High-Base Optical Signal Proccessing

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.


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][2][3][4][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 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][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Miscellaneous optical signal processing functions have been demonstrated, such as wavelength conversion, wavelength (de)multiplexing, wavelength multicasting, data exchange, add/drop, optical addressing, optical switching, optical logic gate, optical computing, optical format conversion, optical correlation, optical equalization, optical regeneration, tunable optical delay, optical coding/decoding, etc. . 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 nonlinear fibers (HNLFs), periodically poled lithium niobate (PPLN) waveguides, chalcogenide (As 2 S 3 ) 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.
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.

High-Base Wavelength Conversion
We demonstrate high-base all-optical wavelength conversions of multicarrier, multilevel modulation signals based on degenerate FWM in a silicon waveguide. Coherent multicarrier,

High-base wavelength conversion [83]
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. 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 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, especially for higher-order modulations such as OFDM 16/32/64/128-QAM. 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 2 31 -1 pseudo random binary sequences (PRBS) and then mapped onto m-QAM constellation. The OFDM m-QAM signal is constructed by 82 subcar-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  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 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.

Shown in
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 S 1 , S2:λ S 2 ) are depicted in Fig. 6. The four-level phase information carried by two DQPSK signals at different wavelengths 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:λ P 1 , P2:λ P 2 ) and signal 1 (S1:λ S 1 ) are fed into the HNLF. P1 and S1 are symmetrical about the zero-dispersion wavelength (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 S 2 + 1 / λ P 2 = 1 / λ S 1 + 1 / λ P 1 ) by the nondegenerate FWM process. Thus, the parametric depletion of S1 is expected with its data information 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 (A S 1  amplitudes between the output signals (A S 1 ' , A S 2 ' ) and input signals and pumps (A S 1 , A S 2 , A P 1 , . 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 S 1 ' = φ S 2 + φ P 2 − φ P 1 and φ S 2 ' = φ S 1 + φ P 1 − φ P 2 . It is worth noting that phase modulation is always applied to the pumps (φ P 1 , φ P 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 P 1 =φ P 2 ), which makes it possible to implement the high-base data exchange of DQPSK or other multilevel modulation signals containing phase information.    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 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.  (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. Figure 11. Concept and principle of simultaneous multichannel, high-base data exchange of DQPSK signals.

Updated Figures
Exchange π/2 π 3π/2 π/2 2 S  2 S  0 π 3π/2 π S2 S2 (a) S1&S2 Data Exchange S1: ON, S2: ON  (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 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.
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 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 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 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. WC (S2-to-S1) Ex. (S2-to-S1) WC (S2-to-S1) Ex. (S2-to-S1) WC (S1-to-S2) Ex. (S1-to-S2) WC (S1-to-S2)

Ch. I Ch. Q
Ex. (S1-to-S2) Applications of Digital Signal Processing through Practical Approach 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 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.  Ex. S2 to S1 (4 ps)

Ch. Q Misalignment
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 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) 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.
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. Figure 11. Concept and principle of simultaneous multichannel, high-base data exchange of DQPSK signals. S1 (before data exchange) S2 (before data exchange) Ch. I Ch. I Ch. Q Ch. Q S1 (after wavelength conversion: S2 to S1) Ch. Q Ch. I Ch. I S2 (after wavelength conversion: S1 to S2) Ch. Q Ch. I Ch. I S2 (after data exchange: S1 to S2) Ch. Q S1 (after data exchange: S2 to S1) 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. 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 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.     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. 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.
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. Fig. 15 is the concept and operation principle of the proposed high-base, multifunctional grooming switch element that could be used at the network nodes. When multiple 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 13 further displays temporal waveforms and balanced eyes of demodulated inphase (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.  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. 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 23channel, 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. Applications of Digital Signal Processing through Practical Approach 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  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 wavelength 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. 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 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.  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; high-base power equalization for all 23 wavelength channels S1-S23).
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.  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 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).

