**Optical Signal Processing for High-Order Quadrature-Amplitude Modulation Formats**

Guo-Wei Lu

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/61681

#### **Abstract**

In this book chapter, optical signal processing technology, including optical wavelength conversion, wavelength exchange and wavelength multicasting, for phase-noise-sensitive high-order quadrature-amplitude modulation (QAM) signals will be discussed. Due to the susceptibility of high-order QAM signals against phase noise, it is imperative to avoid the phase noise in the optical signal processing subsystems. To design high-performance optical signal processing subsystems, both linear and nonlinear phase noise and distor‐ tions are the main concerns in the system design. We will first investigate the effective monitoring approach to optimize the performance of wavelength conversion for avoiding undesired nonlinear phase noise and distortions, and then propose coherent pumping scheme to eliminate the linear phase noise from local pumps in order to realize pumpphase-noise-free wavelength conversion, wavelength exchange and multicasting for high-order QAM signals. All of the discussions are based on experimental investigation.

**Keywords:** Optical Signal Processing, Nonlinear Optics, Advanced Optical Modulation Formats, Quadrature Amplitude Modulation

#### **1. Introduction**

Recently, digital signal processing (DSP) is playing an increasingly important role in coherent detection for reconstructing the complex field of signal and compensating for the transmission impairments. It dramatically simplifies the reception of multi-level and multi-dimensional modulation formats such as high-order quadrature amplitude modulation (QAM), thus making high-order QAM become a promising and practical approach for achieving higher bit rate and higher spectral efficiency. However, optical signal processing is still highly desirable

© 2015 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

and appreciable in order to overcome the electronics bottlenecks, support the transparency and ultra-fast processing in future optical networks. As basic optical network functionalities, all-optical wavelength conversion, wavelength data exchange, and wavelength multicasting play important roles in the all-optical networks to enhance the re-configurability and nonblocking capacity, and facilitate the wavelength management in future transparent optical networks.

On the other hand, recently, lots of advanced modulation formats like single-carrier high-order QAM like 64QAM [1–5] or multi-carrier optical orthogonal frequency-division multiplexing (OFDM) have been introduced and realized in optical communications for enabling spectrallyefficient and ultra-fast optical transmissions. It is desirable to exploit optical signal processing schemes suitable for these advanced optical modulation formats. However, for these highorder QAM signals, the increasing number of states in the constellation makes the signal more sensitive to the intensity and phase noise. It is imperative to suppress phase noise in optical signal processing subsystems to allow compatibility phase-noise sensitive high-order QAM formats.

As one of the basic optical signal processing techniques, several all-optical wavelength conversion (AOWC) schemes have been demonstrated to realize AOWC functions of OFDM, 8ary phase-shift keying (8PSK), 16QAM, and 64QAM by using the second-order nonlinear effect in periodically-poled Lithium Niobate (PPLN) waveguide [6, 7], four-wave mixing (FWM) in highly-nonlinear fibers (HNLF) [8, 9], semiconductor optical amplifier (SOA) [10– 12], or silicon waveguide. However, the implementation penalty of such subsystems varies from 2dB to 4dB at bit-error rate of 10−3 [9, 12], which is non-negligible for optical networks, especially when multiple wavelength conversion nodes are included in the networks. The distortions introduced in the AOWC mainly originate from: i) the phase noise from the pumps due to the finite laser linewidth, referred to as linear phase noise; and ii) other undesired nonlinear distortions or crosstalk co-existed in the nonlinear process, called as nonlinear phase noise or distortion. To suppress the linear phase noise from pumps, the straightforward way is to use narrow-linewidth lasers, such as external-cavity laser (ECL) or fiber laser (FL), as pump sources. However, it increases the implementation cost. On the other hand, since the nonlinear media in the sub-system is operated in the nonlinear operation region, expect the dominant nonlinear effect utilized for implementing optical signal processing functionalities, it is highly possible that other undesired nonlinear effects co-occur in this process, thus deteriorating the quality of the converted signal. For example, for the wavelength conversion based on the FWM in SOA, additional distortion from cross-gain modulation, cross-phase modulation (XPM), and self-phase modulation (SPM) may deteriorate the converted signal, while in the wavelength conversion based on FWM in HNLF, additional undesirable distor‐ tions are mainly from stimulated Brillouin scattering (SBS), SPM or XPM. High-order QAMs, especially going up to 32QAM, 64QAM or beyond, exhibit more sensitive to nonlinear phase noise like SPM or XPM [13]. Therefore, in order to realize a high-quality all-optical wavelength conversion (AOWC) sub-system for high-order QAMs, it is essential to optimize the system performance of AOWC through effective monitoring approach to suppress the distortion introduced by extra undesired nonlinear distortions. In this chapter, it is categorized into two parts. In the first part, the effective monitoring approach is discussed to avoid the undesired nonlinear phase noise and distortions in the optical signal processing subsystem to enable superior performance [14]. Then, a coherent pumping scheme is proposed and discussed in the second part to implement the pump-phase-noise-free wavelength conversion, wavelength exchange, and wavelength multicasting for high-order QAM signals. Figure 1 summarizes the main topics which will be discussed in this book chapter.

**Figure 1.** Topics to be discussed in this book chapter.

and appreciable in order to overcome the electronics bottlenecks, support the transparency and ultra-fast processing in future optical networks. As basic optical network functionalities, all-optical wavelength conversion, wavelength data exchange, and wavelength multicasting play important roles in the all-optical networks to enhance the re-configurability and nonblocking capacity, and facilitate the wavelength management in future transparent optical

4 Applications of Digital Signal Processing through Practical Approach

On the other hand, recently, lots of advanced modulation formats like single-carrier high-order QAM like 64QAM [1–5] or multi-carrier optical orthogonal frequency-division multiplexing (OFDM) have been introduced and realized in optical communications for enabling spectrallyefficient and ultra-fast optical transmissions. It is desirable to exploit optical signal processing schemes suitable for these advanced optical modulation formats. However, for these highorder QAM signals, the increasing number of states in the constellation makes the signal more sensitive to the intensity and phase noise. It is imperative to suppress phase noise in optical signal processing subsystems to allow compatibility phase-noise sensitive high-order QAM

As one of the basic optical signal processing techniques, several all-optical wavelength conversion (AOWC) schemes have been demonstrated to realize AOWC functions of OFDM, 8ary phase-shift keying (8PSK), 16QAM, and 64QAM by using the second-order nonlinear effect in periodically-poled Lithium Niobate (PPLN) waveguide [6, 7], four-wave mixing (FWM) in highly-nonlinear fibers (HNLF) [8, 9], semiconductor optical amplifier (SOA) [10– 12], or silicon waveguide. However, the implementation penalty of such subsystems varies from 2dB to 4dB at bit-error rate of 10−3 [9, 12], which is non-negligible for optical networks, especially when multiple wavelength conversion nodes are included in the networks. The distortions introduced in the AOWC mainly originate from: i) the phase noise from the pumps due to the finite laser linewidth, referred to as linear phase noise; and ii) other undesired nonlinear distortions or crosstalk co-existed in the nonlinear process, called as nonlinear phase noise or distortion. To suppress the linear phase noise from pumps, the straightforward way is to use narrow-linewidth lasers, such as external-cavity laser (ECL) or fiber laser (FL), as pump sources. However, it increases the implementation cost. On the other hand, since the nonlinear media in the sub-system is operated in the nonlinear operation region, expect the dominant nonlinear effect utilized for implementing optical signal processing functionalities, it is highly possible that other undesired nonlinear effects co-occur in this process, thus deteriorating the quality of the converted signal. For example, for the wavelength conversion based on the FWM in SOA, additional distortion from cross-gain modulation, cross-phase modulation (XPM), and self-phase modulation (SPM) may deteriorate the converted signal, while in the wavelength conversion based on FWM in HNLF, additional undesirable distor‐ tions are mainly from stimulated Brillouin scattering (SBS), SPM or XPM. High-order QAMs, especially going up to 32QAM, 64QAM or beyond, exhibit more sensitive to nonlinear phase noise like SPM or XPM [13]. Therefore, in order to realize a high-quality all-optical wavelength conversion (AOWC) sub-system for high-order QAMs, it is essential to optimize the system performance of AOWC through effective monitoring approach to suppress the distortion introduced by extra undesired nonlinear distortions. In this chapter, it is categorized into two

networks.

formats.

### **2. Performance optimization of wavelength conversion of high-order QAM signals**

It is well-known that for high-order QAM signals, the increasing number of states in the constellation makes them more sensitive to the intensity and phase noise. Previously, power penalties of around 4 dB at 5Gbaud [12], and 2 dB at 21Gbaud [9] were experimentally demonstrated for the converted 64QAM at bit-error rate (BER) of 10−3. As shown in Fig. 3, to implement the AOWC for high-order QAMs, a simple degenerate FWM in HNLF is deployed. Input QAM signal serves as probe, while a CW pump works as pump in AOWC. The phase of the converted signal follows the phase relationship: *θ*idler=2*θ*pump−*θ*probe, where *θ*idler, *θ*pump, and *θ*probe are the phase of the idler, pump and probe, respectively. In order to implement an AOWC for QAM signals with minimal power penalty, the phase and intensity noise from both pump and probe should be suppressed. Since high-order QAM signals are sensitive to the phase noise in the system, to avoid the introduced linear phase noise from pump, it is preferred to deploy narrow linewidth light sources for the pump source. In the following experimental demonstration, a tunable external cavity laser (ECL) with the linewidth of around 100 kHz is employed as the light source of the input QAM signal (probe). On the other hand, two fiber lasers (FLs) with a linewidth of around 10 kHz are used as light sources for pump and local oscillator (LO) at the coherent receiver. Since a narrow-linewidth FL was deployed as pump source, the linear phase noise from pump was negligible.

**Figure 2.** Operation principle of wavelength conversion using FWM in HNLF.

In the AOWC subsystem based on FWM in HNLF for high-order QAM signals, the main nonlinear distortions in the converted signal are mainly from the following sources:


which is not suitable for multi-hop optical networks. In our experiment, thanks to the short length (150 m) and high nonlinearity (nonlinear coefficient: 18/W/km) of the deployed HNLF, the measured SBS threshold is around 24 dBm, which allows a high launching power even without applying additional phase dithering. However, the optimization of the pump power is required in order to avoid the SBS distortion in the pump.

As discussed above, the main undesired nonlinear components in the AOWC based on degenerate FWM in HNLF are from SPM of the input QAM (probe) and SBS of the CW pump. In order to eliminate these deleterious components in the converted signal, the launched pump and probe power should be well managed.

#### **2.1. Experimental investigation**

phase noise in the system, to avoid the introduced linear phase noise from pump, it is preferred to deploy narrow linewidth light sources for the pump source. In the following experimental demonstration, a tunable external cavity laser (ECL) with the linewidth of around 100 kHz is employed as the light source of the input QAM signal (probe). On the other hand, two fiber lasers (FLs) with a linewidth of around 10 kHz are used as light sources for pump and local oscillator (LO) at the coherent receiver. Since a narrow-linewidth FL was deployed as pump

> w*idler*

nonlinear distortions in the converted signal are mainly from the following sources:

*Idler*

Phase Transparency *High-order* 

In the AOWC subsystem based on FWM in HNLF for high-order QAM signals, the main

**1.** SPM from the probe signal: Since the input QAM signal, i.e. the probe, exhibits multilevel in amplitude, in the nonlinear operation condition, the probe may experience SPM. The nonlinear phase noise will then be transferred to the converted signal through FWM and finally deteriorate the converted signal. Therefore, it is critical to manage the launched power of probe to avoid the degradation in the converted QAM signal caused by the probe-introduced SPM. However, it will sacrifice the conversion efficiency. There is a tradeoff between conversion efficiency and the quality of the converted signal in the

**2.** XPM from the pump signal: As discussed in [15,16], with limited optical signal-to-noise ratio (OSNR) in pump, the amplitude noise in pump may distort the converted signal by introducing nonlinear phase noise through XPM effect. In our experiment, a FL is used as the pump source. Thanks to the low relative intensity noise (RIN) of the FL, the OSNR of pump source is measured as around 57 dB, which avoids the pump-induced nonlinear

**3.** SBS from the pump signal: In AOWC subsystems based on FWM in HNLF, SBS limits the conversion efficiency unless the pumps' linewidth is broadened to increase the SBS threshold. In an AOWC based on degenerate single-pump FWM, if intentionally applying phase dithering on the pump, it will deteriorate the converted QAM signals. Although it has been shown that the phase dithering could be compensated for at the coherent digital receiver by DSP [17], the applied phase dithering will be accumulat‐ ed in the converted signal as distortions and be further transferred to the next node,

w*pump*w*probe*

*Pump*

w

*QAM signal*

*Probe*

source, the linear phase noise from pump was negligible.

6 Applications of Digital Signal Processing through Practical Approach

**Figure 2.** Operation principle of wavelength conversion using FWM in HNLF.

q*idler*=2q*pump*q*probe*

performance optimization.

phase noise.

Figure 3 depicts the experimental setup used to achieve the AOWC of 36QAM and 64QAM through FWM in HNLF. Since high-order QAM signals are sensitive to the phase noise in the system, it is preferred to employ narrow-linewidth light sources in the experiment, especially for the pump source. Owing to the lack of instruments in the lab, in the experiment, a tunable ECL with a linewidth of around 100 kHz was deployed as a light source of the input QAM signal in the experiment, whereas two FLs with a linewidth of around 10 kHz worked as light sources for the pump and LO at the coherent receiver. To synthesize optical QAM signals, the light from the ECL, operating at 1551.38 nm, was modulated by a single in-phase/quadrature (IQ) modulator, which had a 3 dB bandwidth of around 25 GHz, and a 3.5 V half-wave voltage. Two de-correlated 6- or 8-level driving signals originating from pseudorandom binary sequence (PRBS) streams with a length of 215−1 from an arbitrary waveform generator (AWG) were used to drive the IQ modulator for generating optical 36QAM or 64QAM, respectively. After power amplification, the QAM signal was combined with amplified CW light at 1551.95 nm, and was then fed into a 150 m length of HNLF having an attenuation coefficient of 0.9 dB/ km, a nonlinear coefficient of 18/W/km, a zero-dispersion wavelength of 1548 nm, and a dispersion slope of around 0.02 ps/nm2 /km. Note that, due to the inability to tune the wave‐ length of the FLs used in the experiment, wavelengths of the probe signal and pump could not be set for the optimum FWM efficiency. Nevertheless, owing to the high nonlinear effects and flat-dispersion-profile of the employed HNLF, the experimental results showed high conver‐ sion efficiency, which can ensure the superior performance of the converted signal. The produced idle signal at the wavelength of 1552.52 nm was filtered out and then led to the phasediversity intradyne coherent receiver for the coherent detection and for BER measurement. The coherent receiver included an LO, a 90 degree optical hybrid device, and two balanced photo-detectors (PDs). After detection by the balanced PDs, the data was digitized at 50GSam‐ ples/s by employing a digital storage oscilloscope (Tektronix DP071254) which has the analog bandwidth of 12.5 GHz. The captured data was processed offline through the DSP that included compensation of skew, IQ imbalance, power, data resampling, linear equalization using the finite impulse response (FIR) filtering, carrier phase recovery, and the final harddecision circuits. 89,285 symbols were used for the BER measurement.

**2.1 Experimental investigation** 

As discussed above, the main undesired nonlinear components in the AOWC based on degenerate FWM in HNLF are from SPM of the input QAM (probe) and SBS of the CW pump. In order to eliminate these deleterious components in the converted

signal, the launched pump and probe power should be well managed.

**Figure 3.** Experimental setup of the wavelength conversion of 36QAM and 64QAM signals.

#### **Figure 32.** Experimental setup of the wavelength conversion of 36QAM and 64QAM signals. *2.1.1. AWOC of 36QAM*

Figure 32 depicts the experimental setup used to achieve the AOWC of 36QAM and 64QAM through FWM in HNLF. Since high‐order QAM signals are sensitive to the phase noise in the system, it is preferred to employ narrow‐linewidth light sources in the experiment, especially for the pump source. Owing to the lack of instruments in the lab, in the experiment, a tunable ECL with a linewidth of around 100 kHz was deployed as a light source of the input QAM signal in the experiment, whereas two FLs with a linewidth of around 10 kHz worked as light sources for the pump and LO at the coherent receiver. To synthesize optical QAM signals, the light from the ECL, operating at 1551.38 nm, was modulated by a single in‐phase/quadrature (IQ) modulator, which had a 3 dB3 dB bandwidth of around 25 GHz, and a 3.5 V half‐wave voltage. Two de‐correlated 6‐ or 8‐level driving signals originating from pseudorandom binary sequence (PRBS) streams with a length of 2<sup>15</sup>‐−1 from an arbitrary waveform generator (AWG) were used to drive the IQ modulator for generating optical 36QAM or 64QAM, respectively. After power amplification, the QAM signal was combined with amplified CW light at 1551.95 nm, and was then fed into a 150 m length of HNLF having an attenuation coefficient of 0.9 dB/km, a In order to eliminate possible deleterious components in the converted signal, the launched pump and probe power should be well managed. Figure 4(a) shows the measured EVMs and BERs at the received OSNR of around 25 dB when the probe power was tuned from 7 to 15 dBm and the pump power was fixed at around 20dBm. An improvement in both the EVMs and BERs of the converted 36QAM was observed with an increase in the probe power up to around 11 dBm. After the inflection point (around 11 dBm), both EVMs and BERs increased with the increase of the probe power, which was attributed to the SPM of probe in the nonlinear process. Therefore, we considered setting the probe power to around 11 dBm to avoid the SPM introduced in the probe. As previously mentioned, another main source of distortion is the SBS of the pump in AOWC. To optimize the pump power, we also measured the corresponding EVMs and BERs when the probe power was fixed at 11 dBm and the pump power was tuned from 15 dBm to 23 dBm (Fig. 4(b)). As the launched pump power increased, EVMs and BERs showed similar behavior. We found that it was better to operate the pump power in the range of 17.5–22 dBm. At the pump power of 15.4 dBm, the constellations were relatively noisy due to the low conversion efficiency. However, once the pump power was increased to 22.9 dBm, distortion from SBS started to appear in the measured constellation, acting mainly as intensity noise. To obtain the optimal performance, we set the pump power at 20 dBm in the AOWC of 36QAM. While monitoring the converted 36QAM, EVMs and BERs showed consistent behavior when tuning the probe and pump powers.

nonlinear coefficient of 18/W/km, a zero‐dispersion wavelength of 1548 nm, and a dispersion slope of around 0.02 ps/nm<sup>2</sup> /km. Note that, due to the inability to tune the wavelength of the FLs used in the experiment, wavelengths of the probe signal and pump could not be set for the optimum FWM efficiency. Nevertheless, owing to the high nonlinear effects and flat‐dispersion‐profile of the employed HNLF, the As we discussed previously, the optimal pump and probe power were 20 dBm and 11 dBm for the AOWC of 36QAM. The corresponding optical spectrum under the optimal condition is shown in Fig. 5(i), where a conversion efficiency of about −15 dB was obtained compared with the input probe power. Under the optimal operating condition, the BER performance was measured as the function of OSNR at 0.1 nm for both input and converted signals, and shown in Fig. 5(ii). For the input QAM signals, the power penalty of around 2 dB was obtained compared with theoretical BER measurement at the BER of 10−3, which is better than the previously-reported QAM transmitters [2]. The power penalty is mainly owing to the imper‐ fectness of the transmitter. With respect to the input QAM, a negligible power penalty (<0.3 Optical Signal Processing for High-Order Quadrature-Amplitude Modulation Formats http://dx.doi.org/10.5772/61681 9

**Figure 4.** Measured EVM (triangles) and BER (squares) results of the converted 36QAM signals (**a**) when tuning probe power from 7 to 15 dBm, (**b**) when tuning pump power from 14 to 23 dBm.

**Figure 5.** (**i**) Measured optical spectrum in the optimal condition, (**ii**) measured BER as function of the received OSNR (0.1 nm). Insets: (**a**) input and (**b**) converted 36QAM signals.

dB) was observed at a BER of 10−3. The measured constellations of the input and converted 36QAM are shown in the insets of Fig. 5(ii), where the received OSNR was around 35 dB.

#### *2.1.2. AWOC of 64QAM*

As discussed above, the main undesired nonlinear components in the AOWC based on degenerate FWM in HNLF are from SPM of the input QAM (probe) and SBS of the CW pump. In order to eliminate these deleterious components in the converted

**Figure 32.** Experimental setup of the wavelength conversion of 36QAM and 64QAM

**Figure 3.** Experimental setup of the wavelength conversion of 36QAM and 64QAM signals.

Figure 32 depicts the experimental setup used to achieve the AOWC of 36QAM and 64QAM through FWM in HNLF. Since high‐order QAM signals are sensitive to the phase noise in the system, it is preferred to employ narrow‐linewidth light sources in the experiment, especially for the pump source. Owing to the lack of instruments in the lab, in the experiment, a tunable ECL with a linewidth of around 100 kHz was deployed as a light source of the input QAM signal in the experiment, whereas two FLs with a linewidth of around 10 kHz worked as light sources for the pump and LO at the coherent receiver. To synthesize optical QAM signals, the light from the ECL, operating at 1551.38 nm, was modulated by a single in‐phase/quadrature (IQ) modulator, which had a 3 dB3 dB bandwidth of around 25 GHz, and a 3.5 V half‐wave voltage. Two de‐correlated 6‐ or 8‐level driving signals originating from pseudorandom binary sequence (PRBS) streams with a length of 2<sup>15</sup>‐−1 from an arbitrary waveform generator (AWG) were used to drive the IQ modulator for generating optical 36QAM or 64QAM, respectively. After power amplification, the QAM signal was combined with amplified CW light at 1551.95 nm, and was then fed into a 150 m length of HNLF having an attenuation coefficient of 0.9 dB/km, a nonlinear coefficient of 18/W/km, a zero‐dispersion wavelength of 1548 nm, and a

In order to eliminate possible deleterious components in the converted signal, the launched pump and probe power should be well managed. Figure 4(a) shows the measured EVMs and BERs at the received OSNR of around 25 dB when the probe power was tuned from 7 to 15 dBm and the pump power was fixed at around 20dBm. An improvement in both the EVMs and BERs of the converted 36QAM was observed with an increase in the probe power up to around 11 dBm. After the inflection point (around 11 dBm), both EVMs and BERs increased with the increase of the probe power, which was attributed to the SPM of probe in the nonlinear process. Therefore, we considered setting the probe power to around 11 dBm to avoid the SPM introduced in the probe. As previously mentioned, another main source of distortion is the SBS of the pump in AOWC. To optimize the pump power, we also measured the corresponding EVMs and BERs when the probe power was fixed at 11 dBm and the pump power was tuned from 15 dBm to 23 dBm (Fig. 4(b)). As the launched pump power increased, EVMs and BERs showed similar behavior. We found that it was better to operate the pump power in the range of 17.5–22 dBm. At the pump power of 15.4 dBm, the constellations were relatively noisy due to the low conversion efficiency. However, once the pump power was increased to 22.9 dBm, distortion from SBS started to appear in the measured constellation, acting mainly as intensity noise. To obtain the optimal performance, we set the pump power at 20 dBm in the AOWC of 36QAM. While monitoring the converted 36QAM, EVMs and BERs showed consistent

the wavelength of the FLs used in the experiment, wavelengths of the probe signal and pump could not be set for the optimum FWM efficiency. Nevertheless, owing to the high nonlinear effects and flat‐dispersion‐profile of the employed HNLF, the

As we discussed previously, the optimal pump and probe power were 20 dBm and 11 dBm for the AOWC of 36QAM. The corresponding optical spectrum under the optimal condition is shown in Fig. 5(i), where a conversion efficiency of about −15 dB was obtained compared with the input probe power. Under the optimal operating condition, the BER performance was measured as the function of OSNR at 0.1 nm for both input and converted signals, and shown in Fig. 5(ii). For the input QAM signals, the power penalty of around 2 dB was obtained compared with theoretical BER measurement at the BER of 10−3, which is better than the previously-reported QAM transmitters [2]. The power penalty is mainly owing to the imper‐ fectness of the transmitter. With respect to the input QAM, a negligible power penalty (<0.3

/km. Note that, due to the inability to tune

signal, the launched pump and probe power should be well managed.

**2.1 Experimental investigation** 

8 Applications of Digital Signal Processing through Practical Approach

signals.

*2.1.1. AWOC of 36QAM*

dispersion slope of around 0.02 ps/nm<sup>2</sup>

behavior when tuning the probe and pump powers.

To optimize the performance of AOWC for 64QAM, measurements similar to those described above were performed. Figure 6 (a) depicts the measured EVMs and BERs at the received 25 dB OSNR when the probe power was tuned from 7 to 15 dBm and the pump power was fixed at around 20 dBm. The increase in the launched probe power decreased the BER of the converted signal to around 12.2 dBm owing to the improved OSNR of the converted signals. When the probe power was increased further, the BER started to increase, attributed to the introduced SPM in the probe signal. The BER results with different probe powers suggested to operate the probe power in the range of 9 to 14 dBm. Furthermore, the measured constel‐ lations offered a more perceptive and precise approach for optimizing the performance. The EVMs with the various probe powers were calculated and are plotted in Fig. 6(a). With the increase of the probe power, both BER and EVM results show similar trends. However, according to the EVM and BER results, different optimum probe powers of around 9.2 dBm and 12.4 dBm were obtained, respectively. When the launched probe power was increased to around 12.4 dBm, SPM-induced distortion became visible in the constellation, causing the increase of EVM. However, the SPM-induced spiral rotation in the constellation happens to enlarge the symbol distance between symbols, thus decreasing the BER. Therefore, these results suggested that, to optimize the performance of AOWC, it would be effective to monitor the constellation or EVM, which gives a more intuitive and proper means to optimize the AOWC performance, in order to eliminate the extra undesired nonlinear phase noise intro‐ duced in the process.

**Figure 6.** Measured EVM (triangles) and BER (squares) results of the converted 64QAM signals (**a**) when tuning probe power from 7 to 15 dBm, (**b**) when tuning pump power from 17 to 21 dBm.

For pump power optimization, the EVM and BER results were measured when the launched pump power was increased from 17 to 22 dBm, whereas the pump power was set at around 9 dBm. The measurement was done for optimizing the pump power and is shown in Fig. 6(b). Similar behavior was obtained for the measured EVM and BER values when the pump power was increased. In order to avoid the distortion owing to the SBS, we considered to set the pump power in the range of 17.5–20.5 dBm. It is clear that a high pump power was helpful for obtaining high conversion efficiency, therefore, resulted in a sufficient OSNR for the converted signal. Thus, in this experiment, the pump power was optimized to 20 dBm, which resulted in a conversion efficiency of about -15 dB and also ensured that there was no SBS distortion introduced for the converted signal. The distortion from SBS acted mainly as amplitude noise in the constellations, and became severe once the pump power was increased to more than 20.5 dBm.

To achieve the optimal performance of AOWC for 64QAM signal, the pump and probe power were set at 20 dBm and 9 dBm, respectively. A conversion efficiency of around −15 dB is obtained, as shown in Fig. 7(i). Under the optimized conditions, the BER performance as a function of OSNR was shown in Fig. 7(ii). The implementation penalty compared with the theoretical BER curve was around 2.8 dB for 64QAM, at a BER of 10−3, which is much better Optical Signal Processing for High-Order Quadrature-Amplitude Modulation Formats http://dx.doi.org/10.5772/61681 11

**Figure 7.** (**i**) Measured optical spectrum in the optimal condition, (**ii**) measured BER as function of the received OSNR (0.1 nm). Insets: (**a**) input and (**b**) converted 64QAM signals.

than those of the previously-reported 64QAM transmitters in [3–4]. Similar to that performance of 36QAM AOWC, a negligible power penalty of <0.3 dB was observed with the respect to the input signal at a BER of 10−3 after the conversion. The obtained constellations of the input and converted high-order QAMs at around 35 dB received OSNR and are shown in the insets of Fig. 7(ii).

#### **2.2. Summary**

increase of the probe power, both BER and EVM results show similar trends. However, according to the EVM and BER results, different optimum probe powers of around 9.2 dBm and 12.4 dBm were obtained, respectively. When the launched probe power was increased to around 12.4 dBm, SPM-induced distortion became visible in the constellation, causing the increase of EVM. However, the SPM-induced spiral rotation in the constellation happens to enlarge the symbol distance between symbols, thus decreasing the BER. Therefore, these results suggested that, to optimize the performance of AOWC, it would be effective to monitor the constellation or EVM, which gives a more intuitive and proper means to optimize the AOWC performance, in order to eliminate the extra undesired nonlinear phase noise intro‐

**Figure 6.** Measured EVM (triangles) and BER (squares) results of the converted 64QAM signals (**a**) when tuning probe

For pump power optimization, the EVM and BER results were measured when the launched pump power was increased from 17 to 22 dBm, whereas the pump power was set at around 9 dBm. The measurement was done for optimizing the pump power and is shown in Fig. 6(b). Similar behavior was obtained for the measured EVM and BER values when the pump power was increased. In order to avoid the distortion owing to the SBS, we considered to set the pump power in the range of 17.5–20.5 dBm. It is clear that a high pump power was helpful for obtaining high conversion efficiency, therefore, resulted in a sufficient OSNR for the converted signal. Thus, in this experiment, the pump power was optimized to 20 dBm, which resulted in a conversion efficiency of about -15 dB and also ensured that there was no SBS distortion introduced for the converted signal. The distortion from SBS acted mainly as amplitude noise in the constellations, and became severe once the pump power was increased to more than

To achieve the optimal performance of AOWC for 64QAM signal, the pump and probe power were set at 20 dBm and 9 dBm, respectively. A conversion efficiency of around −15 dB is obtained, as shown in Fig. 7(i). Under the optimized conditions, the BER performance as a function of OSNR was shown in Fig. 7(ii). The implementation penalty compared with the theoretical BER curve was around 2.8 dB for 64QAM, at a BER of 10−3, which is much better

power from 7 to 15 dBm, (**b**) when tuning pump power from 17 to 21 dBm.

duced in the process.

10 Applications of Digital Signal Processing through Practical Approach

20.5 dBm.

We have experimentally demonstrated the AOWC of optical 10-Gbaud (50 Gbps) 36QAM and (60 Gbps) 64QAM through a degenerate FWM effect in HNLF with a power penalty of less than 0.3 dB at a BER of 10−3. In order to optimize the AOWC performance, the converted highorder QAM signals were evaluated by measuring the BER and constellations, i.e., EVM. Since EVM showed higher sensitivity in the presence of nonlinear phase noise, the results suggested the effectiveness of optimizing the AOWC performance by monitoring EVM, rather than BER, especially for high-order QAM signals.

#### **3. Pump-phase-noise-free optical signal processing**

The previous session mainly focuses on how to avoid or suppress the nonlinear noise or distortion in optical signal processing. In this session, the focus is to exploit the approach to eliminate the linear phase noise from the local pumps deployed in optical signal processing subsystems. In optical signal processing subsystems, such as wavelength conversion, wave‐ length exchange or wavelength multicasting, it is inevitable to deploy local pump sources to realize the optical signal processing functionalities. As we discuss before, the linear phase noise from local pumps may introduce phase noise or distortion to the converted signal in optical signal processing subsystem. The most straightforward way is to deploy narrow-linewidth lasers as pump sources. However, it increases the implementation cost of the systems. We will present our proposed coherent pumping scheme. Thanks to the phase noise cancelling effect using this coherent pumping, it allows the use of low-cost distributed feedback (DFB) lasers for high‐order QAM signals.

