**4. Evaluation of parametric amplifiers and its application**

Parametric amplifiers can be based on degenerate FWM (in the single-pump case) and on nondegenerate FWM (in the dual-pump case). FOPA produced gain will reach its maximum, if the phase-matching condition is met or if the phase-mismatch parameter k is equal to zero. In the case of a single-pump FOPA, irrespective of the broad amplification range, the amplification spectrum is not even. In the experimental transmission system, described before, the gain −3dB bandwidth has reached 2.2 THz (see **Figure 9**). It has been found that for ensuring an optimum operation mode of a single-pump FOPA, it is necessary to maintain a small negative linear phase deviation in respect to the zero-dispersion frequency, which would compensate the nonlinear phase mismatch. That is why the pumping radiation wavelength must be slightly larger than the fiber zero-dispersion wavelength (ZDWL).

**Figure 9.** Gain spectrum of the single-pump FOPA with 660 mW 1553.9 nm pumping radiation.

The implementation of the hybrid Raman-SOA solution allows using such mode of the semiconductor amplifier, in which it produces minimum distortions of the amplified signal, whereas the amplification deficit, which occurs after reducing the pumping current value by 43 mA, is compensated by the DRA with a 250 mW 1451.7 nm co-propagating pump. The implementation of the Raman-SOA hybrid solution allows increasing the attainable transmission distance by 12 km. The gain spectrum of the DRA is shown in **Figure 8a**. Eye diagrams for channels with the highest BER value in a system with the SOA amplifier (ninth channel *f* = 193.45 THz) and in a system with the Raman-SOA hybrid amplifier (tenth channel*f* = 193.5 THz) are shown accordingly in **Figure 8b** and **c**. From **Figure 8a**, it can be seen that the DRA produced amplification is large enough to compensate the amplification deficit of 5.3 dB that occurs after reducing the SOA pumping current by 43 mA. SOA amplifier (9th channel) and Raman-SOA hybrid ampli-

After comparing **Figure 8b** and **c**, it has been found that implementation of the Raman-SOA hybrid solution allows obtaining approximately the same BER level as in the case of SOA inline amplifier, but at signal power lower by 1.5 times. This shows that, by using SOA together with the distributed Raman amplifier and introducing relevant SOA pumping current adjustments, it is possible to substantially lower the amount of SOA produced noise and, therefore,

fier (10th channel) be selected, because they are the worst channels.

**4. Evaluation of parametric amplifiers and its application**

amplifier (B) and the tenth channel in the system with the Raman-SOA hybrid amplifier (c).

slightly larger than the fiber zero-dispersion wavelength (ZDWL).

Parametric amplifiers can be based on degenerate FWM (in the single-pump case) and on nondegenerate FWM (in the dual-pump case). FOPA produced gain will reach its maximum, if the phase-matching condition is met or if the phase-mismatch parameter k is equal to zero. In the case of a single-pump FOPA, irrespective of the broad amplification range, the amplification spectrum is not even. In the experimental transmission system, described before, the gain −3dB bandwidth has reached 2.2 THz (see **Figure 9**). It has been found that for ensuring an optimum operation mode of a single-pump FOPA, it is necessary to maintain a small negative linear phase deviation in respect to the zero-dispersion frequency, which would compensate the nonlinear phase mismatch. That is why the pumping radiation wavelength must be

**Figure 8.** DRA produced gain spectrum (A) and eye diagrams of the ninth channel in the system with the SOA in-line

to improve the quality of the amplified signal.

192 Optical Fiber and Wireless Communications

The gain spectrum bandwidth is very dependent on the nonlinearity parameter of the medium and on the pumping radiation power and the length of the gain medium highly nonlinear fibers (HNLFs). Thus, by increasing the fiber length, it is possible to achieve a higher level of amplification, but in this case, the gain spectrum width will be reduced accordingly (the longer the fiber, the larger the accumulated phase mismatch is). Due to this reason, when constructing FOPA amplifiers, it is not recommended to use HNLFs that are longer than 1 km. If they are configured in a way to achieve as wide gain spectrum as possible, it is required to use as short HNLF as possible, but to maintain the achievable amplification level, the pump power must be increased, or a fiber with a higher nonlinearity coefficient must be used. When selecting the pumping radiation parameters, one must keep in mind that, by changing the pumping radiation power, also the nonlinear phase mismatch is changed. Therefore, along with adjusting the pump power, its wavelength also needs to be reconfigured.

The performance of single-pump parametric amplifiers is affected by various factors, which must be taken into account when designing a specific FOPA. It is necessary to selectively choose the pumping radiation parameters to ensure as high amplification efficiency as possible and to avoid occurrence of excessive channel-channel four-wave mixing (CC-FWM) and pumpchannel four-wave mixing (PC-FWM) produced interchannel cross talk, which in its turn is produced due to excessive pumping. The SBS threshold increase is also very important; otherwise, the amplification effectiveness will decrease, and the amplified signal will be distorted.

