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Abstract
We propose a novel all-optical phase shifted quantizer using cascade step-size MMI. The operation principle has been derived in detail. A 3-bit quantizer and a 5-bit quantizer are designed and simulated based on 220-nm SOI platform to verify the feasibility of the scheme, of which the lengths are all below 200 μm. To the best of our knowledge, they have the most compact footprint compared to the existing all-optical quantizers. In the end, the fabrication error analyses of the proposed quantizers are carried out to verify their stability.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Analog-to-digital converter (ADC), like a bridge connecting the real world with the digital world, play a key role in modern signal processing technology, such as high speed optical communication, advanced radar system, and medical imaging. Limited by the timing jitter and comparator bandwidth, conventional electrical ADC is difficult to meet the requirement of high resolution and ultra-bandwidth [1,2]. To overcome these bottlenecks, all-optical ADC schemes, which utilizing photonic technologies to sample and quantize the high speed analog signals, has attracted much attention in recent years. As a key element in all-optical ADCs, optical quantization schemes have been extensively proposed and improved in the past decades. Until now, the high performance optical quantization schemes can be classified into two categories: the phase-shifted optical quantization (PSOQ) in a linear system [3–7], and the optical amplitude quantization (OAQ) using highly nonlinear materials [8–10]. Today in the trend of on-chip integration, the OAQ schemes have disadvantages of high optical power consumption and large footprint due to the reason that high optical power and long propagation path are required to generate the nonlinear effect. Optical ADC (OADC) schemes based on PSOQ can utilize as little as only one modulator to convert the amplitude of the signal into optical phase, and the schemes work in the linear region, which means that the system is simple and stable. However, the research of integratable all-optical quantizer is still at the early stage, there is only a few work have been reported. In [6], a phase-shifted OADC scheme based on 4 × 4 multimode interference (MMI) coupler has been presented. This scheme has an extremely simple structure and can be easily integrated on the SOI platform. However, to avoid redundant coding, only half output channels of the MMI are used as quantization channels, resulting in half optical power wasted. On the other hand, more 4 × 4 MMI couplers were needed to achieve a resolution of above 2 bit, for example, a quantization resolution of 3-bit should be achieved by two 4 × 4 MMI couplers, which lead to a system complexity as quantization precision increases.
In this paper, we propose a novel all-optical quantizer based on cascade step-size MMI (CSS-MMI) structure. By using odd channels as the quantization channels, this device works without any optical power wasting and has a quite compact footprint. The operation principle has been derived in detail and proved by simulation results. A 3-bit quantizer and a 5-bit quantizer are designed and simulated based on 220-nm SOI platform to verify the feasibility of the scheme, of which the lengths are all below 200 μm. This device can be easily fabricated on SOI platform and has potential to be very stable.
2. Principle
2.1 The CSS-MMI
As the schematic view shown in Fig. 1(a), the CSS-MMI consists of two parts, one of which is the first MMI (MMI1st, with length and width of L1 and W1), used to convert the dual injections (Es and Ep, with equal intensity) into three single mode outputs (Es’, Ep1’ and Ep2’) with specific phase differences. While the other part, referred as the second MMI (MMI2nd, with length and width of L2 and W2), is utilized to motivate a multi-modes interference of Es’, Ep1’ and Ep2’. Then, by carefully design of the dimension of the CSS-MMI, odd imaging points can be formed at the output facet and the intensities of each image varies as the phase of Es changes. The transmission curves are shown in Fig. 1(b) and can be utilized for quantization.
Fig. 1 (a) Schematic diagram and main parameters of the CSS-MMI. (b) Transmission curves of CSS-MMI with K outputs.
