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Abstract
Optical computing technology has gained attention as a solution to address the computational latency caused by the resistance-capacitance (RC) delay in processors based on complementary metal-oxide-semiconductor (CMOS). However, many optical computing technologies tend to rely on nonlinear effects, resulting in an increase in the device length and input light intensity to enhance nonlinear efficiency. This study proposed what we believe is a new optical decoder device based on linear effects. The device was composed of two cascaded delay-line interferometers (DLIs) made of a silicon waveguide. Targeting 2-bit binary phase-shift keying (BPSK) signals, it outputs ON state for a specific bit pattern by setting different phase conditions. The experimental results confirmed the functionality of the device, including measurements of the impulse response, evaluation of the phase-shift conditions, and successful decoding operations for a signal at 10 Gbps. The proposed decoder, which does not rely on nonlinear effects, offers advantages in terms of low latency and power consumption.
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1. Introduction
The continuous increase in data traffic within digital infrastructures requires ongoing improvements in the performance of processors based on complementary metal oxide semiconductor (CMOS), in accordance with the principles of the Moore’s law. However, despite these efforts, computational latency is currently at its limit owing to the escalation of the resistance-capacitance (RC) delay resulting from CMOS miniaturization. A proposed solution to overcome this problem involves integrating optics into computers because the propagation of light is unaffected by RC delays. Optical computing is considered a promising solution for significantly reducing the computation latency [1,2].
In the field of optical computing, various studies have been conducted on logical gates [3–26], half-adders [27–31], and decoders [32–35]. Many of these studies depend on nonlinear optical effects, such as semiconductor optical amplifiers (SOAs) [3–7,27–29,32,33], SOA-based Mach-Zehnder interferometers (SOA-MZIs) [8,9], highly nonlinear fibers (HNLFs) [10–12], periodically poled lithium niobates (PPLNs) [13–16], microring resonators (MRRs) [17,18], and waveguide-type devices [19–21,34]. These technologies tend to increase the device length and input light intensity to enhance the efficiency of nonlinear effects. Recently, optical computing technologies that do not rely on nonlinear effects have been realized [22–26,30,31,35]. These approaches enable the realization of compact devices with low input light intensity.
Decoders are highly versatile owing to their applicability to processor instruction decoding. Two types of optical decoder composed of SOA were proposed by Hassan and Yi [32,33], and an optical decoder using photonic crystals was suggested by Tina [34]. However, both approaches rely on optical nonlinearity, resulting in large device lengths and high power consumption. A decoder utilizing linear effects was proposed by Zhiwen and Mir [36,37], but both approaches were not entirely optical as it is driven by electricity. Although an optical decoder utilizing linear effects was proposed by Haraprasad [35], it was limited to 1-bit operation and had practical challenges.
In this study, we proposed a 2-bit optical decoder consisting of silicon waveguides. This decoder operated based on linear effects, enabling low-latency and low-power operations without dependence on nonlinear effects. Furthermore, due to the ability to achieve logical negation through phase rotation, binary phase shift keying (BPSK) signals were targeted. In the decoder, a 2-bit decoding operation was experimentally demonstrated using BPSK-modulated signals at 10 Gbps.
2. Operating principles
A binary decoder is a device that converts binary information from n-bit coded inputs to a $2^n$-th unique output. Figure 1 shows the operating principles of a 2-bit decoder for signals A and B. At the left figure in Fig. 1, signals A and B are modulated using BPSK, and both signals are combined through two phase shifters to generate a single combined signal. Then, by superimposing an assist light onto the combined signal, the target signal is obtained.
Fig. 1. Operating principles of a 2-bit optical decoder with operating example: the decoder generates a combined signal and achieves its functionality by superimposing an assist signal.