One of the most effective solutions of increasing the SBS threshold is phase modulation of the pumping radiation. However, as can be seen from the results shown in **Figure 10**, if the choice of frequencies modulating the pumping radiation phase is not thoroughly considered, a substantial expansion of spectrum of the idler spectral components will occur. Therefore, in systems, in which idlers are used for all-optical signal processing, it must be ensured that the chosen pumping radiation phase-modulation does not produce excessive spectral broadening of idlers (in the results shown in **Figure 10**, idler spectral broadening has reached 54% at the level of −15 dB from the maximum power spectrum). For initiating the FWM process, it is also necessary to preserve the angular momentum among the four photons involved in the parametric interactions, as the parametric gain has explicit polarization dependence.

**Figure 10.** Spectra of the amplified signal (A) and the generated idlers (B) at the output of the single-pump FOPA.

Unlike single-pump FOPAs, dual-pump FOPAs can ensure even amplification over a very broad wavelength band. To achieve even amplification in a broad wavelength band, it is necessary to ensure that the wavelengths of the pumps are placed symmetrically in respect to the gain medium ZDWL, whereas the frequency distance between ZDWL and pumping radiations must be large enough (depending on the specific FOPA configuration), to avoid the impact of PC-FWM-generated components on the quality of the amplified signal.

Since dual-pump FOPAs both degenerate and nondegenerate FWM, for one input signal, it is possible to obtain at least five idlers (see **Figure 11**, where *ω*<sup>1</sup> and *ω*<sup>2</sup> are the pumping source frequencies, but *ω*<sup>3</sup> is the signal), which are directly related to the amplifiable signal frequency. This leads to amplification spectrum depressions at frequencies near the frequencies of the pumps. It has been concluded from the results obtained in this study that at 0.5 mW pump power it is recommended that the amplified signal frequency is at a distance of at least 1.2 THz from pump frequencies.

Just like in the case of single-pump FOPAs, dual-pump FOPAs also require the usage of one of the methods for mitigation of the negative impact of SBS. However, in the dual-pump case, it is important to note that by manipulating with the phase of both pumping radiations it can

**Figure 11.** Optical spectrum at the output of a dual-pump FOPA with 200 mW 191.5 THz pumps and 500 meter long HNLF.

be achieved that the relevant idler will not experience spectral broadening. The amplification efficiency in the case of dual-pump FOPAs is highly dependent on the SRS triggered energy transfer between the pumps. It is not possible to fully avoid this effect. To reduce its impact, normally higher power is used for the pump with the higher frequency than for the other pumping radiation, thus achieving that the average power difference between the pumps is minimum over the entire gain medium.

In traditional WDM transmission system architecture, one optical source is required to produce a single-channel carrier. It is not the most cost-effective solution, as, by increasing the number of transmission channels, the number of required light sources increases accordingly. Due to this reason, an increasing number of studies are conducted to find such transmission system architecture, which would be able to ensure a higher number of signal carriers using fewer optical sources [32–34]. FOPAs during the process of parametric amplification generate idler spectral components, which, in essence, are phase-conjugated copies of the amplified signal. These idlers could be used not only for wavelength conversion or 2R and 3R signal regeneration but also for increasing the number of carriers on the transmitter side of a WDM transmission system.

Unlike single-pump FOPAs, dual-pump FOPAs can ensure even amplification over a very broad wavelength band. To achieve even amplification in a broad wavelength band, it is necessary to ensure that the wavelengths of the pumps are placed symmetrically in respect to the gain medium ZDWL, whereas the frequency distance between ZDWL and pumping radiations must be large enough (depending on the specific FOPA configuration), to avoid the

**Figure 10.** Spectra of the amplified signal (A) and the generated idlers (B) at the output of the single-pump FOPA.

Since dual-pump FOPAs both degenerate and nondegenerate FWM, for one input signal, it

frequency. This leads to amplification spectrum depressions at frequencies near the frequencies of the pumps. It has been concluded from the results obtained in this study that at 0.5 mW pump power it is recommended that the amplified signal frequency is at a distance of at least

Just like in the case of single-pump FOPAs, dual-pump FOPAs also require the usage of one of the methods for mitigation of the negative impact of SBS. However, in the dual-pump case, it is important to note that by manipulating with the phase of both pumping radiations it can

and *ω*<sup>2</sup>

is the signal), which are directly related to the amplifiable signal

are the pumping

impact of PC-FWM-generated components on the quality of the amplified signal.

is possible to obtain at least five idlers (see **Figure 11**, where *ω*<sup>1</sup>

source frequencies, but *ω*<sup>3</sup>

194 Optical Fiber and Wireless Communications

1.2 THz from pump frequencies.

Therefore, a model of a dual-pump FOPA has been introduced for doubling the number of existing carriers in a WDM transmission system. For this reason, a simulation model of a 32-channel DWDM transmission system has been created with 10 Gbps transmission speed per channel, 100 GHz channel spacing, and NRZ-OOK modulation format. This system simulation model is displayed in **Figure 12**. The authors chose SMF length of 20 km, because it is the typical line length of optical access networks. EDFA preamplifier is used here for insertion loss compensation of transmission line and other transmission elements.