**PPLN**

coherent pumping.

as pump sources, and at the same time, ensures the superior performance since it is free of the phase noise from pumps. Here we will demonstrate several pump-phase-noise-free optical signal processing subsystems for high-order QAM signals, including: (a) pump-phase-noisefree wavelength conversion and wavelength exchange for high-order QAMs signals using cascaded second-order nonlinearities in PPLN [18, 19]; and (b) pump-phase-noise-free wavelength multicasting of QAM signals using FWM in HNLF [20]. **3. Pump‐phase‐noise‐free Optical optical Signal signal Processing processing** The previous session mainly focuses on how to avoid or suppress the nonlinear noise or distortion in optical signal processing. In this session, the focus is to exploit the approach to eliminate the linear phase noise from the local pumps deployed in optical signal processing subsystems. In optical signal processing subsystems, such as wavelength conversion, wavelength exchange or wavelength multicasting, it is inevitable to deploy local pump sources to realize the optical signal processing

presence of nonlinear phase noise, the results suggested the effectiveness of

#### **3.1. Pump-phase-noise-free wavelength conversion and wavelength exchange in PPLN** functionalities. As we discuss before, the linear phase noise from local pumps may introduce phase noise or distortion to the converted signal in optical signal

Figure 8 depicts the operation principle of the pump-linewidth-free AOWC. It is based on cascaded second-order nonlinearity in PPLN. Two pumps at *ω*p1 and *ω*p2 are allocated at one side of quasi-phase-matching (QPM) wavelength of PPLN, whereas input signal at *ω*1 is placed symmetrically with pump at *ω*p1 with respect to QPM wavelength. After AOWC, the input signal at *ω*1 is shifted to the frequency *ω*2, with *ω*2=*ω*p1-*ω*p2+*ω*1, where *ω*p1, *ω*p2 and *ω*1 are the frequencies of pump1, pump2, and the input signal, respectively. It is typically employed for performing the data exchange between the two input wavelengths [13], i.e. wavelength exchange. The frequencies *ω*p1 and *ω*<sup>1</sup> have to be arranged symmetrically with the respect to the PPLN's quasi-phase-matching (QPM) wavelength in order to satisfy the phase matching condition and for increasing the conversion efficiency. With the non-depletion assumption, linear mapping between the input and output relationship in complex amplitudes and phase are given by equations (1) and (2), respectively. processing subsystem. The most straightforward way is to deploy narrow‐linewidth lasers as pump sources. However, it increases the implementation cost of the systems. We will present our proposed coherent pumping scheme. Thanks to the phase noise cancelling effect using this coherent pumping, it allows the use of low‐cost distributed feedback (DFB) lasers as pump sources, and at the same time, ensures the superior performance since it is free of the phase noise from pumps. Here we will demonstrate several pump‐phase‐noise‐free optical signal processing subsystems for high‐order QAM signals, including: (a) Pump‐phase‐noise‐free wavelength conversion and wavelength exchange for high‐order QAMs signals using cascaded 2ndsecond‐order nonlinearities in PPLN [18, 19]; and (b) Pump‐phase‐noise‐free wavelength multicasting of QAM signals using FWM in HNLF [20]. **3.1 Pump‐phase‐noise‐free wavelength conversion and wavelength exchange in**

**Fig.Figure 87.** Operation principle of the pump phase‐noise cancellation using

**Figure 8.** Operation principle of the pump phase-noise cancellation using coherent pumping.

$$\mathbf{A}\_{\boldsymbol{\omega}\_{2}} \propto \mathbf{A}\_{\boldsymbol{\omega}\_{1}} \cdot \mathbf{A}\_{\boldsymbol{\omega}\_{p2}}^{\*} \cdot \mathbf{A}\_{\boldsymbol{\omega}\_{p1}} \tag{1}$$

**Formatted:** Font: 10 pt, Font color: Auto

$$
\boldsymbol{\theta}\_{\text{output}} = \boldsymbol{\theta}\_{\text{input}} + \boldsymbol{\Lambda}\boldsymbol{\theta}\_{\text{p1}} - \boldsymbol{\Lambda}\boldsymbol{\theta}\_{\text{p2}} + \mathbf{C} = \boldsymbol{\theta}\_{\text{input}} + \boldsymbol{\Lambda}\boldsymbol{\theta}\_{\text{pump}} + \mathbf{C} \tag{2}
$$

where θoutput, θinput, ∆θp1, ∆θp2, and *C* are the phase of the converted and input signals, the phase noise from pump1 and pump2, and a constant term, respectively, and ∆θpump =∆θp1 -∆θp2. Note that the phase information in each pump is transparently transferred to the converted signal as a subtraction term between them. In order to avoid additional phase noise introduced in the process, the phase noise term from pumps, Δθpump, should be minimized. If the pumps are synthesized by a two-tone generator (TTG) from a single laser source, the phase noise from pumps is eliminated in the converted signal, i.e. Δθpump=0. Hence, the wavelength conversion becomes free of the phase noise from pumps, allowing the use of lower cost lasers and at the same time ensuring a superior performance in terms of noise performance. The TTG may be constructed using either Mach-Zehnder modulators driven by a RF clock, or an optical frequency comb followed by an optical spectrum shaper. The two-tone spacing could vary from a fraction of nanometer to several nanometers, making it possible to cover a relative wide conversion range in the OWC. The TTG generated from a filtered optical frequency comb is more suitable and practical for the OWC based on HNLF.

#### *3.1.1. Pump-phase-noise-free AOWC in PPLN*

**Formatted:** Font: 10 pt, Font color: Auto

as pump sources, and at the same time, ensures the superior performance since it is free of the phase noise from pumps. Here we will demonstrate several pump-phase-noise-free optical signal processing subsystems for high-order QAM signals, including: (a) pump-phase-noisefree wavelength conversion and wavelength exchange for high-order QAMs signals using cascaded second-order nonlinearities in PPLN [18, 19]; and (b) pump-phase-noise-free

**3. Pump‐phase‐noise‐free Optical optical Signal signal Processing processing** The previous session mainly focuses on how to avoid or suppress the nonlinear noise or distortion in optical signal processing. In this session, the focus is to exploit the approach to eliminate the linear phase noise from the local pumps deployed in optical signal processing subsystems. In optical signal processing subsystems, such as wavelength conversion, wavelength exchange or wavelength multicasting, it is inevitable to deploy local pump sources to realize the optical signal processing functionalities. As we discuss before, the linear phase noise from local pumps may introduce phase noise or distortion to the converted signal in optical signal processing subsystem. The most straightforward way is to deploy narrow‐linewidth lasers as pump sources. However, it increases the implementation cost of the systems. We will present our proposed coherent pumping scheme. Thanks to the phase noise cancelling effect using this coherent pumping, it allows the use of low‐cost distributed feedback (DFB) lasers as pump sources, and at the same time, ensures the superior performance since it is free of the phase noise from pumps. Here we will demonstrate several pump‐phase‐noise‐free optical signal processing subsystems for high‐order QAM signals, including: (a) Pump‐phase‐noise‐free wavelength conversion and wavelength exchange for high‐order QAMs signals using cascaded 2ndsecond‐order nonlinearities in PPLN [18, 19]; and (b) Pump‐phase‐noise‐free wavelength multicasting of QAM signals using FWM in HNLF

presence of nonlinear phase noise, the results suggested the effectiveness of optimizing the AOWC performance by monitoring EVM, rather than BER, especially

**3.1. Pump-phase-noise-free wavelength conversion and wavelength exchange in PPLN**

Figure 8 depicts the operation principle of the pump-linewidth-free AOWC. It is based on cascaded second-order nonlinearity in PPLN. Two pumps at *ω*p1 and *ω*p2 are allocated at one side of quasi-phase-matching (QPM) wavelength of PPLN, whereas input signal at *ω*1 is placed symmetrically with pump at *ω*p1 with respect to QPM wavelength. After AOWC, the input signal at *ω*1 is shifted to the frequency *ω*2, with *ω*2=*ω*p1-*ω*p2+*ω*1, where *ω*p1, *ω*p2 and *ω*1 are the frequencies of pump1, pump2, and the input signal, respectively. It is typically employed for performing the data exchange between the two input wavelengths [13], i.e. wavelength exchange. The frequencies *ω*p1 and *ω*<sup>1</sup> have to be arranged symmetrically with the respect to the PPLN's quasi-phase-matching (QPM) wavelength in order to satisfy the phase matching condition and for increasing the conversion efficiency. With the non-depletion assumption, linear mapping between the input and output relationship in complex amplitudes and phase

**3.1 Pump‐phase‐noise‐free wavelength conversion and wavelength exchange in**

**Fig.Figure 87.** Operation principle of the pump phase‐noise cancellation using

 ×

> q

 q= +D -D + = +D + (2)

(1)

2 1 p2 p1 \* A AA A ω ωω ω µ×

output input p1 p2 *C C* input pump

**Figure 8.** Operation principle of the pump phase-noise cancellation using coherent pumping.

 qq

wavelength multicasting of QAM signals using FWM in HNLF [20].

are given by equations (1) and (2), respectively.

coherent pumping.

q

 q

[20].

**PPLN**

for high‐order QAM signals.

12 Applications of Digital Signal Processing through Practical Approach

The experimental set-up is depicted in Fig. 6, showing OWC scheme of 16 and 64 QAM signals. A 5kHz linewidth FL at the wavelength of 1552.52 nm was deployed as the light source to minimize the phase noise from the input signal. And then the light was modulated by an inphase/quadrature (IQ) modulator for generating QAM signals. The two de-correlated 4- or 8 level driving electronics derived from 10-Gbaud PRBS streams with the length of 215−1 were generated from an arbitrary waveform generator (AWG) to drive the IQ modulator, which has a Vπ of 3.5 V and an optical bandwidth of around 25 GHz. Two different pump configurations were adopted for comparison. The two pumps were generated from a single laser source at the wavelength of 1548.08 nm using a TTG in the coherent pump configuration, which consisted of a high extinction-ratio (ER) optical modulator driven by a 25-GHz RF clock. The high-ER modulator was made up on the x-cut LiNbO3 substrate with two embedded active trimmers in each arm and it has the extinction ratio of up to 60 dB. The two phase-correlated coherent pumps were obtained with the 50-GHz frequency separation with a >40-dB spurious suppression ratio. For the case of free-running pumping, two independent free-running lasers at the wavelengths of 1547.88 and 1548.28 nms were used as pumps with 50-GHz spacing. For each of the configurations, we tried either the 500-kHz linewidth ECLs or the 3.5-MHz linewidth DFBs as the laser sources for the pumps.

The optical spectra with and without pumps for wavelength conversion of 64QAM signals after the PPLN are shown in Fig. 10. Similar conversion efficiency (CE) and signal depletion (SD) were obtained for the both free-running pumps (ECL/DFB) and coherent two-tone pumps (ECL/DFB). Here, the CE is defined as the power ratio between the converted signal to the input signal after the PPLN. On the other hand, the SD is the power ratio of the input signal after the PPLN when the both pumps were switched OFF and ON, respectively. The total pump power launched into the PPLN was set to the maximum value of about 28.8 dBm (25.8 dBm for each pump) to maximize both CE and SD, where CE of -6.5 dB and SD of 25 dB were obtained with input signal power of 6 dBm.

**Figure 9.** Experimental set-up for AOWC of 16QAM and 64QAM signals.

**Formatted:** Font: 10 pt, Font color: Auto

**Formatted:** Font: 10 pt, Font color: Auto

**Fig.Figure 109.** Optical spectra measured after PPLN when performing OWC of 64QAM with DFB pump lasers in both free‐running and coherent configurations. **Figure 10.** Optical spectra measured after PPLN when performing OWC of 64QAM with DFB pump lasers in both free-running and coherent configurations.

**Figure 11.** Measured QAM constellations using ECL and DFB pump lasers in coherent two-tone and free-running con‐ figurations (16QAM: OSNR=18 dB, 64QAM: OSNR =34 dB).

**Fig.Figure 110.** Measured QAM constellations using ECL and DFB pump lasers in coherent two‐tone and free‐running configurations (16QAM: OSNR=18dB18 dB,

64QAM: OSNR =34dB34 dB).

**Formatted:** Font: 10 pt, Font color: Auto The constellations of the converted 16/64QAMs signals were re-constructed and observed with different pump lasers and pump configurations. As shown in Fig. 11, for either ECL or DFB pump laser, clear constellations are observed with coherent two-tone pumps. On the other ways, with the ECL pump lasers in free-running configuration, symbol rotation in phase starts to turn into obvious in the 64QAM constellation owing to the additional phase noise from the free-running ECL pumps. Furthermore, the presence of even larger pump phase noise causes clear spreading of the symbols around the unit circle for both formats with DFB free-running pumps, which is more severe for the higher amplitude symbols. From the measured BER curves, the results can also be confirmed as a function of optical signal-to-noise ratio (OSNR) at 0.1 nm for both input and converted 16/64QAM signals, as seen in Fig. 12. For both ECL and DFB pump lasers with coherent pump configuration, negligible power penalties of <0.1 dB for 16QAM and <0.3 dB for 64QAM at BER of 10−3 are observed with the respect of the input signal at 10Gbaud. Although we can get insignificant power penalty of <0.3 dB at BER of 10−3 for 16QAM with ECL as the pump laser, by increasing the modulation level to 64QAM, a 0.5 dB penalty at BER of 10−3 and an error floor at around 3×10−5 are observed in the case of freerunning pumps. Owing to the strong phase noise with the free-running DFB pumps, even at >30 dB OSNR, a BER of around 10−2 is observed for 16QAM. The effectiveness of the pumpphase-noise removal in the OWC for high-order QAM with coherent two-tone pumps is verified by the BER and constellation results.

**Figure 12.** Measured BER vs. OSNR curves for 16/64QAM. Squares: back-to-back (BtB), stars: coherent pumps (ECL), crosses: free-running pumps (ECL), diamonds: coherent pumps (DFB).

#### *3.1.2. Pump-phase-noise-free wavelength exchange in PPLN*

**Figure 11.** Measured QAM constellations using ECL and DFB pump lasers in coherent two-tone and free-running con‐

**Fig.Figure 110.** Measured QAM constellations using ECL and DFB pump lasers in coherent two‐tone and free‐running configurations (16QAM: OSNR=18dB18 dB,

**Fig.Figure 109.** Optical spectra measured after PPLN when performing OWC of 64QAM with DFB pump lasers in both free‐running and coherent configurations.

**Figure 10.** Optical spectra measured after PPLN when performing OWC of 64QAM with DFB pump lasers in both

DFB (free-run. pumps) DFB (coh. pumps) Pumps off

Sig. Pump2

Pump1

Input Sig.

CE = -6.5 dB

Converted

1547 1548 1549 1550 1551 1552 1553 1554

SD =25 dB

Wavelength (nm)

The optical spectra with or without pumps for wavelength conversion of 64QAM signals after the PPLN are shown in Fig.Figure. 109. Similar conversion efficiency (CE) and signal depletion (SD) were obtained for the both free‐running pumps (ECL/DFB) and coherent two‐tone pumps (ECL/DFB). Here, the CE is defined as the power ratio between the converted signal to the input signal after the PPLN. On the other hand, the SD is the power ratio of the input signal after the PPLN when the both pumps were switched OFF and ON, respectively. The total pump power launched into the PPLN was set to the maximum value of about 28.8 dBm (25.8 dBm for each pump) to maximize both CE and SD, where CE of ‐6.5 dB and SD of 25 dB were obtained with

figurations (16QAM: OSNR=18 dB, 64QAM: OSNR =34 dB).

64QAM: OSNR =34dB34 dB).

input signal power of 6 dBm.



Power (dBm)

free-running and coherent configurations.


0

**Figure 9.** Experimental set-up for AOWC of 16QAM and 64QAM signals.

14 Applications of Digital Signal Processing through Practical Approach

**Formatted:** Font: 10 pt, Font color: Auto Wavelength exchange is a kind of optical signal processing technique to realize bidirectional information swapping between different wavelengths. It consists of simultaneous signal depletion and wavelength conversion processes of two participated channel signals. Each of input signals is power consumed and its corresponding power is shifted to the other wave‐ length, finally realizing data exchange between two wavelengths in single device. So far, several works have been demonstrated through non-degenerate FWM in highly-nonlinear fiber [21–24] or cascaded second-order nonlinearities in PPLN waveguide [25–26].

**Figure 13.** Measured constellations of input and converted signals after wavelength exchange (16QAM and QPSK).

Here, we apply the coherent pumping concept to wavelength exchange to demonstrate pump-phase-noise free wavelength exchange in PPLN. For experimental demonstration, an experimental setup similar to the one shown in Fig. 9 was deployed by adding another input signal. Two input signals modulated in 16QAM and QPSK, respectively were launched to PPLN as input signals for performing wavelength exchange. To evaluate the performance of wavelength exchange, BER and constellations were measured. The constellations of the swapped signals with different pump configurations are depicted in Fig. 13. With coherent pumps, clear constellations are observed for both QPSK and 16QAM. However, with DFB free-running pumps, the presence of pump phase noise causes clear spreading of the symbols around the unit circle with which is more severe for the higher amplitude symbols in 16QAM. It implies that with incoherent DFB pumps, the phase noise from pump severely deteriorates the swapped QAM signals. It can also be confirmed from the measured BER curves as a function of OSNR (0.1 nm) for both input and swapped signals. With coherent DFB pump, around 0.6 dB and 3 dB power penalties at BER of 10−3 were obtained for QPSK and 16QAM, respectively. As discussed above, this is mainly attributed to the crosstalk introduced by finite ER (20dB). However, in case of freerunning pumps, although it was still possible to obtain BER curve for swapped QPSK, ~3.4 dB penalty and visible error-floor at BER of 5×10−4 were clearly observed. Due to the susceptibility of 16QAM against phase noise and crosstalk, it becomes impossible to obtain BER plot for the swapped 16QAM. This verifies the effectiveness of the elimination of the pump phase noise in the OWE for high-order QAM with coherent pumps.

Optical Signal Processing for High-Order Quadrature-Amplitude Modulation Formats http://dx.doi.org/10.5772/61681 17

**Figure 14.** Measured BER vs. OSNR of the input and swapped QAM signals.

**in HNLF**

10-3

length, finally realizing data exchange between two wavelengths in single device. So far, several works have been demonstrated through non-degenerate FWM in highly-nonlinear

**BTB Coherent Pump Free-running Pumps**

**(a) (b) (c)**

**(d) (e) (f)**

**Figure 13.** Measured constellations of input and converted signals after wavelength exchange (16QAM and QPSK).

pump phase noise in the OWE for high-order QAM with coherent pumps.

Here, we apply the coherent pumping concept to wavelength exchange to demonstrate pump-phase-noise free wavelength exchange in PPLN. For experimental demonstration, an experimental setup similar to the one shown in Fig. 9 was deployed by adding another input signal. Two input signals modulated in 16QAM and QPSK, respectively were launched to PPLN as input signals for performing wavelength exchange. To evaluate the performance of wavelength exchange, BER and constellations were measured. The constellations of the swapped signals with different pump configurations are depicted in Fig. 13. With coherent pumps, clear constellations are observed for both QPSK and 16QAM. However, with DFB free-running pumps, the presence of pump phase noise causes clear spreading of the symbols around the unit circle with which is more severe for the higher amplitude symbols in 16QAM. It implies that with incoherent DFB pumps, the phase noise from pump severely deteriorates the swapped QAM signals. It can also be confirmed from the measured BER curves as a function of OSNR (0.1 nm) for both input and swapped signals. With coherent DFB pump, around 0.6 dB and 3 dB power penalties at BER of 10−3 were obtained for QPSK and 16QAM, respectively. As discussed above, this is mainly attributed to the crosstalk introduced by finite ER (20dB). However, in case of freerunning pumps, although it was still possible to obtain BER curve for swapped QPSK, ~3.4 dB penalty and visible error-floor at BER of 5×10−4 were clearly observed. Due to the susceptibility of 16QAM against phase noise and crosstalk, it becomes impossible to obtain BER plot for the swapped 16QAM. This verifies the effectiveness of the elimination of the

fiber [21–24] or cascaded second-order nonlinearities in PPLN waveguide [25–26].

**10G**

**12.5G**

**B. 16Q**

**A**

**M**

**B. Q**

**P**

**S**

**K**

16 Applications of Digital Signal Processing through Practical Approach

#### **3.2. Pump-phase-noise-free wavelength multicasting of high-order QAM by FWM in HNLF** 10-4 BER

With the emergence of high-bandwidth point-to-multipoint applications such as highdefinition Internet TV, big-data sharing, and data center migration, the need for wavelength multicasting has arisen recently to improve the network throughput and decrease the blocking probability in optical networks. Through multicasting, the network wavelength resources could be efficiently and flexibly managed in wavelength division multiplexing networks. Recently, it has also shown the application of wavelength multicasting in the all-optical spectrum defragmentation in elastic optical networks (EON) [27]. All-optical multicast through the nonlinearities in HNLF [28–30], SOA [31] and silicon nanowire waveguide [32] has been reported. **Figure 14.** Measured BER vs. OSNR of the input and swapped QAM signals. <sup>0</sup> <sup>2</sup> <sup>4</sup> <sup>6</sup> <sup>8</sup> <sup>10</sup> <sup>12</sup> <sup>14</sup> <sup>16</sup> <sup>18</sup> <sup>20</sup> <sup>22</sup> <sup>10</sup>-6 10-5 OSNR(dB) BtB 12.5GBaud 16QAM BtB 10GBaud QPSK Coh. Pumps WE: 12.5GBaud 16QAM Coh. Pumps WE: 10GBaud QPSK F.-R. Pumps WE:10GBaud QPSK

**3.2 Pump‐phase‐noise‐free wavelength multicasting of high‐order QAM by FWM**

**Figure 15.** Operation principle of wavelength multicasting based on FWM in HNLF. **Figure 15.** Operation principle of wavelength multicasting based on FWM in HNLF.

With the proposed coherent pumping, it is possible to achieve pump-phase-noise-free wavelength multicasting as well. Figure 15 illustrates the operation principle of the proposed pump-phase-noise-free wavelength multicasting scheme based on FWM with coherent multicarrier pump. With the input three pumps at ω1, ω2, ω3, and input signal at ωs, seven multi‐ casted channels, including the original input signal, are uniformly generated with a spacing of ∆ω. The frequency spacing settings of ∆ω and 2∆ω between ω1 and ω2, ω2 and ω<sup>3</sup> could efficiently avoid the overlapping of spectrum among multicasted channels. It finally leads to a uniform frequency allocation of the multicasted signals alongside of the input signal with a spacing of ∆ω, which is important to realizing all-optical spectrum defragmentation [27]. The generated six components next to input signal are the non-degenerate FWM components with the frequencies of ωsij\*, where i,j ∈[1, 2, 3], i≠j, and \* symbolizes the conjugate operation. The following equation shows the resultant phase in the multicasted signal at ωsij\*:

$$
\boldsymbol{\Theta}\_{\text{output}} = \boldsymbol{\Theta}\_{\text{input}} \pm \left( \boldsymbol{\Delta} \boldsymbol{\Theta}\_{\text{pl}} - \boldsymbol{\Delta} \boldsymbol{\Theta}\_{\text{p}\natural} \right) + \boldsymbol{\mathbb{C}} = \boldsymbol{\Theta}\_{\text{input}} \pm \boldsymbol{\Delta} \boldsymbol{\Theta}\_{\text{pump}} + \boldsymbol{\mathbb{C}} \tag{3}
$$

where ∆θpump =∆θpi-∆θpj, and θoutput, θinput, ∆θpi, ∆θpj, and *C* are the phase of the output and input signals, the phase noise from pump i, j where i, j∈[1, 2, 3], and a constant term, respectively. When the pumps are coherent in phase, it is obvious that the phase noise from pumps are eliminated in the multicasted signals, i.e. ∆θpump=0. Therefore, the wavelength multicasting becomes tolerant against the phase noise from the pumps. Hence, lower-cost DFB lasers can be used as pump source. In practice, an optical comb with a spacing of ∆ω could be employed to generate the coherent multi-carrier pump followed by an optical processor. The optical processor could ether be a liquid crystal on silicon (LCoS) device or cascaded band-pass and notch filters to select coherent carriers with desired spacing. The multicasting scale and the channel spacing of multicasted signals could be simply re-configured by programming the optical processor. The coherent pumping concept has been applied to wavelength conversion to remove the phase noise from the local pumps [18]. It is more beneficial and cost-effective when coherent pumping scheme is extended to multicasting with the flexible coherent multicarrier pumping.

**Figure 16.** Experimental setup of pump‐phase‐noise‐free 1 to 7 wavelength **Figure 16.** Experimental setup of pump-phase-noise-free 1 to 7 wavelength multicasting based FWM in HNLF.

To verify the proposed pump‐phase‐noise‐free wavelength multicasting, a 1‐to‐7 multicasting experiment for QPSK and 16QAM signals was conducted with the setup shown in Fig. 16. Different from the setup shown in Fig. 9, a coherent multi‐carrier pump is used as pump source, and a piece of highly‐nonlinear fiber (HNLF) with length of 150 m is deployed as nonlinear media. The deployed HNLF has an attenuation coefficient of 0.9dB/km, a nonlinear coefficient of 18/W/km, a zero‐dispersion wavelength of 1548 nm, a dispersion slope of around 0.02ps/nm2

m) is sufficient to achieve the FWM‐based wavelength multicasting. To retain the coherence of pumps, the short lengths, low and flat dispersion profile of the deployed HNLF are helpful to maintain the coherence of the pumps when propagating in HNLF. The constellations of the input and multicasted QPSK and16QAM signals with different pumping configurations are shown in Fig. 17. Even using DFB as pump laser, clear constellations are observed with coherent 3‐carrier pumping. However, in the case of free‐running DFB pumping, for the newly‐produced components, clear symbol spreading around the unit circle occurred due to the phase noise from DFB pumps. It happens especially for the outer symbols with higher amplitude in 16QAM. The measured BER curves as function of OSNR (0.1 nm) is depicted in Fig. 18. For both QPSK and 16QAM, less than 0.8 dB power penalty was obtained at BER=10<sup>−</sup><sup>3</sup> for all of the seven multicasted signals with respect to the input signal with coherent pumping. On the other hand, owing to the strong phase noise transferred from the noisy pumps with free‐running DFB pumping, error‐floor at BER of 1×10<sup>−</sup><sup>3</sup> and 4×10<sup>−</sup><sup>3</sup> was observed for QPSK and 16QAM, respectively. The effectiveness of the elimination of the pump phase noise is verified in the

multicasting for QAM signals with coherent multi‐carrier pumping.

/m). Thanks to its high nonlinearity, a short length of HNLF (150

/km

multicasting based FWM in HNLF.

4

and low4 (2×10<sup>−</sup>56s

To verify the proposed pump-phase-noise-free wavelength multicasting, a 1-to-7 multicasting experiment for QPSK and 16QAM signals was conducted with the setup shown in Fig. 16. Different from the setup shown in Fig. 9, a coherent multi-carrier pump is used as pump source, and a piece of highly-nonlinear fiber (HNLF) with length of 150 m is deployed as nonlinear media. The deployed HNLF has an attenuation coefficient of 0.9dB/km, a nonlinear coefficient of 18/W/km, a zero-dispersion wavelength of 1548 nm, a dispersion slope of around 0.02ps/nm2 /km and low β4 (2×10−56s4 /m). Thanks to its high nonlinearity, a short length of HNLF (150 m) is sufficient to achieve the FWM-based wavelength multicasting. To retain the coherence of pumps, the short lengths, low and flat dispersion profile of the deployed HNLF are helpful to maintain the coherence of the pumps when propagating in HNLF. The constel‐ lations of the input and multicasted QPSK and16QAM signals with different pumping configurations are shown in Fig. 17. Even using DFB as pump laser, clear constellations are observed with coherent 3-carrier pumping. However, in the case of free-running DFB pump‐ ing, for the newly-produced components, clear symbol spreading around the unit circle occurred due to the phase noise from DFB pumps. It happens especially for the outer symbols with higher amplitude in 16QAM. The measured BER curves as function of OSNR (0.1 nm) is depicted in Fig. 18. For both QPSK and 16QAM, less than 0.8 dB power penalty was obtained at BER=10−3 for all of the seven multicasted signals with respect to the input signal with coherent pumping. On the other hand, owing to the strong phase noise transferred from the noisy pumps with free-running DFB pumping, error-floor at BER of 1×10−3 and 4×10−3 was observed for QPSK and 16QAM, respectively. The effectiveness of the elimination of the pump phase noise is verified in the multicasting for QAM signals with coherent multi-carrier pumping.

pump-phase-noise-free wavelength multicasting scheme based on FWM with coherent multicarrier pump. With the input three pumps at ω1, ω2, ω3, and input signal at ωs, seven multi‐ casted channels, including the original input signal, are uniformly generated with a spacing of ∆ω. The frequency spacing settings of ∆ω and 2∆ω between ω1 and ω2, ω2 and ω<sup>3</sup> could efficiently avoid the overlapping of spectrum among multicasted channels. It finally leads to a uniform frequency allocation of the multicasted signals alongside of the input signal with a spacing of ∆ω, which is important to realizing all-optical spectrum defragmentation [27]. The generated six components next to input signal are the non-degenerate FWM components with the frequencies of ωsij\*, where i,j ∈[1, 2, 3], i≠j, and \* symbolizes the conjugate operation. The

following equation shows the resultant phase in the multicasted signal at ωsij\*:

 qq

q

carrier pumping.

 q

18 Applications of Digital Signal Processing through Practical Approach

multicasting based FWM in HNLF.

4

and low4 (2×10<sup>−</sup>56s

output input pi pj ( ) *C C* input pump

where ∆θpump =∆θpi-∆θpj, and θoutput, θinput, ∆θpi, ∆θpj, and *C* are the phase of the output and input signals, the phase noise from pump i, j where i, j∈[1, 2, 3], and a constant term, respectively. When the pumps are coherent in phase, it is obvious that the phase noise from pumps are eliminated in the multicasted signals, i.e. ∆θpump=0. Therefore, the wavelength multicasting becomes tolerant against the phase noise from the pumps. Hence, lower-cost DFB lasers can be used as pump source. In practice, an optical comb with a spacing of ∆ω could be employed to generate the coherent multi-carrier pump followed by an optical processor. The optical processor could ether be a liquid crystal on silicon (LCoS) device or cascaded band-pass and notch filters to select coherent carriers with desired spacing. The multicasting scale and the channel spacing of multicasted signals could be simply re-configured by programming the optical processor. The coherent pumping concept has been applied to wavelength conversion to remove the phase noise from the local pumps [18]. It is more beneficial and cost-effective when coherent pumping scheme is extended to multicasting with the flexible coherent multi-

**Figure 16.** Experimental setup of pump‐phase‐noise‐free 1 to 7 wavelength

**Figure 16.** Experimental setup of pump-phase-noise-free 1 to 7 wavelength multicasting based FWM in HNLF.

To verify the proposed pump‐phase‐noise‐free wavelength multicasting, a 1‐to‐7 multicasting experiment for QPSK and 16QAM signals was conducted with the setup shown in Fig. 16. Different from the setup shown in Fig. 9, a coherent multi‐carrier pump is used as pump source, and a piece of highly‐nonlinear fiber (HNLF) with length of 150 m is deployed as nonlinear media. The deployed HNLF has an attenuation coefficient of 0.9dB/km, a nonlinear coefficient of 18/W/km, a zero‐dispersion wavelength of 1548 nm, a dispersion slope of around 0.02ps/nm2

m) is sufficient to achieve the FWM‐based wavelength multicasting. To retain the coherence of pumps, the short lengths, low and flat dispersion profile of the deployed HNLF are helpful to maintain the coherence of the pumps when propagating in HNLF. The constellations of the input and multicasted QPSK and16QAM signals with different pumping configurations are shown in Fig. 17. Even using DFB as pump laser, clear constellations are observed with coherent 3‐carrier pumping. However, in the case of free‐running DFB pumping, for the newly‐produced components, clear symbol spreading around the unit circle occurred due to the phase noise from DFB pumps. It happens especially for the outer symbols with higher amplitude in 16QAM. The measured BER curves as function of OSNR (0.1 nm) is depicted in Fig. 18. For both QPSK and 16QAM, less than 0.8 dB power penalty was obtained at BER=10<sup>−</sup><sup>3</sup> for all of the seven multicasted signals with respect to the input signal with coherent pumping. On the other hand, owing to the strong phase noise transferred from the noisy pumps with free‐running DFB pumping, error‐floor at BER of 1×10<sup>−</sup><sup>3</sup> and 4×10<sup>−</sup><sup>3</sup> was observed for QPSK and 16QAM, respectively. The effectiveness of the elimination of the pump phase noise is verified in the

multicasting for QAM signals with coherent multi‐carrier pumping.

/m). Thanks to its high nonlinearity, a short length of HNLF (150

/km

 q

 q= ± D -D + = ±D + (3)

**Figure 17.** Measured constellations of input and converted signals with coherent pumping and free-running pumping schemes. QPSK: (a)~(c); 16QAM: (d)~(f).

**Figure 18.** Measured BER vs. OSNR curves for (a) QPSK and (b) 16QAM multicasting systems.

#### **3.3. Summary**

In this section, in order to avoid the phase noise introduced from local pumps, coherent pumping concept has been proposed. Through experimental demonstration based on either cascaded second-order nonlinearities in PPLN or third-order nonlinearity in HNLF, we have successfully demonstrated that, even using low-cost noisy DFB lasers as pump source, the phase noise from local pumps could be effectively avoided in optical signal processing for high-order QAM signals, including wavelength conversion, wavelength exchange, and wavelength multicasting. However, in cases of free-running DFB pumps, it is impossible to obtain clear constellations for QAM signals, especially for 16QAM and 64QAM signals, which was significantly deteriorated by the large phase noise from DFB pumps.

#### **4. Future works**

To properly conduct optical signal processing for advanced high-order QAM signals, several issues have been addressed in this chapter. We also discussed proposed coherent pumping schemes for realizing the phase-noise-free optical signal processing for high-order QAM signals. For further study and investigation, the following aspects could be considered.

**1.** Phase-noise-free processing for multi-carrier high-order signals

Here, the study and investigation of phase-noise-free optical signal processing are mainly focusing on the single-carrier high-order modulation formats like high-order QAMs. It is also applicable to the multi-carrier high-order signals, such as coherent optical OFDM (CO-OFDM) with subcarriers modulated in high-order QAMs. Such QAM-CO-OFDM also suffers from the susceptibility against phase noise, especially for CO-OFDM with high-order QAM subcarrier modulations [33]. Therefore, it is highly desirable to further apply the coherent pumping concept to demonstrate the phase-noise-free processing for multi-carrier high-order signals in the near future.

**2.** Reconfigurable coherent optical multi-carrier

As we point out in the above sections, coherent optical multi-carrier could be produced by an optical comb followed by optical signal processing, which is usually an LCoS-based compo‐ nent. It is cost effective to share multi-carrier for multi-channel signal processing. However, it is still costly to include LCoS-based optical processor in optical signal processing subsystems. Thus, it is interesting to further develop cost-effective coherent multi-carrier with reconfigur‐ able tone number and spacing. It will be one of key components for realizing reconfigurable optical signal processing in the future.