The light power of the target signal is derived by defining the two BPSK signals A and B and a probe light (assist light) in the following form:
where $P_S$, $P_P$, $\omega _S$, and $\omega _P$ represent the light power and the angular frequencies of the signal and the probe, and $\phi _A$, $\phi _B$, and $\phi _P$ are the phases of the signal A, signal B, and the probe, respectively. Here, the notation varies depending on the amounts of $\phi _A$ and $\phi _B$. Specifically, when $\phi _A$ and $\phi _B$ have a phase of 0, they are denoted as $E_{\overline {A}}$ and $E_{\overline {B}}$, while when $\phi _A$ and $\phi _B$ have a phase of $\pi$, they are denoted as $E_{A}$ and $E_{B}$. The target signals for all patterns of signals A and B could be summarized in the following manner:Here, it is assumed that both frequencies of the signal and the probe are the same ($\omega _S$=$\omega _P$). Additionally, the intensity of the two signals and probe is 1 ($P_S=P_P=1$), and the probe phase is 0 ($\phi _P=0$). Consequently, for all possible patterns of the two phase shifters $\theta _A$ and $\theta _B$, the intensity of the target signal is given as follows:
According to the above equations, different target signals maximize depending on the pattern of phase amounts $\theta _A$ and $\theta _B$.
The operating example for all possible patterns of $\theta _A$ and $\theta _B$ is illustrated on the right side of Fig. 1. The combined signal has three different values depending on the pattern of signals A and B. Specifically, when the constellation of codes 0 and 1 in BPSK is given with respect to the real axis at 0 and $\pi$, the constellation of the combined signal consists of three points: 0 phase, the origin, and $\pi$ phase. More precisely, when both signals A and B are 0, it corresponds to 0 phase (00); when A is 0 and B is 1, or vice versa, it corresponds to the origin (01 or 10); and when both are 1, it corresponds to $\pi$ phase (11) as shown in Fig. 1(#1). Consequently, by superimposing an assist light onto the combined signal, the constellations are shifted and the four target signals are obtained (Fig. 1(#5)). Similarly, with different phase values in the two phase shifters, the position of the constellation in the target signal changes (Figs. 1(#6–#8)). Thus, specific codes can be located at the 0-phase position via phase rotation [38,39].
According to Eqs. (6) to (9), the ratio of light power is given by 4:1:1:0 from the highest to the lowest when square-law detection is applied. The extinction ratio between the maximum intensity and the other is described as
3. Device
The proposed decoder generated a combined signal and achieved functionality by superimposing the assist signal. Figure 2 shows a top-view microscopic image and a schematic of the 2-bit optical decoder device. The device consisted of two serially cascaded delay-line interferometers (DLIs). The first was used to generate the combined signal, and the second was used to superimpose the assist signal. While the structure differs from that shown in Fig. 1, it ultimately generates an equivalent signal. Each DLI was constructed using a silicon waveguide.
Fig. 2. Photomicrograph of the 2-bit optical decoder device: (a) schematic of the optical decoder with operating examples.
The structure of the device is explained herein using an operating example. The silicon waveguide was positioned at the center of a cladding layer composed of SiO$_2$. Its cross section is rectangular with a width of 440 nm and a thickness of 220 nm to provide single-mode propagation for transverse electric (TE) light. Four BPSK symbols were input into the device, which were separated into two parts. The symbols on the upper branch passed through a delay line and propagated for a distance equivalent to the time interval of one symbol. Considering that the last two of the four BPSK symbols were signals A and B, they were aligned on the same time axis, and each passed through a phase shifter. The phase shifter consisted of a TiN heater located 1.2 $\mu$m on the silicon waveguide. When a voltage was applied to the heater, the phase of the propagating light shifted through the thermo-optic effect. After passing through each phase shifter, signals A and B were combined to generate a combined signal. Similarly, an assist signal was generated at a point two symbols before. Here, the assist signal was set to have a phase of 0 after the combination.