The main feature in the simulation model, which is presented in **Figure 12**, is that the FOPA is placed before the transmitter block or at the 32-channel modulator inputs. The optical

**Figure 12.** Simulation model of the 32 channel 10 Gbps WDM transmission system with the provided multicarrier source solution, which is based on wavelength conversion using a dual-pump FOPA.

multicarrier source consists of continuous radiation lasers (CW1–CW16), an optical attenuator, two powerful pumping sources, two optical splitters, and a 500 m long HNLF. One of the main goals of this experiment is to obtain 32 carriers with even frequency distribution (equal channel spacing), which can be achieved by using idlers *ω*<sup>4</sup> . Taking into account that the distribution of idlers *ω*<sup>4</sup> and the initial light source frequencies are symmetrical in respect to the gain medium ZDWL, it has been decided to place the carrier with the lowest frequency higher by 50 GHz than the HNLF ZDWL (193 THz). Therefore, the frequencies of the 16 initial carriers are distributed in a range from 193.05 to 194.55 THz with 100 GHz channel spacing (see **Figure 13a**). The optical flow sent through the parametric amplifier is not modulated and basically represents a continuous radiation set. At the output of the HNLF, a combination is obtained consisting of 16 initial carriers, 16 idlers *ω*<sup>4</sup> (generated as a result of parametric processes), 2 pumps, and other third-order spectral components (see **Figure 13b** and **c**). The pump power for both pumps is set to 400 mW each (26 dBm), and 190 and 196 THz frequencies are temporarily chosen.

**Figure 13.** Optical spectrum at the input of the FOPA when initial carrier power is set to 0 dBm (A) and optical spectra at the output of the HNLF when the power of the initial carriers is set to 0 dBm (B) and to −10 dBm (C).

It has been found that when given an excessively high level of input signal power, CC-FWM processes will trigger explicit interchannel cross talk (see **Figure 13b**). Due to this reason, when the idlers obtained as a result of parametric processes are used for increasing the number of carriers, it is necessary to limit the power of the carriers at the amplifier input. Based on the obtained results, the power level of the initial carriers at the input of the amplifier is reduced to −10 dBm. The alignment of idlers in respect to the central frequencies of the throughput band of demultiplexer filters is achieved by changing the frequency of the first pumping radiation (frequency obtained in simulations −196.01 THz). With the aforementioned amplifier configuration, the maximum power level difference among all the 32 channels has been reduced to 1.9 dB.

To assess the performance of the proposed system architecture solution, BER value dependence on the received signal power in the channel with the poorest signal quality (the highest BER) is obtained. These results are compared to the corresponding results obtained in a system with traditional architecture (with 32 laser sources, which function in a continuous radiation mode). The obtained results are shown in **Figure 14**. It has been found that power penalty of 1.8 dB exists between the system with the proposed multicarrier source and the conventional 32-channel solution. It is important to note that part of the obtained power penalty is directly related to the large amount of ASE produced by the EDFA used as a preamplifier for ensuring the necessary signal power at the input of the received block.

multicarrier source consists of continuous radiation lasers (CW1–CW16), an optical attenuator, two powerful pumping sources, two optical splitters, and a 500 m long HNLF. One of the main goals of this experiment is to obtain 32 carriers with even frequency distribution

**Figure 12.** Simulation model of the 32 channel 10 Gbps WDM transmission system with the provided multicarrier source

to the gain medium ZDWL, it has been decided to place the carrier with the lowest frequency higher by 50 GHz than the HNLF ZDWL (193 THz). Therefore, the frequencies of the 16 initial carriers are distributed in a range from 193.05 to 194.55 THz with 100 GHz channel spacing (see **Figure 13a**). The optical flow sent through the parametric amplifier is not modulated and basically represents a continuous radiation set. At the output of the HNLF, a combination

processes), 2 pumps, and other third-order spectral components (see **Figure 13b** and **c**). The pump power for both pumps is set to 400 mW each (26 dBm), and 190 and 196 THz frequen-

**Figure 13.** Optical spectrum at the input of the FOPA when initial carrier power is set to 0 dBm (A) and optical spectra at

the output of the HNLF when the power of the initial carriers is set to 0 dBm (B) and to −10 dBm (C).

and the initial light source frequencies are symmetrical in respect

. Taking into account that

(generated as a result of parametric

(equal channel spacing), which can be achieved by using idlers *ω*<sup>4</sup>

solution, which is based on wavelength conversion using a dual-pump FOPA.

is obtained consisting of 16 initial carriers, 16 idlers *ω*<sup>4</sup>

the distribution of idlers *ω*<sup>4</sup>

196 Optical Fiber and Wireless Communications

cies are temporarily chosen.