**3.** Other nonlinear media to realize optical signal processing

The experimental demonstration reported here is mainly focusing on HNLF and PPLN devices. Obviously, it could also be implemented in other nonlinear media like SOA especially quantum-dot SOA [34], and silicon waveguides [35].

#### **5. Conclusion**

**Figure 18.** Measured BER vs. OSNR curves for (a) QPSK and (b) 16QAM multicasting systems.

20 Applications of Digital Signal Processing through Practical Approach

was significantly deteriorated by the large phase noise from DFB pumps.

**1.** Phase-noise-free processing for multi-carrier high-order signals

In this section, in order to avoid the phase noise introduced from local pumps, coherent pumping concept has been proposed. Through experimental demonstration based on either cascaded second-order nonlinearities in PPLN or third-order nonlinearity in HNLF, we have successfully demonstrated that, even using low-cost noisy DFB lasers as pump source, the phase noise from local pumps could be effectively avoided in optical signal processing for high-order QAM signals, including wavelength conversion, wavelength exchange, and wavelength multicasting. However, in cases of free-running DFB pumps, it is impossible to obtain clear constellations for QAM signals, especially for 16QAM and 64QAM signals, which

To properly conduct optical signal processing for advanced high-order QAM signals, several issues have been addressed in this chapter. We also discussed proposed coherent pumping schemes for realizing the phase-noise-free optical signal processing for high-order QAM signals. For further study and investigation, the following aspects could be considered.

Here, the study and investigation of phase-noise-free optical signal processing are mainly focusing on the single-carrier high-order modulation formats like high-order QAMs. It is also applicable to the multi-carrier high-order signals, such as coherent optical OFDM (CO-OFDM) with subcarriers modulated in high-order QAMs. Such QAM-CO-OFDM also suffers from the susceptibility against phase noise, especially for CO-OFDM with high-order QAM subcarrier modulations [33]. Therefore, it is highly desirable to further apply the coherent pumping concept to demonstrate the phase-noise-free processing for multi-carrier high-order signals in

**3.3. Summary**

**4. Future works**

the near future.

Local pump lasers are indispensable for conducting optical signal processing for optical signals. For phase-noise-sensitive advanced modulation formats, the phase noise from local pumps are critical to be considered in order to realize superior optical signal processing. In this chapter, optical signal processing technology for high-order QAM signals has been discussed, with focus on wavelength conversion, wavelength exchange and wavelength multicasting for high-order QAM signals. To design high-performance optical signal process‐ ing subsystems, both linear and nonlinear phase noise and distortions are the main concerns in the system design. We first investigated the effective monitoring approach to optimize the performance of wavelength conversion for avoiding undesired nonlinear phase noise and distortions. Then, in the following sections, we discussed our proposed coherent pumping scheme to eliminate the linear phase noise from local pumps in order to realize pump-phasenoise-free wavelength conversion, wavelength exchange and multicasting for high-order QAM signals. Experimental demonstrations were present to verify the feasibility of the proposed coherent pumping schemes.

#### **Acknowledgements**

We acknowledge Takahide Sakamoto, Tetsuya Kawanishi, André Albuquerque, Benjamin J. Puttnam, Miguel Drummond, Rogério Nogueira, Atsushi Kanno, Satoshi Shinada, Naoya Wada for their collaborations, and the generous support of Grant-in-Aid for Scientific Research (C) (15K06033), and Grant-in-Aid for Young Scientist (A) (25709031) from the Ministry of Education, Science, Sports and Culture (MEXT), Japan.

#### **Author details**

Guo-Wei Lu\*

Address all correspondence to: gordon.guoweilu@gmail.com

Tokai University, Japan

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Address all correspondence to: gordon.guoweilu@gmail.com

22 Applications of Digital Signal Processing through Practical Approach

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## **High-Base Optical Signal Proccessing**

### Jian Wang and Alan E. Willner

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/61504

#### **Abstract**

Optical signal processing is a promising technique to enable fast data information proc‐ essing in the optical domain. Traditional optical signal processing functions pay more at‐ tention to binary modulation formats (i.e., binary numbers) with single-bit information contained in one symbol. The ever-growing data traffic has propelled great success in high-speed optical signal transmission by using advanced multilevel modulation formats (i.e., high-base numbers), which encode multiple-bit information in one symbol with re‐ sultant enhanced transmission capacity and efficient spectrum usage. A valuable chal‐ lenge would be to perform various optical signal processing functions for multilevel modulation formats, i.e., high-base optical signal processing. In this chapter, we review recent research works on high-base optical signal processing for multilevel modulation formats by exploiting degenerate and nondegenerate four-wave mixing in highly nonlin‐ ear fibers or silicon photonic devices. Grooming high-base optical signal processing func‐ tions including high-base wavelength conversion, high-base data exchange, high-base optical computing, and high-base optical coding/decoding are demonstrated. High-base optical signal processing may facilitate advanced data management and superior net‐ work performance.

**Keywords:** High-base optical signal processing, multilevel modulation format, four-wave mixing, wavelength conversion, data exchange, optical computing, coding/decoding

#### **1. Introduction**

The arrival of the era of big data has fuelled the increasing demand on both high-speed signal transmission and fast signal processing, which are known as two themes of great importance for optical communications. The advances in fiber-optic technologies have resulted in great success in delivering high-speed data signals in optical fiber transmission links [1-5]. The rapid development of photonics technologies has also promoted increasing interest for optical signal processing, which is regarded as a promising solution to facilitate high-speed signal processing

© 2015 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

in the optical domain and to eliminate complicated, inefficient, low-latency, and powerconsuming optical-to-electrical-to-optical (O-E-O) conversions [6]. At network nodes of advanced photonic networks, different optical signal processing functions might be required to enable increased network flexibility and efficiency. Remarkably, nonlinear optics has offered great potential to develop optical signal processing in high-speed photonic networks using various optical nonlinearities [6-20]. Miscellaneous optical signal processing functions have been demonstrated, such as wavelength conversion, wavelength (de)multiplexing, wave‐ length multicasting, data exchange, add/drop, optical addressing, optical switching, optical logic gate, optical computing, optical format conversion, optical correlation, optical equaliza‐ tion, optical regeneration, tunable optical delay, optical coding/decoding, etc. [21-53]. These optical signal processing operations are enabled by exploiting different nonlinear effects in different nonlinear optical devices. The typical nonlinear effects include cross-gain modulation (XGM), self-phase modulation (SPM), cross-phase modulation (XPM), two-photon absorption (TPA), degenerate and nondegenerate four-wave mixing (FWM), second-harmonic generation (SHG), sum-frequency generation (SFG), difference-frequency generation (DFG), cascaded second-harmonic generation and difference-frequency generation (cSHG/DFG), and cascaded sum- and difference-frequency generation (cSFG/DFG). Typical nonlinear optical devices based on different platforms include semiconductor optical amplifiers (SOAs), highly nonlin‐ ear fibers (HNLFs), periodically poled lithium niobate (PPLN) waveguides, chalcogenide (As2S3) waveguides, silicon waveguides, and photonic crystal waveguides. It is noted that most of previous research efforts are dedicated to optical signal processing for binary modulation formats such as on–off keying (OOK), differential phase-shift keying (DPSK), and binary phase-shift keying (BPSK). Despite favorable operation performance achieved for binary optical signal processing, it suffers limited bitrate and low spectral efficiency since only singlebit information is carried by each symbol for binary modulation formats.

With the rapid growth of global broadband and mobile data traffic, high transmission capacity and high spectral efficiency are highly desirable. Fortunately, recent advances in multilevel modulation formats, coherent detection, and digital signal processing have led to tremendous increase in transmission capacity and spectral efficiency [54-63]. Beyond great progress in highspeed signal transmission, processing multilevel modulation formats in the optical domain could be another interesting topic compatible with superior network performance and advanced data management. Typically, multilevel modulation formats contain multiple bits in one symbol, e.g., 2, 3, and 4 bits in one symbol for quadrature phase-shift keying (QPSK), 8-ary phase-shift keying (8PSK), star 8-ary quadrature amplitude modulation (Star-8QAM), 16-ary phase-shift keying (16PSK), star 16-ary quadrature amplitude modulation (Star-16QAM), and square 16-ary quadrature amplitude modulation (Square-16QAM) (Fig. 1). Moreover, multiple points in the constellation plane can be used to represent high-base numbers, e.g., quaternary number for QPSK, octal numbers for 8PSK and Star-8QAM, and hexadecimal numbers for 16PSK, Star-16QAM and Square-16QAM (Fig. 1). Despite great success in transmission links using multilevel modulation formats [64-69], there have been relatively limited research efforts dedicated to their manipulation in the optical domain (i.e., high-base optical signal processing). In this scenario, a laudable goal would be to develop miscellaneous high-base optical signal processing functions for multilevel modulation formats [70-86]. The aforementioned optical nonlinearities in various nonlinear optical devices would be promising candidates to facilitate grooming high-base optical signal processing operations. 69], there have been relatively limited research efforts dedicated to their manipulation in the optical domain (i.e., high‐base optical signal processing). In this scenario, a laudable goal would be to develop miscellaneous high‐base optical signal processing functions for

(Square‐16QAM) (Fig. 1). Moreover, multiple points in the constellation plane can be used

In this chapter, we provide a comprehensive report of our recent research works on high-base optical signal processing for multilevel modulation formats by exploiting optical nonlinearities [71, 73-75, 77, 79, 80, 83, 85, 86]. The demonstrated high-base optical signal processing functions include wavelength conversion using degenerate FWM in a silicon waveguide [83], data exchange using degenerate/nondegenerate FWM in HNLFs or silicon-organic hybrid slot waveguides [71, 73, 74, 86], optical computing using degenerate/nondegenerate FWM in HNLFs or silicon–organic hybrid slot waveguides [75, 77, 80, 85], and optical coding/decoding using degenerate FWM in HNLFs [79]. multilevel modulation formats [70‐86]. The aforementioned optical nonlinearities in various nonlinear optical devices would be promising candidates to facilitate grooming high‐base optical signal processing operations. In this chapter, we provide a comprehensive report of our recent research works on high‐base optical signal processing for multilevel modulation formats by exploiting optical nonlinearities. The demonstrated high‐base optical signal processing functions include wavelength conversion using degenerate FWM in a silicon waveguide, data exchange using degenerate/nondegenerate FWM in HNLFs or silicon‐organic hybrid slot waveguides, optical computing using degenerate/nondegenerate FWM in HNLFs or silicon–organic

hybrid slot waveguides, and optical coding/decoding using degenerate FWM in HNLFs.

Fig. 1. Schematic constellations of advanced multilevel modulation formats representing high‐base (quaternary, octal, hexadecimal) numbers (QPSK, Star‐8QAM/8PSK, 16PSK/Star‐ 16QAM/Square‐16QAM). **Figure 1.** Schematic constellations of advanced multilevel modulation formats representing high-base (quaternary, oc‐ tal, hexadecimal) numbers (QPSK, Star-8QAM/8PSK, 16PSK/Star-16QAM/Square-16QAM).

#### **2. High‐Base Wavelength Conversion 2. High-base wavelength conversion [83]**

in the optical domain and to eliminate complicated, inefficient, low-latency, and powerconsuming optical-to-electrical-to-optical (O-E-O) conversions [6]. At network nodes of advanced photonic networks, different optical signal processing functions might be required to enable increased network flexibility and efficiency. Remarkably, nonlinear optics has offered great potential to develop optical signal processing in high-speed photonic networks using various optical nonlinearities [6-20]. Miscellaneous optical signal processing functions have been demonstrated, such as wavelength conversion, wavelength (de)multiplexing, wave‐ length multicasting, data exchange, add/drop, optical addressing, optical switching, optical logic gate, optical computing, optical format conversion, optical correlation, optical equaliza‐ tion, optical regeneration, tunable optical delay, optical coding/decoding, etc. [21-53]. These optical signal processing operations are enabled by exploiting different nonlinear effects in different nonlinear optical devices. The typical nonlinear effects include cross-gain modulation (XGM), self-phase modulation (SPM), cross-phase modulation (XPM), two-photon absorption (TPA), degenerate and nondegenerate four-wave mixing (FWM), second-harmonic generation (SHG), sum-frequency generation (SFG), difference-frequency generation (DFG), cascaded second-harmonic generation and difference-frequency generation (cSHG/DFG), and cascaded sum- and difference-frequency generation (cSFG/DFG). Typical nonlinear optical devices based on different platforms include semiconductor optical amplifiers (SOAs), highly nonlin‐ ear fibers (HNLFs), periodically poled lithium niobate (PPLN) waveguides, chalcogenide (As2S3) waveguides, silicon waveguides, and photonic crystal waveguides. It is noted that most of previous research efforts are dedicated to optical signal processing for binary modulation formats such as on–off keying (OOK), differential phase-shift keying (DPSK), and binary phase-shift keying (BPSK). Despite favorable operation performance achieved for binary optical signal processing, it suffers limited bitrate and low spectral efficiency since only single-

28 Applications of Digital Signal Processing through Practical Approach

bit information is carried by each symbol for binary modulation formats.

With the rapid growth of global broadband and mobile data traffic, high transmission capacity and high spectral efficiency are highly desirable. Fortunately, recent advances in multilevel modulation formats, coherent detection, and digital signal processing have led to tremendous increase in transmission capacity and spectral efficiency [54-63]. Beyond great progress in highspeed signal transmission, processing multilevel modulation formats in the optical domain could be another interesting topic compatible with superior network performance and advanced data management. Typically, multilevel modulation formats contain multiple bits in one symbol, e.g., 2, 3, and 4 bits in one symbol for quadrature phase-shift keying (QPSK), 8-ary phase-shift keying (8PSK), star 8-ary quadrature amplitude modulation (Star-8QAM), 16-ary phase-shift keying (16PSK), star 16-ary quadrature amplitude modulation (Star-16QAM), and square 16-ary quadrature amplitude modulation (Square-16QAM) (Fig. 1). Moreover, multiple points in the constellation plane can be used to represent high-base numbers, e.g., quaternary number for QPSK, octal numbers for 8PSK and Star-8QAM, and hexadecimal numbers for 16PSK, Star-16QAM and Square-16QAM (Fig. 1). Despite great success in transmission links using multilevel modulation formats [64-69], there have been relatively limited research efforts dedicated to their manipulation in the optical domain (i.e., high-base optical signal processing). In this scenario, a laudable goal would be to develop miscellaneous high-base optical signal processing functions for multilevel modulation formats

We demonstrate high‐base all‐optical wavelength conversions of multicarrier, multilevel modulation signals based on degenerate FWM in a silicon waveguide. Coherent multicarrier, We demonstrate high-base all-optical wavelength conversions of multicarrier, multilevel modulation signals based on degenerate FWM in a silicon waveguide. Coherent multicarrier, multilevel modulations, i.e., orthogonal frequency-division multiplexing (OFDM) combined with advanced multilevel quadrature amplitude modulation (mQAM), are employed in the experiment.

Shown in Fig. 2(a) is the schematic cross section of a typical silicon waveguide. The calculated mode distribution using finite element method (FEM) is depicted in Fig. 2(b), from which one can see the tight light confinement in the top silicon region due to the high contrast index of the silicon waveguide. The measured scanning electron microscope (SEM) images of the fabricated silicon waveguide and grating coupling region are shown in Fig. 2(c) and (d). We fabricate the silicon waveguide on a silicon-on-insulator (SOI) wafer, on the top of which the silicon thickness is 340 nm with a 2-μm-thick buried oxide (BOX) layer. Using electron-beam lithography (EBL), followed by induced coupled plasma (ICP) etching, the desired silicon waveguide is formed for on-chip, high-base wavelength conversion.

**Figure 2.** (a) Cross section and (b) calculated mode distribution of a typical silicon waveguide. (c)(d) Measured scan‐ ning electron microscope (SEM) images of the fabricated silicon waveguide and grating coupling region.

Figure 3 illustrates the wavelength conversion process based on degenerate FWM in a silicon waveguide. One OFDM m-QAM carrying data signal and one continuous-wave (CW) pump are launched into the silicon waveguide. When propagating along the silicon waveguide, pump photons are annihilated to create signal photons and newly converted idler photons through degenerate FWM process. At the output of the silicon waveguide, the converted idler takes the OFDM m-QAM data information carried by the input signal and the wavelength conversion from input signal to output idler is achieved. It is noted that the performance degradation of high-base wavelength conversion by degenerate FWM process can be ascribed to the accumulated phase noise transferred from the input pump and signal. Since the constellations of higher-order modulations (e.g., 16/32/64/128-QAM) inherently have a smaller phase noise tolerance due to the smaller spacing between adjacent constellation points, it is challengeable to realize high-base wavelength conversion of OFDM m-QAM signals, espe‐ cially for higher-order modulations such as OFDM 16/32/64/128-QAM.

Shown in Fig. 4 is the experimental setup for high-base wavelength conversion of OFDM 16/32/64/128-QAM signals using a silicon waveguide. At the transmitter, an external cavity laser (ECL1) at 1563.849 nm is modulated by a single-polarization optical I/Q modulator. An arbitrary waveform generator (AWG) running at 10 GS/s sampling rate is used to produce the electrical OFDM m-QAM signal (m=16, 32, 64, 128). The transmitted OFDM signal is generated off-line from a data sequence of 231-1 pseudo random binary sequences (PRBS) and then mapped onto m-QAM constellation. The OFDM m-QAM signal is constructed by 82 subcar‐

fabricated silicon waveguide and grating coupling region are shown in Fig. 2(c) and (d). We fabricate the silicon waveguide on a silicon-on-insulator (SOI) wafer, on the top of which the silicon thickness is 340 nm with a 2-μm-thick buried oxide (BOX) layer. Using electron-beam lithography (EBL), followed by induced coupled plasma (ICP) etching, the desired silicon

**Figure 2.** (a) Cross section and (b) calculated mode distribution of a typical silicon waveguide. (c)(d) Measured scan‐

Figure 3 illustrates the wavelength conversion process based on degenerate FWM in a silicon waveguide. One OFDM m-QAM carrying data signal and one continuous-wave (CW) pump are launched into the silicon waveguide. When propagating along the silicon waveguide, pump photons are annihilated to create signal photons and newly converted idler photons through degenerate FWM process. At the output of the silicon waveguide, the converted idler takes the OFDM m-QAM data information carried by the input signal and the wavelength conversion from input signal to output idler is achieved. It is noted that the performance degradation of high-base wavelength conversion by degenerate FWM process can be ascribed to the accumulated phase noise transferred from the input pump and signal. Since the constellations of higher-order modulations (e.g., 16/32/64/128-QAM) inherently have a smaller phase noise tolerance due to the smaller spacing between adjacent constellation points, it is challengeable to realize high-base wavelength conversion of OFDM m-QAM signals, espe‐

Shown in Fig. 4 is the experimental setup for high-base wavelength conversion of OFDM 16/32/64/128-QAM signals using a silicon waveguide. At the transmitter, an external cavity laser (ECL1) at 1563.849 nm is modulated by a single-polarization optical I/Q modulator. An arbitrary waveform generator (AWG) running at 10 GS/s sampling rate is used to produce the electrical OFDM m-QAM signal (m=16, 32, 64, 128). The transmitted OFDM signal is generated off-line from a data sequence of 231-1 pseudo random binary sequences (PRBS) and then mapped onto m-QAM constellation. The OFDM m-QAM signal is constructed by 82 subcar‐

ning electron microscope (SEM) images of the fabricated silicon waveguide and grating coupling region.

cially for higher-order modulations such as OFDM 16/32/64/128-QAM.

waveguide is formed for on-chip, high-base wavelength conversion.

30 Applications of Digital Signal Processing through Practical Approach

**Figure 3.** Illustration of high-base wavelength conversion of OFDM m-QAM signals based on degenerate FWM in a silicon waveguide.

riers, in which 78 subcarriers are used to carry the payloads with m-QAM signal, while 4 subcarriers are selected as the pilots with 4-QAM loading to estimate the phase noise. Another inverse fast Fourier transform (IFFT) with a size of 256 is used to convert the signal to time domain. No cyclic prefix (CP) is used as the signal passes through a system without dispersiondominated devices. For the channel estimation, 10 training symbols are used for every 468 payload symbols in a manner of [A 0], where "A" denotes one OFDM m-QAM symbol. Another ECL (ECL2) employed as the pump is set at 1560.61 nm with a 6-dBm output power. Two polarization controllers (PC1, PC2) are used to adjust the polarization states of signal and pump, respectively. After the signal amplification by an erbium-doped fiber amplifier (EDFA1) with a maximum output power of 27 dBm and pump amplification by a second EDFA (EDFA2) with a maximum output power of 30 dBm, the signal and pump are combined with a wavelength selective switch (WSS) and then vertically coupled into the silicon waveguide, in which degenerate FWM process takes place to enable the wavelength conversion from the signal to the converted idler. In the experiment, the signal is amplified to 25.5 dBm by EDFA1 and the pump is amplified to 27 dBm by EDFA2. The WSS not only combines the amplified signal and pump together but also suppresses the amplified spontaneous emission (ASE) noise from two EDFAs. After the wavelength conversion, the signal, pump, and newly converted idler are vertically coupled out from the silicon waveguide. After the amplification by a third EDFA (EDFA3), the converted idler is filtered using a tunable optical filter (TOF) with a bandwidth of 0.4 nm. A variable optical attenuator (VOA) and one more EDFA (EDFA4) are employed to adjust the received optical signal-to-noise ratio (OSNR) for proper detection by the coherent receiver. At the receiver, the optical signal is first mixed with a local oscillator (LO) by an optical hybrid and detected by a typical balanced coherent receiver. The line width of the employed laser sources including ECL1, ECL2, and LO in the experiment is around 100 kHz. The obtained two radio frequency (RF) signals for the IQ components are sent into a Tektronix real-time digital oscilloscope acquired at 50 GS/s and processed off-line with a MATLAB program. The offline digital processing of the received signal includes: 1) carrier frequency offset estimation and OFDM window synchronization; 2) fast Fourier transform (FFT); 3) channel estimation; 4) phase noise estimation (crucial to m-QAM signal); 5) constel‐ lation decision and bit-error rate (BER) calculation.

**Figure 4.** Experimental setup for high-base wavelength conversion of OFDM m-QAM signals using a silicon wave‐ guide. ECL: external cavity laser; AWG: arbitrary waveform generator; PC: polarization controller; TOF: tunable opti‐ cal filter; VOA: variable optical attenuator; LO: local oscillator; EDFA: erbium-doped fiber amplifier.

In order to characterize the performance of high-base wavelength conversion of OFDM m-QAM signals, we measure the BER curves as a function of received OSNR for back-to-back (Bto-B) and converted idler. Shown in Fig. 5(a)-(d) are measured BER performance for high-base wavelength conversions of OFDM 16-QAM, OFDM 32-QAM, OFDM 64-QAM, and OFDM 128-QAM, respectively. As shown in Fig. 5(a), for OFDM 16-QAM wavelength conversion the required OSNR at the 7% forward error correction (FEC) threshold (BER=1x10-3) is 7.8 and 10.8 dB for the B-to-B signal and converted idler, respectively. The observed OSNR penalty is around 3 dB for OFDM 16-QAM wavelength conversion. Similarly, the received OSNR penalties of ~4 dB at 7% FEC threshold in Fig. 5(b), ~3.5 dB in Fig. 5(c) at 20% FEC threshold and ~4.5 dB in Fig. 5(d) at 20% FEC threshold are observed for high-base wavelength conver‐ sions of OFDM 32-QAM, OFDM 64-QAM, and OFDM 128-QAM, respectively. The right insets of Fig. 5(a)-(d) depict corresponding constellations of the B-to-B signals and converted idlers at the given OSNR values. One can see clear constellations of converted idlers, indicating favorable operation performance achieved for on-chip, high-base, all-optical wavelength conversions of multicarrier, multilevel modulation (OFDM 16/32/64/128-QAM) signals using a silicon waveguide.

#### **3. High-base optical data exchange [71, 73, 74, 86]**

We propose and demonstrate high-base all-optical data exchange of advanced multilevel modulation signals based on degenerate/nondegenerate FWM in HNLFs or silicon–organic hybrid slot waveguides.

MATLAB program. The offline digital processing of the received signal includes: 1) carrier frequency offset estimation and OFDM window synchronization; 2) fast Fourier transform (FFT); 3) channel estimation; 4) phase noise estimation (crucial to m-QAM signal); 5) constel‐

**Figure 4.** Experimental setup for high-base wavelength conversion of OFDM m-QAM signals using a silicon wave‐ guide. ECL: external cavity laser; AWG: arbitrary waveform generator; PC: polarization controller; TOF: tunable opti‐

In order to characterize the performance of high-base wavelength conversion of OFDM m-QAM signals, we measure the BER curves as a function of received OSNR for back-to-back (Bto-B) and converted idler. Shown in Fig. 5(a)-(d) are measured BER performance for high-base wavelength conversions of OFDM 16-QAM, OFDM 32-QAM, OFDM 64-QAM, and OFDM 128-QAM, respectively. As shown in Fig. 5(a), for OFDM 16-QAM wavelength conversion the required OSNR at the 7% forward error correction (FEC) threshold (BER=1x10-3) is 7.8 and 10.8 dB for the B-to-B signal and converted idler, respectively. The observed OSNR penalty is around 3 dB for OFDM 16-QAM wavelength conversion. Similarly, the received OSNR penalties of ~4 dB at 7% FEC threshold in Fig. 5(b), ~3.5 dB in Fig. 5(c) at 20% FEC threshold and ~4.5 dB in Fig. 5(d) at 20% FEC threshold are observed for high-base wavelength conver‐ sions of OFDM 32-QAM, OFDM 64-QAM, and OFDM 128-QAM, respectively. The right insets of Fig. 5(a)-(d) depict corresponding constellations of the B-to-B signals and converted idlers at the given OSNR values. One can see clear constellations of converted idlers, indicating favorable operation performance achieved for on-chip, high-base, all-optical wavelength conversions of multicarrier, multilevel modulation (OFDM 16/32/64/128-QAM) signals using

We propose and demonstrate high-base all-optical data exchange of advanced multilevel modulation signals based on degenerate/nondegenerate FWM in HNLFs or silicon–organic

cal filter; VOA: variable optical attenuator; LO: local oscillator; EDFA: erbium-doped fiber amplifier.

**3. High-base optical data exchange [71, 73, 74, 86]**

lation decision and bit-error rate (BER) calculation.

32 Applications of Digital Signal Processing through Practical Approach

a silicon waveguide.

hybrid slot waveguides.

**Figure 5.** Measured BER versus received OSNR for high-base wavelength conversions of multicarrier, multilevel mod‐ ulation signals. (a) OFDM 16-QAM. (b) OFDM 32-QAM. (c) OFDM 64-QAM. (d) OFDM 128-QAM.

We first demonstrate high-base optical data exchange of 100-Gbit/s return-to-zero differential QPSK (RZ-DQPSK) signals. The concept and principle for high-base optical data exchange of DQPSK modulation signals between two different wavelengths (S1:*λ<sup>S</sup>* <sup>1</sup>, S2:*λ<sup>S</sup>* <sup>2</sup>) are depicted in Fig. 6. The four-level phase information carried by two DQPSK signals at different wave‐ lengths is swapped after the data exchange, as shown in Fig. 6(a). To perform high-base optical data exchange of DQPSK signals carrying phase information, the optical data exchange operation is expected to be phase transparent. Using the parametric depletion effect in a single HNLF, one may realize phase-transparent optical data exchange. Figure 6(b) depicts the principle of operation of parametric depletion. Two CW pumps (P1:*λP*1, P2:*λP*2) and signal 1 (S1:*λ<sup>S</sup>* <sup>1</sup>) are fed into the HNLF. P1 and S1 are symmetrical about the zero-dispersion wave‐ length (ZDM) of HNLF. When propagating along the HNLF, the photons of P1 and S1 are annihilated to create the photons of P2 and S2 (1 / *λ<sup>S</sup>* <sup>2</sup> + 1 / *λP*<sup>2</sup> =1 / *λ<sup>S</sup>* <sup>1</sup> + 1 / *λP*1) by the nonde‐ generate FWM process. Thus, the parametric depletion of S1 is expected with its data infor‐ mation copied onto a newly generated S2. Similarly, the depletion of S2 accompanied by the creation of S1 is realized during the nondegenerate FWM process when sending two pumps and S2 into the HNLF. Figure 6(c) shows the principle of operation of optical data exchange. Two pumps and two signals are simultaneously launched into the HNLF. When P1(P2) and S1(S2) are almost symmetrical about the ZDW of HNLF, S1(S2) can be consumed to produce S2(S1) by appropriately adjusting the power of two pumps. As a consequence, one can implement optical data exchange between two signals (S1, S2).

Remarkably, under the nondepletion approximation and proper control of pump powers, one can easily derive linear relationships (*AS* <sup>1</sup> ' ∝ *AS* <sup>2</sup> ⋅ *AP*<sup>2</sup> ⋅ *AP*<sup>1</sup> \* , *AS* <sup>2</sup> ' ∝ *AS* <sup>1</sup> ⋅ *AP*<sup>1</sup> ⋅ *AP*<sup>2</sup> \* ) of complex amplitudes between the output signals (*AS* <sup>1</sup> ' , *AS* <sup>2</sup> ' ) and input signals and pumps (*AS* <sup>1</sup>, *AS* 2, *AP*1, *AP*2). The linear complex amplitude relationships imply that nondegenerate FWM-based highbase data exchange has the characteristic of transparency to the modulation format including the phase transparency. We can further obtain the phase relationships of *φ<sup>S</sup>* <sup>1</sup> '=*φ<sup>S</sup>* <sup>2</sup> + *φP*<sup>2</sup> −*φ <sup>P</sup>*<sup>1</sup> and *φ<sup>S</sup>* <sup>2</sup> '=*φ<sup>S</sup>* <sup>1</sup> + *φP*<sup>1</sup> −*φ <sup>P</sup>*2. It is worth noting that phase modulation is always applied to the pumps (*φ <sup>P</sup>*1, *φ <sup>P</sup>*2) to effectively suppress the stimulated Brillouin scattering (SBS) effect in HNLF. As a result, the pump power is efficiently utilized in the nondegenerate FWM process, which benefits the effective parametric depletion and data exchange. Remarkably, the pump phase transfer to the exchanged signals might cause serious trouble for the DQPSK data exchange. Fortunately, according to the deduced phase relationships, it is possible to cancel the pump phase transfer by applying the precisely identical phase modulation to the two pumps (i.e., *φ <sup>P</sup>*1=*φ <sup>P</sup>*2), which makes it possible to implement the high-base data exchange of DQPSK or other multilevel modulation signals containing phase information. *Updated Figures* 

Figure 6. (a) Concept of high-base optical data exchange of DQPSK modulation signals. (b)(c) Principle of nondegenerate FWM-based parametric depletion and high-base optical data exchange. **Figure 6.** (a) Concept of high-base optical data exchange of DQPSK modulation signals. (b)(c) Principle of nondegener‐ ate FWM-based parametric depletion and high-base optical data exchange.

S1 (before data exchange) S2 (before data exchange) Ch. I Ch. I Ch. Q Ch. Q Ch. I S1 (after wavelength conversion: S2 to S1) Ch. Q Ch. I S1 (after data exchange: S2 to S1) Ch. Q (a1) (b1) (c1) (d1) (a2) (b2) (c2) (d2) In the experiment, two CW pumps (P1: 1564.4 nm, P2: 1558.6 nm) together with two 100-Gbit/ s RZ-DQPSK signals (S1: 1539.4 nm, S2: 1545.4 nm) are coupled into a 1-km piece of HNLF with a nonlinear coefficient of 9.1 W-1·km-1, a ZDW of ~1552 nm, and a fiber loss of 0.45 dB/km. The DQPSK optical data exchange is realized in the HNLF based on the parametric depletion effect of the nondegenerate FWM process. For the 100-Gbit/s DQPSK optical data exchange, shown in Fig. 7 are the measured temporal waveforms of demodulated channel I (Ch. I) and channel Q (Ch. Q). One can clearly see from Fig. 7 that after the nondegenerate FWM-based optical data exchange, the data information swapping between two 100-Gbit/s RZ-DQPSK signals is successfully implemented. Additionally, when looking at the temporal waveforms

Ch. I S2 (after wavelength conversion: S1 to S2) Ch. Q

(e2)

(f2)

**Ch. I Ch. Q** 

**Ch. I Ch. Q** 

**Ch. I Ch. Q**

**Ch. I Ch. Q** 

**DQPSK 0 1 1 0 0 1**

**DQPSK 1 0 0 1 0 1**

**DQPSK 1 0 0 1 1 1** 

**DQPSK** 

*<sup>P</sup>* t

**1 1 1 0 0 0**

**1 0 1 0 0 0**

**0 0 1 1 1 0**

**1 0 1 1 1 1** 

**1 0 0 0 1 1** 

t t

t t

t t

t

(e1)

(f1)

**1 1 1** 

**0**

**0 0**

t t

t t

t t

t t

**1 1** 

**1 1 1**

**1 1 1 1 1 1 1** 

**1 0 0 0**

**0 0 0** 

**1 1 1**

**0 0 0 0 0 0** 

**1 1**

**0 0** 

**1 1**

**1**

**0**

**0 0** 

**1 1** 

**0 0**

Ch. I S2 (after data exchange: S1 to S2) Ch. Q

Figure 7. Measured temporal waveforms of demodulated channel I (Ch. I) and channel Q (Ch. Q) for high-base optical data exchange of 100-Gbit/s DQPSK signals. (a1)(a2) S1 is ON, P1 is OFF, and P2 is OFF. (b1)(b2) S2 is ON, P1 is OFF, and P2 is OFF. (c1)(c2) S2 to S1 wavelength conversion. S1 is OFF, S2 is ON, P1 is ON, and P2 is ON. (d1)(d2) S2 to S1 data exchange. S1 is ON, S2 is ON, P1 is ON, and P2 is ON. (e1)(e2) S1 to S2 wavelength conversion. S1 is ON, S2 is OFF, P1 is ON, and P2 is ON. (f1)(f2) S1 to S2 data exchange. S1 is ON, S2 is ON, P1 is

**HNLF**

S1 S2 Pump

> S1 S2

**S2 S2** 

**FWM**

**Multi-channel**

**IN OUT**

**Data Exchange** 

**S1 S1** 

Figure 11. Concept and principle of simultaneous multichannel, high-base data exchange of DQPSK signals.

