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Abstract
All-optical canonical logic unit (CLU) is the basic building block of high-speed optical logic operation and complex optical computing. By utilizing the parallelism of optical signals, multichannel multicasting of all-optical CLUs can expand the capacity of the computing system effectively. Here, we propose and experimentally demonstrate the 40 Gb/s all-optical reconfigurable two-input CLUs generated in seven wavelength channels via four-wave mixing (FWM) in the nonlinearity-enhanced silicon waveguide. By introducing reverse-biased PIN junctions to reduce nonlinear loss, the output power of converted light can be increased over 10 dB. Moreover, pumped by two optical signals and a continuous wave beam, a full set of reconfigurable CLUs is multicasted in seven parallel wavelength channels. All logic signals with error-free performance are realized. Attributing to the rate transparency of FWM and parallel multicasting of logic functions, the proposed scheme offers more flexibility and expandability in future high-speed optical logic processing and complex optical computing.
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1. Introduction
With the rapid development of optical communication networks and the exponentially growing demand for computing capacity, all-optical signal processing is considered as the key technology to break through the bottleneck of bandwidth limitation caused by electrical-optical conversion [1]. All-optical logic operation is one of the urgent difficulties in all-optical signal processing, which has enormous potential in future complex optical computing [2]. More recently, some optical logic function devices through linear effects have been proposed, such as the arithmetic logic units and full adders based on electronic-photonic inspired logic [3–5]. However, the operation speeds of these schemes are limited by electrical-optical conversions of modulators since the logic operations are mainly performed in the electrical domain. Compared with electronic-photonic logic devices, the logic operation based on nonlinearity is fully implemented in the optical domain, enabling the high-speed signal processing [6]. Many works of logic operations via various nonlinear effects including cross-gain modulation (XGM) [7], cross-phase modulation (XPM) [8], and four-wave mixing (FWM) [9] have been reported. These applications realize basic logic operations including AND [10], OR [11], NOT [12], and XOR [13], and complex logic functions including encoder [14], comparator [15], and full adder/subtractor [16]. Among these devices, the complex logic functions are commonly realized by specific combination of canonical logic units (CLUs), which are also called logic minterms [17]. All-optical CLUs have attracted wide attention attributing to their advantages of flexibility and expandability [7,11,16]. In previous works, based on two-input CLUs, the all-optical two-bit multiplier and reconfigurable logic gates are realized in highly nonlinear fiber (HNLF) [18] and silicon waveguide [19], respectively.
By fully utilizing parallelism of optical signals, multichannel multicasting of CLUs can expand the capacity, and reduce power consumption and complexity of optical computing systems. With the superiority of rate transparency and multichannel parallel processing, FWM is widely used for CLUs multicasting [20,21]. CLUs multicasting circuits have been developed towards high-efficiency and miniaturization. The previous work has demonstrated the multicasting of two-input CLUs via FWM in HNLF [22], but small nonlinear coefficient and long length of HNLF prevent the integration of logic devices seriously. Many on-chip platforms feature large nonlinear coefficient, such as silicon [13], indium phosphide [23], silicon nitride [24], and their compounds [25]. Among them, silicon is a more appropriate candidate for achieving more wavelength channels of integrated CLUs multicasting due to its high accessibility and CMOS-compatibility. However, the two-photon absorption (TPA) and free carriers absorption (FCA) in silicon waveguides hinder the implementation of high-efficiency nonlinear process, mainly limited by optical power in waveguide [26]. The FCA effect can be significantly reduced by providing reverse-biased PIN junctions to sweep away the free carriers generated by the TPA, thereby enhancing the nonlinearity of the silicon waveguide [27]. Nevertheless, simultaneously achieving high-efficiency and miniaturization of CLUs multicasting circuits remains challenged.
In this paper, by introducing silicon waveguide with reverse-biased PIN junctions to enhance FWM effect, we propose and experimentally demonstrate the 40 Gb/s all-optical reconfigurable two-input CLUs multicasting in seven wavelength channels. Removing carriers can reduce the nonlinear loss and increase the output power of converted light by more than 10 dB. Based on the proposed waveguide and delay interferometer (DI), the full set of reconfigurable two-input CLUs in seven wavelength channels is demonstrated, and all logic signals with error-free performance are obtained. Due to the rate transparency of FWM and parallel multicasting of logic functions, the proposed scheme paves the way for future high-speed optical logic processing and high-capacity optical computing circuit.