There are at least two alternatives to the proposed system architecture, which can produce more than one carrier per optical source: spectrum-sliced systems [33, 35] and systems, which are based on FWM use for producing third-order spectral components (without the initial carriers) [34, 36]. Nevertheless, the use of idlers *ω*<sup>4</sup> produced by FOPA for doubling the number of carriers in WDM systems ensures the best carrier signal stability and, therefore, the highest quality of the transmittable signal.

**Figure 14.** BER value dependence on the power of the detected signal for the 12th channel (*f* =192.55 THz; *λ* = 1557 nm) in the system with the proposed multicarrier source solution (solid line) and in the system with traditional architecture (dashed line).

It has been found that for dual-pump FOPAs the maximum amplification efficiency is achieved when both pumps are linearly polarized with the same state of polarization (SOP) and their SOP corresponds to the SOP of the amplified signal. However, when the SOP of both linearly polarized pumps is orthogonal to the SOP of the amplified signal, amplification decreases to its minimum value, and in a broad frequency region, it is equal to zero. The results obtained in this paper have shown that the same situation is observed also in the case of single-pump FOPAs.

This property of parametric amplifiers can be used for emphasizing one state of polarization from a combination of two orthogonally polarized optical components. The key problem, which is observed when the FOPA is used for emphasizing a specific state of polarization, is ensuring the conservation of the relative positioning of signal and pump SOP throughout the entire length of HNLF. This problem occurs due to the following reasons:


It is not possible to completely avoid changes in relative positioning of the SOP of the signal and the SOP of the pump. To demonstrate this, a simulation model is introduced, where a single-pump FOPA (500 mW, 1533.9 nm) amplifies a signal with −31 dBm total optical power at the input of the HNLF. At first, both the signal and the pump are linearly co-polarized. During the simulation, the SOP of the pump is rotated in respect to the SOP of the amplified signal, and the power of the signal is observed at the output of the FOPA. It has been found that by using polarization-maintaining fibers, under the influence of SPM and XPM, a change in the relative positioning of the signal SOP and the pump SOP is observed. As a result of this change, even when the signal is orthogonally polarized in respect to the SOP of the pump at the input of the HNLF, the signal obtains 1.5–1.6 dB gain. When the SOP of the amplified signal is co-polarized with the SOP of the pump, the obtained amplification reaches 18.3 dB, which is by 16.7 dB higher than in case of orthogonal relative positioning of the SOP at the input of the HNLF.

As it has already been previously mentioned, the polarization dependence of the parametric gain can be used for emphasizing radiation with a specific SOP from the flow of orthogonally polarized optical components, which in its turn can be used for emphasizing polarizationmultiplexed signals and 2PolSK to NRZ-OOK modulation format conversion.

For conversion of 2PolSK signal to NRZ-OOK modulation format, cases of single-channel and multichannel systems are considered. To avoid changes in relative positioning of the states of polarization between pumping radiations, single-pump parametric amplifiers are used in both cases. In both cases, the FOPA is placed at the receiver (or receiver block) input.

It has been found that for dual-pump FOPAs the maximum amplification efficiency is achieved when both pumps are linearly polarized with the same state of polarization (SOP) and their SOP corresponds to the SOP of the amplified signal. However, when the SOP of both linearly polarized pumps is orthogonal to the SOP of the amplified signal, amplification decreases to its minimum value, and in a broad frequency region, it is equal to zero. The results obtained in this paper have shown that the same situation is observed also in the case of single-pump

This property of parametric amplifiers can be used for emphasizing one state of polarization from a combination of two orthogonally polarized optical components. The key problem, which is observed when the FOPA is used for emphasizing a specific state of polarization, is ensuring the conservation of the relative positioning of signal and pump SOP throughout the

• Due to the effect of fiber birefringence, SOP of optical radiation changes along the fiber, and, as result, random SOP rotation is observed. It is very difficult to compensate such a random SOP change, as the rotation rate is affected by various factors, such as temperature, the frequency of the transmitted radiation, internal and external mechanical loads, etc. It is possible to avoid rotation of SOP of the pumps and the amplified signal by using

• When the amplified signal and the pumps are propagating in the gain medium, additionally to fiber birefringence, their states of polarization are also affected by self-phase modulation (SPM) and cross-phase modulation (XPM) nonlinear effects. Therefore, when configuring the parametric amplifier, it is first necessary to avoid excessing pumping; otherwise, it can lead to a more explicit occurrence of SPM and XPM, which decreases the efficiency of