**S4 S4** 

 *S*1*S* 2

**S1 Pump**

*S* 4

S3 S4

S3 S4

Pump

*S* 3

**S2 S3 S4** 

**S3 S3** 

ON, and P2 is ON.

**DQPSK** 

**DQPSK** 

**DQPSK** 

**DQPSK** 

**Ch. I Ch. Q**

**Ch. I Ch. Q**

**Ch. I Ch. Q**

**Ch. I Ch. Q**

**S1**

3

after wavelength conversion with only S1 or S2 present and the temporal waveforms after data exchange with both S1 and S2 present, the performance degradation of temporal waveforms after data exchange is observed with increased noise. Such phenomenon can be explained with the fact that the beating effect between the newly converted signal and original residual signal induces added noise. Figure 6. (a) Concept of high-base optical data exchange of DQPSK modulation signals. (b)(c) Principle of **S1&S2 Data Exchange** *S*1 *S* 2 *P*2 *P*1 **ZDW (c)** *P*1 **ZDW Parametric Depletion (b)** *S*1 *S* 2 *P*2

nondegenerate FWM-based parametric depletion and high-base optical data exchange.

π/2 π <sup>3</sup>π/2 π/2

**DQPSK Pumps** 

**S1: ON, S2: OFF** 

 *S*1 *S* 2

**S1** 

**DQPSK** 

*Updated Figures* 

<sup>0</sup>π π <sup>3</sup>π/2 π/2 π <sup>3</sup>π/2 π/2

**Data Exchange** 

**Input Output** 

**DQPSK DQPSK** 

**S2 S2 (a)**

 *S*1 *S* 2 <sup>0</sup> π π <sup>3</sup>π/2

**DQPSK Pumps** 

amplitudes between the output signals (*AS* <sup>1</sup>

34 Applications of Digital Signal Processing through Practical Approach

**S1** 

 *S*1 *S* 2

Ch. I

(a1)

(b1)

(c1)

(d1)

(e1)

(f1)

**1 1 1** 

**0**

**0 0**

t t

t t

t t

t t

**1 1** 

**1 1 1**

**1 1 1 1 1 1 1** 

**1 0 0 0**

**0 0 0** 

**1 1 1**

**0 0 0 0 0 0** 

**1 1**

**0 0** 

**1 1** 

**0 0**

**0**

**0 0** 

**1 1**

**1**

Ch. I

Ch. I

and *φ<sup>S</sup>* <sup>2</sup>

ON, and P2 is ON.

**DQPSK** 

**DQPSK** 

**DQPSK** 

**DQPSK** 

**Ch. I Ch. Q**

**Ch. I Ch. Q**

**Ch. I Ch. Q**

**Ch. I Ch. Q** ' , *AS* <sup>2</sup> '

the phase transparency. We can further obtain the phase relationships of *φ<sup>S</sup>* <sup>1</sup>

DQPSK or other multilevel modulation signals containing phase information.

*AP*2). The linear complex amplitude relationships imply that nondegenerate FWM-based highbase data exchange has the characteristic of transparency to the modulation format including

pumps (*φ <sup>P</sup>*1, *φ <sup>P</sup>*2) to effectively suppress the stimulated Brillouin scattering (SBS) effect in HNLF. As a result, the pump power is efficiently utilized in the nondegenerate FWM process, which benefits the effective parametric depletion and data exchange. Remarkably, the pump phase transfer to the exchanged signals might cause serious trouble for the DQPSK data exchange. Fortunately, according to the deduced phase relationships, it is possible to cancel the pump phase transfer by applying the precisely identical phase modulation to the two pumps (i.e., *φ <sup>P</sup>*1=*φ <sup>P</sup>*2), which makes it possible to implement the high-base data exchange of

*Updated Figures* 

<sup>0</sup>π π <sup>3</sup>π/2 π/2 π <sup>3</sup>π/2 π/2

**Data Exchange** 

**Input Output** 

**DQPSK DQPSK** 

**S2 S2 (a)**

 *S*1 *S* 2 <sup>0</sup> π π <sup>3</sup>π/2

**S1&S2 Data Exchange**

 *P*2 *P*1

(a2)

(b2)

(c2)

(d2)

(e2)

(f2)

**Ch. I Ch. Q** 

**Ch. I Ch. Q** 

**Ch. I Ch. Q**

**Ch. I Ch. Q** 

**DQPSK 0 1 1 0 0 1**

**DQPSK 1 0 0 1 0 1**

**DQPSK 1 0 0 1 1 1** 

**DQPSK** 

*<sup>P</sup>* t

**1 1 1 0 0 0**

**1 0 1 0 0 0**

**0 0 1 1 1 0**

**1 0 1 1 1 1** 

**1 0 0 0 1 1** 

t t

t t

t t

t

Ch. Q

Ch. Q

**S1**

**S1: ON, S2: ON** 

**DQPSK Pumps** 

**(c)**

**ZDW**

Figure 6. (a) Concept of high-base optical data exchange of DQPSK modulation signals. (b)(c) Principle of

**Figure 6.** (a) Concept of high-base optical data exchange of DQPSK modulation signals. (b)(c) Principle of nondegener‐

S1 (before data exchange)

In the experiment, two CW pumps (P1: 1564.4 nm, P2: 1558.6 nm) together with two 100-Gbit/ s RZ-DQPSK signals (S1: 1539.4 nm, S2: 1545.4 nm) are coupled into a 1-km piece of HNLF with a nonlinear coefficient of 9.1 W-1·km-1, a ZDW of ~1552 nm, and a fiber loss of 0.45 dB/km. The DQPSK optical data exchange is realized in the HNLF based on the parametric depletion effect of the nondegenerate FWM process. For the 100-Gbit/s DQPSK optical data exchange, shown in Fig. 7 are the measured temporal waveforms of demodulated channel I (Ch. I) and channel Q (Ch. Q). One can clearly see from Fig. 7 that after the nondegenerate FWM-based optical data exchange, the data information swapping between two 100-Gbit/s RZ-DQPSK signals is successfully implemented. Additionally, when looking at the temporal waveforms

S2 (before data exchange)

Ch. I S1 (after wavelength conversion: S2 to S1) Ch. Q

S1 (after data exchange: S2 to S1) Ch. Q

Ch. I S2 (after wavelength conversion: S1 to S2) Ch. Q

Ch. I S2 (after data exchange: S1 to S2) Ch. Q

*P*1

*P*2

 *S*1 *S* 2

Figure 7. Measured temporal waveforms of demodulated channel I (Ch. I) and channel Q (Ch. Q) for high-base optical data exchange of 100-Gbit/s DQPSK signals. (a1)(a2) S1 is ON, P1 is OFF, and P2 is OFF. (b1)(b2) S2 is ON, P1 is OFF, and P2 is OFF. (c1)(c2) S2 to S1 wavelength conversion. S1 is OFF, S2 is ON, P1 is ON, and P2 is ON. (d1)(d2) S2 to S1 data exchange. S1 is ON, S2 is ON, P1 is ON, and P2 is ON. (e1)(e2) S1 to S2 wavelength conversion. S1 is ON, S2 is OFF, P1 is ON, and P2 is ON. (f1)(f2) S1 to S2 data exchange. S1 is ON, S2 is ON, P1 is

**HNLF**

S1 S2 Pump

> S1 S2

**S2 S2** 

**FWM**

**Multi-channel**

**IN OUT**

**Data Exchange** 

**S1 S1** 

Figure 11. Concept and principle of simultaneous multichannel, high-base data exchange of DQPSK signals.

**S4 S4** 

 *S*1*S* 2

**S1 Pump**

*S* 4

S3 S4

S3 S4

Pump

*S* 3

**S2 S3 S4** 

**S3 S3** 

nondegenerate FWM-based parametric depletion and high-base optical data exchange.

π/2 π <sup>3</sup>π/2 π/2

**DQPSK Pumps** 

**(b)**

**S1: ON, S2: OFF** 

**ZDW**

**Parametric Depletion** 

ate FWM-based parametric depletion and high-base optical data exchange.

 *S*1 *S* 2

'=*φ<sup>S</sup>* <sup>1</sup> + *φP*<sup>1</sup> −*φ <sup>P</sup>*2. It is worth noting that phase modulation is always applied to the

) and input signals and pumps (*AS* <sup>1</sup>, *AS* 2, *AP*1,

'=*φ<sup>S</sup>* <sup>2</sup> + *φP*<sup>2</sup> −*φ <sup>P</sup>*<sup>1</sup>

3

S1 (before data exchange) S2 (before data exchange) Ch. I Ch. I Ch. Q Ch. Q Ch. I S1 (after wavelength conversion: S2 to S1) Ch. Q Ch. I Ch. I S2 (after wavelength conversion: S1 to S2) Ch. Q Ch. I S2 (after data exchange: S1 to S2) Ch. Q S1 (after data exchange: S2 to S1) Ch. Q (a1) (b1) (c1) (d1) (e1) (f1) (a2) (b2) (c2) (d2) (e2) (f2)

Figure 7. Measured temporal waveforms of demodulated channel I (Ch. I) and channel Q (Ch. Q) for high-base optical data exchange of 100-Gbit/s DQPSK signals. (a1)(a2) S1 is ON, P1 is OFF, and P2 is OFF. (b1)(b2) S2 is ON, P1 is OFF, and P2 is OFF. (c1)(c2) S2 to S1 wavelength conversion. S1 is OFF, S2 is ON, P1 is ON, and P2 is ON. (d1)(d2) S2 to S1 data exchange. S1 is ON, S2 is ON, P1 is ON, and P2 is ON. (e1)(e2) S1 to S2 wavelength conversion. S1 is ON, S2 is OFF, P1 is ON, and P2 is ON. (f1)(f2) S1 to S2 data exchange. S1 is ON, S2 is ON, P1 is **Figure 7.** Measured temporal waveforms of demodulated channel I (Ch. I) and channel Q (Ch. Q) for high-base optical data exchange of 100-Gbit/s DQPSK signals. (a1)(a2) S1 is ON, P1 is OFF, and P2 is OFF. (b1)(b2) S2 is ON, P1 is OFF, and P2 is OFF. (c1)(c2) S2 to S1 wavelength conversion. S1 is OFF, S2 is ON, P1 is ON, and P2 is ON. (d1)(d2) S2 to S1 data exchange. S1 is ON, S2 is ON, P1 is ON, and P2 is ON. (e1)(e2) S1 to S2 wavelength conversion. S1 is ON, S2 is OFF, P1 is ON, and P2 is ON. (f1)(f2) S1 to S2 data exchange. S1 is ON, S2 is ON, P1 is ON, and P2 is ON

ON, and P2 is ON. **HNLF Multi-channel Data Exchange FWM DQPSK 1 1 1 1 1 0 Ch. I Ch. Q 1 1 1 1 1 1 1 0 0 0 0 0 Ch. I Ch. Q 1 1 1 1 1 0 0 0 0 0 0 0 DQPSK Ch. I Ch. Q DQPSK 0 1 1 0 0 1 DQPSK 1 0 0 1 1 1 1 0 1 1 1 1 Ch. I Ch. Q DQPSK 1 0 0 1 0 1 1 0 0 0 1 1**  t t t t t t t t **S1 S1 S2 S2**  S1 S2 Pump S3 S4 S1 S2 S3 S4 Pump **IN OUT** Shown in Fig. 8 is the measured BER performance and balanced eyes for high-base optical data exchange of 100-Gbit/s DQPSK signals. One can see from Fig. 8 that for wavelength conversion with only S1 or S2 and two pumps present, the power penalty is assessed to be less than 1.2 dB at a BER of 10-9. In contrast, for data exchange with both two signals and two pumps present, the power penalty is measured to be less than 5 dB at a BER of 10-9. It is expected that the extra power penalty of the high-base data exchange compared to the wavelength conversion could be due to the beating effect between the newly converted signal and the original residual signal.

Figure 11. Concept and principle of simultaneous multichannel, high-base data exchange of DQPSK signals. *S* 4 **S1 Pump** *S*1*S* 2 *S* 3 **S2 S3 S4 Ch. I Ch. Q 1 1 1 0 0 0 Ch. I Ch. Q 1 1 1 1 1 1 0 0 0 0 0 0 DQPSK Ch. I Ch. Q 1 1 1 0 0 0 DQPSK Ch. I Ch. Q 0 0 1 1 1 0 1 0 1 0 0 0** t t t t t t t *<sup>P</sup>* t **S3 S3 S4 S4**  We further investigate the tolerance of pump misalignment and the dynamic range of input signal power for the 100-Gbit/s RZ-DQPSK data exchange. Shown in Fig. 9 is the measured relative power penalty as a function of the pump misalignment. One can clearly see that the performance degradation of wavelength conversion and data exchange becomes severe when the pump misalignment is larger than +/-2 ps. Actually, under relatively large pump phase misalignment, the residual phase due to incomplete pump phase cancellation is transferred to the phase noise added to the wavelength converted signal and data exchanged signal, resulting in the degradation of operation performance. Under different pump phase misalignments, the measured typical balanced eyes of demodulated signals after data exchange are also shown in

converted signal and the original residual signal.

ON, and P2 is ON.

performance degradation of temporal waveforms after data exchange is observed with increased noise. Such phenomenon can be explained with the fact that the beating effect between the newly converted signal and original residual signal induces added noise.

Fig. 7. Measured temporal waveforms of demodulated channel I (Ch. I) and channel Q (Ch. Q) for high‐base optical data exchange of 100‐Gbit/s DQPSK signals. (a1)(a2) S1 is ON, P1 is OFF, and P2 is OFF. (b1)(b2) S2 is ON, P1 is OFF, and P2 is OFF. (c1)(c2) S2 to S1 wavelength conversion. S1 is OFF, S2 is ON, P1 is ON, and P2 is ON. (d1)(d2) S2 to S1 data exchange. S1 is ON, S2 is ON, P1 is ON, and P2 is ON. (e1)(e2) S1 to S2 wavelength conversion. S1 is ON, S2 is OFF, P1 is ON, and P2 is ON. (f1)(f2) S1 to S2 data exchange. S1 is ON, S2 is ON, P1 is

Shown in Fig. 8 is the measured BER performance and balanced eyes for high‐base optical data exchange of 100‐Gbit/s DQPSK signals. One can see from Fig. 8 that for wavelength conversion with only S1 or S2 and two pumps present, the power penalty is assessed to be less than 1.2 dB at a BER of 10‐9. In contrast, for data exchange with both two signals and two pumps present, the power penalty is measured to be less than 5 dB at a BER

to the wavelength conversion could be due to the beating effect between the newly

Fig. 8. BER curves and balanced eyes for high‐base data exchange of 100‐Gbit/s DQPSK signals. (a) Ch. I. (b) Ch. Q. **Figure 8.** BER curves and balanced eyes for high-base data exchange of 100-Gbit/s DQPSK signals. (a) Ch. I. (b) Ch. Q.

the insets of Fig. 9. By comparing the balanced eyes shown in Fig. 8 with perfectly aligned two pumps, one can observe the performance degradation with added noise under pump phase misalignment of 3 ps and 4 ps. Especially, one can observe almost completely closed eyes of demodulated signals after data exchange under an even larger time misalignment of 10 ps between the two pumps. Consequently, precise time alignment between two pumps and resultant perfect pump phase cancellation is important and highly desired to obtain favorable operation performance for phase-transparent optical data exchange.

The measured received power versus the input signal power at a BER of 10-9 is shown in Fig. 10. Less than 3.5-dB fluctuation of the received power is observed at a BER of 10-9 when varying the input signal power from -12.0 to 8.1 dBm. Thus, the dynamic range of the input signal power is estimated to be around 20 dB for high-base optical data exchange of 100-Gbit/s RZ-DQPSK signals based on nondegenerated FWM process.

We then propose and demonstrate a simple alternative method to perform high-base data exchange between multichannel DQPSK signals using bidirectional degenerate FWM in a single HNLF accompanied by optical filtering. The concept and operation principle of multichannel, high-base optical data exchange is illustrated in Fig. 11. Four-channel DQPSK signals (S1-S4) and a single CW pump are used. Degenerate FWM process is employed. Note that four-channel DQPSK signals (S1-S4) are symmetrical about the CW pump. For multi‐ channel data exchange, one would expect to see simultaneous data information swapping between S1 and S4, S2 and S3. Generally speaking, for data exchange operation with two signals present, it is impossible to separate the newly converted signals from the original signals by unidirectional degenerate FWM process, so it is difficult to realize optical data

under an even larger time misalignment of 10 ps between the two pumps. Consequently, precise time alignment between two pumps and resultant perfect pump phase cancellation is important and highly desired to obtain favorable operation performance for phase‐

The measured received power versus the input signal power at a BER of 10‐9 is shown in Fig. 10. Less than 3.5‐dB fluctuation of the received power is observed at a BER of 10‐9

100‐Gbit/s RZ‐DQPSK signals based on nondegenerated FWM process.

transparent optical data exchange.

DQPSK signals. (a) Ch. I. (b) Ch. Q.

of 100‐Gbit/s DQPSK signals. (a) Ch. I. (b) Ch. Q.

Fig. 9. Impact of pump phase misalignment on the performance of high‐base data exchange of 100‐Gbit/s DQPSK signals. (a) Ch. I. (b) Ch. Q. **Figure 9.** Impact of pump phase misalignment on the performance of high-base data exchange of 100-Gbit/s DQPSK signals. (a) Ch. I. (b) Ch. Q. Fig. 9. Impact of pump phase misalignment on the performance of high‐base data exchange

the insets of Fig. 9. By comparing the balanced eyes shown in Fig. 8 with perfectly aligned two pumps, one can observe the performance degradation with added noise under pump phase misalignment of 3 ps and 4 ps. Especially, one can observe almost completely closed eyes of demodulated signals after data exchange under an even larger time misalignment of 10 ps between the two pumps. Consequently, precise time alignment between two pumps and resultant perfect pump phase cancellation is important and highly desired to obtain favorable

Fig. 8. BER curves and balanced eyes for high‐base data exchange of 100‐Gbit/s DQPSK

**Figure 8.** BER curves and balanced eyes for high-base data exchange of 100-Gbit/s DQPSK signals. (a) Ch. I. (b) Ch. Q.

WC (S2-to-S1) Ex. (S2-to-S1) WC (S2-to-S1) Ex. (S2-to-S1)

**S1 B-to-B**

Ex. (S1-to-S2)

**S2 B-to-B**

WC (S1-to-S2) Ex. (S1-to-S2) WC (S1-to-S2)

**S2 B-to-B**

**Ch. I Ch. Q**

performance degradation of temporal waveforms after data exchange is observed with increased noise. Such phenomenon can be explained with the fact that the beating effect between the newly converted signal and original residual signal induces added noise.

Fig. 7. Measured temporal waveforms of demodulated channel I (Ch. I) and channel Q (Ch. Q) for high‐base optical data exchange of 100‐Gbit/s DQPSK signals. (a1)(a2) S1 is ON, P1 is OFF, and P2 is OFF. (b1)(b2) S2 is ON, P1 is OFF, and P2 is OFF. (c1)(c2) S2 to S1 wavelength conversion. S1 is OFF, S2 is ON, P1 is ON, and P2 is ON. (d1)(d2) S2 to S1 data exchange. S1 is ON, S2 is ON, P1 is ON, and P2 is ON. (e1)(e2) S1 to S2 wavelength conversion. S1 is ON, S2 is OFF, P1 is ON, and P2 is ON. (f1)(f2) S1 to S2 data exchange. S1 is ON, S2 is ON, P1 is

Shown in Fig. 8 is the measured BER performance and balanced eyes for high‐base optical data exchange of 100‐Gbit/s DQPSK signals. One can see from Fig. 8 that for wavelength conversion with only S1 or S2 and two pumps present, the power penalty is assessed to be less than 1.2 dB at a BER of 10‐9. In contrast, for data exchange with both two signals and two pumps present, the power penalty is measured to be less than 5 dB at a BER of 10‐9. It is expected that the extra power penalty of the high‐base data exchange compared to the wavelength conversion could be due to the beating effect between the newly

ON, and P2 is ON.

signals. (a) Ch. I. (b) Ch. Q.

converted signal and the original residual signal.

36 Applications of Digital Signal Processing through Practical Approach

 **S1 B-to-B** 

The measured received power versus the input signal power at a BER of 10-9 is shown in Fig. 10. Less than 3.5-dB fluctuation of the received power is observed at a BER of 10-9 when varying the input signal power from -12.0 to 8.1 dBm. Thus, the dynamic range of the input signal power is estimated to be around 20 dB for high-base optical data exchange of 100-Gbit/s RZ-

We then propose and demonstrate a simple alternative method to perform high-base data exchange between multichannel DQPSK signals using bidirectional degenerate FWM in a single HNLF accompanied by optical filtering. The concept and operation principle of multichannel, high-base optical data exchange is illustrated in Fig. 11. Four-channel DQPSK signals (S1-S4) and a single CW pump are used. Degenerate FWM process is employed. Note that four-channel DQPSK signals (S1-S4) are symmetrical about the CW pump. For multi‐ channel data exchange, one would expect to see simultaneous data information swapping between S1 and S4, S2 and S3. Generally speaking, for data exchange operation with two signals present, it is impossible to separate the newly converted signals from the original signals by unidirectional degenerate FWM process, so it is difficult to realize optical data

operation performance for phase-transparent optical data exchange.

DQPSK signals based on nondegenerated FWM process.

Fig. 10. Dynamic range of input signal power for high‐base data exchange of 100‐Gbit/s DQPSK signals. (a) Ch. I. (b) Ch. Q. **Figure 10.** Dynamic range of input signal power for high-base data exchange of 100-Gbit/s DQPSK signals. (a) Ch. I. (b) Ch. Q.

exchange function based on unidirectional degenerate FWM in a single HNLF. We propose a possible solution by exploiting bidirectional degenerate FWM process in a single HNLF together with optical filtering. As illustrated in Fig. 11, taking four-channel optical data exchange as an example, there are four-channel DQPSK signals (S1-S4) at the input. 1) With optical filtering, S1 and S2 are selected and fed into the HNLF together with the CW pump from the left side. When propagating along the HNLF, S4 and S3 are generated by the degenerate FWM wavelength conversion process. After the generation of S4 and S3, the original S1, S2, and CW pump are suppressed, while the newly converted S4 and S3 are selected We then propose and demonstrate a simple alternative method to perform high‐base data exchange between multichannel DQPSK signals using bidirectional degenerate FWM in a single HNLF accompanied by optical filtering. The concept and operation principle of multichannel, high‐base optical data exchange is illustrated in Fig. 11. Four‐channel DQPSK signals (S1‐S4) and a single CW pump are used. Degenerate FWM process is employed. Note that four‐channel DQPSK signals (S1‐S4) are symmetrical about the CW pump. For multichannel data exchange, one would expect to see simultaneous data information swapping between S1 and S4, S2 and S3. Generally speaking, for data exchange operation with two signals present, it is impossible to separate the newly converted signals from the

original signals by unidirectional degenerate FWM process, so it is difficult to realize optical data exchange function based on unidirectional degenerate FWM in a single HNLF. We propose a possible solution by exploiting bidirectional degenerate FWM process in a single HNLF together with optical filtering. As illustrated in Fig. 11, taking four‐channel optical data exchange as an example, there are four‐channel DQPSK signals (S1‐S4) at the input. 1) (b1)

**S1** 

 *S*1 *S* 2

Ch. I

ON, and P2 is ON.

nondegenerate FWM-based parametric depletion and high-base optical data exchange.

π/2 π <sup>3</sup>π/2 π/2

**DQPSK Pumps** 

**S1: ON, S2: OFF (b)**

**ZDW**

**Parametric Depletion** 

 *S*1 *S* 2

by optical filtering at the right side of HNLF. 2) At the same time, with optical filtering at the input, S3 and S4 are selected and sent into the HNLF together with CW pump from the right side. During the propagation through the HNLF, S2 and S1 are created by the degenerate FWM wavelength conversion process. After producing S2 and S1, the original S3, S4 and CW pump are removed, while the newly generated S2 and S1 are selected via optical filtering at the left side of HNLF. For the selected S4 and S3 (carrying data information of original S1 and S2) from the left side and selected S2 and S1 (carrying data information of original S3 and S4) from the right side of the HNLF, it is noted that data information carried by S1 and S4, S2 and S3 are swapped. As a result, by employing a single HNLF, exploiting bidirectional degenerate FWM process, and using optical filtering, simultaneous four-channel optical data exchange between S1 and S4 as well as S2 and S3 can be implemented. The combined S1-S4 from the left and right sides of the HNLF correspond to the output four-channel signals after optical data exchange. Remarkably, since the degenerate FWM process has distinct phase-conjugation property, for DQPSK signals the in-phase (Ch. I) and quadrature (Ch. Q) components are also swapped after the optical data exchange operation. Figure 7. Measured temporal waveforms of demodulated channel I (Ch. I) and channel Q (Ch. Q) for high-base optical data exchange of 100-Gbit/s DQPSK signals. (a1)(a2) S1 is ON, P1 is OFF, and P2 is OFF. (b1)(b2) S2 is ON, P1 is OFF, and P2 is OFF. (c1)(c2) S2 to S1 wavelength conversion. S1 is OFF, S2 is ON, P1 is ON, and P2 is ON. (d1)(d2) S2 to S1 data exchange. S1 is ON, S2 is ON, P1 is ON, and P2 is ON. (e1)(e2) S1 to S2 wavelength conversion. S1 is ON, S2 is OFF, P1 is ON, and P2 is ON. (f1)(f2) S1 to S2 data exchange. S1 is ON, S2 is ON, P1 is Ch. I S1 (after wavelength conversion: S2 to S1) Ch. Q Ch. I Ch. I S2 (after wavelength conversion: S1 to S2) Ch. Q Ch. I S2 (after data exchange: S1 to S2) Ch. Q S1 (after data exchange: S2 to S1) Ch. Q (c1) (d1) (e1) (f1) (c2) (d2) (e2) (f2)

Figure 6. (a) Concept of high-base optical data exchange of DQPSK modulation signals. (b)(c) Principle of

S2 (before data exchange)

*P*1

*P*2

 *S*1 *S* 2

*Updated Figures* 

<sup>0</sup>π π <sup>3</sup>π/2 π/2 π <sup>3</sup>π/2 π/2

**Data Exchange** 

**Input Output** 

**DQPSK DQPSK** 

**S2 S2 (a)**

 *S*1 *S* 2 <sup>0</sup> π π <sup>3</sup>π/2

**S1&S2 Data Exchange**

 *P*2 *P*1

(a2)

(b2)

Ch. Q

Ch. Q

**S1**

**S1: ON, S2: ON** 

**DQPSK Pumps** 

**(c)**

**ZDW**

Figure 11. Concept and principle of simultaneous multichannel, high-base data exchange of DQPSK signals. **Figure 11.** Concept and principle of simultaneous multichannel, high-base data exchange of DQPSK signals.

In the experiment, the bidirectional degenerate FWM in a single HNLF is enabled by a fiber loop mirror configuration, which consists of an HNLF with a length of 460 m, two optical bandpass filters, and optical fiber couplers. The typical parameters of the HNLF are as follows: ZDW: ~1556 nm; nonlinear coefficient: 20 W-1·km-1; dispersion slope (*S*): ~0.026 ps/nm2 /km. Compared to the nondegenerate FWM-based data exchange with two pumps, single pump with its wavelength (1554.94 nm) close to the ZDW of HNLF is employed in the bidirectional degenerate FWM-based multichannel, high-base data exchange. ITU-grid-compatible fourchannel 100-Gbit/s RZ-DQPSK signals (S1: 1546.12 nm, S2: 1547.72 nm, S3: 1562.23 nm, S4: 1563.86 nm) are employed for multichannel, high-base data exchange.

3

Shown in Fig. 12(a) is the measured spectrum of input four-channel, 100-Gbit/s RZ-DQPSK signals. S1(S2) and S4(S3) are symmetrical about the CW pump. The measured spectrum after

4

four-channel optical data exchange with the CW pump ON is shown in Fig. 12(b) (solid blue line). For reference, the measured spectrum of residual signals with the CW pump OFF is also shown in Fig. 12(b) (dashed red line). It is expected that the residual signals are caused by the Rayleigh scattering in the HNLF. From Fig. 12(b), one can measure the extinction ratio of the newly exchanged signals to the residual signals to be 18.4 dB for S1, 19.5 dB for S2, 17 dB for S3, and 17 dB for S4, respectively.

by optical filtering at the right side of HNLF. 2) At the same time, with optical filtering at the input, S3 and S4 are selected and sent into the HNLF together with CW pump from the right side. During the propagation through the HNLF, S2 and S1 are created by the degenerate FWM wavelength conversion process. After producing S2 and S1, the original S3, S4 and CW pump are removed, while the newly generated S2 and S1 are selected via optical filtering at the left side of HNLF. For the selected S4 and S3 (carrying data information of original S1 and S2) from the left side and selected S2 and S1 (carrying data information of original S3 and S4) from the right side of the HNLF, it is noted that data information carried by S1 and S4, S2 and S3 are swapped. As a result, by employing a single HNLF, exploiting bidirectional degenerate FWM process, and using optical filtering, simultaneous four-channel optical data exchange between S1 and S4 as well as S2 and S3 can be implemented. The combined S1-S4 from the left and right sides of the HNLF correspond to the output four-channel signals after optical data exchange. Remarkably, since the degenerate FWM process has distinct phase-conjugation property, for DQPSK signals the in-phase (Ch. I) and quadrature (Ch. Q) components are also swapped after

Ch. I S1 (after wavelength conversion: S2 to S1) Ch. Q

S1 (after data exchange: S2 to S1) Ch. Q

Ch. I S2 (after wavelength conversion: S1 to S2) Ch. Q

Ch. I S2 (after data exchange: S1 to S2) Ch. Q

S2 (before data exchange)

Figure 7. Measured temporal waveforms of demodulated channel I (Ch. I) and channel Q (Ch. Q) for high-base optical data exchange of 100-Gbit/s DQPSK signals. (a1)(a2) S1 is ON, P1 is OFF, and P2 is OFF. (b1)(b2) S2 is ON, P1 is OFF, and P2 is OFF. (c1)(c2) S2 to S1 wavelength conversion. S1 is OFF, S2 is ON, P1 is ON, and P2 is ON. (d1)(d2) S2 to S1 data exchange. S1 is ON, S2 is ON, P1 is ON, and P2 is ON. (e1)(e2) S1 to S2 wavelength conversion. S1 is ON, S2 is OFF, P1 is ON, and P2 is ON. (f1)(f2) S1 to S2 data exchange. S1 is ON, S2 is ON, P1 is

**HNLF**

S1 S2 Pump

> S1 S2

**S2 S2** 

**FWM**

**Multi-channel**

**IN OUT**

**Data Exchange** 

**S1 S1** 

Figure 11. Concept and principle of simultaneous multichannel, high-base data exchange of DQPSK signals.

**Figure 11.** Concept and principle of simultaneous multichannel, high-base data exchange of DQPSK signals.

In the experiment, the bidirectional degenerate FWM in a single HNLF is enabled by a fiber loop mirror configuration, which consists of an HNLF with a length of 460 m, two optical bandpass filters, and optical fiber couplers. The typical parameters of the HNLF are as follows: ZDW: ~1556 nm; nonlinear coefficient: 20 W-1·km-1; dispersion slope (*S*): ~0.026 ps/nm2

Compared to the nondegenerate FWM-based data exchange with two pumps, single pump with its wavelength (1554.94 nm) close to the ZDW of HNLF is employed in the bidirectional degenerate FWM-based multichannel, high-base data exchange. ITU-grid-compatible fourchannel 100-Gbit/s RZ-DQPSK signals (S1: 1546.12 nm, S2: 1547.72 nm, S3: 1562.23 nm, S4:

Shown in Fig. 12(a) is the measured spectrum of input four-channel, 100-Gbit/s RZ-DQPSK signals. S1(S2) and S4(S3) are symmetrical about the CW pump. The measured spectrum after

**S4 S4** 

 *S*1*S* 2

1563.86 nm) are employed for multichannel, high-base data exchange.

**S1 Pump**

*S* 4

S3 S4

S3 S4

Pump

*S* 3

**S2 S3 S4** 

**S3 S3** 

Figure 6. (a) Concept of high-base optical data exchange of DQPSK modulation signals. (b)(c) Principle of

S1 (before data exchange)

*P*1

*P*2

 *S*1 *S* 2

nondegenerate FWM-based parametric depletion and high-base optical data exchange.

