**5. Passive Si-photonic components for all-optical signal processing**

In this section we discuss the implementation of passive WPT-OFDM system components based on the Si photonics and a novel hierarchical architecture of the 1Tb/s WPT-OFDM transmission system that can be realized by using these components.

#### **5.1. SOI optical components**

The practical implementation of all-optical signal processing would require some extent of device integration. Much effort is dedicated over the last two decades to the development of photonic integrated circuits (PICs), which bring together multiple discrete devices on a single substrate. Integration helps to minimize the losses associated with the coupling of light in and out of devices, to enhance functionality, and to reduce cost and footprint. Numerous material platforms are prevalent in PICs, such as LiNbO₃, GaAs, InP and SiO₂. Among those platforms, the SOI wafer structure stands out as an advantageous choice for the realization of passive devices, such as couplers, interferometers, arrayed-waveguide gratings etc [24], [25]. Silicon is a low-cost material with an excellent crystalline quality, high thermal conductivity and high optical damage threshold. It is transparent over a broad range of wavelengths of 1.1-7 μm, including the telecommunication wavelengths. The silica SiO₂ lower cladding of SOI wafers provides a large contrast in refractive index with respect to silicon, which allows for the tight confinement of light into sub-micron structures. The fabrication of photonic devices in SOI can benefit from the advanced manufacturing technology of electronic integrated circuits. Silicon photonic devices may lead to a true merger of optics alongside electronics in unified devices. The realization of modulation of light on the silicon material platform is more challenging. The concentration of free charges in silicon changes the real and imaginary parts of the refractive index, and this effect in pure silicon is more strongly pronounced than the Pockels effect, the Kerr effect and the Franz-Keldysh effect [26]. Most of the fast modulators integrated on Si are based on free-carrier concentration variations [27]. Optical modulation using SiGe/Si and allsilicon phase shifters based on carrier depletion has been investigated theoretically and experimentally [27]. An all-silicon phase-shifter based on carrier depletion in a doped layer inserted into a PIN diode has been demonstrated [28]. SiGe/Si and all-silicon modulators can be integrated in rib waveguides and in MZIs [27]. Another modulation technique for SOI optical devices is based on the thermo-optic effect, in which the refractive index n of silicon is varied by applying heat to the material [24]. The thermo-optic coefficient in silicon is given by 4 1 *dn dT* / 1.86 10 *K* , and the refractive coefficient variation of <sup>3</sup> *n* 1.1 10 for the controllable temperature increase of 6K [24]. It has been shown experimentally that a 500μm length device thermally isolated from the substrate can provide a phase shift of radians for an applied power of 10mW [24].

#### **5.2. Example of SOI MZM for all-optical signal processing**

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communication system.

**5.1. SOI optical components** 

an applied power of 10mW [24].

The results clearly show that WPT-OFDM provides the efficient transmission up to 500km without CP with 5% GI, while the FFT based CO-OFDM may achieve the same distance with the CP length of 25% of the symbol interval which substantially reduces SE of the

In this section we discuss the implementation of passive WPT-OFDM system components based on the Si photonics and a novel hierarchical architecture of the 1Tb/s WPT-OFDM

The practical implementation of all-optical signal processing would require some extent of device integration. Much effort is dedicated over the last two decades to the development of photonic integrated circuits (PICs), which bring together multiple discrete devices on a single substrate. Integration helps to minimize the losses associated with the coupling of light in and out of devices, to enhance functionality, and to reduce cost and footprint. Numerous material platforms are prevalent in PICs, such as LiNbO₃, GaAs, InP and SiO₂. Among those platforms, the SOI wafer structure stands out as an advantageous choice for the realization of passive devices, such as couplers, interferometers, arrayed-waveguide gratings etc [24], [25]. Silicon is a low-cost material with an excellent crystalline quality, high thermal conductivity and high optical damage threshold. It is transparent over a broad range of wavelengths of 1.1-7 μm, including the telecommunication wavelengths. The silica SiO₂ lower cladding of SOI wafers provides a large contrast in refractive index with respect to silicon, which allows for the tight confinement of light into sub-micron structures. The fabrication of photonic devices in SOI can benefit from the advanced manufacturing technology of electronic integrated circuits. Silicon photonic devices may lead to a true merger of optics alongside electronics in unified devices. The realization of modulation of light on the silicon material platform is more challenging. The concentration of free charges in silicon changes the real and imaginary parts of the refractive index, and this effect in pure silicon is more strongly pronounced than the Pockels effect, the Kerr effect and the Franz-Keldysh effect [26]. Most of the fast modulators integrated on Si are based on free-carrier concentration variations [27]. Optical modulation using SiGe/Si and allsilicon phase shifters based on carrier depletion has been investigated theoretically and experimentally [27]. An all-silicon phase-shifter based on carrier depletion in a doped layer inserted into a PIN diode has been demonstrated [28]. SiGe/Si and all-silicon modulators can be integrated in rib waveguides and in MZIs [27]. Another modulation technique for SOI optical devices is based on the thermo-optic effect, in which the refractive index n of silicon is varied by applying heat to the material [24]. The thermo-optic coefficient in silicon is given by 4 1 *dn dT* / 1.86 10 *K* , and the refractive coefficient variation of <sup>3</sup> *n* 1.1 10 for the controllable temperature increase of 6K [24]. It has been shown experimentally that a 500μm