It is not possible to completely avoid changes in relative positioning of the SOP of the signal and the SOP of the pump. To demonstrate this, a simulation model is introduced, where a single-pump FOPA (500 mW, 1533.9 nm) amplifies a signal with −31 dBm total optical power at the input of the HNLF. At first, both the signal and the pump are linearly co-polarized. During the simulation, the SOP of the pump is rotated in respect to the SOP of the amplified signal, and the power of the signal is observed at the output of the FOPA. It has been found that by using polarization-maintaining fibers, under the influence of SPM and XPM, a change in the relative positioning of the signal SOP and the pump SOP is observed. As a result of this change, even when the signal is orthogonally polarized in respect to the SOP of the pump at the input of the HNLF, the signal obtains 1.5–1.6 dB gain. When the SOP of the amplified signal is co-polarized with the SOP of the pump, the obtained amplification reaches 18.3 dB, which is by 16.7 dB higher than in case of orthogonal relative positioning of the SOP at the

As it has already been previously mentioned, the polarization dependence of the parametric gain can be used for emphasizing radiation with a specific SOP from the flow of orthogonally polarized optical components, which in its turn can be used for emphasizing polarization-

multiplexed signals and 2PolSK to NRZ-OOK modulation format conversion.

entire length of HNLF. This problem occurs due to the following reasons:

polarization-maintaining HNLF as the gain medium.

the FWM process in the gain medium.

input of the HNLF.

FOPAs.

198 Optical Fiber and Wireless Communications

At first, a single-channel transmission system simulation model is introduced with 2PolSK modulation format, 150 km long optical fiber, a FOPA preamplifier (which simultaneously performs modulation format and wavelength conversion functionality), and two receivers for detecting the converted NRZ-OOK signal at signal and idler frequencies. The introduced simulation model is displayed in **Figure 15**.

In case of a single-channel system, the primary task is to assess the new modulation format conversion solution created within the scope of this paper, by obtaining a power penalty introduced specifically by the process conversion of the modulation format. Based on the obtained results, 535 mW, 1554.1 nm pumping radiation is chosen, the phase of which is modulated with the following frequency tones: 180 MHz, 420 MHz, 1.087 GHz, and 2.133 GHz. Such configuration ensures 14.8 dB gain for the logical "1" component of 2PolSK signal, which is sufficient for ensuring BER value below the 10−12 mark for the obtained NRZ-OOK signal.

Based on the obtained results, it has been concluded that the idler requires lower pump power to ensure BER values below the 10−12 mark, even though the gain for idler is lower by 0.8 dB than the signal (see **Figure 16**). Therefore, in the case of a single-channel system, it is recommended to process the idler spectral component as the informative signal. These results can be explained by the fact that the signal at its initial frequency contains the orthogonally polarized logical "0" component, which for the obtained NRZ-OOK signal is interpreted as noise.

It has been found that the power of the obtained NRZ-OOK signal that is necessary to ensure BER value below 10−12 is −23.65 dBm, whereas the necessary idler power is −23.8 dBm (see **Figure 17**). In a standard single-channel system with NRZ-OOK modulation format, the signal power required to ensure BER value below the 10−12 threshold has reached −24 dBm. Thus, there is a power penalty of 0.4 dB between the NRZ-OOK signal from the standard

**Figure 15.** Simulation model of the single-channel transmission system, where a single-pump FOPA with linearly polarized pumping radiation is used for 2PolSK to NRZ-OOK modulation format conversion.

**Figure 16.** Gain spectrum produced by the single-pump FOPA with linearly polarized pumping radiation at signal frequencies (solid line) and at idler frequencies (dotted line).

**Figure 17.** BER value dependence on the detected signal power in the standard single-channel transmission system (dashed line) and in the system with modulation format conversion at the initial signal frequency (solid line) and at idler frequency (dotted line).

single-channel system and the converted signal. It is important to note that the power penalty between the NRZ-OOK signal from the standard single-channel system and the generated idler is lower by 0.1 dB (only 0.2 dB). These results are explained by the fact that the idler produced during the FWM process does not contain the logical "0" component of the initial 2PolSK signal, which in this case is interpreted as noise for the converted NRZ signal. The obtained power penalty values are also attributable to the relative intensity noise, which is transferred from the pumping radiation to the amplifiable signal, as well as to the phase SOP mismatch between the pump and the amplified signal that occurs due to SPM and XPM.

In the case of the multichannel system, the goal is to assess the performance of the developed modulation format conversion solution in the presence of interchannel cross talk. When converting 2PolSK signal to NRZ-OOK modulation format, using FOPA with linearly polarized pumping radiation, one must pay special attention to the control of the level of interchannel cross talk produced by the CC-FWM interactions because if the SOP pumping radiation and SOP signal coincidence, the FWM process takes place with its maximum efficiency, including also production of the CC-FWM interchannel cross talk.