π/2 π <sup>3</sup>π/2 π/2

**DQPSK Pumps** 

**S1: ON, S2: OFF (b)**

**ZDW**

**Parametric Depletion** 

 *S*1 *S* 2

**S1** 

 *S*1 *S* 2

Ch. I

(a1)

38 Applications of Digital Signal Processing through Practical Approach

(b1)

(c1)

(d1)

(e1)

(f1)

**1 1 1** 

**0**

**0 0**

t t

t t

t t

t t

**1 1** 

**1 1 1**

**1 1 1 1 1 1 1** 

**1 0 0 0**

**1 1** 

**0 0**

**0 0 0** 

**1 1 1**

**0 0 0 0 0 0** 

**1 1**

**1**

**0**

Ch. I

Ch. I

*Updated Figures* 

<sup>0</sup>π π <sup>3</sup>π/2 π/2 π <sup>3</sup>π/2 π/2

**Data Exchange** 

**Input Output** 

**DQPSK DQPSK** 

**S2 S2 (a)**

 *S*1 *S* 2 <sup>0</sup> π π <sup>3</sup>π/2

**S1&S2 Data Exchange**

 *P*2 *P*1

(a2)

(b2)

(c2)

(d2)

(e2)

(f2)

**Ch. I Ch. Q** 

**Ch. I Ch. Q** 

**Ch. I Ch. Q**

**Ch. I Ch. Q** 

**DQPSK 0 1 1 0 0 1**

**DQPSK 1 0 0 1 0 1**

**DQPSK 1 0 0 1 1 1** 

**DQPSK** 

*<sup>P</sup>* t

**1 1 1 0 0 0**

**1 0 1 0 0 0**

**0 0 1 1 1 0**

**1 0 1 1 1 1** 

**1 0 0 0 1 1** 

t t

t t

t t

t

/km.

Ch. Q

Ch. Q

**S1**

**S1: ON, S2: ON** 

**DQPSK Pumps** 

**(c)**

**ZDW**

the optical data exchange operation.

**1 1**

**DQPSK** 

**DQPSK** 

**DQPSK** 

**DQPSK** 

**Ch. I Ch. Q**

**Ch. I Ch. Q**

**Ch. I Ch. Q**

**Ch. I Ch. Q**

ON, and P2 is ON.

Figure 12. Spectra for four-channel, high-base data exchange of DQPSK signals. (a) Input four-channel, 100-Gbit/s RZ-DQPSK signals. (b) Spectra measured in the absence (dashed curve: Rayleigh scattering)/presence (solid curve: after data exchange) of CW pump. **Figure 12.** Spectra for four-channel, high-base data exchange of DQPSK signals. (a) Input four-channel, 100-Gbit/s RZ-DQPSK signals. (b) Spectra measured in the absence (dashed curve: Rayleigh scattering)/presence (solid curve: after data exchange) of CW pump.

**Ch. I Ch. Q Ch. I S2 Back to Back Ch. Q S1 Back to Back Ch. Q Ch. I Ch. Q S3 to S2 Exchange Ch. I S4 to S1 Exchange S1 S1 S2 S2**  Figure 13 further displays temporal waveforms and balanced eyes of demodulated in-phase (Ch. I) and quadrature (Ch. Q) components of 100-Gbit/s RZ-DQPSK signals before and after four-channel high-base optical data exchange. One can clearly confirm the successful imple‐ mentation of simultaneous four-channel, 100-Gbit/s RZ-DQPSK optical data exchange between S1 and S4 as well as S2 and S3. Meanwhile, one can also see that for DQPSK signals, the Ch. I and Ch. Q components are swapped after optical data exchange, which is due to the optical phase-conjugation property of the degenerate FWM process.

**Ch. I S3 Back to Back Ch. Q Ch. Q S2 to S3 Exchange Ch. I S3 S3**  Figure 14 plots the BER curves for four-channel, high-base data exchange of 100-Gbit/s RZ-DQPSK signals. Less than 4.7-dB power penalty is observed at a BER of 10-9, which could be caused by the beating effect between the newly exchanged signals and the original residual signals.

Figure 13. Waveforms and balanced eyes of demodulated in-phase (Ch. I) and quadrature (Ch. Q) components for four-channel, high-base data exchange of 100-Gbit/s DQPSK signals. **Ch. I S4 Back to Back Ch. Q Ch. Q S1 to S4 Exchange Ch. I S4 S4**  Grating Unequalized N×100-Gbit/s By exploiting bidirectional degenerate FWM progress with a single pump in a single HNLF and employing liquid crystal on silicon (LCoS) technology in a double-pass configuration, we further propose a terabit-scale network grooming switch element, which can simultaneously perform multiple optical signal processing functions, e.g., high-base add/drop, high-base optical data exchange, and high-base power equalization. Using 23-channel, 100-Gbit/s RZ-DQPSK signals, we demonstrate reconfigurable 2.3-Tbit/s network grooming switch operation in the experiment. Remarkably, simultaneous implementation of all these high-base optical signal processing functions can potentially enhance the efficiency and flexibility of network management.

3

DQPSK Signals 1 2 7 3 6 4 5 Shown in Fig. 15 is the concept and operation principle of the proposed high-base, multifunc‐ tional grooming switch element that could be used at the network nodes. When multiple

New Signal Mirror

**Input**

Exchange

12 7 3 4 5 6

**Outpu**

for Add

Equalization:1-7

1

~7 **LCoS** 

Pump

Exchange

<sup>2</sup> <sup>3</sup> <sup>6</sup> <sup>7</sup>

3 6 <sup>7</sup> <sup>1</sup> <sup>4</sup>

**HNLF** 

5

A B C D E

<sup>4</sup> <sup>5</sup>

Fiber Array 2 Input/Output

Figure 15. Concept and principle of LCoS+HNLF-based multifunctional, high-base grooming switch (add/drop,

data exchange, power equalization).

1 Drop

1

Add

1540 1555 1570

**S1 S2 S3 S4**

curve: after data exchange) of CW pump.

Power (dBm)

10dB/div

RZ-DQPSK signals. (b) Spectra measured in the absence (dashed curve: Rayleigh scattering)/presence (solid

Figure 13 further displays temporal waveforms and balanced eyes of demodulated in‐

Fig. 12. Spectra for four‐channel, high‐base data exchange of DQPSK signals. (a) Input four‐

(a) **S1S2 S3 S4**

18.4

10dB/div

Power (dBm)

dB 19.5

dB

(b)

1540 1555 1570 Wavelength (nm)

17

Exchange

dB 17 dB

Figure 13. Waveforms and balanced eyes of demodulated in-phase (Ch. I) and quadrature (Ch. Q) components for four-channel, high-base data exchange of 100-Gbit/s DQPSK signals. **Figure 13.** Waveforms and balanced eyes of demodulated in-phase (Ch. I) and quadrature (Ch. Q) components for four-channel, high-base data exchange of 100-Gbit/s DQPSK signals. be caused by the beating effect between the newly exchanged signals and the original residual signals.

Unequalized

for Add

100‐Gbit/s DQPSK signals.

and flexibility of network management.

1 **Outpu** New Signal Mirror Exchange Fig. 14. Measured BER curves for simultaneous four‐channel, high‐base data exchange of **Figure 14.** Measured BER curves for simultaneous four-channel, high-base data exchange of 100-Gbit/s DQPSK signals.

Pump

wavelength-division multiplexed (WDM) channels with unequalized power levels arrive at the network nodes, one would expect to flexibly manipulate these signals in the optical domain, in order to reduce the network latency and enhance the network efficiency. The typical favorable grooming optical signal processing functions are as follows: 1) optical data exchange between two or multiple channels of interest; 2) dropping of one or multiple channels of interest and adding of corresponding one or multiple channels with new data information; 3) power equalization for all the WDM channels. Moreover, it is also expected that these optical signal processing functions (optical data exchange, add/drop, power equalization) could be switchable, selective, and reconfigurable. For simplicity, shown in Fig. 15 is an example with Figure 15. Concept and principle of LCoS+HNLF-based multifunctional, high-base grooming switch (add/drop, data exchange, power equalization). <sup>4</sup> <sup>5</sup> 1 Drop <sup>2</sup> <sup>3</sup> <sup>6</sup> <sup>7</sup> By exploiting bidirectional degenerate FWM progress with a single pump in a single HNLF and employing liquid crystal on silicon (LCoS) technology in a double‐pass configuration, we further propose a terabit‐scale network grooming switch element, which can simultaneously perform multiple optical signal processing functions, e.g., high‐base add/drop, high‐base optical data exchange, and high‐base power equalization. Using 23‐ channel, 100‐Gbit/s RZ‐DQPSK signals, we demonstrate reconfigurable 2.3‐Tbit/s network grooming switch operation in the experiment. Remarkably, simultaneous implementation of all these high‐base optical signal processing functions can potentially enhance the efficiency

7-channel WDM signals. A wavelength selective switch (WSS) using a two-dimensional (2D) array of LCoS pixels is employed in the setup. The operation principle of the LCoS-based WSS is as follows. By changing the voltages loaded to the LCoS, one can adjust the phase retardance of each pixel of LCoS. The 2D LCoS array includes two axes with one horizontal wavelength axis and the other vertical displacement axis. The input 7-channel 100-Gbit/s DQPSK signals with unequalized power levels are sent to the port A of the input/output fiber array through a circulator. A diffraction grating collecting the input signals from port A then disperses different wavelength channels to different horizontal positions of the LCoS. Along the vertical direction, many pixels (~400 pixels) are covered due to the divergence of the light. The manipulation mechanism relies on the control of the LCoS. Since the phase shift of each pixel of LCoS can be adjusted by varying its applied voltage, it is possible to flexibly manipulate the phase front of the light through the control of the 2D array of LCoS pixels. By appropriately adjusting the independent pixel voltage, the propagation direction of different wavelength channels can be flexibly controlled, i.e., different wavelength channels can be delivered to different spatial positions at the output ports (e.g., S1 sent to port B, S4 and S5 sent to port C, S2 and S3 sent to port D, S6 and S7 sent to port E). Meanwhile, the power levels of different wavelength channels delivered to the desired fiber array ports (port B, port C, port D, port E) can be also adjusted. After separating and delivering different wavelength channels to different output fiber array ports together with flexible power control, various grooming optical signal processing functions can be carried out on these output fiber array ports: 1) highbase optical data exchange between port D and port E; 2) high-base wavelength add and drop at port B; 3) high-base power equalization of all wavelength channels. For the high-base optical data exchange between port D and port E, simultaneous multichannel, high-base optical data exchange between S2 and S7 and between S3 and S6 can be implemented by exploiting bidirectional degenerate FWM through a single HNLF. When compared to the similar optical data exchange scheme using degenerate FWM and employing optical band-pass filters to select desired wavelength channels, here the channel separation and selection are accomplished by LCoS. When compared to the optical data exchange approach using parametric depletion effect of nondegenerate FWM process with two pumps, here only single pump is employed in the setup. In particular, the simultaneous multichannel optical data exchange operation is switchable when employing the programmable LCoS. For the high-base wavelength add and drop, the S1 DQPSK signal is dropped at port B and a new S1 with updated data information is also added to port B through a circulator. For the high-base power equalization, the flexible attenuation control for all WDM channels is available by programming LCoS. Besides optical data exchange (S2 and S7, S3 and S6) and add/drop (S1) operations on the channels of interest, other channels (S4 and S5) without undergoing these operations should be kept and delivered back. A fiber loop structure could be employed at the port C. Remarkably, after multiple grooming optical signal processing operations, it is preferred that all the signals are sent back to the same input/output fiber array port A, which not only imports unequalized multiple WDM signals but also exports all the signals after the grooming switching. Such function can be implemented simply by running the LCoS device in a double-pass configuration assisted by use of some optical circulators. As shown in Fig. 15, if we consider the dashed boxes as a grooming switch unit based on HNLF and LCoS, it is actually a multifunctional, high-base

wavelength-division multiplexed (WDM) channels with unequalized power levels arrive at the network nodes, one would expect to flexibly manipulate these signals in the optical domain, in order to reduce the network latency and enhance the network efficiency. The typical favorable grooming optical signal processing functions are as follows: 1) optical data exchange between two or multiple channels of interest; 2) dropping of one or multiple channels of interest and adding of corresponding one or multiple channels with new data information; 3) power equalization for all the WDM channels. Moreover, it is also expected that these optical signal processing functions (optical data exchange, add/drop, power equalization) could be switchable, selective, and reconfigurable. For simplicity, shown in Fig. 15 is an example with

**Figure 14.** Measured BER curves for simultaneous four-channel, high-base data exchange of 100-Gbit/s DQPSK signals.

Fig. 14. Measured BER curves for simultaneous four‐channel, high‐base data exchange of

New Signal Mirror

<sup>4</sup> <sup>5</sup>

By exploiting bidirectional degenerate FWM progress with a single pump in a single HNLF and employing liquid crystal on silicon (LCoS) technology in a double‐pass configuration, we further propose a terabit‐scale network grooming switch element, which can simultaneously perform multiple optical signal processing functions, e.g., high‐base add/drop, high‐base optical data exchange, and high‐base power equalization. Using 23‐ channel, 100‐Gbit/s RZ‐DQPSK signals, we demonstrate reconfigurable 2.3‐Tbit/s network grooming switch operation in the experiment. Remarkably, simultaneous implementation of all these high‐base optical signal processing functions can potentially enhance the efficiency

1

~7

Figure 15. Concept and principle of LCoS+HNLF-based multifunctional, high-base grooming switch (add/drop,

Figure 13. Waveforms and balanced eyes of demodulated in-phase (Ch. I) and quadrature (Ch. Q) components for

**Figure 13.** Waveforms and balanced eyes of demodulated in-phase (Ch. I) and quadrature (Ch. Q) components for

Grating

**S4 S4** 

Figure 14 plots the BER curves for four‐channel, high‐base data exchange of 100‐Gbit/s RZ‐DQPSK signals. Less than 4.7‐dB power penalty is observed at a BER of 10‐9, which could be caused by the beating effect between the newly exchanged signals and the original

Fig. 13. Waveforms and balanced eyes of demodulated in‐phase (Ch. I) and quadrature (Ch. Q) components for four‐channel, high‐base data exchange of 100‐Gbit/s DQPSK signals.

four-channel, high-base data exchange of 100-Gbit/s DQPSK signals.

four-channel, high-base data exchange of 100-Gbit/s DQPSK signals.

1

Add

1 Drop

1

Unequalized N×100-Gbit/s DQPSK Signals

> 2 7 3 6 4 5

**Input**

Exchange

12 7 3 4 5 6

**Outpu**

for Add

Equalization:1-7

Figure 12. Spectra for four-channel, high-base data exchange of DQPSK signals. (a) Input four-channel, 100-Gbit/s RZ-DQPSK signals. (b) Spectra measured in the absence (dashed curve: Rayleigh scattering)/presence (solid

Figure 13 further displays temporal waveforms and balanced eyes of demodulated in‐ phase (Ch. I) and quadrature (Ch. Q) components of 100‐Gbit/s RZ‐DQPSK signals before and after four‐channel high‐base optical data exchange. One can clearly confirm the successful implementation of simultaneous four‐channel, 100‐Gbit/s RZ‐DQPSK optical data exchange between S1 and S4 as well as S2 and S3. Meanwhile, one can also see that for DQPSK signals, the Ch. I and Ch. Q components are swapped after optical data exchange, which is due to the optical phase‐conjugation property of the degenerate FWM process.

Fig. 12. Spectra for four‐channel, high‐base data exchange of DQPSK signals. (a) Input four‐ channel, 100‐Gbit/s RZ‐DQPSK signals. (b) Spectra measured in the absence (dashed curve:

**S1 S1** 

**S2 S2** 

**S3 S3** 

**S1 Back to Back Ch. Q**

Rayleigh scattering)/presence (solid curve: after data exchange) of CW pump.

(a) **S1S2 S3 S4**

18.4

10dB/div

Power (dBm)

**Ch. I**

**Ch. I**

**Ch. I**

**Ch. I**

3 6 <sup>7</sup> <sup>1</sup> <sup>4</sup>

**HNLF** 

5

A B C D E

**LCoS** 

Pump

Exchange

<sup>2</sup> <sup>3</sup> <sup>6</sup> <sup>7</sup>

Fiber Array 2 Input/Output

dB 19.5

dB

**Ch. Q S3 to S2 Exchange** 

**Ch. Q S2 to S3 Exchange** 

**Ch. Q S1 to S4 Exchange** 

(b)

1540 1555 1570 Wavelength (nm)

**S4 to S1 Exchange** 

17

Exchange

dB 17 dB

curve: after data exchange) of CW pump.

**Ch. I** 

**Ch. Q** 

**Ch. Q** 

**Ch. Q** 

**Ch. Q** 

residual signals.

Power (dBm)

10dB/div

**S1 S2 S3 S4**

1540 1555 1570 Wavelength (nm)

40 Applications of Digital Signal Processing through Practical Approach

**Ch. I S2 Back to Back** 

**Ch. I S3 Back to Back** 

**Ch. I S4 Back to Back** 

data exchange, power equalization).

and flexibility of network management.

100‐Gbit/s DQPSK signals.

grooming optical signal processing element with great reconfigurability. Simultaneous reconfigurable high-base add/drop, high-base optical data exchange, and high-base power equalization are implemented by exploiting bidirectional degenerate FWM in a single HNLF and double-pass programmable LCoS technology.

**Figure 15.** Concept and principle of LCoS+HNLF-based multifunctional, high-base grooming switch (add/drop, data exchange, power equalization).

Similar operation principle is adopted for reconfigurable 2.3-Tbit/s network grooming switch with 23x100-Gbit/s RZ-DQPSK channels. In the experiment, ITU-grid-compatible 23 wave‐ length channels (from S1: 1531.12 nm to S23: 1566.31 nm) each carrying 100-Gbit/s RZ-DQPSK modulation signal with a channel spacing of 200 GHz are utilized. A 520-m piece of HNLF with a ZDW of ~1555 nm and a nonlinear coefficient (γ) of 20 W-1·km-1 is employed. The single pump wavelength is set to be 1555.75 nm for bidirectional degenerate FWM.

Figure 16 shows the measured optical spectrum and balanced eyes for input unequalized 23 wavelength channels each carrying a 100-Gbit/s RZ-DQPSK signal. The observed power fluctuation of all 23 wavelength channels is assessed to be around 9.1 dB. The insets of Fig. 16 depict measured typical balanced eyes for the demodulated in-phase (Ch. I) and quadrature (Ch. Q) components of 100-Gbit/s RZ-DQPSK signals.

We first perform 2.3-Tbit/s grooming switch with single-channel, high-base add/drop and twochannel high-base optical data exchange. The measured optical spectrum together with typical balanced eyes for 100-Gbit/s RZ-DQPSK signals after the multifunctional, high-base grooming switch is shown in Fig. 17. Three high-base grooming optical signal processing functions are implemented as follows: 1) high-base optical data exchange between S12 and S21; 2) high-base

5

5

grooming optical signal processing element with great reconfigurability. Simultaneous reconfigurable high-base add/drop, high-base optical data exchange, and high-base power equalization are implemented by exploiting bidirectional degenerate FWM in a single HNLF

Grating

1

~7 **LCoS** 

Pump

Exchange

<sup>2</sup> <sup>3</sup> <sup>6</sup> <sup>7</sup>

3 6 <sup>7</sup> <sup>1</sup> <sup>4</sup>

**HNLF** 

5

A B C D E

<sup>4</sup> <sup>5</sup>

**Figure 15.** Concept and principle of LCoS+HNLF-based multifunctional, high-base grooming switch (add/drop, data

Similar operation principle is adopted for reconfigurable 2.3-Tbit/s network grooming switch with 23x100-Gbit/s RZ-DQPSK channels. In the experiment, ITU-grid-compatible 23 wave‐ length channels (from S1: 1531.12 nm to S23: 1566.31 nm) each carrying 100-Gbit/s RZ-DQPSK modulation signal with a channel spacing of 200 GHz are utilized. A 520-m piece of HNLF with a ZDW of ~1555 nm and a nonlinear coefficient (γ) of 20 W-1·km-1 is employed. The single

Figure 16 shows the measured optical spectrum and balanced eyes for input unequalized 23 wavelength channels each carrying a 100-Gbit/s RZ-DQPSK signal. The observed power fluctuation of all 23 wavelength channels is assessed to be around 9.1 dB. The insets of Fig. 16 depict measured typical balanced eyes for the demodulated in-phase (Ch. I) and quadrature

We first perform 2.3-Tbit/s grooming switch with single-channel, high-base add/drop and twochannel high-base optical data exchange. The measured optical spectrum together with typical balanced eyes for 100-Gbit/s RZ-DQPSK signals after the multifunctional, high-base grooming switch is shown in Fig. 17. Three high-base grooming optical signal processing functions are implemented as follows: 1) high-base optical data exchange between S12 and S21; 2) high-base

Fiber Array 2 Input/Output

and double-pass programmable LCoS technology.

42 Applications of Digital Signal Processing through Practical Approach

1

Add

1 Drop

(Ch. Q) components of 100-Gbit/s RZ-DQPSK signals.

exchange, power equalization).

1

Unequalized N×100-Gbit/s DQPSK Signals

> 2 7 3 6 4 5

**Input**

Exchange

12 7 3 4 5 6

**Output**

for Add

Equalization:1-7

New Signal Mirror

pump wavelength is set to be 1555.75 nm for bidirectional degenerate FWM.

**Ch. I**  Figure 16. Measured optical spectrum and balanced eyes for input unequalized 23-channel 100-Gbit/s RZ-DQPSK **Figure 16.** Measured optical spectrum and balanced eyes for input unequalized 23-channel 100-Gbit/s RZ-DQPSK signals.

**Ch. I** 

**Ch. I** 

**Ch. I** 

**<1dB**

**Ch. I** 

dropping of the original S18 and high-base adding of new S18 with updated data information; 3) high-base power equalization for all 23-channel 100-Gbit/s RZ-DQPSK signals (power fluctuation: <1 dB). We also measure power penalties at a BER of 10-9 as shown in Fig. 18 for the multichannel, multifunctional grooming switch. **Ch.Q Ch.Q Ch.Q Ch.Q Ch.Q S1 Equalized 23×100-Gbit/s RZ-DQPSK S12 S18 S21S23 Data Exchange Add S18 Drop**

Figure 16. Measured optical spectrum and balanced eyes for input unequalized 23-channel 100-Gbit/s RZ-DQPSK

high-base grooming switch (high-base optical data exchange between S12 and S21; high-base add/drop for S18; high-base power equalization for all 23 wavelength channels S1-S23). **Figure 17.** Measured optical spectrum and balanced eyes for 100-Gbit/s RZ-DQPSK signals after multifunctional, highbase grooming switch (high-base optical data exchange between S12 and S21; high-base add/drop for S18; high-base power equalization for all 23 wavelength channels S1-S23). Data Exchange S12 S21

Equalization

Figure 17. Measured optical spectrum and balanced eyes for 100-Gbit/s RZ-DQPSK signals after multifunctional,

Equalization Data Exchange S12 S21 Due to the programmable LCoS employed in the configuration, the proposed multichannel, multifunctional grooming switch is reconfigurable. For instance, one can perform switchable simultaneous multichannel optical data exchange simply by changing the wavelength channels of interest sent to the fiber array port D and port E. S1-S11, S13-S17 S19, S20, S22, S23

> S1-S11, S13-S17 S19, S20, S22, S23

Figure 18. Measured power penalties at a BER of 10-9 for the multichannel, multifunctional high-base grooming switch (high-base optical data exchange between S12 and S21; high-base add/drop for S18; high-base power

Figure 18. Measured power penalties at a BER of 10-9 for the multichannel, multifunctional high-base grooming switch (high-base optical data exchange between S12 and S21; high-base add/drop for S18; high-base power

S18 Add S18

S18 Add S18

**S6S7 Drop** 

**S6S7 Drop**  Drop

Drop

S21 S22 S23

Aft. Ex. (Ch. Q)

S21 S22 S23

S10 S11 S12

S10 S11 S12

Aft. Ex. (Ch. I)

S21 S22 S23

S21 S22 S23

S10 S11 S12

S10 S11 S12

Aft. Ex. (Ch. I)

Aft. Ex. (Ch. Q)

equalization for all 23 wavelength channels S1-S23).

**S6 S7 Exchange** 

**Six-Channel** 

equalization for all 23 wavelength channels S1-S23).

**Six-Channel** 

**S6 S7 Exchange** 

**Add** 

**Add** 

**Equalized 23×100-Gbit/s RZ-DQPSK** 

**Equalized 23×100-Gbit/s RZ-DQPSK** 

**S10-S12 S21-S23** 

**S10-S12 S21-S23** 

**S1** 

**<1dB**

**S1** 

**<1dB**

1

signals.

signals.

high-base power equalization for all 23 wavelength channels S1-S23).

signals.

Figure 17. Measured optical spectrum and balanced eyes for 100-Gbit/s RZ-DQPSK signals after multifunctional,

**Ch. I Ch.Q Ch. I Ch.Q** 

Figure 16. Measured optical spectrum and balanced eyes for input unequalized 23-channel 100-Gbit/s RZ-DQPSK

**Equalized 23×100-Gbit/s RZ-DQPSK** 

**Data Exchange Add**

**23×100-Gbit/s RZ-DQPSK** 

**S12** 

**Ch. I** 

**Ch.Q**

**S23** 

**9.1dB**

**S18 Drop**

**Ch. I** 

**S21** 

**S18** 

**Ch. I** 

**Ch.Q**

**S12 S18 S21S23**

**Ch.Q**

**Unequalized S1** 

**Ch. I** 

**Ch. I** 

**Ch.Q**

**Ch.Q**

**S1** 

**<1dB**

Figure 18. Measured power penalties at a BER of 10-9 for the multichannel, multifunctional high-base grooming switch (high-base optical data exchange between S12 and S21; high-base add/drop for S18; high-base power equalization for all 23 wavelength channels S1-S23). **Figure 18.** Measured power penalties at a BER of 10-9 for the multichannel, multifunctional high-base grooming switch (high-base optical data exchange between S12 and S21; high-base add/drop for S18; high-base power equalization for all 23 wavelength channels S1-S23).

We also demonstrate 2.3-Tbit/s grooming switch with two-channel add/drop and six-channel optical data exchange. Shown in Fig. 19 is the measured optical spectrum and typical balanced eyes for 100-Gbit/s RZ-DQPSK signals after the multifunctional, high-base grooming switch: 1) simultaneous six-channel, high-base optical data exchange between S10 and S23, S11 and S22, S12 and S21; 2) simultaneous two-channel, high-base dropping of the original S6 and S7 and high-base adding of new S6 and S7 with updated data information; 3) high-base power equalization with power fluctuation less than 1 dB for all 23 wavelength channels. Shown in the inset of Fig. 19 is the measured optical spectrum of dropped two wavelength channels of S6 and S7. Figure 20 plots the measured BER performance for simultaneous multichannel, high-base optical data exchange and high-base add/drop. The observed power penalties are assessed to be less than 1.2 dB for two-channel high-base add, 0.5 dB for two-channel highbase drop, and 5 dB for six-channel high-base optical data exchange at a BER of 10-9. **S1 Equalized 23×100-Gbit/s RZ-DQPSK S10-S12 S21-S23 <1dB Six-Channel Add S6 S7 Exchange**  S21 S22 S23 S10 S11 S12 S21 S22 S23 S10 S11 S12 Aft. Ex. (Ch. I) Aft. Ex. (Ch. Q) **S6S7 Drop** 

In addition to high-base data exchange based on degenerate/nondegenerate FWM in HNLFs, we also propose and simulate ultrahigh-speed high-base data exchange using nondegenerate FWM in a silicon–organic hybrid slot waveguide. The working principle is also based on the parametric depletion effect of nondegenerate FWM as in an HNLF. The designed silicon– organic hybrid slot waveguide offers tight light confinement, enhanced nonlinearity, and negligible TPA and free-carrier absorption (FCA). Using nonlinear coupled-mode equations under the slowly varying envelope approximation and taking full consideration of groupvelocity mismatching (GVM), group-velocity dispersion (GVD), TPA, FCA, and free-carrier dispersion (FCD), the proposed silicon–organic hybrid slot waveguide based high-base data exchange is simulated. In the following simulations, two 640 Gbaud 213-1 pseudorandom binary sequence (PRBS) 16-QAM/64-QAM signals (λSA: 1542 nm, λSB: 1544 nm) and two pumps (λP1: 1548 nm, λP2: 1550 nm) are sent into a 17-mm-long silicon–organic hybrid slot waveguide, in which 16-QAM/64-QAM data exchange is realized based on the nondegenerate FWM process. Note that the high-speed 640 Gbaud 16-QAM/64-QAM signal could be optical time-

5

Figure 16. Measured optical spectrum and balanced eyes for input unequalized 23-channel 100-Gbit/s RZ-DQPSK

**Equalized 23×100-Gbit/s RZ-DQPSK** 

**Data Exchange Add**

**23×100-Gbit/s RZ-DQPSK** 

**S12** 

**Ch. I** 

**Ch.Q**

**S23** 

**9.1dB**

**S18 Drop**

**Ch. I** 

**S21** 

**S18** 

**Ch. I** 

**Ch.Q**

**S12 S18 S21S23**

S18 Add S18

Data Exchange S12 S21

Drop

**Ch.Q**

**Unequalized S1** 

**Ch. I** 

**Ch. I** 

**Ch.Q**

**Ch.Q**

**S1** 

**<1dB**

Figure 17. Measured optical spectrum and balanced eyes for 100-Gbit/s RZ-DQPSK signals after multifunctional, high-base grooming switch (high-base optical data exchange between S12 and S21; high-base add/drop for S18;

> Equalization S1-S11, S13-S17 S19, S20, S22, S23

**Ch. I Ch.Q Ch. I Ch.Q** 

high-base power equalization for all 23 wavelength channels S1-S23).

equalization for all 23 wavelength channels S1-S23).

for all 23 wavelength channels S1‐S23).

between S10 and S23, S11 and S22, S12 and S21.

signals.

**Figure 19.** Measured optical spectrum and balanced eyes for 100-Gbit/s RZ-DQPSK signals after multichannel, multi‐ functional high-base grooming switch (simultaneous six-channel, high-base optical data exchange between S10 and S23, S11 and S22, S12 and S21; simultaneous two-channel, high-base add/drop for S6 and S7; high-base power equali‐ zation for all 23 wavelength channels S1-S23). after multichannel, multifunctional high‐base grooming switch (simultaneous six‐channel, high‐base optical data exchange between S10 and S23, S11 and S22, S12 and S21; simultaneous two‐channel, high‐base add/drop for S6 and S7; high‐base power equalization

Fig. 19. Measured optical spectrum and balanced eyes for 100‐Gbit/s RZ‐DQPSK signals

We also demonstrate 2.3-Tbit/s grooming switch with two-channel add/drop and six-channel optical data exchange. Shown in Fig. 19 is the measured optical spectrum and typical balanced eyes for 100-Gbit/s RZ-DQPSK signals after the multifunctional, high-base grooming switch: 1) simultaneous six-channel, high-base optical data exchange between S10 and S23, S11 and S22, S12 and S21; 2) simultaneous two-channel, high-base dropping of the original S6 and S7 and high-base adding of new S6 and S7 with updated data information; 3) high-base power equalization with power fluctuation less than 1 dB for all 23 wavelength channels. Shown in the inset of Fig. 19 is the measured optical spectrum of dropped two wavelength channels of S6 and S7. Figure 20 plots the measured BER performance for simultaneous multichannel, high-base optical data exchange and high-base add/drop. The observed power penalties are assessed to be less than 1.2 dB for two-channel high-base add, 0.5 dB for two-channel high-

Figure 18. Measured power penalties at a BER of 10-9 for the multichannel, multifunctional high-base grooming switch (high-base optical data exchange between S12 and S21; high-base add/drop for S18; high-base power

**Figure 18.** Measured power penalties at a BER of 10-9 for the multichannel, multifunctional high-base grooming switch (high-base optical data exchange between S12 and S21; high-base add/drop for S18; high-base power equalization for

S18 Add S18

**S6S7 Drop** 

Data Exchange

S12 S21

Drop

S21 S22 S23

S21 S22 S23

S10 S11 S12

S10 S11 S12

Aft. Ex. (Ch. I)

Aft. Ex. (Ch. Q)

Figure 16. Measured optical spectrum and balanced eyes for input unequalized 23-channel 100-Gbit/s RZ-DQPSK

**Equalized 23×100-Gbit/s RZ-DQPSK** 

**Data Exchange Add**

**23×100-Gbit/s RZ-DQPSK** 

**S12** 

**Ch. I** 

**Ch.Q**

**S23** 

**9.1dB**

**S18 Drop**

**Ch. I** 

**S21** 

**S18** 

**Ch. I** 

**Ch.Q**

**S12 S18 S21S23**

**Ch.Q**

**Unequalized S1** 

**Ch. I** 

**Ch. I** 

**Ch.Q**

**Ch.Q**

**S1** 

**<1dB**

Figure 17. Measured optical spectrum and balanced eyes for 100-Gbit/s RZ-DQPSK signals after multifunctional, high-base grooming switch (high-base optical data exchange between S12 and S21; high-base add/drop for S18;

> Equalization S1-S11, S13-S17 S19, S20, S22, S23

**Ch. I Ch.Q Ch. I Ch.Q** 

high-base power equalization for all 23 wavelength channels S1-S23).