**5. Passive Si-photonic components for all-optical signal processing** 

transmission system that can be realized by using these components.

length device thermally isolated from the substrate can provide a phase shift of

radians for

In this section we present an example of the SOI based MZI which can realize the WPT operation. The most basic family of wavelet shapes is the Haar transform, proposed initially by Alfred Haar in 1910 [19]. The Haar wavelet and scaling functions *t t* , and the filter coefficients h[n], g[n] have the form, respectively [13], [19].

$$\nu\left(t\right) = \begin{cases} 1, 0 \le t < \frac{1}{2} \\ -1, \frac{1}{2} \le t < 1; \phi\left(t\right) = \begin{cases} 1, & 0 \le t < 1 \\ 0, & t < 0, t \ge 1 \end{cases} \tag{27}$$

$$h\boxed{n} = \frac{1}{\sqrt{2}}(-1,1) \, \_\prime g\boxed{n} = \frac{1}{\sqrt{2}}(1,1) \tag{28}$$

Note that the equivalent definitions *h n* 1,1 / 2 , 1, 1 / 2 *g n* also may be used [21]. Since it is the simplest to implement, we adapt it in the proposed realization of the WPT based CO-OFDM photonic integrated circuit. An n-points signal is decomposed into two groups of n/2 samples. The first group is the sum of pairs of c[n] of the original signal, and can be described as the output of a discrete low-pass filter (LPF) followed by a downsampling operation by a factor of two. The second group describes the differences between pairs d[n], and can be represented as the output of a discrete high-pass filter (HPF) followed by factor of two down-sampling operation [14]. The Haar WPT can be described by the scheme shown in Figure 3. Here s[n] is the input signal, g[n] and h[n] are the discrete HPF and LPF impulse responses.

**Figure 3.** Two levels Haar wavelet-packet decomposition (WPD)

The inverse operation recovers the original signal from its decomposition coefficients. Its scheme is shown in Figure 4. Here S[n] is the output signal, g[n] and h[n] are the discrete HPF and LPF impulse responses, c[n] and d[n] are the approximation and detail coefficients respectively mentioned above.

**Figure 4.** Haar inverse wavelet-packet decomposition (IWPD) transform

The realization of Haar wavelet packet decomposition (WPD) transform and the corresponding inverse wavelet packet decomposition (IWPD) in an optical integrated circuit was theoretically suggested by Gabriella Cincotti and co-workers [14], [22], [29], [30]. The method is based on the following MZI delay line architecture shown in Figure 5.

**Figure 5.** Optical implementation of Haar WPD / IWPD based on MZI. Left: Haar-IWPD used for the transmitter unit. Right: Haar-WPD used for the receiver unit.

The IWPD is represented by the optical field *out*<sup>2</sup> *E t* at the lower output of a MZI that is driven by two inputs 1,2 *S t* .

$$E\_{out2}\left(t\right) = \frac{1}{2}\left[-j\mathbf{S}\_1\left(t\right) + \mathbf{S}\_2\left(t\right)\right] + \frac{1}{2}\left[-j\mathbf{S}\_1\left(t-\tau\right) - \mathbf{S}\_2\left(t-\tau\right)\right] \tag{29}$$

Expression (29) shows that a single MZI could provide the sum and the difference of its two input fields, in series, in one of its output ports. The operation is equivalent to the LPF and HPF operation of the inverse Haar IWPD. Similarly, the same MZI can generate the sum of successive values in one of its input ports at one output *out*<sup>2</sup> *E t* , and the difference of the same values at the other output *out*<sup>1</sup> *E t* , in parallel.