2. Operational principle and device design
2.1 Principle of reconfigurable CLUs multicasting
The schematic diagram of reconfigurable CLUs multicasting is shown in Fig. 1(a). DI is an asymmetric Mach-Zehnder interferometer with a differential delay of τ in one arm, causing the complementary comb-like spectra in two output ports. Two input differential phase-shift keying (DPSK) signals are demodulated to on-off keying (OOK) signals when their wavelengths align with peaks or notches of comb-like spectra [28]. So two pairs of complementary OOK signals A, $\bar{A}$ and B, $\bar{B}$ can output from two ports of DI. By changing different signals as input, different CLUs are realized. When A, B are chosen as input signals, CLU carrying information of $AB$ is generated via FWM processes [17]. For the implementation of multichannel multicasting, an extra continuous wave (CW) beam is introduced and coupled with signals A, B via dense wavelength division multiplexer (DWDM). Then they are launched into the nonlinearity-enhanced waveguide to produce degenerate, non-degenerate and high-order FWM processes, generating CLUs multicasting.
The wavelength distribution of reconfigurable CLUs multicasting is shown in Fig. 1(b). In order to enhance FWM conversion efficiency and reduce crosstalk, we set A, B and CW at channel 6, 7, and 12. ${E_A}$ is the complex-amplitude light field of incident signal A, and so on for signal B and CW.The frequency spacing between adjacent channels is equal. Based on various FWM processes, converted signals in seven wavelength channels are produced simultaneously. For the degenerate FWM processes, when A and B act as pumps, the converted signals carrying the amplitude information of $AB$ are generated at channel 5 and 8, marked as $2{\omega _A} - {\omega _B}$ and $2{\omega _B} - {\omega _A}$. As shown in Fig. 1(b), the converted light in channel 5 is denoted by $E_A^2E_B^\ast $, the product of the square of ${E_A}$ and the conjugate of ${E_B}$. For the nondegenerate FWM processes, the converted signals of $AB$ are achieved at channel 1, when A, B are selected as pumps and CW as signal, marked as ${\omega _A} + {\omega _B} - {\omega _{CW}}$. Other converted signals are realized at channel 11 (${\omega _A} + {\omega _{CW}} - {\omega _B}$) and 13 (${\omega _B} + {\omega _{CW}} - {\omega _A}$). Due to the strong nonlinearity of the waveguide, high-order FWM processes can occur between incident pumps and converted signals. When $AB$ at channel 5 and CW act as pumps, B acts as signal, high-order converted signal carrying information of $AB$ is generated at channel 10, marked as ${\omega _{AB,\; CH5}} + {\omega _{CW}} - {\omega _B}$. Simultaneously, another high-order converted signal $AB$ is also generated at channel 10 with pumps of A, CW and signal of $AB$ at channel 8, marked as ${\omega _A} + {\omega _{CW}} - {\omega _{AB,\; CH8}}$. Thus the signal $AB$ at channel 10 is produced by the superposition of two high-order converted signals. Similarly, two high-order converted signals from ${\omega _B} + {\omega _{CW}} - {\omega _{AB,\; CH5}}$ and ${\omega _{AB,\; CH8}} + {\omega _{CW}} - {\omega _A}$ are superposed at channel 14, generating signal $AB$. Overall, seven channels of CLU are realized via various FWM processes simultaneously. By choosing different input signals, a full set of two-input CLUs is obtained in seven channels.
2.2 Device design
As described in the introduction, reverse-biased PIN junctions can be implemented to reduce nonlinear loss and enhance nonlinearity. The 4 cm silicon waveguide with reverse-biased PIN junctions is fabricated using 130 nm CMOS technology in Chongqing United Microelectronics Center (CUMEC). The schematic diagram of the waveguide cross-section is shown in Fig. 2(a). Based on a 220 nm-SOI platform with cladding silica layer thickness of 2 µm, the etching depth of vertical coupling grating coupler is 70 nm, and the etching depth of slab area is 150 nm. Two heavy doping areas act as ohmic contact, and the width of total doping area is 6.8 µm. The distance between two doping areas is 1.35 µm, which makes a tradeoff between the loss caused by doping and the performance of carrier removing. Figure 2(b) shows the simulated mode profile of the ridge waveguide. The dispersion coefficient is calculated to be -1766 ps/nm/km. The microscopic image of the fabricated waveguide is shown in Fig. 2(c), and spiral-shape curling of waveguide is used to reduce footprint. Figure 2(d) shows the measured spectra of reference grating and nonlinear waveguide. The peak loss of a pair of grating couplers is 10 dB at 1540.5 nm, and linear loss of the 4 cm nonlinear waveguide is about 4 dB.
Fig. 2. (a) Schematic diagram of the waveguide cross-section. (b) Simulated mode profile of ridge waveguide. (c) Microscopic image of the fabricated waveguide. (d) Measured spectra of reference grating and nonlinear waveguide.