44 Applications of Digital Signal Processing through Practical Approach

equalization for all 23 wavelength channels S1-S23).

all 23 wavelength channels S1-S23).

**Six-Channel** 

**S6 S7 Exchange** 

**Add** 

**Equalized 23×100-Gbit/s RZ-DQPSK** 

**S10-S12 S21-S23** 

**S1** 

**<1dB**

signals.

base drop, and 5 dB for six-channel high-base optical data exchange at a BER of 10-9.

In addition to high-base data exchange based on degenerate/nondegenerate FWM in HNLFs, we also propose and simulate ultrahigh-speed high-base data exchange using nondegenerate FWM in a silicon–organic hybrid slot waveguide. The working principle is also based on the parametric depletion effect of nondegenerate FWM as in an HNLF. The designed silicon– organic hybrid slot waveguide offers tight light confinement, enhanced nonlinearity, and negligible TPA and free-carrier absorption (FCA). Using nonlinear coupled-mode equations under the slowly varying envelope approximation and taking full consideration of groupvelocity mismatching (GVM), group-velocity dispersion (GVD), TPA, FCA, and free-carrier dispersion (FCD), the proposed silicon–organic hybrid slot waveguide based high-base data exchange is simulated. In the following simulations, two 640 Gbaud 213-1 pseudorandom binary sequence (PRBS) 16-QAM/64-QAM signals (λSA: 1542 nm, λSB: 1544 nm) and two pumps (λP1: 1548 nm, λP2: 1550 nm) are sent into a 17-mm-long silicon–organic hybrid slot waveguide, in which 16-QAM/64-QAM data exchange is realized based on the nondegenerate FWM process. Note that the high-speed 640 Gbaud 16-QAM/64-QAM signal could be optical time-

5

Fig. 20. Measured BER performance for (a)(b) simultaneous two‐channel, high‐base add/drop (S6 and S7) and (c)(d) simultaneous six‐channel, high‐base optical data exchange **Figure 20.** Measured BER performance for (a)(b) simultaneous two-channel, high-base add/drop (S6 and S7) and (c)(d) simultaneous six-channel, high-base optical data exchange between S10 and S23, S11 and S22, S12 and S21.

division multiplexed (OTDM) signal from 64 low-speed 10 Gbaud tributaries in practical applications. In addition to high‐base data exchange based on degenerate/nondegenerate FWM in HNLFs, we also propose and simulate ultrahigh‐speed high‐base data exchange using

The obtained results (symbol sequences) for high-base optical data exchange of 640 Gbaud (2.56 Tbit/s) 16-QAM signals are shown in Fig. 21. One can easily confirm the successful nondegenerate FWM in a silicon–organic hybrid slot waveguide. The working principle is also based on the parametric depletion effect of nondegenerate FWM as in an HNLF. The designed silicon–organic hybrid slot waveguide offers tight light confinement, enhanced

nonlinearity, and negligible TPA and free‐carrier absorption (FCA). Using nonlinear coupled‐mode equations under the slowly varying envelope approximation and taking full consideration of group‐velocity mismatching (GVM), group‐velocity dispersion (GVD), TPA, FCA, and free‐carrier dispersion (FCD), the proposed silicon–organic hybrid slot waveguide based high‐base data exchange is simulated. In the following simulations, two 640 Gbaud 213‐1 pseudorandom binary sequence (PRBS) 16‐QAM/64‐QAM signals (λSA: 1542 nm, λSB: 1544 nm) and two pumps (λP1: 1548 nm, λP2: 1550 nm) are sent into a 17‐mm‐long silicon– organic hybrid slot waveguide, in which 16‐QAM/64‐QAM data exchange is realized based on the nondegenerate FWM process. Note that the high‐speed 640 Gbaud 16‐QAM/64‐QAM

realization of the proposed high-base optical data exchange of 16-QAM signals by comparing the 10 symbol sequences for two signals (SA, SB) before optical data exchange (Bef. Ex.) and after optical data exchange (Aft. Ex.). Figure 22 shows simulated constellations for high-base optical data exchange of 16-QAM signals. For a signal-to-noise ratio (SNR) of 10 dB the error vector magnitude (EVM) is also assessed in Fig. 22. The simulated EVM and BER performance versus SNR for high-base optical data exchange of 640 Gbaud (2.56 Tbit/s) 16-QAM signals is shown in Fig. 23(a) and (b). For reference we also plot in Fig. 23(b) the theoretical 16-QAM BER curve. By comparing the simulated BER curves of two signals before and after optical data exchange, one can see negligible SNR penalty induced by the high-base optical data exchange operation at a BER of 2x10-3, which is the enhanced forward error correction (EFEC) threshold.

Fig. 21. Simulated symbol sequences for high‐base optical data exchange of 640 Gbaud (2.56 Tbit/s) 16‐QAM signals. **Figure 21.** Simulated symbol sequences for high-base optical data exchange of 640 Gbaud (2.56 Tbit/s) 16-QAM signals.

**Bef. Ex. SA Bef. Ex. SB Aft. Ex. (SB to SA) Aft. Ex. (SA to SB)**  We further simulate high-base optical data exchange of 640 Gbaud (3.84 Tbit/s) 64-QAM signals. The obtained results (symbol sequences) for high-base optical data exchange of 640 Gbaud (3.84 Tbit/s) 64-QAM signals are shown in Fig. 24. One can also confirm the successful implementation of the proposed high-base optical data exchange of 64-QAM signals by comparing the 10 symbol sequences for two signals (SA, SB) before optical data exchange (Bef. Ex.) and after optical data exchange (Aft. Ex.).

Fig. 22. Simulated constellations of (a)(b) input and (c)(d) output signals for high‐base

**EVM: 12.1 EVM: 12.1 EVM: 12 EVM: 12**

optical data exchange of 640 Gbaud (2.56 Tbit/s) 16‐QAM signals.

6

S10 and S23, S11 and S22, S12 and S21; simultaneous two-channel, high-base add/drop for S6 and S7; high-base

power equalization for all 23 wavelength channels S1-S23).

realization of the proposed high-base optical data exchange of 16-QAM signals by comparing the 10 symbol sequences for two signals (SA, SB) before optical data exchange (Bef. Ex.) and after optical data exchange (Aft. Ex.). Figure 22 shows simulated constellations for high-base optical data exchange of 16-QAM signals. For a signal-to-noise ratio (SNR) of 10 dB the error vector magnitude (EVM) is also assessed in Fig. 22. The simulated EVM and BER performance versus SNR for high-base optical data exchange of 640 Gbaud (2.56 Tbit/s) 16-QAM signals is shown in Fig. 23(a) and (b). For reference we also plot in Fig. 23(b) the theoretical 16-QAM BER curve. By comparing the simulated BER curves of two signals before and after optical data exchange, one can see negligible SNR penalty induced by the high-base optical data exchange operation at a BER of 2x10-3, which is the enhanced forward error correction (EFEC) threshold.

Fig. 21. Simulated symbol sequences for high‐base optical data exchange of 640 Gbaud (2.56

**Figure 21.** Simulated symbol sequences for high-base optical data exchange of 640 Gbaud (2.56 Tbit/s) 16-QAM signals.

We further simulate high-base optical data exchange of 640 Gbaud (3.84 Tbit/s) 64-QAM signals. The obtained results (symbol sequences) for high-base optical data exchange of 640 Gbaud (3.84 Tbit/s) 64-QAM signals are shown in Fig. 24. One can also confirm the successful implementation of the proposed high-base optical data exchange of 64-QAM signals by comparing the 10 symbol sequences for two signals (SA, SB) before optical data exchange (Bef.

**Bef. Ex. SA Bef. Ex. SB Aft. Ex. (SB to SA) Aft. Ex. (SA to SB)** 

**Symbol Sequence**

**In-Phase**

**In-Phase**

**In-Phase**

Fig. 22. Simulated constellations of (a)(b) input and (c)(d) output signals for high‐base

**EVM: 12.1 EVM: 12.1 EVM: 12 EVM: 12**

optical data exchange of 640 Gbaud (2.56 Tbit/s) 16‐QAM signals.

Ex.) and after optical data exchange (Aft. Ex.).

 **Aft. Ex. (SA to SB) In-Phase**

Tbit/s) 16‐QAM signals.

**Quadrature**

**Quadrature**

**Quadrature**

**Quadrature**

 **Bef. Ex. SB** 

**Aft. Ex. (SB to SA)** 

 **Bef. Ex. SA**

46 Applications of Digital Signal Processing through Practical Approach

Figure 22. Simulated constellations of (a)(b) input and (c)(d) output signals for high-base optical data exchange of 640 Gbaud (2.56 Tbit/s) 16-QAM signals. **Bef. Ex. SA Bef. Ex. SB Aft. Ex. (SB to SA) Aft. Ex. (SA to SB) Figure 22.** Simulated constellations of (a)(b) input and (c)(d) output signals for high-base optical data exchange of 640 Gbaud (2.56 Tbit/s) 16-QAM signals. Fig. 22. Simulated constellations of (a)(b) input and (c)(d) output signals for high‐base

optical data exchange of 640 Gbaud (2.56 Tbit/s) 16‐QAM signals.

Fig. 23. Simulated (a) EVM and (b) BER versus SNR for high‐base optical data exchange of 640 Gbaud (2.56 Tbit/s) 16‐QAM signals. We further simulate high‐base optical data exchange of 640 Gbaud (3.84 Tbit/s) 64‐ **Figure 23.** Simulated (a) EVM and (b) BER versus SNR for high-base optical data exchange of 640 Gbaud (2.56 Tbit/s) 16-QAM signals.

QAM signals. The obtained results (symbol sequences) for high‐base optical data exchange of 640 Gbaud (3.84 Tbit/s) 64‐QAM signals are shown in Fig. 24. One can also confirm the

Fig. 24. Simulated symbol sequences for high‐base optical data exchange of 640 Gbaud (3.84 Tbit/s) 64‐QAM signals. **Figure 24.** Simulated symbol sequences for high-base optical data exchange of 640 Gbaud (3.84 Tbit/s) 64-QAM signals. DQPSK DQPSK Wavelength Idler2 Idler1 Idler3

Idler5

Fig. 25. Simulated constellations of (a)(b) input and (c)(d) output signals for high‐base

**EVM: 7.5 EVM: 7.5 EVM: 8.0 EVM: 8.1** 

optical data exchange of 640 Gbaud (3.84 Tbit/s) 64‐QAM signals.

2x10‐<sup>3</sup> which is the EFEC threshold.

Figure 25 shows simulated constellations for high‐base optical data exchange of 64‐ QAM signals. For an SNR of 14 dB the EVM is also evaluated in Figure 25. The simulated EVM and BER performance versus SNR for high‐base optical data exchange of 640 Gbaud (2.56 Tbit/s) 64‐QAM signals is shown in Fig. 26(a) and (b). For reference we also plot in Fig. 26(b) the theoretical 64‐QAM BER curve. By comparing the simulated BER curves of two signals before and after optical data exchange, one can see that the SNR penalty induced by the high‐base optical data exchange operation is assessed to be less than 2 dB at a BER of

Idler4

Idler6

**Bef. Ex. SA Bef. Ex. SB Aft. Ex. (SB to SA) Aft. Ex. (SA to SB)** 

power equalization for all 23 wavelength channels S1-S23).

640 Gbaud (2.56 Tbit/s) 16-QAM signals.

640 Gbaud (3.84 Tbit/s) 64-QAM signals.

Tbit/s) 64-QAM signals.

Figure 25 shows simulated constellations for high-base optical data exchange of 64-QAM signals. For an SNR of 14 dB the EVM is also evaluated in Fig. 25. The simulated EVM and BER performance versus SNR for high-base optical data exchange of 640 Gbaud (2.56 Tbit/s) 64- QAM signals is shown in Fig. 26(a) and (b). For reference we also plot in Fig. 26(b) the theoretical 64-QAM BER curve. By comparing the simulated BER curves of two signals before and after optical data exchange, one can see that the SNR penalty induced by the high-base optical data exchange operation is assessed to be less than 2 dB at a BER of 2x10-3 which is the EFEC threshold. Figure 22. Simulated constellations of (a)(b) input and (c)(d) output signals for high-base optical data exchange of **Bef. Ex. SA Bef. Ex. SB Aft. Ex. (SB to SA) Aft. Ex. (SA to SB) (a) EVM: 12 (b) EVM: 12 (c) EVM: 12.1 (d) EVM: 12.1**  S10 and S23, S11 and S22, S12 and S21; simultaneous two-channel, high-base add/drop for S6 and S7; high-base power equalization for all 23 wavelength channels S1-S23). **Bef. Ex. SA Bef. Ex. SB Aft. Ex. (SB to SA) Aft. Ex. (SA to SB)** 

Figure 19. Measured optical spectrum and balanced eyes for 100-Gbit/s RZ-DQPSK signals after multichannel,

Figure 19. Measured optical spectrum and balanced eyes for 100-Gbit/s RZ-DQPSK signals after multichannel, multifunctional high-base grooming switch (simultaneous six-channel, high-base optical data exchange between

**(a) EVM: 12 (b) EVM: 12 (c) EVM: 12.1 (d) EVM: 12.1** 

Figure 25. Simulated constellations of (a)(b) input and (c)(d) output signals for high-base optical data exchange of 640 Gbaud (3.84 Tbit/s) 64-QAM signals. **Figure 25.** Simulated constellations of (a)(b) input and (c)(d) output signals for high-base optical data exchange of 640 Gbaud (3.84 Tbit/s) 64-QAM signals. Figure 25. Simulated constellations of (a)(b) input and (c)(d) output signals for high-base optical data exchange of **EVM: 7.5 EVM: 8.0 (a) (b) EVM: 7.5 (c) (d) EVM: 8.1** 

A, B, A+B, A-B, B-A, -A, -B, 2B: quaternary numbers (a) 1 (π/2) Q Figure 26. Simulated (a) EVM and (b) BER versus SNR for high-base optical data exchange of 640 Gbaud (3.84 Tbit/s) 64-QAM signals. A, B, A+B, A-B, B-A, -A, -B, 2B: quaternary numbers **Figure 26.** Simulated (a) EVM and (b) BER versus SNR for high-base optical data exchange of 640 Gbaud (3.84 Tbit/s) 64-QAM signals.

Q

0 (0)

I

#### A-B: 2, 3, 2, 0 2 (π) 3 (3π/2) A+B: 0, 1, 2, 2 0 (0) I **4. High-base optical computing [75, 77, 80, 85]**

1 (π/2)

B: 3, 1, 0, 3

A-B

A-B

A: 1, 0, 2, 3 B: 3, 1, 0, 3 Nonlinear Device B-A: 2, 1, 2, 0 - A : 3, 0, 2, 1 - B : 1, 3, 0, 1 A: 1, 0, 2, 3 Nonlinear Device A-B: 2, 3, 2, 0 B-A: 2, 1, 2, 0 - A : 3, 0, 2, 1 2 (π) 3 (3π/2) We propose and demonstrate high-base optical computing of advanced multilevel modulation signals based on degenerate/nondegenerate FWM in HNLFs or silicon–organic hybrid slot waveguides.

> Sig. A A+B B-A CW Pump

Sig. B

Sig. B

2B Idler6

2B Idler6

Idler2 Idler1 Idler3

Idler2 Idler1 Idler3

Sig. A A+B B-A CW Pump



Degenerate/non-degenerate four-wave mixing (FWM)

Degenerate/non-degenerate four-wave mixing (FWM)

(b)

(b)



2B : 2, 2, 0, 2


2B : 2, 2, 0, 2

A+B: 0, 1, 2, 2

(a)

DQPSK DQPSK Wavelength

DQPSK DQPSK Wavelength

6

6

We first demonstrate high-speed two-input high-base optical computing (addition/subtrac‐ tion/complement/doubling) of quaternary numbers using optical nonlinearities and DQPSK signals. Figure 22. Simulated constellations of (a)(b) input and (c)(d) output signals for high-base optical data exchange of 640 Gbaud (2.56 Tbit/s) 16-QAM signals. **Bef. Ex. SA Bef. Ex. SB Aft. Ex. (SB to SA) Aft. Ex. (SA to SB)** 

**(a) EVM: 12 (b) EVM: 12 (c) EVM: 12.1 (d) EVM: 12.1** 

Figure 19. Measured optical spectrum and balanced eyes for 100-Gbit/s RZ-DQPSK signals after multichannel, multifunctional high-base grooming switch (simultaneous six-channel, high-base optical data exchange between S10 and S23, S11 and S22, S12 and S21; simultaneous two-channel, high-base add/drop for S6 and S7; high-base

**Bef. Ex. SA Bef. Ex. SB Aft. Ex. (SB to SA) Aft. Ex. (SA to SB)** 

power equalization for all 23 wavelength channels S1-S23).

Figure 25 shows simulated constellations for high-base optical data exchange of 64-QAM signals. For an SNR of 14 dB the EVM is also evaluated in Fig. 25. The simulated EVM and BER performance versus SNR for high-base optical data exchange of 640 Gbaud (2.56 Tbit/s) 64- QAM signals is shown in Fig. 26(a) and (b). For reference we also plot in Fig. 26(b) the theoretical 64-QAM BER curve. By comparing the simulated BER curves of two signals before and after optical data exchange, one can see that the SNR penalty induced by the high-base optical data exchange operation is assessed to be less than 2 dB at a BER of 2x10-3 which is the

Figure 19. Measured optical spectrum and balanced eyes for 100-Gbit/s RZ-DQPSK signals after multichannel, multifunctional high-base grooming switch (simultaneous six-channel, high-base optical data exchange between S10 and S23, S11 and S22, S12 and S21; simultaneous two-channel, high-base add/drop for S6 and S7; high-base

**Bef. Ex. SA Bef. Ex. SB Aft. Ex. (SB to SA) Aft. Ex. (SA to SB)** 

Figure 22. Simulated constellations of (a)(b) input and (c)(d) output signals for high-base optical data exchange of

**(a) EVM: 12 (b) EVM: 12 (c) EVM: 12.1 (d) EVM: 12.1** 

Figure 22. Simulated constellations of (a)(b) input and (c)(d) output signals for high-base optical data exchange of

**Bef. Ex. SA Bef. Ex. SB Aft. Ex. (SB to SA) Aft. Ex. (SA to SB)** 

**Bef. Ex. SA Bef. Ex. SB Aft. Ex. (SB to SA) Aft. Ex. (SA to SB)** 

**(a) EVM: 12 (b) EVM: 12 (c) EVM: 12.1 (d) EVM: 12.1** 

**Bef. Ex. SA Bef. Ex. SB Aft. Ex. (SB to SA) Aft. Ex. (SA to SB)** 

Figure 25. Simulated constellations of (a)(b) input and (c)(d) output signals for high-base optical data exchange of

**Figure 25.** Simulated constellations of (a)(b) input and (c)(d) output signals for high-base optical data exchange of 640

**EVM: 7.5 EVM: 8.0 (a) (b) EVM: 7.5 (c) (d) EVM: 8.1** 

Figure 25. Simulated constellations of (a)(b) input and (c)(d) output signals for high-base optical data exchange of

**EVM: 7.5 EVM: 8.0 (a) (b) EVM: 7.5 (c) (d) EVM: 8.1** 

Figure 26. Simulated (a) EVM and (b) BER versus SNR for high-base optical data exchange of 640 Gbaud (3.84

A, B, A+B, A-B, B-A, -A, -B, 2B: quaternary numbers

Figure 26. Simulated (a) EVM and (b) BER versus SNR for high-base optical data exchange of 640 Gbaud (3.84

**Figure 26.** Simulated (a) EVM and (b) BER versus SNR for high-base optical data exchange of 640 Gbaud (3.84 Tbit/s)

A, B, A+B, A-B, B-A, -A, -B, 2B: quaternary numbers

We propose and demonstrate high-base optical computing of advanced multilevel modulation signals based on degenerate/nondegenerate FWM in HNLFs or silicon–organic hybrid slot

0 (0)

I

0 (0)

I

Sig. A A+B B-A CW Pump

Sig. B

Sig. B

2B Idler6

2B Idler6

Idler2 Idler1 Idler3

Idler2 Idler1 Idler3

Sig. A A+B B-A CW Pump

Degenerate/non-degenerate four-wave mixing (FWM)

Degenerate/non-degenerate four-wave mixing (FWM)

Nonlinear Device

Nonlinear Device



2 (π) 3 (3π/2)

Q

2 (π) 3 (3π/2)

Q

1 (π/2)

1 (π/2)

DQPSK DQPSK Wavelength

DQPSK DQPSK Wavelength

**EFEC Threshold** 

**EFEC Threshold** 

(b)

(b)

A+B: 0, 1, 2, 2 A-B: 2, 3, 2, 0 B-A: 2, 1, 2, 0

A+B: 0, 1, 2, 2 A-B: 2, 3, 2, 0 B-A: 2, 1, 2, 0


2B : 2, 2, 0, 2


2B : 2, 2, 0, 2



(a)

**(a) (b)**

**(a) (b)**

A: 1, 0, 2, 3

**4. High-base optical computing [75, 77, 80, 85]**

B: 3, 1, 0, 3

B: 3, 1, 0, 3

A: 1, 0, 2, 3

A-B

A-B

Figure 19. Measured optical spectrum and balanced eyes for 100-Gbit/s RZ-DQPSK signals after multichannel, multifunctional high-base grooming switch (simultaneous six-channel, high-base optical data exchange between S10 and S23, S11 and S22, S12 and S21; simultaneous two-channel, high-base add/drop for S6 and S7; high-base

EFEC threshold.

640 Gbaud (2.56 Tbit/s) 16-QAM signals.

640 Gbaud (2.56 Tbit/s) 16-QAM signals.

640 Gbaud (3.84 Tbit/s) 64-QAM signals.

640 Gbaud (3.84 Tbit/s) 64-QAM signals.

Gbaud (3.84 Tbit/s) 64-QAM signals.

Tbit/s) 64-QAM signals.

Tbit/s) 64-QAM signals.

64-QAM signals.

waveguides.

power equalization for all 23 wavelength channels S1-S23).

48 Applications of Digital Signal Processing through Practical Approach

power equalization for all 23 wavelength channels S1-S23).

The concept and principle of operation of quaternary optical computing are shown in Fig. 27. As depicted in Fig. 27(a), DQPSK modulation signals have four-phase levels, i.e., 0, π/2, π, 3π/2, which can be used to represent quaternary numbers, i.e., 0, 1, 2, 3. For two input signals A and B carrying quaternary numbers, it is expected that multiple outputs carrying different quaternary optical computing results could be achieved by employing a single nonlinear device. As depicted in Fig. 27(b), one can exploit three nondegenerate FWM processes and three degenerate FWM processes in a single HNLF with low and flat dispersion to implement simultaneous multiple quaternary optical computing functions. When launching signal A, signal B, and one CW pump into the HNLF, six converted idlers can be obtained with three idlers (idler 1-3) produced by three nondegenerate FWM processes and the other three idlers (idler 4-6) created by three degenerate FWM processes. For the six idlers generated by six FWM processes, one can derive the electrical field (E) and optical phase (Φ) relationships under the nondepletion approximation expressed as Ei1∝EA EB ECW\* , Φi1=ΦA+ΦB-ΦCW (1), Ei2∝EA EB \* ECW, Φi2=ΦA-ΦB+ΦCW (2), Ei3∝E<sup>A</sup> \* EB ECW, Φi3=ΦB-ΦA+ΦCW (3), Ei4∝ECW ECW EA \* , Φi3=2ΦCW-Φ<sup>A</sup> (4), Ei5∝ECW ECW EB \* , Φi5=2ΦCW-ΦB (5), Ei6∝E<sup>B</sup> EB ECW\* , Φi6=2ΦB-ΦCW (6). Remarkably, since optical phase has a periodicity of 2π due to its phase wrap characteristic, one can clearly see from Eqs. (1)-(6) that the six converted idlers actually take modulo 4 functions of quaternary optical computing, i.e., idler 1 for quaternary addition (A+B), idler 2 for quaternary subtraction (A-B), idler 3 for quaternary subtraction (B-A), idler 4 for quaternary complement (-A), idler 5 for quaternary complement (-B), and idler 6 for quaternary doubling (2B). Figure 25. Simulated constellations of (a)(b) input and (c)(d) output signals for high-base optical data exchange of 640 Gbaud (3.84 Tbit/s) 64-QAM signals. Figure 26. Simulated (a) EVM and (b) BER versus SNR for high-base optical data exchange of 640 Gbaud (3.84 Tbit/s) 64-QAM signals. **EVM: 7.5 EVM: 8.0 (a) (b) EVM: 7.5 (c) (d) EVM: 8.1 (a) (b) EFEC Threshold** 

**Figure 27.** (a) Concept and (b) principle of two-input high-base optical computing (quaternary addition/subtraction/ complement/doubling) using a single nonlinear device and DQPSK signals.

6

Shown in Fig. 28 are measured spectra. One CW pump (1553.2 nm) and two 100-Gbit/s 27 -1 RZ-DQPSK signals (A: 1546.6 nm, B: 1555.5 nm) are fed into a 460-m-long HNLF. The ZDW, dispersion slope (*S*) and nonlinear coefficient (γ) of the HNLF are ~1556 nm, ~0.026 ps/nm2 /km, and 20 W-1 km-1, respectively. The employed HNLF has low and flat dispersion, which benefits simultaneous multiple FWM processes. As a consequence, it is possible to simultaneously generate six idlers (idler 1: 1544.3 nm, idler 2: 1548.9 nm, idler 3: 1562.2 nm, idler 4: 1559.9 nm, idler 5: 1550.9 nm, idler 6: 1557.7 nm) corresponding to simultaneous addition (A+B), subtrac‐ tion (A-B, B-A), complement (-A, -B), and doubling (2B) of quaternary numbers (A, B). Figure 27. (a) Concept and (b) principle of two-input high-base optical computing (quaternary

addition/subtraction/complement/doubling) using a single nonlinear device and DQPSK signals.

Figure 28. Measured spectra (a) before HNLF and (b) after HNLF for 50-Gbaud two-input quaternary optical computing (addition, subtraction, complement, doubling). A: 0,1,0,3,2 A+B-C: 0,0,1,1,3 **Figure 28.** Measured spectra (a) before HNLF and (b) after HNLF for 50-Gbaud two-input quaternary optical comput‐ ing (addition, subtraction, complement, doubling).

Sig.A A+C-B B+C-A Wavelength Idler1 Idler2 Idler3 Sig.C Non-Degenerate Four-Wave Mixing (FWM) B: 2,2,2,3,3 A+C-B: 0,2,3,1,1 B+C-A: 0,0,3,1,3 A+B-C 0 (0) 1 (π/2) 2 (π) I Q Sig.B C: 2,3,1,1,2 Nonlinear Device A B C DQPSK: Quaternary Base Numbers A+B+C: 0,2,3,3,3 In order to confirm the quaternary optical computing (addition, subtraction, complement, doubling), the waveforms and balanced eyes of the demodulated in-phase (Ch. I) and quad‐ rature (Ch. Q) components of two-input 100-Gbit/s RZ-DQPSK signals and six converted idlers by multiple FWM processes are recorded. A 50-GHz delay-line interferometer (DLI) is used to demodulate 100-Gbit/s RZ-DQPSK. A relative delay of 20 ps is introduced between the two arms of the 50-GHz DLI. Remarkably, quaternary numbers can be represented by the combi‐ nation of Ch. I and Ch. Q (i.e., 00: '0', 01: '1', 11: '2', 10: '3'). By exploiting multiple degenerate and nondegenerate FWM processes, one can clearly see from Figs. 29 and 30 that simultaneous 50-Gbaud quaternary optical computing of addition (A+B), dual-directional subtraction (A-B, B-A), complement (-A, -B), and doubling (2B) are successfully implemented with 100-Gbit/s DQPSK signals.

Figure 33. Concept and principle of three-input (A, B, C) optical quaternary addition and subtraction (A+B-C, A+C-B, B+C-A, A+B+C) using nondegenerate FWM and DQPSK signals. 3 (3π/2) Sig.A A+B+C Wavelength Idler1 Sig.B -Sig.C A B -C The BER performance of the quaternary optical computing is characterized as shown in Fig. 31. The measured power penalty at a BER of 10-9 is less than 4 dB for addition (A+B), 3 dB for subtraction (A-B, B-A), 2 dB for complement (-A, -B), and 3.1 dB for doubling (2B), respectively. Remarkably, one can see that the quaternary addition, subtraction, and doubling show relatively large power penalties compared to the quaternary complement. Such interesting phenomenon can be briefly explained as follows. According to the relationships of electrical fields, the distortions of input signals are transferred into converted idlers (i.e., computing results). Actually, the degradations of quaternary addition/subtraction, complement, and doubling are respectively induced by the accumulated distortions from signal A and signal B, distortion from single signal B, and twice distortions from signal B. Additionally, the BER curves of two-output signals from the HNLF are also plotted in Fig. 31(c) and (d) for reference.

One can clearly see that the two signals suffer negligible performance degradations during high-base arithmetical operations.

Shown in Fig. 28 are measured spectra. One CW pump (1553.2 nm) and two 100-Gbit/s 27

RZ-DQPSK signals (A: 1546.6 nm, B: 1555.5 nm) are fed into a 460-m-long HNLF. The ZDW, dispersion slope (*S*) and nonlinear coefficient (γ) of the HNLF are ~1556 nm, ~0.026 ps/nm2

and 20 W-1 km-1, respectively. The employed HNLF has low and flat dispersion, which benefits simultaneous multiple FWM processes. As a consequence, it is possible to simultaneously generate six idlers (idler 1: 1544.3 nm, idler 2: 1548.9 nm, idler 3: 1562.2 nm, idler 4: 1559.9 nm, idler 5: 1550.9 nm, idler 6: 1557.7 nm) corresponding to simultaneous addition (A+B), subtrac‐ tion (A-B, B-A), complement (-A, -B), and doubling (2B) of quaternary numbers (A, B).

Figure 27. (a) Concept and (b) principle of two-input high-base optical computing (quaternary

A-B

CW (a) (b)

Sig. A

Idler2

Idler1 Idler5

A+B -B

CW Pump

Wavelength (nm) 1543 1553 1563

A+C-B B+C-A

Sig.C

Sig.B -Sig.C

Idler1 Idler2 Idler3

Sig.B

Non-Degenerate Four-Wave Mixing (FWM)

Nonlinear Device

A B C

A B -C

Wavelength

Wavelength

Sig. B

Idler6

2B


B-A

Idler4 Idler3

A+B-C: 0,0,1,1,3 A+C-B: 0,2,3,1,1 B+C-A: 0,0,3,1,3

A+B+C: 0,2,3,3,3

Figure 28. Measured spectra (a) before HNLF and (b) after HNLF for 50-Gbaud two-input quaternary optical

**Figure 28.** Measured spectra (a) before HNLF and (b) after HNLF for 50-Gbaud two-input quaternary optical comput‐

In order to confirm the quaternary optical computing (addition, subtraction, complement, doubling), the waveforms and balanced eyes of the demodulated in-phase (Ch. I) and quad‐ rature (Ch. Q) components of two-input 100-Gbit/s RZ-DQPSK signals and six converted idlers by multiple FWM processes are recorded. A 50-GHz delay-line interferometer (DLI) is used to demodulate 100-Gbit/s RZ-DQPSK. A relative delay of 20 ps is introduced between the two arms of the 50-GHz DLI. Remarkably, quaternary numbers can be represented by the combi‐ nation of Ch. I and Ch. Q (i.e., 00: '0', 01: '1', 11: '2', 10: '3'). By exploiting multiple degenerate and nondegenerate FWM processes, one can clearly see from Figs. 29 and 30 that simultaneous 50-Gbaud quaternary optical computing of addition (A+B), dual-directional subtraction (A-B, B-A), complement (-A, -B), and doubling (2B) are successfully implemented with 100-Gbit/s

Power (dBm)

10dB/div

Figure 33. Concept and principle of three-input (A, B, C) optical quaternary addition and subtraction (A+B-C,

The BER performance of the quaternary optical computing is characterized as shown in Fig. 31. The measured power penalty at a BER of 10-9 is less than 4 dB for addition (A+B), 3 dB for subtraction (A-B, B-A), 2 dB for complement (-A, -B), and 3.1 dB for doubling (2B), respectively. Remarkably, one can see that the quaternary addition, subtraction, and doubling show relatively large power penalties compared to the quaternary complement. Such interesting phenomenon can be briefly explained as follows. According to the relationships of electrical fields, the distortions of input signals are transferred into converted idlers (i.e., computing results). Actually, the degradations of quaternary addition/subtraction, complement, and doubling are respectively induced by the accumulated distortions from signal A and signal B, distortion from single signal B, and twice distortions from signal B. Additionally, the BER curves of two-output signals from the HNLF are also plotted in Fig. 31(c) and (d) for reference.

Sig.A

Sig.A

A+B-C

A+B+C

Idler1

A: 0,1,0,3,2

B: 2,2,2,3,3

C: 2,3,1,1,2

addition/subtraction/complement/doubling) using a single nonlinear device and DQPSK signals.

Wavelength (nm) 1543 1553 1563

Sig. A Sig. B

Pump

50 Applications of Digital Signal Processing through Practical Approach

computing (addition, subtraction, complement, doubling).

ing (addition, subtraction, complement, doubling).

0 (0)

Q

DQPSK: Quaternary Base Numbers

I

3 (3π/2)

1 (π/2)

2 (π)

DQPSK signals.

Power (dBm)

10dB/div

A+C-B, B+C-A, A+B+C) using nondegenerate FWM and DQPSK signals.