To assess the performance of the proposed solution in the presence of interchannel cross talk, a 16-channel 10 Gbps DWDM transmission system is introduced with 2PolSK initial modulation format and 100 GHz channel spacing (see **Figure 18**). In this system, the access network is divided into two branches, eight channels in each. The first branch consists of eight channels, occupying frequency range from 194.5 THz (1541 nm in wavelength) to 195.2 THz (1536 nm), whereas the second branch is occupying frequency range from 196.2 THz (1528 nm) to 196.9 THz (1523 nm). Only those results are included in this paper, which are obtained in the second access network branch, where the signal is divided among eight receivers using an optical splitter with 10.5 dB attenuation.

Based on the obtained results, in the second access network branch, 790 mW 1554.15 nm pumping radiation is used, the phase of which is modulated with the same frequency tones as in the case of a single-channel system: 180 MHz, 420 MHz, 1.087 GHz, and 2.133 GHz. It has been found that to ensure BER values below the 10−12 threshold, all eight idlers require pump power that is by 35 mW higher than in the case of the signals at their initial frequency. The obtained gain for the idler spectral components is lower by at least 2.2 dB, whereas the gain spectrum slope near its maximum is higher than in the initial signal frequency band (see **Figure 19**). The obtained level of amplification in the initial signal frequency band changes in the range from 30.3 to 30.9 dB among all eight channels; thus, the amplification difference between the channels reaches 0.6 dB. Between the idler spectral components, such difference has reached 2.6 dB (from 26.1 to 28.7 dB), but the biggest amplification difference between the signal at its initial frequency and the corresponding idler has reached 4.2 dB. This explains the need for pump power exceeding 35 mW to ensure BER values below the 10−12 mark in the idler frequency band.

single-channel system and the converted signal. It is important to note that the power penalty between the NRZ-OOK signal from the standard single-channel system and the generated idler is lower by 0.1 dB (only 0.2 dB). These results are explained by the fact that the idler produced during the FWM process does not contain the logical "0" component of the initial 2PolSK signal, which in this case is interpreted as noise for the converted NRZ signal. The obtained power penalty values are also attributable to the relative intensity noise, which is transferred from the pumping radiation to the amplifiable signal, as well as to the phase SOP mismatch between the pump and the amplified signal that occurs due to SPM and XPM.

**Figure 17.** BER value dependence on the detected signal power in the standard single-channel transmission system (dashed line) and in the system with modulation format conversion at the initial signal frequency (solid line) and at idler frequency

**Figure 16.** Gain spectrum produced by the single-pump FOPA with linearly polarized pumping radiation at signal

frequencies (solid line) and at idler frequencies (dotted line).

200 Optical Fiber and Wireless Communications

(dotted line).

In the case of the multichannel system, the goal is to assess the performance of the developed modulation format conversion solution in the presence of interchannel cross talk. When converting 2PolSK signal to NRZ-OOK modulation format, using FOPA with linearly polarized

**Figure 18.** Simulation model of the 16-channel WDM transmission system with two access network branches, where in each branch the FOPA preamplifier is used for 2PolSK to NRZ-OOK (on-off keying) modulation format conversion.

**Figure 19.** Gain spectrum ensured by the FOPA with 790 mW 1554.15 nm linearly polarized pumping radiation at initial signal frequencies (1) and idler frequencies (2).

To assess the performance of the proposed solution, the results obtained in the second branch of the access network are compared to the standard eight-channel DWDM system without signal amplification. The detected signal power required to ensure a certain BER value in the fifth channel of the second access network branch both at the initial signal and idler frequencies is compared with the same results obtained in the standard eight-channel DWDM system. As seen in **Figure 20**, in a system with modulation format conversion, to ensure BER values below the 10−12 mark, the required signal power is at least −23.5 dBm. In the standard eight-channel system, the corresponding required power level is −23.9 dBm; therefore, in this case, the power penalty between the signal with the converted modulation format and the signal from the standard eight-channel solution is 0.4 dB. It must be particularly emphasized that, contrary to the single-channel system, in the multichannel system, the idler BER values are higher than those of signals at their initial frequencies—when receiving the idler corresponding to the fifth channel, at least −23.15 dBm is required to ensure a BER value below the 10−12 threshold, which is more by 0.3 dB than receiving the signal of the fifth channel at its initial frequency.

It has been found that in case of the idler, larger amplitude fluctuations are observed, which densify the logical "0" and "1" component levels of the eye diagrams. The cause behind generating noise of such range is CC-FWM produced interchannel cross talk, which is produced as a result of parametric amplification and creates third-order spectral components, the frequencies of which correspond to the frequencies of the amplified signals. As mentioned previously, the gain difference between the idlers is much larger (by 2 dB) than between the signals at their initial frequencies. Therefore, more explicit manifestation of CC-FWM processes is observed, which also produces additional interchannel cross talk. Moreover, the cross talk caused by CC-FWM is not only transferred from signals at their initial frequencies to the idlers but is also generated between the idlers.