S18
Drop S18 Add S18 Drop Equalization S1-S11, S13-S17 S19, S20, S22, S23 Data Exchange S12 S21  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 .
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 siliconorganic 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 2 13 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; 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). S18 Add S18 Drop Equalization S1-S11, S13-S17 S19, S20, S22, S23 Data Exchange S12 S21 S1 Equalized 23×100-Gbit/s RZ-DQPSK S10-S12 S21-S23 <1dB Six-Channel Add S6 S7 Exchange S23 S22 S21 S12 S11 S10 S23 S22 S21 S12 S11 S10  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). division multiplexed (OTDM) signal from 64 low-speed 10 Gbaud tributaries in practical applications.
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 5 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).
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 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 2 13 -1 pseudorandom binary sequence (PRBS) 16-QAM/64-QAM signals (λSA: 1542 nm, λSB: 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. 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. 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 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 power equalization for all 23 wavelength channels S1-S23).      High-Base Optical Signal Proccessing http://dx.doi.org/10.5772/61504 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 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 power equalization for all 23 wavelength channels S1-S23).    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 power equalization for all 23 wavelength channels S1-S23).

High-base optical computing [75, 77, 80, 85]
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.
We first demonstrate high-speed two-input high-base optical computing (addition/subtraction/complement/doubling) of quaternary numbers using optical nonlinearities and DQPSK signals.
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 (6). Remarkably, since optical phase has a periodicity of 2π due to its phase wrap characteristic, one can clearly see from Eqs.       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. 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). 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). Fig. 29. Demodulated waveforms and balanced eyes for 50-Gbaud two-input quaternary addition and dual-directional subtraction 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. 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 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.

Shown in
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) Fig. 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.   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 degenerate 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 performance 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 accumulated 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 nondegenerate 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 Figure 28. Measured spectra (a) before HNLF and (b) after HNLF for 50-Gbaud two-input quaternary optical computing (addition, subtraction, complement, doubling). 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 four-  phase 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.     In addition to two-/three-input high-base optical computing based on degenerate/nondegenerate 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. 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 m 2 and 5500 w -1 m -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. In the following simulations, three 40-Gbaud 2 13 -1 PRBS 16-PSK signals (λ A : 1546 nm, λ B : 1552 nm, λ C : 1550 nm) are adopted. A 1-mm-long silicon-organic hybrid slot waveguide is employed. 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.

High-base coding/decoding [79]
We propose and demonstrate high-base optical coding/decoding of advanced multilevel modulation signals based on degenerate FWM in HNLFs.  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 Thus, the phase of the decoded signal As a consequence, the decoded signal (Di) recovers the original signal (Pi) after the decoding process. The decoding algorithm is determined by 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 hexadecimal 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. 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.  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 C i = − Φ P i ) and ( − ( − Φ P i ) = Φ P i ), 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 C i = 2Φ K i − Φ P i ) for the symbol-wise hexadecimal coding process and decoding algorithm ( 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 constellation 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.

Shown in
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 modulation 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. 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 In-phase quadrature In-phase quadrature In-phase quadrature In-phase quadrature In-phase quadrature 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 symbol-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-modulated pump; (f) decoded signal using a (0, π/4) phase-modulated 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 performance changes slightly. Such interesting phenomenon can be briefly explained as follows. For the symbol-wise hexadecimal coding process with the coding algorithm ofΦ C i = 2Φ K i − Φ P i , 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  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 K i − Φ C i = 2Φ K i − (2Φ K i − Φ P i ) = Φ P i 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).  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%.

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.
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 doublepass LCoS technology accompanied by bidirectional degenerate FWM in a single HNLF has 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 C i = 2Φ K i − Φ P i . 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 K i − Φ C i = 2Φ K i − (2Φ K i − Φ P i ) = Φ P i . Figure 52(c) shows measured BER of symbol-wise 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%.

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.