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respectively mentioned above.

The inverse operation recovers the original signal from its decomposition coefficients. Its scheme is shown in Figure 4. Here S[n] is the output signal, g[n] and h[n] are the discrete HPF and LPF impulse responses, c[n] and d[n] are the approximation and detail coefficients

The realization of Haar wavelet packet decomposition (WPD) transform and the corresponding inverse wavelet packet decomposition (IWPD) in an optical integrated circuit was theoretically suggested by Gabriella Cincotti and co-workers [14], [22], [29], [30]. The

**Figure 5.** Optical implementation of Haar WPD / IWPD based on MZI. Left: Haar-IWPD used for the

The IWPD is represented by the optical field *out*<sup>2</sup> *E t* at the lower output of a MZI that is

2 12 1 2

Expression (29) shows that a single MZI could provide the sum and the difference of its two input fields, in series, in one of its output ports. The operation is equivalent to the LPF and

(29)

2 2 *out E t jS t S t jS t S t*

1 1

method is based on the following MZI delay line architecture shown in Figure 5.

**Figure 4.** Haar inverse wavelet-packet decomposition (IWPD) transform

transmitter unit. Right: Haar-WPD used for the receiver unit.

driven by two inputs 1,2 *S t* .

$$E\_{out1}\left(t\right) = \frac{1}{2}\left[S\_1\left(t\right) - S\_1\left(t-\tau\right)\right]; \\ E\_{out2}\left(t\right) = -j\frac{1}{2}\left[S\_1\left(t\right) + S\_1\left(t-\tau\right)\right] \tag{30}$$

The latter configuration described by expression (30) can realize the Haar WPD. Hence, MZIs can function as a basic building block of a discrete Haar WPD and IWPD. As can be seen in equations (29) and (30), the MZI realization of the WPD includes an additional relative phase shift of 90° in between the two inputs/outputs, which is not part of the Haar formalism. This additional phase must be compensated for. Furthermore, the optical path lengths connecting between cascaded MZIs cannot be controlled at the fabrication stage to a sub-wavelength precision. Hence, metallic resistors must be deposited in proximity to the waveguides [31], [32]. The driving of currents through the resistors would locally heat the nearby silicon structure, and modify its refractive index through the thermo-optic effect mentioned above [24]. A schematic drawing of a single MZI with the thermo-optic phaseshifters is shown in Figure 6.

**Figure 6.** A schematic drawing of a single MZI stage used in a Haar WPD receiver including three thermo-optic phase-shifters

Three-stage MZI-based photonic integrated circuits for the realization of Haar WPT-OFDM encoding and decoding based on the single MZI stage are shown in Figures 7, 8.

In the Haar WPT-OFDM encoder presented in Figure 7, S₁-S₈ are low rate input data channels, with a seven-bits zero padding. The output is the multiplexed Haar transform signal.

**Figure 7.** All-optical Haar WP Encoder used as optical transmitter

In the all-optical Haar WP Decoder shown in Figure 8, the input signal is constructed from eight data channels, which are recovered individually at the eight outputs. The output channels must be down sampled by factor of 8.

**Figure 8.** All-optical Haar WP Decoder used as an optical receiver

The all-optical WP encoder calculates the Haar IWPD of eight coefficients, incoming from eight parallel input values. The reconstructed signal appears in series at the output of the circuit. Note that padding by seven zeros is necessary between successive bits at each input, so that the transform coefficients of one input parallel word do not overrun those of the next word at the output [9], [33], [34]. The zero padding is the optical-domain equivalent of the up-sampling that is part of a digital IWPD. Similarly, a proper gating is necessary at the each of the eight outputs of the decoder circuit, since the original data is only reconstructed at specific time slots within the symbol duration [33]. The remainder of the symbol duration is occupied by noise-like ISI.

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**Figure 7.** All-optical Haar WP Encoder used as optical transmitter

**Figure 8.** All-optical Haar WP Decoder used as an optical receiver

channels must be down sampled by factor of 8.