It has also been found that the pumping radiation-phase modulation leads to spectral expansion of the idlers by approximately 40%, which, accordingly, results in additional interchannel

Evaluation of Parametric and Hybrid Amplifier Applications in WDM Transmission Systems http://dx.doi.org/10.5772/67607 203

**Figure 20.** BER value dependence on the detected signal power in the standard eight-channel transmission system (3) and in the fifth channel on the second branch of the multichannel system with modulation format conversion at the initial signal frequency (1) and idler frequency (2).

To assess the performance of the proposed solution, the results obtained in the second branch of the access network are compared to the standard eight-channel DWDM system without signal amplification. The detected signal power required to ensure a certain BER value in the fifth channel of the second access network branch both at the initial signal and idler frequencies is compared with the same results obtained in the standard eight-channel DWDM system. As seen in **Figure 20**, in a system with modulation format conversion, to ensure BER values below the 10−12 mark, the required signal power is at least −23.5 dBm. In the standard eight-channel system, the corresponding required power level is −23.9 dBm; therefore, in this case, the power penalty between the signal with the converted modulation format and the signal from the standard eight-channel solution is 0.4 dB. It must be particularly emphasized that, contrary to the single-channel system, in the multichannel system, the idler BER values are higher than those of signals at their initial frequencies—when receiving the idler corresponding to the fifth channel, at least −23.15 dBm is required to ensure a BER value below the 10−12 threshold, which is more by 0.3 dB than receiving the signal of the fifth channel at its

**Figure 19.** Gain spectrum ensured by the FOPA with 790 mW 1554.15 nm linearly polarized pumping radiation at initial

It has been found that in case of the idler, larger amplitude fluctuations are observed, which densify the logical "0" and "1" component levels of the eye diagrams. The cause behind generating noise of such range is CC-FWM produced interchannel cross talk, which is produced as a result of parametric amplification and creates third-order spectral components, the frequencies of which correspond to the frequencies of the amplified signals. As mentioned previously, the gain difference between the idlers is much larger (by 2 dB) than between the signals at their initial frequencies. Therefore, more explicit manifestation of CC-FWM processes is observed, which also produces additional interchannel cross talk. Moreover, the cross talk caused by CC-FWM is not only transferred from signals at their initial frequencies to the

It has also been found that the pumping radiation-phase modulation leads to spectral expansion of the idlers by approximately 40%, which, accordingly, results in additional interchannel

initial frequency.

signal frequencies (1) and idler frequencies (2).

202 Optical Fiber and Wireless Communications

idlers but is also generated between the idlers.

cross talk. Interchannel cross talk caused by the CC-FWM interactions and idler spectral broadening is the main reason why, in the case of idlers, the power penalty in relation to the standard system is larger by 0.4 dB than for signals at their initial frequencies.

The second studied application of parametric gain polarization dependence is the emphasizing of a signal with a specific SOP from a combination of two polarization-multiplexed NRZ-OOK signals. For this purpose, a two-channel 10 Gbps transmission system with NRZ-OOK modulation format and polarization multiplexing is introduced (see **Figure 21**). Both signals, the SOP of which are mutually orthogonally allocated, are transmitted using the same frequency −196.5 THz.

**Figure 21.** Simulation model of the two-channel optical transmission system with FOPA for division and amplification of polarization-multiplexed signals.

Based on the obtained results, a decision has been made to use 530 mW 1553.9 nm pumping radiation in the case of both FOPA, because this is the lowest pump power that can ensure BER values below the 10−12 threshold in both the first and the second channel. Previously described results have shown that phase modulation of the pump can cause spectral broadening of idlers. In a situation, when the probability that both orthogonally polarized optical radiations are observed simultaneously in the logical "1" level is high, the mutual deviations of the SOP of optical components have a bigger impact on the quality of the amplified signal than in the case when such simultaneous transmission of logical "1" is not performed (e.g., in the case of 2PolSK signal). Therefore, it is important to minimize the phase mismatch between the pumping radiation and the amplified signals, which can also cause a change of the relative positioning of SOP between the signal and the pump. Bearing in mind this fact and having observed the FOPA produced gain spectrum and in the OSNR at the output of the amplifier, the following frequency tones have been selected for pumping-radiation phase modulation: 0.13 GHz, 0.42 GHz, 1.087 GHz, and 1.94 GHz. The obtained signal gain in the first channel has reached 20 dB, whereas in the second channel, it has reached 20.1 dB. Idler component gain maximum is lower by 0.7 dB (see **Figure 22**).