Subsequently, the combined and assist signals were input into the following DLI: Here, they are also split into two parts; however, owing to the delay lines corresponding to the time intervals of the two symbols, interference occurs between the combined and assist signals. Thus, the constellation of the combined signals shifted, and a decoding operation obtained. This is how the decoder operation is carried out in our device. In addition, the processing delay is determined by the length of the waveguide, and the power consumption is determined by the losses of the device
4. Results
4.1 Experimental setup
An experiment was conducted to demonstrate a 2-bit decoding operation using the fabricated silicon device. The measurement setup is shown in Fig. 3. A lithium niobate modulator (T.SBXH1.5PL-25PD-ADC, Sumicem) was driven by a pulse pattern generator (D3186, Advantest) to modulate a 1550 nm wavelength light emitted from a tunable laser diode (TSL-210, santec), generating a 10 Gbps non-return to zero (NRZ) BPSK signal. After adjusting the polarization state to the TE mode, the optical signal was input into the silicon device through a lensed fiber. Voltage was applied to the two phase-shifters in the device using probe electrodes, providing phase shifts of 0-0, 0-$\pi$, $\pi$-0, and $\pi$-$\pi$ for signals A and B. Different signal sequences were generated for each condition. As shown in Fig. 2, the fundamental signal was a 4-bit BPSK signal, where the first two bits represented the assist signal, and the remaining two bits represented signals A and B. The assist signal was configured to have a phase of 0 after the phase shift and set to different patterns for each condition. Furthermore, to adjust the occurrence rate of 0 and $\pi$ in BPSK to 1/2, 4-bits of dummy signals were added. An 8-bit sequence was generated for the four possible patterns of signals A and B, resulting in a 32-bit signal sequence. Furthermore, by using four different dummy signals to observe the pattern effect, a final 128-bit signal sequence was achieved. After the decoding operation, the optical signal was received through a lensed fiber via a spot-size converter. Subsequently, the signal was amplified to 0 dBm, and after the removal of the amplified spontaneous emission (ASE) noise, it was input to a photodetector (PD). Square-law detection was performed at the PD (DX20AF, Thorlabs), and the operational waveform was observed using an oscilloscope (86100B, Agilent).
Fig. 3. Experimental setup (TLD: tunable laser diode; PC: polarization controller; LNM: LiNbO$_3$ modulator; EDFA: erbium-doped fiber amplifier; OBPF: optical band-pass filter; Att: optical attenuator; VS: voltage source; PD: photodetector; PPG: pulse pattern generator; OSC: oscilloscope).
4.2 Experimental results
Before demonstrating the operation of the decoder, device characteristics were evaluated. Initially, impulse response was measured. A single pulse with a width of 2 ps was generated by using a mode-locked laser with a light of 1550 nm wavelength. Subsequently, the pulse was input to the device, and the waveform from the output port was observed using an oscilloscope. Figure 4 illustrates the input and output waveforms. Figure 4(b) shows that the output waveform was divided into four parts. As shown in the figure, the output pulses had the same intensity, and each time delay was approximately 100 ps. The Free Spectral Range (FSR) of the two DLIs was as designed, 10 GHz and 5 GHz, respectively. The first DLI contributes to the synchronization of signals A and B, while the second DLI contributes to the synchronization of the combined signal and the assist light.
Subsequently, we evaluated the phase-shift conditions. Figure 5(a) shows the transmission spectra observed at the monitor port in the first DLI. The solid line represents the conditions with applied voltages to the two phase-shifters: $V_A$ = 1.1 V and $V_B$ = 0.0 V, whereas the dashed line represents the conditions with VA = 1.1 V and VB = 3.6 V. Here, the solid line suppressed the wavelength at 1550 nm, and the dashed line allowed transmission. In other words, the solid line indicates an anti-phase condition at the monitor port and an in-phase condition at the port opposite to the monitor port (the port connected to the second DLI). Similarly, the dashed line indicates the anti-phase condition at the opposite port. Therefore, it indicates that the solid line corresponded to 0-0 shift for signals A and B, whereas the dashed line corresponded to 0-$\pi$ shift. Similarly, in Fig. 5(b), the solid and dashed lines represent the conditions for $\pi$-$\pi$ shift ($V_A$ = 2.6 V and $V_B$ = 3.6 V) and $\pi$-0 shift ($V_A$ = 2.6 V and $V_B$ = 0.0 V). Figure 5(c) is a spectrum of the BPSK signal before input, and Figs. 5(d)–(g) show the BPSK signal spectra obtained at the monitor port for 0-0, 0-$\pi$, $\pi$-0, and $\pi$-$\pi$ shifts. In the 0-0 and $\pi$-$\pi$ shifts, the carrier was suppressed, whereas in the 0-$\pi$ and $\pi$-0 shifts, the carrier was emphasized. However, considering that the port opposite to the monitor port was connected to the following DLI, the 0-0 and $\pi$-$\pi$ shifts were in-phase and the 0-$\pi$ and $\pi$-0 shifts were anti-phase. This confirmed that the phase conditions were set correctly.