3. Experiments and results
3.1 Nonlinearity enhancement of silicon waveguide with reverse-biased PIN junctions
The nonlinear performance of the silicon waveguide with reverse-biased PIN junctions is characterized by the power of converted light generated by the degenerate FWM processes between two CW beams [29]. The experimental setup for FWM performance measurement is shown in Fig. 3(a). Two CW beams with respective wavelengths of 1549.05 nm and 1552.25 nm are amplified by adjustable erbium-doped optical fiber amplifiers (EDFAs) and then injected into the nonlinearity-enhanced waveguide. A DWDM with free spectral range (FSR) of 1.6 nm is used to couple the CW beams and polarization controllers (PCs) are used to adjust polarization of incident CW beams to the transverse electric (TE) mode. Voltage supporting reverse-biased PIN junctions is provided by a direct current (DC) power. The optical power of coupled beams measured after DWDM is defined as incident power of the waveguide. When incident power is 23 dBm, the FWM spectra measured with 25 V reverse bias voltage (red) and no reverse bias voltage (blue) are shown in Fig. 3(b). By applying reverse bias voltage to PIN junctions, carriers produced by nonlinear absorption are removed, and the optical powers of pump and converted light have been significantly improved. As illustrated in Fig. 3(b), the optical power of left converted light without reverse bias voltage (blue) is measured as -30.14 dBm, while the optical power with 25 V reverse bias voltage (red) is -19.25 dBm, providing a 10.89 dB improvement. For the right pump, optical power without reverse bias voltage is -5.6 dBm, while the optical power with 25 V reverse bias voltage is 1.68 dBm, providing a 7.28 dB improvement.
Fig. 3. (a) Experimental setup for the FWM performance measurement. (b) Spectra measured with 25 V reverse bias voltage (red) and no reverse bias voltage (blue) when incident power is 23 dBm. (c) Optical power variation curves of converted light with reverse bias voltage when incident power is 23 dBm (purple), 20 dBm (yellow), 15 dBm (red), and 10 dBm (blue).
Figure 3(c) shows the optical power variation curves of left converted light with reverse bias voltage, when incident power is 23 dBm (purple), 20 dBm (yellow), 15 dBm (red), and 10 dBm (blue), respectively. Points representing no reverse bias voltage are drawn on the far left. When incident power is smaller than 15 dBm, the output power of converted light hardly increases with the reverse bias voltage increasing; when incident power is 20 dBm, the output power of converted light increases by 3 dB; while incident power is 23 dBm, the output power of converted light can increase over 10 dB.
3.2 40 Gb/s seven-channel reconfigurable CLUs multicasting
By utilizing parallelism of optical signals and nonlinearity enhancement of silicon waveguide, integrated CLUs multicasting can give more possibilities to on-chip optical computing systems. Here, we experimentally demonstrate the 40 Gb/s reconfigurable two-input CLUs multichannel multicasting, and the experimental setup is shown in Fig. 4. The 27−1 pseudorandom binary sequence (PRBS) signal at 40 Gb/s is generated by the bit pattern generator (BPG), driving the Mach-Zehnder modulators (MZMs) to modulate two return-to-zero differential phase-shift keying (RZ-DPSK) optical signals with the duty cycle of 33%. The wavelengths of two RZ-DPSK signals are 1545.32 nm and 1546.92 nm. After amplified by EDFA1, two RZ-DPSK optical signals are sent to DI and demodulated to two pairs of complementary RZ-OOK signals A, $\bar{A}$ and B, $\bar{B}$. These input signals are demultiplexed by two DWDMs. When different signals are chosen as input, different CLUs are realized. An optical delay line (ODL) is introduced to decorrelate and align two signals. Two RZ-OOK signals are amplified by EDFAs, then coupled with a CW beam at 1556.55 nm via DWDM. Optical powers of A, B, and CW measured after DWDM are 20.44 dBm, 20.64 dBm, and 21.4 dBm, respectively. Then the mixed signals are injected into the silicon waveguide to produce various FWM processes. The FWM spectra measured by the optical spectrum analyzer (OSA) are shown in Fig. 5. Seven CLUs signals are generated at 1535.69 nm, 1543.72 nm, 1548.92 nm, 1553.35 nm, 1554.95 nm, 1558.15 nm, and 1559.75 nm, respectively, marked as CH1 to CH7. The output CLUs are extracted by a tunable bandpass filter (TBPF1), then amplified by EDFA5. TBPF2 is used to filter noise caused by EDFA5, and the 3 dB bandwidths of two TBPFs are both 1.6 nm. The filtered converted signals are characterized by the communication signal analyzer (CSA).