To assess the performance of the proposed solution, BER value dependence on the received signal power is obtained, and these results are compared with the same results obtained in a standard single-channel transmission system with NRZ-OOK modulation format without optical signal amplification. It can be concluded from the results shown in **Figure 23** that there is a power penalty of 0.8 dB between the signal detected in the first channel and the signal from the standard single-channel NRZ-OOK system. The power penalty for the idler spectral component has reached 0.5 dB.

Unlike the system with modulation format conversion, in this case, a situation has been observed, when, given the same frequency, it is possible that the logical "1" of orthogonally polarized components is observed simultaneously in both channels. Thus, the effect of orthogonally polarized radiation on the divided signal quality is higher than in a system with modulation format conversion. This is the fact, which mainly explains a larger power penalty value than

**Figure 22.** FOPA produced on-off gain for the first channel at idler frequencies (left side) and at the initial signal frequencies (right side).

Based on the obtained results, a decision has been made to use 530 mW 1553.9 nm pumping radiation in the case of both FOPA, because this is the lowest pump power that can ensure BER values below the 10−12 threshold in both the first and the second channel. Previously described results have shown that phase modulation of the pump can cause spectral broadening of idlers. In a situation, when the probability that both orthogonally polarized optical radiations are observed simultaneously in the logical "1" level is high, the mutual deviations of the SOP of optical components have a bigger impact on the quality of the amplified signal than in the case when such simultaneous transmission of logical "1" is not performed (e.g., in the case of 2PolSK signal). Therefore, it is important to minimize the phase mismatch between the pumping radiation and the amplified signals, which can also cause a change of the relative positioning of SOP between the signal and the pump. Bearing in mind this fact and having observed the FOPA produced gain spectrum and in the OSNR at the output of the amplifier, the following frequency tones have been selected for pumping-radiation phase modulation: 0.13 GHz, 0.42 GHz, 1.087 GHz, and 1.94 GHz. The obtained signal gain in the first channel has reached 20 dB, whereas in the second channel, it has reached 20.1 dB. Idler component

To assess the performance of the proposed solution, BER value dependence on the received signal power is obtained, and these results are compared with the same results obtained in a standard single-channel transmission system with NRZ-OOK modulation format without optical signal amplification. It can be concluded from the results shown in **Figure 23** that there is a power penalty of 0.8 dB between the signal detected in the first channel and the signal from the standard single-channel NRZ-OOK system. The power penalty for the idler spectral

Unlike the system with modulation format conversion, in this case, a situation has been observed, when, given the same frequency, it is possible that the logical "1" of orthogonally polarized components is observed simultaneously in both channels. Thus, the effect of orthogonally polarized radiation on the divided signal quality is higher than in a system with modulation format conversion. This is the fact, which mainly explains a larger power penalty value than

**Figure 22.** FOPA produced on-off gain for the first channel at idler frequencies (left side) and at the initial signal frequencies

gain maximum is lower by 0.7 dB (see **Figure 22**).

component has reached 0.5 dB.

204 Optical Fiber and Wireless Communications

(right side).

**Figure 23.** BER value dependence on the power of the detected signal in the standard single-channel system (3) and in the first channel of the system with the chosen FOPA configuration of the signal at its initial frequency (1) and of the idler (2).

in a single-channel system with modulation format conversion. A lower power penalty value in the case of idler component is explained by the fact that the orthogonally polarized radiation of the second channel is not included in the parametric amplification and idler generation process, and, therefore, it is not reflected in the idler itself. Irrespective of the fact that the amplification of orthogonally polarized (second channel) radiation is much lower (1–2 dB), its power level is still sufficiently high to affect the BER value of the divided signal, which in our case produces an additional power penalty of 0.3 dB. The idler use has allowed achieving a lower power penalty in respect to the standard single-channel system with the NRZ-OOK modulation format, whereas to achieve a BER value below the 10−12 threshold, it is necessary to use pump power that is larger by 10 mW than that when receiving the initial signal with 196.5 THz frequency.

Upon comparing the amplification spectra in a single-channel system with modulation format conversion and in a system with polarization-multiplexed signal division, it has been concluded that the amplification obtained in the latter case is larger by 5.2 dB (14.8 and 20 dB, respectively), irrespective of the fact that the pumping radiation power differs only by 5 mW. This is explained by the following two factors:


Upon summing up all the information presented in this chapter, it can be concluded that polarization dependence of the parametric amplification can be used for emphasizing optical radiation with a specific state of polarization from a flow of two orthogonally polarized optical radiations. FOPA with linearly polarized pumping radiation can be used both for 2PolSK signal conversion into NRZ-OOK modulation format and for signal emphasizing from a flow of two polarization-multiplexed optical signals. In both cases, such FOPA configurations have been found, which ensure that the BER values of the processed signal are below the 10−12 mark, and at the same time, none of the proposed solutions cause power penalty that exceeds 1.8 dB in comparison with the relevant standard solutions.