In the all-optical Haar WP Decoder shown in Figure 8, the input signal is constructed from eight data channels, which are recovered individually at the eight outputs. The output

The all-optical WP encoder calculates the Haar IWPD of eight coefficients, incoming from eight parallel input values. The reconstructed signal appears in series at the output of the circuit. Note that padding by seven zeros is necessary between successive bits at each input, so that the transform coefficients of one input parallel word do not overrun those of the next word at the output [9], [33], [34]. The zero padding is the optical-domain equivalent of the up-sampling that is part of a digital IWPD. Similarly, a proper gating is necessary at the each of the eight outputs of the decoder circuit, since the original data is only reconstructed A WPT based CO-OFDM communication network, employing the encoding and decoding PICs, is shown in Figure 9. Light from a CW laser diode is split in eight paths. Light in each path is individually modulated by a separate stream of data, which are prepared with the necessary zero padding as described above. The eight channels are multiplexed by the WPT-OFDM PIC. At the other end of the link, each of the eight outputs of the WPT-OFDM decoder PIC is separately gated by an electro-optic switch and detected.

The SOI waveguide is a basic component of the Si photonic systems. We calculated the modal profile of such a waveguide in a single mode regime for each polarization of the optical wave. The SOI waveguide cross-section and the modal profile are shown in Figure 10. The analysis of such waveguides can be carried out only by numerical methods [35]. We used the commercial software modeling (COMSOL). The modal field distribution (Figure 10b) clearly shows the electric field confinement in the waveguide core.

A basic building block of a MZI is a directional coupler. Couplers are realized by bringing two SOI waveguides in close proximity for a certain length Z₀. The degrees of freedom in the design are the length and gap between the SOI waveguide cores. A relatively large gap of the order of magnitude of 300nm is advantageous with respect to fabrication imperfections. COMSOL simulations were used to calculate the coupling coefficient *ab* between two waveguides separated by a chosen gap. An even splitting ratio of incoming optical power between the two outputs is obtained when the two waveguides remain in proximity over a length / 4 *ab L* . The simulation results are shown in Figure 11.

**Figure 9.** WPT based CO-OFDM data channel based on transmitter and receiver PICs

(b)

**Figure 10.** A single mode SOI-based waveguide; (a) schematic diagram; (b) COMSOL simulation of the transverse profile for the EM mode field super-imposed on the waveguide cross section

Consider now the differential delays of the MZIs. As discussed earlier, different stages in the cascaded MZI PIC require different delays. The basic delay unit is T/8, where T is the symbol duration. For a data rate of 2.5 GSymbols/s for each of the eight multiplexed channels, the fundamental delay unit is 50psec, which corresponds to a physical length of about 3.5mm in SOI waveguides. The heat dissipation from aluminium heaters in proximity of the SOI waveguides was simulated, once more using COMSOL. Figure 12 shows the resulting temperature profile. The Al heaters are heated by an external current up to 60°C. Simulation results show that a temperature in the Si core of the SOI waveguide is 40°C compared to 20°C in the unheated regions. This temperature difference stems from the attachment of the back end of the PIC to a 20°C heat sink.

**Figure 10.** A single mode SOI-based waveguide; (a) schematic diagram; (b) COMSOL simulation of the

(b)

(a)

Consider now the differential delays of the MZIs. As discussed earlier, different stages in the cascaded MZI PIC require different delays. The basic delay unit is T/8, where T is the symbol duration. For a data rate of 2.5 GSymbols/s for each of the eight multiplexed channels, the fundamental delay unit is 50psec, which corresponds to a physical length of about 3.5mm in SOI waveguides. The heat dissipation from aluminium heaters in proximity of the SOI waveguides was simulated, once more using COMSOL. Figure 12 shows the resulting temperature profile. The Al heaters are heated by an external current up to 60°C. Simulation results show that a temperature in the Si core of the SOI waveguide is 40°C compared to 20°C in the unheated regions. This temperature difference stems from the

transverse profile for the EM mode field super-imposed on the waveguide cross section

attachment of the back end of the PIC to a 20°C heat sink.

All-Optical Signal Processing for High Spectral Efficiency (SE) Optical Communication 361

**Figure 11.** Coupler dimensions design with COMSOL software simulations: (a) an example of a threedimensional modelling of a directional coupler; (b) calculated coupling length that is required between two parallel waveguides as a function of the gap size. The coupling length for the chosen gap size of 300 nm is approximately 110µm

**Figure 12.** Cross section of heat dissipation in an SOI waveguide with the aluminium heaters located in both sides of the SOI waveguide