7

/km,


Fig. 29. Demodulated waveforms and balanced eyes for 50‐Gbaud two‐input quaternary addition and dual‐directional subtraction using 100‐Gbit/s DQPSK signals. **Figure 29.** Demodulated waveforms and balanced eyes for 50-Gbaud two-input quaternary addition and dual-direc‐ tional subtraction using 100-Gbit/s DQPSK signals.

Shown in Fig. 32 are measured constellations for input/output signals and output computing results. An optical complex spectrum analyzer (APEX AP2440A) is employed in the experi‐ ment. One can clearly see from Fig. 32 that the quaternary addition (A+B), quaternary sub‐ traction (A-B, B-A), and quaternary complement (-A, -B) have four-phase levels (0, π/2, π, 3π/2) while the quaternary doubling (2B) has two-phase levels (0, π). Fig. 29. Demodulated waveforms and balanced eyes for 50‐Gbaud two‐input quaternary

quaternary subtraction (A‐B, B‐A), and quaternary complement (‐A, ‐B) have four‐phase

levels (0, π/2, π, 3π/2) while the quaternary doubling (2B) has two‐phase levels (0, π).

addition and dual‐directional subtraction using 100‐Gbit/s DQPSK signals.

Shown in Fig. 32 are measured constellations for input/output signals and output computing results. An optical complex spectrum analyzer (APEX AP2440A) is employed in

converted idlers (i.e., computing results). Actually, the degradations of quaternary addition/subtraction, complement, and doubling are respectively induced by the accumulated distortions from signal A and signal B, distortion from single signal B, and twice distortions from signal B. Additionally, the BER curves of two‐output signals from the HNLF are also plotted in Fig. 31(c) and (d) for reference. One can clearly see that the two signals suffer negligible performance degradations during high‐base arithmetical operations.


Fig. 30. Demodulated waveforms and balanced eyes for 50‐Gbaud quaternary complement and doubling using 100‐Gbit/s DQPSK signals. **Figure 30.** Demodulated waveforms and balanced eyes for 50-Gbaud quaternary complement and doubling using 100- Gbit/s DQPSK signals.

We then demonstrate high-speed three-input high-base optical computing (addition and subtraction) of quaternary numbers using multiple nondegenerate FWM processes in a single HNLF and DQPSK signals. Figure 33 illustrates the concept and operation principle.

Shown in Fig. 34 are measured spectra for 50-Gbaud three-input quaternary optical computing (addition, subtraction). Figure 34(a) depicts the spectrum for degenerate FWM, which enables the conversion from C to –C (i.e., quaternary complement). In the experiment, the wavelengths of CW pump, input signal C (Sig. C) and converted signal (–Sig. C) are 1552.0, 1548.7, and 1555.5 nm, respectively. Figure 34(b) shows the typical spectrum for three-input quaternary optical computing, i.e., quaternary hybrid addition and subtraction (A+B-C, A+C-B, B+C-A). In the experiment, the wavelengths of three input 100-Gbit/s RZ-DQPSK signals (A, B, C) are 1546.6 (Sig. A), 1553.2 (Sig. B), and 1555.5 nm (Sig. C), respectively. It is clearly shown that three converted idlers, i.e., idler 1 at 1544.3 nm, idler 2 at 1548.9 nm, and idler 3 at 1562.2 nm, are generated by three nondegenerate FWM processes. Actually, idler 1, idler 2, and idler 3 correspond to A+B-C, A+C-B, and B+C-A, respectively. Figure 34(c) displays the spectrum for

converted idlers (i.e., computing results). Actually, the degradations of quaternary addition/subtraction, complement, and doubling are respectively induced by the accumulated distortions from signal A and signal B, distortion from single signal B, and twice distortions from signal B. Additionally, the BER curves of two‐output signals from the HNLF are also plotted in Fig. 31(c) and (d) for reference. One can clearly see that the two signals suffer negligible performance degradations during high‐base arithmetical operations.

Shown in Fig. 32 are measured constellations for input/output signals and output computing results. An optical complex spectrum analyzer (APEX AP2440A) is employed in the experiment. One can clearly see from Fig. 32 that the quaternary addition (A+B), quaternary subtraction (A‐B, B‐A), and quaternary complement (‐A, ‐B) have four‐phase

levels (0, π/2, π, 3π/2) while the quaternary doubling (2B) has two‐phase levels (0, π).

addition and dual‐directional subtraction using 100‐Gbit/s DQPSK signals.

and doubling using 100‐Gbit/s DQPSK signals.

signals.

Fig. 29. Demodulated waveforms and balanced eyes for 50‐Gbaud two‐input quaternary

Shown in Fig. 32 are measured constellations for input/output signals and output computing results. An optical complex spectrum analyzer (APEX AP2440A) is employed in the experi‐ ment. One can clearly see from Fig. 32 that the quaternary addition (A+B), quaternary sub‐ traction (A-B, B-A), and quaternary complement (-A, -B) have four-phase levels (0, π/2, π,

Fig. 29. Demodulated waveforms and balanced eyes for 50‐Gbaud two‐input quaternary

Fig. 30. Demodulated waveforms and balanced eyes for 50‐Gbaud quaternary complement

**Figure 30.** Demodulated waveforms and balanced eyes for 50-Gbaud quaternary complement and doubling using 100-

We then demonstrate high-speed three-input high-base optical computing (addition and subtraction) of quaternary numbers using multiple nondegenerate FWM processes in a single

Shown in Fig. 34 are measured spectra for 50-Gbaud three-input quaternary optical computing (addition, subtraction). Figure 34(a) depicts the spectrum for degenerate FWM, which enables the conversion from C to –C (i.e., quaternary complement). In the experiment, the wavelengths of CW pump, input signal C (Sig. C) and converted signal (–Sig. C) are 1552.0, 1548.7, and 1555.5 nm, respectively. Figure 34(b) shows the typical spectrum for three-input quaternary optical computing, i.e., quaternary hybrid addition and subtraction (A+B-C, A+C-B, B+C-A). In the experiment, the wavelengths of three input 100-Gbit/s RZ-DQPSK signals (A, B, C) are 1546.6 (Sig. A), 1553.2 (Sig. B), and 1555.5 nm (Sig. C), respectively. It is clearly shown that three converted idlers, i.e., idler 1 at 1544.3 nm, idler 2 at 1548.9 nm, and idler 3 at 1562.2 nm, are generated by three nondegenerate FWM processes. Actually, idler 1, idler 2, and idler 3 correspond to A+B-C, A+C-B, and B+C-A, respectively. Figure 34(c) displays the spectrum for

HNLF and DQPSK signals. Figure 33 illustrates the concept and operation principle.

**Doubling: 2B (DPSK)**

and doubling using 100‐Gbit/s DQPSK signals.

Gbit/s DQPSK signals.

**Ch. Q**

**Ch. Q** 

levels (0, π/2, π, 3π/2) while the quaternary doubling (2B) has two‐phase levels (0, π).

Shown in Fig. 32 are measured constellations for input/output signals and output computing results. An optical complex spectrum analyzer (APEX AP2440A) is employed in the experiment. One can clearly see from Fig. 32 that the quaternary addition (A+B), quaternary subtraction (A‐B, B‐A), and quaternary complement (‐A, ‐B) have four‐phase

converted idlers (i.e., computing results). Actually, the degradations of quaternary addition/subtraction, complement, and doubling are respectively induced by the accumulated distortions from signal A and signal B, distortion from single signal B, and twice distortions from signal B. Additionally, the BER curves of two‐output signals from the HNLF are also plotted in Fig. 31(c) and (d) for reference. One can clearly see that the two signals suffer negligible performance degradations during high‐base arithmetical operations.

3π/2) while the quaternary doubling (2B) has two-phase levels (0, π).

**Complement: -A Ch. I**

**Complement: -B Ch. I** 

**Quaternary number (-A)**

52 Applications of Digital Signal Processing through Practical Approach

**Quaternary number (-B)**

addition and dual‐directional subtraction using 100‐Gbit/s DQPSK signals.

Fig. 31. Measured BER curves for input/output signals (A, B), quaternary addition (A+B), **Figure 31.** Measured BER curves for input/output signals (A, B), quaternary addition (A+B), dual-directional subtrac‐ tion (A-B, B-A), complement (-A, -B), and doubling (2B).

Fig. 32. Measured constellations for 50‐Gbaud two‐input quaternary optical computing (addition, dual‐directional subtraction, complement, doubling) with 100‐Gbit/s DQPSK **Figure 32.** Measured constellations for 50-Gbaud two-input quaternary optical computing (addition, dual-directional subtraction, complement, doubling) with 100-Gbit/s DQPSK signals.

three-input quaternary addition of A+B+C. In the experiment, the converted signal (-Sig. C) by degenerate FWM shown in Fig. 34(a) is selected and used as the input signal shown in Fig. 34(b), i.e., -Sig. C is employed instead of Sig. C as shown in Fig. 34(c). After the nondegenerate FWM process, the converted idler 1 carrying quaternary addition result of A+B+C is obtained. We then demonstrate high‐speed three‐input high‐base optical computing (addition and subtraction) of quaternary numbers using multiple nondegenerate FWM processes in a single HNLF and DQPSK signals. Figure 33 illustrates the concept and operation principle.

To verify the successful realization of three-input quaternary optical computing (addition, subtraction), the waveforms and balanced eye diagrams of the demodulated in-phase (Ch. I) A: 0,1,0,3,2 A+B-C: 0,0,1,1,3 A+C-B: 0,2,3,1,1

A+C- B+C-A


Non-Degenerate Four-Wave Mixing (FWM)

A B C

A B -C

Nonlinear

Wavelength

B+C-A: 0,0,3,1,3

A+B+C: 0,2,3,3,3

Fig. 33. Concept and principle of three‐input (A, B, C) optical quaternary addition and subtraction (A+B‐C, A+C‐B, B+C‐A, A+B+C) using nondegenerate FWM and DQPSK signals.

Sig.A

Idler1 Idler2

A+B-C

A+B+C Idler1

0

Q

 DQPSK: Quaternary Base Numbers

I

3 (3π/2)

1 (π/2)

2 (π)

B: 2,2,2,3,3

C: 2,3,1,1,2

Power (dBm)

10dB/div

Wavelength (nm)

Sig. A Sig. B

Pump

Figure 27. (a) Concept and (b) principle of two-input high-base optical computing (quaternary

A-B

CW (a) (b)

Sig. A

Idler2

Idler1 Idler5

A+B -B

CW Pump

Wavelength (nm)

Sig. B

Idler6

2B


B-A

Idler4 Idler3

Figure 28. Measured spectra (a) before HNLF and (b) after HNLF for 50-Gbaud two-input quaternary optical

Power (dBm)

10dB/div

addition/subtraction/complement/doubling) using a single nonlinear device and DQPSK signals.

Figure 33. Concept and principle of three-input (A, B, C) optical quaternary addition and subtraction (A+B-C, A+C-B, B+C-A, A+B+C) using nondegenerate FWM and DQPSK signals. **Figure 33.** Concept and principle of three-input (A, B, C) optical quaternary addition and subtraction (A+B-C, A+C-B, B +C-A, A+B+C) using nondegenerate FWM and DQPSK signals.

and quadrature (Ch. Q) components of three-input 100-Gbit/s RZ-DQPSK signals and threeoutput converted idlers by nondegenerate FWM processes are recorded. Figure 35 depicts the measured sequences of input signals and converted idlers. It is clearly shown that the degen‐ erate FWM process enables 50-Gbaud conversion from C to –C (i.e., quaternary complement) and three nondegenerate FWM processes perform three-input quaternary optical computing, i.e., hybrid quaternary addition and subtraction (A+B-C, A+C-B, B+C-A, A+B+C).

We measure the BER curves as shown in Fig. 36 for 50-Gbaud three-input quaternary optical computing (A+B-C, A+C-B, B+C-A). It is shown from Figs. 36(a) and (b) that the power penalties at a BER of 10-9 of three-input quaternary optical computing (A+B-C, A+C-B, B+C-A) are measured to be less than 6 dB. Shown in Fig. 37 are the measured BER curves for 50-Gbaud conversion from C to –C (i.e., quaternary complement) and 50-Gbaud three-input quaternary addition (A+B+C). The observed power penalty is negligible for the conversion from C to –C. For the quaternary addition of A+B+C, the power penalty at a BER of 10-9 is assessed to be less than 6 dB. Similar to two-input quaternary optical computing, it is believed that the perform‐ ance degradations of three-input quaternary optical computing (i.e., quaternary hybrid addition and subtraction of A+B-C, A+C-B, B+C-A, and A+B+C) are mainly caused by accu‐ mulated distortions originated from three-input signals (A, B, C or –C). Such phenomenon can be explained according to the electrical field and linear optical phase relationships of nonde‐ generate FWM processes. Shown in Fig. 36(c)(d) and Fig. 37(a)(b) are measured BER curves for three output signals (A, B, C or –C) from HNLF after three-input quaternary optical 7

8

and quadrature (Ch. Q) components of three-input 100-Gbit/s RZ-DQPSK signals and threeoutput converted idlers by nondegenerate FWM processes are recorded. Figure 35 depicts the measured sequences of input signals and converted idlers. It is clearly shown that the degen‐ erate FWM process enables 50-Gbaud conversion from C to –C (i.e., quaternary complement) and three nondegenerate FWM processes perform three-input quaternary optical computing,

Figure 33. Concept and principle of three-input (A, B, C) optical quaternary addition and subtraction (A+B-C,

**Figure 33.** Concept and principle of three-input (A, B, C) optical quaternary addition and subtraction (A+B-C, A+C-B, B

Figure 27. (a) Concept and (b) principle of two-input high-base optical computing (quaternary

A-B

CW (a) (b)

Sig. A

Idler2

Idler1 Idler5

A+B -B

CW Pump

Wavelength (nm) 1543 1553 1563

A+C-B B+C-A

Sig.C

Sig.B -Sig.C

Idler1 Idler2 Idler3

Sig.B

Non-Degenerate Four-Wave Mixing (FWM)

Nonlinear Device

A B C

A B -C

Wavelength

Wavelength

Sig. B

Idler6

2B


B-A

Idler4 Idler3

A+B-C: 0,0,1,1,3 A+C-B: 0,2,3,1,1 B+C-A: 0,0,3,1,3

A+B+C: 0,2,3,3,3

Figure 28. Measured spectra (a) before HNLF and (b) after HNLF for 50-Gbaud two-input quaternary optical

Power (dBm)

10dB/div

addition/subtraction/complement/doubling) using a single nonlinear device and DQPSK signals.

Wavelength (nm) 1543 1553 1563

Sig. A Sig. B

Pump

computing (addition, subtraction, complement, doubling).

54 Applications of Digital Signal Processing through Practical Approach

0 (0)

Q

DQPSK: Quaternary Base Numbers

I

3 (3π/2)

1 (π/2)

2 (π)

Power (dBm)

10dB/div

We measure the BER curves as shown in Fig. 36 for 50-Gbaud three-input quaternary optical computing (A+B-C, A+C-B, B+C-A). It is shown from Figs. 36(a) and (b) that the power penalties at a BER of 10-9 of three-input quaternary optical computing (A+B-C, A+C-B, B+C-A) are measured to be less than 6 dB. Shown in Fig. 37 are the measured BER curves for 50-Gbaud conversion from C to –C (i.e., quaternary complement) and 50-Gbaud three-input quaternary addition (A+B+C). The observed power penalty is negligible for the conversion from C to –C. For the quaternary addition of A+B+C, the power penalty at a BER of 10-9 is assessed to be less than 6 dB. Similar to two-input quaternary optical computing, it is believed that the perform‐ ance degradations of three-input quaternary optical computing (i.e., quaternary hybrid addition and subtraction of A+B-C, A+C-B, B+C-A, and A+B+C) are mainly caused by accu‐ mulated distortions originated from three-input signals (A, B, C or –C). Such phenomenon can be explained according to the electrical field and linear optical phase relationships of nonde‐ generate FWM processes. Shown in Fig. 36(c)(d) and Fig. 37(a)(b) are measured BER curves for three output signals (A, B, C or –C) from HNLF after three-input quaternary optical 7

i.e., hybrid quaternary addition and subtraction (A+B-C, A+C-B, B+C-A, A+B+C).

Sig.A

Sig.A

A+B-C

A+B+C

Idler1

A: 0,1,0,3,2

B: 2,2,2,3,3

C: 2,3,1,1,2

A+C-B, B+C-A, A+B+C) using nondegenerate FWM and DQPSK signals.

+C-A, A+B+C) using nondegenerate FWM and DQPSK signals.

Degenerate FWM process (C to –C conversion); (b) three-input quaternary hybrid addition and subtraction (idler 1: A+B-C, idler 2: A+C-B, idler 3: B+C-A) by degenerate FWM process; (c) three-input quaternary addition (idler: A+B+C) by degenerate FWM process. **Figure 34.** Measured spectra for 50-Gbaud three-input quaternary optical computing (addition, subtraction). (a) De‐ generate FWM process (C to –C conversion); (b) three-input quaternary hybrid addition and subtraction (idler 1: A+B-C, idler 2: A+C-B, idler 3: B+C-A) by degenerate FWM process; (c) three-input quaternary addition (idler: A+B+C) by degenerate FWM process.

Figure 34. Measured spectra for 50-Gbaud three-input quaternary optical computing (addition, subtraction). (a)

computing. For the three signals during the three-input quaternary optical computing operations, no significant performance degradations are observed in the experiment.

We also measure the constellation diagrams for three-input/output 100-Gbit/s RZ-DQPSK signals (A, B, C/-C) and six converted idlers corresponding to quaternary hybrid addition and subtraction of A+B-C, A+C-B, B+C-A, and A+B+C. An optical complex spectrum analyzer (APEX AP2440A) is employed in the experiment. From Fig. 38 one can clearly observe fourphase levels (i.e., 0, π/2, π, 3π/2) of all input/output signal and output idlers. These four-phase levels can represent quaternary base numbers.

Figure 35. Demodulated temporal waveforms and balanced eye diagrams for 50-Gbaud three-input (A, B, C) quaternary addition and subtraction (A+B-C, A+C-B, B+C-A, A+B+C). **Figure 35.** Demodulated temporal waveforms and balanced eye diagrams for 50-Gbaud three-input (A, B, C) quaterna‐ ry addition and subtraction (A+B-C, A+C-B, B+C-A, A+B+C).

phase levels (i.e., 0, π/2, π, 3π/2) of all input/output signal and output idlers. These four-phase

**Ch. I** 

**Ch. Q** 

**Ch. Q** 

**Ch. Q** 

**Ch. Q** 

**Ch. I** 

**Quaternary number (A+B-C)** 

**Output: A+C-B Ch. I** 

**Quaternary number (A+C-B)** 

**Quaternary number (B+C-A)**

**Quaternary number (A+B+C)** 

**Output : B+C-A** 

**Output : A+B+C** 

**Ch. I Ch. Q** 

**Ch. I Ch. Q** 

**Ch. I Ch. Q** 

**Ch. I Ch. Q Ch. I Ch. Q** 

**Output : A+B-C** 

Figure 35. Demodulated temporal waveforms and balanced eye diagrams for 50-Gbaud three-input (A, B, C)

**Figure 35.** Demodulated temporal waveforms and balanced eye diagrams for 50-Gbaud three-input (A, B, C) quaterna‐

**Ch. Q** 

quaternary addition and subtraction (A+B-C, A+C-B, B+C-A, A+B+C).

ry addition and subtraction (A+B-C, A+C-B, B+C-A, A+B+C).

levels can represent quaternary base numbers.

56 Applications of Digital Signal Processing through Practical Approach

**Ch. Q** 

**Ch. I** 

**Ch. Q** 

**Ch. I** 

**Ch. Q** 

**Ch. I** 

**Ch. Q** 

**Quaternary number (A)** 

**Quaternary number (B)** 

**Quaternary number (C)** 

**Quaternary number (-C)** 

**Input : Signal B Ch. I** 

**Input : Signal A** 

**Ch. I** 

**Ch. Q** 

**Ch. I Ch. Q**

**Input : - Signal C Ch. I** 

**Ch. I** 

**Input : Signal C** 

Fig. 36. Measured BER curves for 50‐Gbaud three‐input quaternary optical computing. (a)(b) Hybrid addition and subtraction of A+B‐C, A+C‐B, and B+C‐A. (c)(d) Output signals (Sig. A, Sig. B, Sig. C) from HNLF. (a)(c) Ch. I. (b)(d) Ch. Q. B‐to‐B: back‐to‐back. **Figure 36.** Measured BER curves for 50-Gbaud three-input quaternary optical computing. (a)(b) Hybrid addition and subtraction of A+B-C, A+C-B, and B+C-A. (c)(d) Output signals (Sig. A, Sig. B, Sig. C) from HNLF. (a)(c) Ch. I. (b)(d) Ch. Q. B-to-B: back-to-back.

(b)(d) Ch. Q. B‐to‐B: back‐to‐back. Fig. 37. Measured BER curves for 50‐Gbaud conversion from C to –C and three‐input quaternary addition of A+B+C. (a)(b) Conversion from C to –C. (c)(d) A+B+C. (a)(c) Ch. I. (b)(d) Ch. Q. B‐to‐B: back‐to‐back. **Figure 37.** Measured BER curves for 50-Gbaud conversion from C to –C and three-input quaternary addition of A+B +C. (a)(b) Conversion from C to –C. (c)(d) A+B+C. (a)(c) Ch. I. (b)(d) Ch. Q. B-to-B: back-to-back.

(k)

Output Output

Output Output

Input Sig. C (d)

(h)

(l)

 A+B+C Output

**-**Sig. C Output

 Input  **-**Sig.

Input Sig. B

Sig. A Sig. B Sig. C

A+B-C A+C- B+C-

(f) (g)

(a) (b)

(e)

(i) (j)

Input Sig. A

Output

Output

quaternary addition of A+B+C. (a)(b) Conversion from C to –C. (c)(d) A+B+C. (a)(c) Ch. I.

Figure 38. Measured constellation diagrams for 50-Gbaud three-input quaternary addition and subtraction. **Figure 38.** Measured constellation diagrams for 50-Gbaud three-input quaternary addition and subtraction.

In addition to two-/three-input high-base optical computing based on degenerate/nondegen‐ erate FWM in HNLFs, we also propose and simulate three-input high-base optical computing (hexadecimal addition and subtraction) in a single silicon–organic hybrid slot waveguide based on nondegenerate FWM processes.

Shown in Fig. 39(a) is the schematic 3D structure of the proposed silicon–organic hybrid slot waveguide. It has a sandwich structure formed by a low-refractive-index PTS [polymer poly (bis para-toluene sulfonate) of 2, 4-hexadiyne-1,6 diol] layer inserted between two highrefractive-index silicon layers. The cladding of the structure is air. The substrate is silicon dioxide. In the designed silicon–organic hybrid slot waveguide, the waveguide width is W=250 nm, the upper silicon height is Hu=180 nm, the lower silicon height is Hl=180 nm, and the slot height is Hs=25 nm. We plot in Fig. 39(b)-(d) the quasi-TM mode distribution together with its normalized power density along x and y directions. It is clearly shown that the mode is highly confined in the nanoscale nonlinear organic slot region (i.e., tight light confinement). As a consequence, high nonlinearity and instantaneous Kerr response are achievable without impairments by TPA and FCA. Using finite-element method, we assess the effective mode area and nonlinearity to be 7.7x10-14 m2 and 5500 w-1m-1, which can potentially facilitate efficient high-base optical signal processing (e.g., hexadecimal addition/subtraction). Figure 40 illustrates the operation principle which is similar to that in HNLFs. Instead of using DQPSK

for quaternary optical computing, here 16PSK signals are used to achieve hexadecimal optical computing.

**Figure 39.** (a) 3D structure, (b) mode distribution, (c)(d) normalized power density along x and y directions of a sili‐ con–organic hybrid slot waveguide.

In the following simulations, three 40-Gbaud 213-1 PRBS 16-PSK signals (λA: 1546 nm, λB: 1552 nm, λC: 1550 nm) are adopted. A 1-mm-long silicon–organic hybrid slot waveguide is em‐ ployed. Figure 41 shows simulation results for three-input 40-Gbaud (160-Gbit/s) hexadecimal addition/subtraction. Twenty-symbol sequences are plotted in Fig. 41, which confirms the successful implementation of three-input hexadecimal addition/subtraction (A+B-C, A+C-B, B +C-A, A+B+C, A-B-C, B-A-C). The constellations are also shown in Fig. 42 with assessed EVM under an OSNR of 28 dB for input signals. The observed degradation of EVM for hexadecimal addition/subtraction can be ascribed to the accumulated noise from input 16-PSK signals and impairments from nonlinear interactions inside the silicon–organic hybrid slot waveguide. We further investigate the EVM of input signals and output idlers against the OSNR of input signals as shown in Fig. 43(a) and (b). The EVM penalties are assessed to be less than 4.5 for hexadecimal addition/subtraction under an OSNR of 28 dB.

10

Figure 38. Measured constellation diagrams for 50-Gbaud three-input quaternary addition and subtraction.

In addition to two-/three-input high-base optical computing based on degenerate/nondegen‐ erate FWM in HNLFs, we also propose and simulate three-input high-base optical computing (hexadecimal addition and subtraction) in a single silicon–organic hybrid slot waveguide

Shown in Fig. 39(a) is the schematic 3D structure of the proposed silicon–organic hybrid slot waveguide. It has a sandwich structure formed by a low-refractive-index PTS [polymer poly (bis para-toluene sulfonate) of 2, 4-hexadiyne-1,6 diol] layer inserted between two highrefractive-index silicon layers. The cladding of the structure is air. The substrate is silicon dioxide. In the designed silicon–organic hybrid slot waveguide, the waveguide width is W=250 nm, the upper silicon height is Hu=180 nm, the lower silicon height is Hl=180 nm, and the slot height is Hs=25 nm. We plot in Fig. 39(b)-(d) the quasi-TM mode distribution together with its normalized power density along x and y directions. It is clearly shown that the mode is highly confined in the nanoscale nonlinear organic slot region (i.e., tight light confinement). As a consequence, high nonlinearity and instantaneous Kerr response are achievable without impairments by TPA and FCA. Using finite-element method, we assess the effective mode area

high-base optical signal processing (e.g., hexadecimal addition/subtraction). Figure 40 illustrates the operation principle which is similar to that in HNLFs. Instead of using DQPSK

**Figure 38.** Measured constellation diagrams for 50-Gbaud three-input quaternary addition and subtraction.

A+B-C A+C-B B+C-A

(c)

(k)

Output Output

Output Output

Input Sig. C

and 5500 w-1m-1, which can potentially facilitate efficient

(d)

(h)

(l)

A+B+C Output

**-**Sig. C Output

Input **-**Sig. C

Input Sig. B

Sig. A Sig. B Sig. C

(f) (g)

(a) (b)

(i) (j)

(e)

Input Sig. A

58 Applications of Digital Signal Processing through Practical Approach

Output

Output

based on nondegenerate FWM processes.

and nonlinearity to be 7.7x10-14 m2

**Figure 40.** (a) Concept and (b)(c)(d) operation principle of three-input hexadecimal addition/subtraction.

**Figure 41.** Simulated symbol sequence for three-input 40-Gbaud (160-Gbit/s) hexadecimal addition/subtraction using silicon–organic hybrid slot waveguide.

**Figure 42.** Simulated constellations for three-input 40-Gbaud (160-Gbit/s) hexadecimal addition/subtraction using sili‐ con–organic hybrid slot waveguide.

**Figure 43.** Simulated EVM vs. OSNR for 40-Gbaud (160-Gbit/s) hexadecimal addition/subtraction using silicon–organic hybrid slot waveguide.

#### **5. High-base coding/decoding [79]**

**Figure 41.** Simulated symbol sequence for three-input 40-Gbaud (160-Gbit/s) hexadecimal addition/subtraction using

**Figure 40.** (a) Concept and (b)(c)(d) operation principle of three-input hexadecimal addition/subtraction.

60 Applications of Digital Signal Processing through Practical Approach

silicon–organic hybrid slot waveguide.

We propose and demonstrate high-base optical coding/decoding of advanced multilevel modulation signals based on degenerate FWM in HNLFs.

Figure 44 illustrates the concept and principle of the proposed symbol-wise hexadecimal coding/decoding using degenerate FWM and 16-QAM signals. Symbol-wise hexadecimal coding/decoding can be regarded as the constellation manipulation in the I/Q plane. The pump, original signal, coded signal and decoded signal are denoted by Ki, Pi, Ci, and Di, respectively. In the symbol-wise hexadecimal coding/decoding the pump can be CW or phase modulated. Illustrated in Fig. 44(a1) and (b1) are the symbol-wise hexadecimal coding, in which a CW or phase-modulated pump (Ki) and a 16-QAM signal (Pi) are launched into a nonlinear device such as HNLF to take part in the nonlinear interaction such as degenerate FWM process. 16-QAM signal can represent a hexadecimal number. When propagating along the HNLF, the degenerate FWM process generates a coded signal (Ci). Note that the electrical field (*EC <sup>i</sup>* ) of the coded signal (Ci) satisfies the relationship of *EC <sup>i</sup>* ∝*EK <sup>i</sup>* <sup>2</sup> <sup>⋅</sup>*EP <sup>i</sup>* \* . From the electrical fields a linear phase relationship of Φ*<sup>C</sup> <sup>i</sup>* =2Φ*<sup>K</sup> <sup>i</sup>* −Φ*<sup>P</sup> <sup>i</sup>* is achieved, i.e., twice the pump phase modulation (2Φ*<sup>K</sup> <sup>i</sup>* ) and the conjugated phase of the original signal (−Φ*<sup>P</sup> <sup>i</sup>* ) contribute together to the phase of the coded signal. Consequently, the coding algorithm simultaneously relies on the pump phase modulation and degenerate-FWM-induced phase conjugation. For the CW pump-assisted symbol-wise hexadecimal coding as shown in Fig. 44(a1), all constel‐ lation points in the I/Q plane are moved to their symmetrical positions with respect to the Iaxis because of the phase conjugation property of degenerate FWM. Actually, hexadecimal code conversion from one number to another is achieved simply by conjugated degenerate FWM process. For the symbol-wise hexadecimal coding exploiting a phase-modulated pump, i.e. (0, π/4) phase modulation, as illustrated in Fig. 44(b1), all constellation points are mapped symmetrically with respect to the I-axis. Meanwhile, the pump phase modulation also introduces additional symbol-varying coding. When the constellation point of 16-QAM in one symbol meets the π/4 pump phase modulation, it will rotate in a counter-clockwise direction by π/2. As a result, the coding algorithm becomes Φ*<sup>C</sup> <sup>i</sup>* =2Φ*<sup>K</sup> <sup>i</sup>* −Φ*<sup>P</sup> <sup>i</sup>* which determines the rule of hexadecimal coding.

**Figure 44.** Concept and operation principle of variable symbol-wise hexadecimal coding/decoding by use of optical nonlinearity and 16-QAM. (a1)(a2) Symbol-wise hexadecimal coding/decoding assisted by CW pump; (b1)(b2) symbolwise hexadecimal coding/decoding assisted by (0, π/4) phase-modulated pump; (a1)(b1) Coding; (a2)(b2) Decoding.