Fig. 5. Signal spectra: transmission spectra of the fist DLI at the monitor port for (a) 0-0 and 0-$\pi$ shifts and (b) $\pi$-$\pi$ and $\pi$-0 shifts. Spectrum of the BPSK signal (c) before input. Spectra of the BPSK signal at the monitor port for (d) 0-0 shift, (e) 0-$\pi$ shift, (f) $\pi$-0 shift, and (g) $\pi$-$\pi$ shift.
Figure 6 illustrates the operating waveforms and eye patterns of the 2-bit decoder. Figures 6(a)–(d) represent the operating waveforms for 0-0, 0-$\pi$, $\pi$-0, and $\pi$-$\pi$ shifts, respectively. At the top of the operating waveforms, the bit patterns of input signals A and B are collectively shown. The highlighted areas in each waveform correspond to the target signal associated with signals A and B, which correspond to 00, 01, 10, and 11, respectively. For each condition, the most intense signal corresponded to different combinations of signals A and B. In other words, the device turns On state for a specific pattern of 2-bit codes by providing four different phase conditions: 0-0, 0-$\pi$, $\pi$-0, and $\pi$-$\pi$. This represented the operation of the decoder, confirming that the decoder operation was realized in the optical domain.
Fig. 6. Operating waveforms and eye patterns of the 2-bit optical decoder: (a) 0-0 shift, (b) 0-$\pi$ shifts, (c) $\pi$-0 shift, and (d) $\pi$-$\pi$ shifts.
In Fig. 6(a), the highlighted signals correspond to patterns 00, 01, 10, and 11 from left to right, with a relative intensity ratio of approximately 4:1:1:0. This aligns with the square-law detection of the constellation in the 0-0 shift shown in Fig. 1(#5). Similarly, as shown in Figs. 6(b)–(d), the relationship between the relative intensity ratios and constellation accurately matched the operating principle shown in Fig. 1(#6–#8). The extinction ratio was calculated from the eye pattern, resulting in $ER^{0-0}$ = 7.3 dB, $ER^{0-\pi }$ = 7.5 dB, $ER^{\pi -0}$ = 7.2 dB, and $ER^{\pi -\pi }$ = 7.2 dB. These values were approximately equal to the theoretical values. Additionally, multiple regression analysis was conducted on the ON and OFF levels of the eye pattern. As a result, it was found that the OFF level contributes more to the extinction ratio.
5. Conclusion
In conclusion, we proposed a 2-bit optical decoder for BPSK-modulated signals using two cascaded DLIs with silicon waveguides. This device operated as a decoder that sets ON state for a specific pattern of 2-bit codes by providing four different phase-shift conditions: 0-0, 0-$\pi$, $\pi$-0, and $\pi$-$\pi$. In the experiments, the decoder successfully operated using 10 Gbps BPSK-modulated signals. The extinction ratio during this operation was exceeded 7 dB for all conditions, which is in close agreement with the theoretical value. As this approach is independent of nonlinear effects, it provides potential advantages in reducing latency and improving power efficiency in future digital infrastructures.
Funding
Japan Society for the Promotion of Science ( JP21K14557).
Acknowledgment
This study was supported by JSPS KAKENHI (grant number: JP21K14557).
Disclosures
The authors declare no conflicts of interest.
Data availability
The 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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