When $\bar{A}$ and $\bar{B}$ are chosen as input signals, we get logic signals $\bar{A}\bar{B}$ at CH1 to CH7. Original input signals and logic signals $\bar{A}\bar{B}$ are characterized in Fig. 6. The temporal waveforms and eye diagrams of original signals are shown in Fig. 6(a). Complementary OOK signals demodulated by DI have high quality, providing switchable input signals. Figure 6(b) shows the temporal waveforms and eye diagrams of logic signals $\bar{A}\bar{B}$ at CH1 to CH7. The logic levels are clearly identified, and the logic sequences are correct with wide-open eyes. The bit error rate (BER) curves of original signals and logic signals $\bar{A}\bar{B}$ are shown in Fig. 6(c). All signals with error-free performance (BER = 10−9) are realized, and the power penalty is less than 9.5 dB. The different slopes of BER lines are caused by the different signal qualities of seven-channel logic signals. Specifically, CLUs in CH2 and CH3 are generated by the degenerate FWM processes with pumps of $\bar{A}$ and $\bar{B}$, thus the slopes of their BER curves are similar. The curves of CH5 and CH6 are approximately parallel since they are all generated by the nondegenerate FWM processes. For CH1, CH4, and CH7, their optical powers are significantly lower than other channels, resulting in slightly poor eye diagram qualities and different slopes of BER curves. The 3 dB bandwidths of two TBPFs are both 1.6 nm as previously mentioned. To analyze the sensitivity of the CLU’s BER with wavelength offset between TBPF center and CLU, a simulation model is built and the wavelength offsets from -0.8 nm to 0.8 nm are numerically analyzed. The simulation results are shown in Fig. 7, indicating the wavelength offsets within 0.37 nm will have no effect on the BER.
Fig. 6. Temporal waveforms and eye diagrams of (a) original signals, (b) seven-channel logic signals $\bar{A}\bar{B}$. (c) BER curves of original signals and logic signals $\bar{A}\bar{B}$.
Fig. 7. Simulation results of CLU’s BER variation curve with wavelength offset between TBPF center and CLU.
By changing input signals, logic signals carrying the reconfigurable CLUs are generated in seven wavelength channels. Due to the similar situation of different inputs, here we just characterize the full set of two-input CLUs signals at CH1, CH2, and CH7. The temporal waveforms and eye diagrams of $AB$, $\bar{A}B$, $A\bar{B}$, and $\bar{A}\bar{B}$ are shown in Fig. 8(a) - (d). The clearly identified logic levels and wide-open eyes of all CLUs signals are observed, meanwhile, the BER curves of different CLUs signals are as shown in Fig. 8(e). The different slopes of the BER lines are caused by different pump signals. All CLUs signals with error-free performance are obtained, and the power difference is less than 7.5 dB, which confirms the practicability of reconfigurable CLU multicasting for high-speed signal processing.
Fig. 8. (a) - (d) Temporal waveforms and eye diagrams of the full set of CLUs $AB$, $\bar{A}B$, $A\bar{B}$, and $\bar{A}\bar{B}$. (e) BER curves of different CLUs signals.
The FWM conversion efficiency of our proposed nonlinear waveguide is -20 dB, as illustrated in Fig. 3(b). According to the comparison in Table 1, the FWM conversion efficiency of silicon-based waveguides is not the highest in various nonlinear mediums. For discrete platforms such as HNLF and semiconductor optical amplifiers (SOA), the FWM conversion efficiency is generally high as -10 dB and -5 dB, but they are difficult to integrate, which heavily prevents their on-chip applications. For the new nonlinearity platforms of silicon nitride and AlGaAsOI, they also have the high conversion efficiency as -10 dB. Nevertheless, their production processes are still immature. Although silicon platform is not optimal in terms of FWM conversion efficiency, the high accessibility, CMOS-compatibility, and mature production process of silicon waveguide with reverse-biased PIN junctions still ensure it as the more appropriate candidate for achieving more wavelength channels of integrated CLUs multicasting.
Table 1. FWM Conversion efficiency of various nonlinear mediums
4. Conclusion
In summary, we have proposed and experimentally demonstrated the 40 Gb/s seven-channel all-optical reconfigurable CLUs multicasting in the silicon waveguide. By introducing reverse-biased PIN junctions, the output power of converted light generated by FWM can be increased over 10 dB, contributing to the performance improvement of optical signal processing systems. A full set of two-input CLUs signals is obtained in seven wavelength channels, and all logic signals with error-free performance are realized. The proposed scheme implements the all-optical integrated reconfigurable CLUs multicasting with high efficiency, showing anticipated prospects in future high-speed parallel optical computing systems.
Funding
National Key Research and Development Program of China (No. 2019YFB2203102); China National Funds for Distinguished Young Scientists (No. 61905083); China Postdoctoral Science Foundation (No. 2019M652631); Natural Science Foundation of Guangdong Province (2020A1515011492); Key Technologies Research and Development Program of Shenzhen (JSGG20201102173200001).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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