Figure 44(a2) and (b2) illustrate the symbol-wise hexadecimal decoding. The pump (Ki) and the coded signal (Ci) are fed into another nonlinear device such as HNLF to participate in the nonlinear interaction such as degenerate FWM process which generates the decoded signal (Di). It is noted that the electrical field of the decoded signal (Di) satisfies the relationship of *ED <sup>i</sup>* ∝*EK <sup>i</sup>* <sup>2</sup> <sup>⋅</sup>*EC <sup>i</sup>* \* <sup>∝</sup>*EK <sup>i</sup>* <sup>2</sup> <sup>⋅</sup>*EK <sup>i</sup>* \* <sup>2</sup> <sup>⋅</sup>*EP <sup>i</sup>* <sup>=</sup> <sup>|</sup> *EK <sup>i</sup>* <sup>|</sup> <sup>4</sup> <sup>⋅</sup>*EP <sup>i</sup>* <sup>∝</sup>*EP <sup>i</sup>* . Thus, the phase of the decoded signal (Di) meets the relationship of Φ*<sup>D</sup> <sup>i</sup>* =2Φ*<sup>K</sup> <sup>i</sup>* −Φ*<sup>C</sup> <sup>i</sup>* =2Φ*<sup>K</sup> <sup>i</sup>* −(2Φ*<sup>K</sup> <sup>i</sup>* −Φ*<sup>P</sup> <sup>i</sup>* )=Φ*<sup>P</sup> <sup>i</sup>* . As a consequence, the decoded signal (Di) recovers the original signal (Pi) after the decoding process. The decoding algorithm is determined by Φ*<sup>D</sup> <sup>i</sup>* =2Φ*<sup>K</sup> <sup>i</sup>* −Φ*<sup>C</sup> <sup>i</sup>* =2Φ*<sup>K</sup> <sup>i</sup>* −(2Φ*<sup>K</sup> <sup>i</sup>* −Φ*<sup>P</sup> <sup>i</sup>* )=Φ*<sup>P</sup> <sup>i</sup>* . Remarkably, the decoding algorithm corresponds to the constellation manipulation in the complex plane. The concept and principle shown in Fig. 44 indicate that the constellation of a 16-QAM signal can be manipulated by employing optical nonlinearity, which enables the symbol-wise hexadec‐ imal coding/decoding. Moreover, exploiting a CW or (0, π/4) phase-modulated pump can facilitate optical variable symbol-wise hexadecimal coding/decoding assisted by optical nonlinearity.

modulated. Illustrated in Fig. 44(a1) and (b1) are the symbol-wise hexadecimal coding, in which a CW or phase-modulated pump (Ki) and a 16-QAM signal (Pi) are launched into a nonlinear device such as HNLF to take part in the nonlinear interaction such as degenerate FWM process. 16-QAM signal can represent a hexadecimal number. When propagating along the HNLF, the degenerate FWM process generates a coded signal (Ci). Note that the electrical

<sup>2</sup> <sup>⋅</sup>*EP <sup>i</sup>*

which determines the rule

**I** 

**Q** 

**Decoded Signal (Di)** 

**Decoding (b2)** 

**Decoded Signal** 

**(Di)** 

**Q** 

**(a2) Decoding** 

**Nonlinear Device** 

**Ki Ci** 

**Nonlinear Device** 

**Pump (Ki) I** 

**Ki Ci** 

**Di** 

t (sym)

**Di** 

\* . From the

) contribute

) of the coded signal (Ci) satisfies the relationship of *EC <sup>i</sup>* ∝*EK <sup>i</sup>*

by π/2. As a result, the coding algorithm becomes Φ*<sup>C</sup> <sup>i</sup>* =2Φ*<sup>K</sup> <sup>i</sup>* −Φ*<sup>P</sup> <sup>i</sup>*

**Q** 

**Coded Signal (Ci)** 

**Q** 

**Coded Signal (Ci)** 

**(a1) Coding** 

**Pump (Ki)** 

<sup>π</sup> <sup>π</sup> <sup>π</sup> <sup>0</sup> <sup>0</sup> <sup>4</sup> <sup>4</sup> <sup>4</sup>

1 2 3 4 5

**Figure 44.** Concept and operation principle of variable symbol-wise hexadecimal coding/decoding by use of optical nonlinearity and 16-QAM. (a1)(a2) Symbol-wise hexadecimal coding/decoding assisted by CW pump; (b1)(b2) symbolwise hexadecimal coding/decoding assisted by (0, π/4) phase-modulated pump; (a1)(b1) Coding; (a2)(b2) Decoding.

**Q** 

0 0

1 2 3 4 5

**Q** 

**Coded Signal** 

t (sym)

 **(Ci)** 

**I** 

**Coded Signal (Ci)** 

**I** 

**Coding (b1)** 

**Nonlinear Device** 

**Pump (Ki) I** 

**Nonlinear Device** 

**Pump (Ki) I** 

**Ci** 

0 0 0 0 0 0 **CW CW** 

**Pi Ki** 

**Ci** 

**Pi Ki** 

electrical fields a linear phase relationship of Φ*<sup>C</sup> <sup>i</sup>* =2Φ*<sup>K</sup> <sup>i</sup>* −Φ*<sup>P</sup> <sup>i</sup>* is achieved, i.e., twice the pump

together to the phase of the coded signal. Consequently, the coding algorithm simultaneously relies on the pump phase modulation and degenerate-FWM-induced phase conjugation. For the CW pump-assisted symbol-wise hexadecimal coding as shown in Fig. 44(a1), all constel‐ lation points in the I/Q plane are moved to their symmetrical positions with respect to the Iaxis because of the phase conjugation property of degenerate FWM. Actually, hexadecimal code conversion from one number to another is achieved simply by conjugated degenerate FWM process. For the symbol-wise hexadecimal coding exploiting a phase-modulated pump, i.e. (0, π/4) phase modulation, as illustrated in Fig. 44(b1), all constellation points are mapped symmetrically with respect to the I-axis. Meanwhile, the pump phase modulation also introduces additional symbol-varying coding. When the constellation point of 16-QAM in one symbol meets the π/4 pump phase modulation, it will rotate in a counter-clockwise direction

) and the conjugated phase of the original signal (−Φ*<sup>P</sup> <sup>i</sup>*

field (*EC <sup>i</sup>*

phase modulation (2Φ*<sup>K</sup> <sup>i</sup>*

62 Applications of Digital Signal Processing through Practical Approach

of hexadecimal coding.

**I** 

**Original Signal (Pi)** 

t (sym)

**I** 

**Original Signal (Pi)** 

t (sym)

**Q** 

0 0

1 2 3 4 5

**Q** 

<sup>π</sup> <sup>π</sup> <sup>π</sup> <sup>0</sup> <sup>0</sup> <sup>4</sup> <sup>4</sup> <sup>4</sup>

1 2 3 4 5

Shown in Fig. 45 is the experimental setup for the proposed optical symbol-wise hexadecimal coding/decoding. A 10-Gbaud (40-Gbit/s) 16-QAM signal is prepared via the vector addition of two copies of QPSK signal using an I/Q QPSK modulator, polarization controllers (PCs), a tunable differential group delay (DGD) element, and a polarizer (Pol.). A 10-Gbit/s phasemodulated pump with (0, π/4) binary phase modulation, which is synchronized with the 10- Gbaud 16-QAM signal, is provided by employing a phase modulator (PM) driven by PRBS patterns. Note that the PM is not utilized for the CW pump-assisted hexadecimal coding/ decoding. For the hexadecimal coding process, the 16-QAM signal (Pi) and the CW/phasemodulated pump (Ki) are launched into a 460-m piece of HNLF. The ZDW, dispersion slope (*S*) and nonlinear coefficient (γ) of the HNLF employed in the experiment are ~1556 nm, ~0.026 ps/nm2 /km, and 20 W-1·km-1, respectively. When the 16-QAM signal (Pi) and the CW/phasemodulated pump (Ki) propagate along the HNLF, a coded signal (Ci) is generated by degen‐ erate FWM process. The coded signal (Ci) takes the result of hexadecimal coding. For the hexadecimal decoding process, the coded signal (Ci) and the CW/phase-modulated pump (Ki) are fed into another 520-m piece of HNLF which has a ZDW of ~1555 nm, *S* of ~0.026 ps/nm2 / km, and γ of 20 W-1·km-1. When the coded signal (Ci) and the CW/phase-modulated pump transmit through the HNLF, a decoded signal (Di) is obtained by degenerate FWM process. The decoded signal (Di) recovers the original signal corresponding to hexadecimal decoding. In the experimental setup, BPFs at the output of HNLFs are employed to suppress unwanted frequency components and pick up coded/decoded signals. For coherent detection of 16-QAM signals, an optical modulation analyzer (Agilent N4391A) and a digital phosphor oscilloscope (Tektronix DPO72004) with a 50-Gs/s sample rate and a 20-GHz electrical bandwidth are employed in the experiment.

The measured spectra for optical variable symbol-wise hexadecimal coding/decoding are shown in Fig. 46. Both, CW pump and (0, π/4) phase-modulated pump are employed in the experiment. The original signal (Pi), pump (Ki), coded signal (Ci), and decoded signal (Di) have wavelengths of 1557.0, 1555.6, 1554.2, and 1557.0 nm, respectively. We set the power of the original signal for coding and the coded signal for decoding to be around 10.8 dBm. For

**Figure 45.** Experimental setup for high-base coding/decoding. Degenerate FWM in HNLF, 16-QAM signal and CW/ phase-modulated pumps are employed to enable symbol-wise hexadecimal coding/decoding. QPSK: quadrature phase-shift keying; QAM: quadrature amplitude modulation; HNLF: highly nonlinear fiber; CW: continuous-wave; PC: polarization controller; EDFA: erbium-doped fiber amplifier; DGD: differential group delay; Pol.: polarizer; BPF: band-pass filter; ODL: tunable optical delay line; PM: phase modulator; OC: optical coupler.

the symbol-wise hexadecimal coding/decoding using a CW pump, the power of CW pump is ~12.8 dBm. The conversion efficiency is assessed to be about -15.4 dB for the symbol-wise hexadecimal coding while -14.9 dB for the symbol-wise hexadecimal decoding. For the symbolwise hexadecimal coding/decoding using a (0, π/4) phase-modulated pump, the power of the (0, π/4) phase-modulated pump is ~9.8 dBm. The symbol-wise hexadecimal coding has a conversion efficiency of about -20.9 dB, while the symbol-wise hexadecimal decoding shows a conversion efficiency of around -19.1 dB.

Figure 47 depicts observed constellation diagrams and in-phase (I) and quadrature (Q) components for optical variable symbol-wise hexadecimal coding/decoding. Figure 47(a) shows the 10-Gbaud 16-QAM signal corresponding to the back-to-back (B-B) case. The EVM is measured to be 5.5%rms. The 16 constellation points can be clearly seen in the complex I/Q plane. Note that hexadecimal numbers can be represented by these 16 constellation points. For the symbol-wise hexadecimal coding/decoding using a CW pump, the phase-conjugated degenerate FWM process determines the coding and decoding algorithms to be (Φ*<sup>C</sup> <sup>i</sup>* = −Φ*<sup>P</sup> <sup>i</sup>* ) and (−(−Φ*<sup>P</sup> <sup>i</sup>* )=Φ*<sup>P</sup> <sup>i</sup>* ), respectively. The constellations in the complex I/Q plane are manipulated following the coding and decoding algorithms. Figure 47(b) and (c) show the constellation diagrams of coded signal with an EVM of 6.3%rms and decoded signal with an EVM of 6.4%rms, respectively. For the symbol-wise hexadecimal coding/decoding using a phasemodulated pump, a (0, π/4) pump phase modulation with an EVM of 5.0%rms is employed in the experiment, as shown in Fig. 47(d). The constellation diagrams of the coded signal with an EVM of 7.8%rms and decoded signal with an EVM of 6.4%rms are shown in Fig. 47(e) and (f). The constellation manipulation in the complex I/Q plane follows the coding algorithm (Φ*<sup>C</sup> <sup>i</sup>* =2Φ*<sup>K</sup> <sup>i</sup>* −Φ*<sup>P</sup> <sup>i</sup>* ) for the symbol-wise hexadecimal coding process and decoding algorithm (2Φ*<sup>K</sup> <sup>i</sup>* −Φ*<sup>C</sup> <sup>i</sup>* =2Φ*<sup>K</sup> <sup>i</sup>* −(2Φ*<sup>K</sup> <sup>i</sup>* −Φ*<sup>P</sup> <sup>i</sup>* )=Φ*<sup>P</sup> <sup>i</sup>* ) for the symbol-wise hexadecimal decoding process. Remarkably, for phase-modulated pump-assisted symbol-wise hexadecimal coding/decod‐ ing, the pump phase modulation and phase conjugation of degenerate FWM contribute together to the coding and decoding algorithms.

**Figure 46.** Measured spectra for high-base coding/decoding. Degenerate FWM in HNLF, 16-QAM signal and CW/ phase-modulated pumps are employed to enable symbol-wise hexadecimal coding/decoding. (a1)(a2) Symbol-wise hexadecimal coding/decoding using a CW pump; (b1)(b2) symbol-wise hexadecimal coding/decoding using a (0, π/4) phase-modulated pump; (a1)(b1) symbol-wise hexadecimal coding; (a2)(b2) symbol-wise hexadecimal decoding.

the symbol-wise hexadecimal coding/decoding using a CW pump, the power of CW pump is ~12.8 dBm. The conversion efficiency is assessed to be about -15.4 dB for the symbol-wise hexadecimal coding while -14.9 dB for the symbol-wise hexadecimal decoding. For the symbolwise hexadecimal coding/decoding using a (0, π/4) phase-modulated pump, the power of the (0, π/4) phase-modulated pump is ~9.8 dBm. The symbol-wise hexadecimal coding has a conversion efficiency of about -20.9 dB, while the symbol-wise hexadecimal decoding shows

**Figure 45.** Experimental setup for high-base coding/decoding. Degenerate FWM in HNLF, 16-QAM signal and CW/ phase-modulated pumps are employed to enable symbol-wise hexadecimal coding/decoding. QPSK: quadrature phase-shift keying; QAM: quadrature amplitude modulation; HNLF: highly nonlinear fiber; CW: continuous-wave; PC: polarization controller; EDFA: erbium-doped fiber amplifier; DGD: differential group delay; Pol.: polarizer; BPF:

ODL

**Original Signal** 

**(Pi)** 

Q

Figure 47 depicts observed constellation diagrams and in-phase (I) and quadrature (Q) components for optical variable symbol-wise hexadecimal coding/decoding. Figure 47(a) shows the 10-Gbaud 16-QAM signal corresponding to the back-to-back (B-B) case. The EVM is measured to be 5.5%rms. The 16 constellation points can be clearly seen in the complex I/Q plane. Note that hexadecimal numbers can be represented by these 16 constellation points. For the symbol-wise hexadecimal coding/decoding using a CW pump, the phase-conjugated degenerate FWM process determines the coding and decoding algorithms to be (Φ*<sup>C</sup> <sup>i</sup>* = −Φ*<sup>P</sup> <sup>i</sup>*

following the coding and decoding algorithms. Figure 47(b) and (c) show the constellation diagrams of coded signal with an EVM of 6.3%rms and decoded signal with an EVM of 6.4%rms, respectively. For the symbol-wise hexadecimal coding/decoding using a phasemodulated pump, a (0, π/4) pump phase modulation with an EVM of 5.0%rms is employed in the experiment, as shown in Fig. 47(d). The constellation diagrams of the coded signal with an EVM of 7.8%rms and decoded signal with an EVM of 6.4%rms are shown in Fig. 47(e) and (f). The constellation manipulation in the complex I/Q plane follows the coding algorithm

Remarkably, for phase-modulated pump-assisted symbol-wise hexadecimal coding/decod‐ ing, the pump phase modulation and phase conjugation of degenerate FWM contribute

)=Φ*<sup>P</sup> <sup>i</sup>*

), respectively. The constellations in the complex I/Q plane are manipulated

) for the symbol-wise hexadecimal coding process and decoding algorithm

) for the symbol-wise hexadecimal decoding process.

1% tap

1% tap 1% tap

**Decoding** 

**Coding** 

**Di** 

1% tap 1% tap

**Coded Signal (Ci)** 

**HNLF 1** 

16-QAM

I

**HNLF 2** 

)

a conversion efficiency of around -19.1 dB.

PC PM

**Pump (Ki)** 

I /Q

I Q

Pump BPF

Fast axis

64 Applications of Digital Signal Processing through Practical Approach

**16-QAM Generation** 

Tunable DGD

Pol.

EDFA OC

band-pass filter; ODL: tunable optical delay line; PM: phase modulator; OC: optical coupler.

QPSK

Signal CW

CW

and (−(−Φ*<sup>P</sup> <sup>i</sup>*

(Φ*<sup>C</sup> <sup>i</sup>* =2Φ*<sup>K</sup> <sup>i</sup>* −Φ*<sup>P</sup> <sup>i</sup>*

)=Φ*<sup>P</sup> <sup>i</sup>*

(2Φ*<sup>K</sup> <sup>i</sup>* −Φ*<sup>C</sup> <sup>i</sup>* =2Φ*<sup>K</sup> <sup>i</sup>* −(2Φ*<sup>K</sup> <sup>i</sup>* −Φ*<sup>P</sup> <sup>i</sup>*

together to the coding and decoding algorithms.

To confirm the implementation of optical variable symbol-wise hexadecimal coding/decoding, the complex amplitudes (i.e., in-phase and quadrature components) of symbol sequence for different signals are recorded in the experiment. As shown in Fig. 48, for symbol-wise hexadecimal coding/decoding using a CW pump, by comparing the symbol sequence of coded signal and original signal, one can clearly see that all the constellation points in the complex I/Q plane are mapped to their symmetrical positions with respect to the I-axis. This constella‐ tion manipulation is determined by the coding algorithm of CW pump-assisted hexadecimal coding. Additionally, by comparing the symbol sequence of decoded signal and original signal one can confirm that the decoded signal recovers the original signal.

As shown in Fig. 49, for symbol-wise hexadecimal coding/decoding using a (0, π/4) phasemodulated pump, the corresponding coding algorithm manipulates the constellation points in the complex I/Q plane as follows. All the constellation points in the complex I/Q plane are first flipped to their symmetrical points with respect to the I-axis. Then, a counter-clockwise rotation of π/2 is introduced to the constellation points, which meet the pump phase modu‐ lation of π/4. One can expect enhanced security for the symbol-wise hexadecimal coding using a phase-modulated pump owing to the added coding algorithm contribution from the pump. When compared to the symbol-wise hexadecimal coding using a CW pump, the phasemodulated pump-assisted symbol-wise hexadecimal coding is not so straightforward.

**Figure 47.** Measured constellation diagrams and in-phase (I) and quadrature (Q) components for high-base coding/ decoding. Degenerate FWM in HNLF, 16-QAM signal, and CW/phase-modulated pumps are employed to enable sym‐ bol-wise hexadecimal coding/decoding. (a) Back-to-back (B-B) 16-QAM signal; (b) coded signal using a CW pump; (c) decoded signal using CW pump; (d) (0, π/4) phase-modulated pump; (e) coded signal using a (0, π/4) phase-modulat‐ ed pump; (f) decoded signal using a (0, π/4) phase-modulated pump.

Nevertheless, the hexadecimal coding process is still verified from Fig. 49, i.e., the symbol sequence relationship of coded signal and original signal follows the coding algorithm of (0, π/4) phase-modulated pump-assisted symbol-wise hexadecimal coding. In addition, for the symbol-wise hexadecimal decoding process, the decoded signal recovers the information carried by the original signal. From the obtained results as shown in Figs. 48 and 49, one can clearly confirm the successful realization of 10-Gbaud optical variable symbol-wise hexadec‐ imal coding/decoding by exploiting degenerate FWM in HNLF, 16-QAM signal, and CW/ phase-modulated pumps.

**Figure 48.** Measured complex amplitudes (i.e., in-phase and quadrature components) of symbol sequence for optical symbol-wise hexadecimal coding/decoding using a CW pump.

The BER performance is characterized for CW/phase-modulated pump-assisted optical variable symbol-wise hexadecimal coding/decoding. Shown in Fig. 50(a) are measured BER curves for the symbol-wise hexadecimal coding/decoding using a CW pump. OSNR penalty is used for performance evaluation defined by the ratio of the received OSNR of the coded signal to that of the back-to-back (B-B) signal. The measured OSNR penalty at a BER of 2e-3 is ~0.6 dB for CW pump-assisted symbol-wise hexadecimal coding. The measured OSNR penalty at a BER of 2e-3 for CW pump-assisted symbol-wise hexadecimal decoding, i.e., the ratio of the received OSNR of the decoded signal to that of the B-B signal, is around 1.1 dB. Shown in Fig. 50(b) are measured BER curves for the symbol-wise hexadecimal coding/decoding using a (0, π/4) phase-modulated pump. From Fig. 50(b) one can see that the OSNR penalty at a BER of 2e-3 is measured to be ~1.2 dB for symbol-wise hexadecimal coding process and ~0.9 dB for symbol-wise hexadecimal decoding process, respectively.

We study the BER performance of symbol-wise hexadecimal coding/decoding as a function of the pump phase modulation depth. Figure 51(a) and (b) show measured results for symbolwise hexadecimal coding and decoding, respectively. The OSNR is fixed around 20 dB. For the symbol-wise hexadecimal coding process as shown in Fig. 51(a), the coding operation performance is sensitive to the pump phase modulation depth. In contrast, for the symbolwise hexadecimal decoding process as shown in Fig. 51(b), the decoding operation perform‐ ance changes slightly. Such interesting phenomenon can be briefly explained as follows. For the symbol-wise hexadecimal coding process with the coding algorithm ofΦ*<sup>C</sup> <sup>i</sup>* =2Φ*<sup>K</sup> <sup>i</sup>* −Φ*<sup>P</sup> <sup>i</sup>* , twice phase modulation of the pump is added to the coded signal. As a result, any change of the pump phase modulation depth and resultant offset from π/4 pump phase modulation can cause the deviation of the constellation points of 16-QAM from their standard positions. Thus, the coding performance is degraded for symbol-wise hexadecimal coding process. To maintain

Nevertheless, the hexadecimal coding process is still verified from Fig. 49, i.e., the symbol sequence relationship of coded signal and original signal follows the coding algorithm of (0, π/4) phase-modulated pump-assisted symbol-wise hexadecimal coding. In addition, for the symbol-wise hexadecimal decoding process, the decoded signal recovers the information carried by the original signal. From the obtained results as shown in Figs. 48 and 49, one can clearly confirm the successful realization of 10-Gbaud optical variable symbol-wise hexadec‐ imal coding/decoding by exploiting degenerate FWM in HNLF, 16-QAM signal, and CW/

**Figure 47.** Measured constellation diagrams and in-phase (I) and quadrature (Q) components for high-base coding/ decoding. Degenerate FWM in HNLF, 16-QAM signal, and CW/phase-modulated pumps are employed to enable sym‐ bol-wise hexadecimal coding/decoding. (a) Back-to-back (B-B) 16-QAM signal; (b) coded signal using a CW pump; (c) decoded signal using CW pump; (d) (0, π/4) phase-modulated pump; (e) coded signal using a (0, π/4) phase-modulat‐

EVM: 7.8%rms

**Coding** (b)

(c)

EVM: 6.4%rms

(f) **Decoding** 

EVM: 6.4%rms

In-phase quadrature In-phase quadrature

**Decoding** 

EVM: 6.3%rms

In-phase quadrature In-phase quadrature In-phase quadrature

**Coding** (e)

phase-modulated pumps.

**Signal (B-B)** (a)

66 Applications of Digital Signal Processing through Practical Approach

EVM: 5.5%rms

**Phase Pump** (d)

π/4

ed pump; (f) decoded signal using a (0, π/4) phase-modulated pump.

EVM: 5.0%rms

**Figure 49.** Measured complex amplitudes of symbol sequence for optical symbol-wise hexadecimal coding/decoding using a phase-modulated pump. A binary phase modulation of (0, π/4) is applied to the pump.

**Figure 50.** Measured BER curves for optical variable symbol-wise hexadecimal coding/decoding. (a) CW pump; (b) (0, π/4) phase-modulated pump.

the BER below 2e-3 (EFEC threshold), the tolerance of the pump phase modulation offset is assessed to be about 0.023π, as shown in Fig. 51(a). For the symbol-wise hexadecimal decoding process with the decoding algorithm of 2Φ*<sup>K</sup> <sup>i</sup>* −Φ*<sup>C</sup> <sup>i</sup>* =2Φ*<sup>K</sup> <sup>i</sup>* −(2Φ*<sup>K</sup> <sup>i</sup>* −Φ*<sup>P</sup> <sup>i</sup>* )=Φ*<sup>P</sup> <sup>i</sup>* algorithms, it is easy to understand that the BER performance of the decoded signal is independent on the pump phase modulation, i.e., insensitive to the modulation depth of the pump as shown in Fig. 51(b).

**Figure 51.** Measured dependence of BER performance on the phase modulation depth of pump. (a) symbol-wise hexa‐ decimal coding; (b) symbol-wise hexadecimal decoding. seen that the performance of decoding process is dependent on the offset in the time domain between the pump for decoding and that for coding. To maintain the BER below 2e‐3 (EFEC threshold), the tolerance of the relative pump offset to the symbol period is assessed to be

about 20%.

Fig. 52. Measured BER performance of symbol‐wise hexadecimal coding/decoding versus signal/pump offset in the time domain. (a) Measured BER of coding as a function of the offset in the time domain between the signal and the pump for coding. The pump for decoding is not involved; (b) Measured BER of decoding as a function of the offset in the time domain between the signal and the pump for decoding. The pump for decoding is **Figure 52.** Measured BER performance of symbol-wise hexadecimal coding/decoding versus signal/pump offset in the time domain. (a) Measured BER of coding as a function of the offset in the time domain between the signal and the pump for coding. The pump for decoding is not involved; (b) Measured BER of decoding as a function of the offset in the time domain between the signal and the pump for decoding. The pump for decoding is aligned to the pump for coding; (c) Measured BER of decoding as a function of the offset in the time domain between the pump for decoding and the pump for coding. The pump for coding is aligned to the signal.

aligned to the pump for coding; (c) Measured BER of decoding as a function of the offset in

the time domain between the pump for decoding and the pump for coding. The pump for coding is aligned to the signal. **6. Conclusion** In this chapter, we have reviewed recent research efforts toward high‐base optical signal processing by adopting multilevel modulation signals and exploiting optical nonlinearities. 1) High‐Base Wavelength Conversion: On‐chip, high‐base, all‐optical wavelength conversion of multicarrier, multilevel modulation signals has been demonstrated using degenerate FWM in a silicon waveguide and OFDM m‐QAM signals. Impressive operation performance of on‐chip 3.2 Gbaud/s OFDM 16/32/64/128‐QAM wavelength conversion has been achieved in the experiment. We further evaluate the BER performance of symbol-wise hexadecimal coding/decoding versus the signal offset and pump offset in the time domain, as shown in Fig. 52. In the experiment, the OSNR is fixed around 20 dB. Figure 52(a) depicts the measured BER of symbolwise hexadecimal coding as a function of the offset in the time domain between the signal and the pump for coding. Note that the pump for decoding is not involved. It is shown that the coding is sensitive to the signal offset from the pump. This is predictable according to the coding algorithm of Φ*<sup>C</sup> <sup>i</sup>* =2Φ*<sup>K</sup> <sup>i</sup>* −Φ*<sup>P</sup> <sup>i</sup>* . To keep the BER below 2e-3 (EFEC threshold), the tolerance of the relative signal offset to the symbol period is measured to be about 10%. Figure 52(b) plots the measured BER of symbol-wise hexadecimal decoding as a function of the offset in the time domain between the signal and the pump for decoding. The pump for decoding is aligned to the pump for coding. One can clearly see that the BER performance is insensitive to the signal offset in the time domain. This is easy to understand based on the decoding algorithm of 2Φ*<sup>K</sup> <sup>i</sup>* −Φ*<sup>C</sup> <sup>i</sup>* =2Φ*<sup>K</sup> <sup>i</sup>* −(2Φ*<sup>K</sup> <sup>i</sup>* −Φ*<sup>P</sup> <sup>i</sup>* )=Φ*<sup>P</sup> <sup>i</sup>* . Figure 52(c) shows measured BER of symbol-wise

2) High‐Base Optical Data Exchange: Phase‐transparent, high‐base optical data exchange between two 100‐Gbit/s DQPSK signals has been demonstrated using the parametric depletion effect of nondegenerate FWM in an HNLF. Simultaneous multichannel data exchange has been proposed and demonstrated using bidirectional degenerate FWM in a single HNLF. Moreover, a reconfigurable Tbit/s network switching element using double‐ pass LCoS technology accompanied by bidirectional degenerate FWM in a single HNLF has been proposed. 2.3‐Tbit/s multifunctional grooming switch has been demonstrated in the experiment, performing simultaneous selective high‐base add/drop, high‐base switchable data exchange, and high‐base power equalization, for ITU‐grid‐compatible 23‐channel 100‐

the BER below 2e-3 (EFEC threshold), the tolerance of the pump phase modulation offset is assessed to be about 0.023π, as shown in Fig. 51(a). For the symbol-wise hexadecimal decoding

**Figure 50.** Measured BER curves for optical variable symbol-wise hexadecimal coding/decoding. (a) CW pump; (b) (0,

**Figure 49.** Measured complex amplitudes of symbol sequence for optical symbol-wise hexadecimal coding/decoding

using a phase-modulated pump. A binary phase modulation of (0, π/4) is applied to the pump.

68 Applications of Digital Signal Processing through Practical Approach

easy to understand that the BER performance of the decoded signal is independent on the pump phase modulation, i.e., insensitive to the modulation depth of the pump as shown in

)=Φ*<sup>P</sup> <sup>i</sup>*

algorithms, it is

process with the decoding algorithm of 2Φ*<sup>K</sup> <sup>i</sup>* −Φ*<sup>C</sup> <sup>i</sup>* =2Φ*<sup>K</sup> <sup>i</sup>* −(2Φ*<sup>K</sup> <sup>i</sup>* −Φ*<sup>P</sup> <sup>i</sup>*

(a) (b)

Fig. 51(b).

π/4) phase-modulated pump.

hexadecimal decoding as a function of the offset in the time domain between the pump for decoding and that for coding. The pump for coding is aligned to the signal. It can be clearly seen that the performance of decoding process is dependent on the offset in the time domain between the pump for decoding and that for coding. To maintain the BER below 2e-3 (EFEC threshold), the tolerance of the relative pump offset to the symbol period is assessed to be about 20%.

#### **6. Conclusion**

In this chapter, we have reviewed recent research efforts toward high-base optical signal processing by adopting multilevel modulation signals and exploiting optical nonlinearities.


decoding assisted by a CW pump or a phase-modulated pump has been demonstrated in the experiment. The former takes the coding through the phase conjugation of degenerate FWM, and the latter offers enhanced coding via the combined contributions from the phase modulation of the pump and the phase-conjugated FWM.

Beyond high-base wavelength conversion, data exchange, optical computing, and optical coding/decoding based on degenerate/nondegenerate FWM in HNLFs or silicon waveguides, with future improvements, other different optical nonlinearities on various nonlinear optical device platforms would also be employed to flexibly manipulate the amplitude and phase information of advanced multilevel modulation signals, which might open diverse interesting applications in robust high-base optical signal processing.

## **Acknowledgements**

hexadecimal decoding as a function of the offset in the time domain between the pump for decoding and that for coding. The pump for coding is aligned to the signal. It can be clearly seen that the performance of decoding process is dependent on the offset in the time domain between the pump for decoding and that for coding. To maintain the BER below 2e-3 (EFEC threshold), the tolerance of the relative pump offset to the symbol period is assessed to be about

In this chapter, we have reviewed recent research efforts toward high-base optical signal processing by adopting multilevel modulation signals and exploiting optical nonlinearities. **1.** High-Base Wavelength Conversion: On-chip, high-base, all-optical wavelength conver‐ sion of multicarrier, multilevel modulation signals has been demonstrated using degen‐ erate FWM in a silicon waveguide and OFDM m-QAM signals. Impressive operation performance of on-chip 3.2 Gbaud/s OFDM 16/32/64/128-QAM wavelength conversion

**2.** High-Base Optical Data Exchange: Phase-transparent, high-base optical data exchange between two 100-Gbit/s DQPSK signals has been demonstrated using the parametric depletion effect of nondegenerate FWM in an HNLF. Simultaneous multichannel data exchange has been proposed and demonstrated using bidirectional degenerate FWM in a single HNLF. Moreover, a reconfigurable Tbit/s network switching element using double-pass LCoS technology accompanied by bidirectional degenerate FWM in a single HNLF has been proposed. 2.3-Tbit/s multifunctional grooming switch has been demon‐ strated in the experiment, performing simultaneous selective high-base add/drop, highbase switchable data exchange, and high-base power equalization, for ITU-gridcompatible 23-channel 100-Gbit/s RZ-DQPSK signals. Additionally, ultrahigh-speed high-base optical data exchange of 640 Gbaud (2.56 Tbit/s) 16-QAM and 640 Gbaud (3.84 Tbit/s) 64-QAM signals has been proposed and simulated by exploiting non-degenerate

**3.** High-Base Optical Computing: By adopting 100-Gbit/s two-input RZ-DQPSK signals (A, B) and exploiting three degenerate FWM processes and three nondegenerate FWM processes in an HNLF, simultaneous 50-Gbaud two-input quaternary addition (A+B), dual-directional subtraction (A-B, B-A), complement (-A, -B), and doubling (2B) have been demonstrated in the experiment. By employing 100-Gbit/s three-input RZ-DQPSK signals (A, B, C/-C) and three nondegenerate FWM processes in an HNLF, 50-Gbaud three-input quaternary hybrid addition and subtraction (A+B-C, A+C-B, B+C-A, A+B+C) have been demonstrated in the experiment. Furthermore, three-input (A, B, C) 40-Gbaud (160-Gbit/ s) optical hexadecimal addition/subtraction (A+B-C, A+C-B, B+C-A, A+B+C, A-B-C, B-A-C) has also been proposed and simulated based on nondegenerate FWM in a silicon–

**4.** High-Base Optical Coding/Decoding: By exploiting degenerate FWM in an HNLF and adopting 16-QAM signal, 10-Gbaud optical variable symbol-wise hexadecimal coding/

20%.

**6. Conclusion**

has been achieved in the experiment.

70 Applications of Digital Signal Processing through Practical Approach

FWM in a silicon-organic hybrid slot waveguide.

organic hybrid slot waveguide.

This work was supported by the National Natural Science Foundation of China (NSFC) under grants 61222502, 11574001, 11274131, and 61077051; the Program for New Century Excellent Talents in University (NCET-11-0182); the National Basic Research Program of China (973 Program) under grant 2014CB340004; the Wuhan Science and Technology Plan Project under grant 2014070404010201; the Fundamental Research Funds for the Central Universities (HUST) under grants 2012YQ008 and 2013ZZGH003. The authors thank the Center of Micro-Fabrica‐ tion and Characterization (CMFC) of WNLO for the support in the manufacturing process of silicon waveguides. The authors also thank the facility support of the Center for Nanoscale Characterization and Devices of WNLO.

#### **Author details**

Jian Wang1\* and Alan E. Willner2

\*Address all correspondence to: jwang@hust.edu.cn

1 Wuhan National Laboratory for Optoelectronics, School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan, Hubei, China

2 Department of Electrical Engineering, University of Southern California, Los Angeles, California, USA

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