Assuming that the injected lights are represented as
in which P, ω and φ0 represent the power, angular frequency and the initial phase of the injections, respectively. ΔФsignal is the phase variation of Es, which is induced by the phase modulation for electrical signal. The outputs of MMI1st can be described asEs’ is injected at the middle position of MMI2nd, while Ep1’ and Ep2’ are injected at special positions as
where K is the number of output channels. The outputs from each channel of MMI2nd can be written asin whichwhere a equals to K ± 2 or K corresponding to the situation when Ep1’, Ep2’ or Es’ is injected, respectively. i represents the serial number of output channels, and i = 1,2,3...K.According to the self-imaging theory [11], N self-images of equal intensities can usually be formed at the length
Where M defines the number of possible lengths with N images, Lc is the coupling length between the lowest order modes of MMI. Here, we choose the lengthin which Lc1 is the coupling length for MMI1st. From Eqs. (6) and (7), we can see that two-images (Ep1’ and Ep2’) for non-central injection (Ep) and the second one-image (Es’) for central injection (Es) can be formed at the same length of MMI1st simultaneously. In this case, Eq. (2) can be used to calculate the transmission relationship between the inputs and outputs of MMI1st.Actually, MMI1st is utilized to provide the incident lights at specific positions for MMI2nd. As we choose the length
where Lc2 is the coupling length of MMI2nd. At this length, K images of equal intensities can be formed when Es’ is injected, and 2K images are formed when Ep1’ or Ep2’ is injected individually. However, according to [12], if Ep1’ or Ep2’ is injected at specific positions as shown in Eq. (3), images overlap takes place and the number of images reduces by half, which means that also K images are formed at length L2. If both Ep1’ and Ep2’ are injected (Es’ = 0), the intensities of each image can be calculated according to Eqs. (4) and (5)which means that the K images also have equal intensities, with the values equal to the intensities when only Es’ is injected. Hence, when Es and Ep are injected simultaneously with same power, K images can be formed at the output facet, and complete destructive interference takes place. Through Eqs. (4) and (5), output power at each channel can be expressed asFrom Eq. (10), we can see that the output power of each channel varies sinusoidally with ΔФsignal increases, as shown in Fig. 1(b). Besides, there is a fixed phase shift of 2π/K between the transmission curves of the output channels, which means the curves can be utilized for phase-shifted quantization.
2.2 CSS-MMI based OADC scheme
Figure 2 shows the schematic diagram of the an OADC scheme based on CSS-MMI. It consists of a phase-shifted optical sampling and quantization module, an electric decision module, and a data processing module. Sampling pulse generated by a mode-locked laser is split into two parts by a 1 × 2 MMI coupler. One part is then modulated by a phase modulator (PM) driven by analog signal and referred to as Es, and another part is referred to as the reference light Ep with no phase modulation. Hence, a phase difference ΔФsignal relevant to the amplitude of the analog signal is induced between Es and Ep. Through the quantization for the phase difference by CSS-MMI, the output signal from each channel is detected by a photodetector (PD) and compared with a threshold by the electric decision module, then binary codes corresponding to the analog signal can be obtained. Note that for the PSOQ schemes with K quantization channels to achieve N = log2(2K) bit quantization, the quantized analog amplitude must be at least expressed by K binary codes, which leads to a very long digital number as resolution increases. To fix this problem, a data processing module is needed, in which a series of XOR operation would be executed to convert the binary codes from K output channels with similar periods into binary codes of N channels with different periods. The examples of detailed processing are introduced in the following sections.
3. Simulation results
3.1 3-bit quantization
To verify the feasibility of the proposed quantizer, we design a 3-bit quantizer as an example based on above principle. CSS-MMI of 5 output channels are used here to achieve 3-bit quantization. The CSS-MMI is based on SOI platform with 220 nm thick-silicon layer and 2 μm thick buried oxide layer. The cross section of waveguide and the schematic diagram of proposed device are shown in Figs. 3(a) and 3(b), respectively. The main description and the size of parameters of CSS-MMI are listed in Table 1.
Fig. 3 (a) Cross section of the silicon nanowaveguide. (b) 3D schematic of 3-bit quantizer using CSS-MMI
Table 1. Main parameters of CSS-MMI for the 3-bit quantizer.
Three-dimensional beam propagation method (3-D BPM) based on SOI is used to simulate the performance of the proposed device, as it is a quick and accurate method to simulate the transmission performance for the devices with footprint of hundreds of microns. The operation wavelength is λ = 1550 nm. Figures 4(a) and 4(b) show the simulation results when the light Es or Ep is injected with TE polarization, respectively, which shows that optical power is split into all 5 output channels equally in both cases. When Es and Ep are injected simultaneously, meanwhile an electrical signal with the amplitude increasing linearly was added to the PM, the interference curves as a function of ΔФsignal and corresponding code table are shown in Fig. 4(c).
Fig. 4 Optical field distribution when the light (a) Es or (b) Ep is injected into CSS-MMI, respectively. (c)Transmission characteristics of 5 outputs as a function of ΔФsignal and corresponding code table.
The insertion loss (IL) of CSS-MMI is around 0.1 dB at 1.55 μm and the equivalent effective number of bit (ENOB) can be calculated as [8]
Where PFS is the maximum phase difference induced by the analog signal, Δstep-i is the phase error for each quantization level. The ENOB of proposed quantizer can be estimated to be 3.32 bit.Fabrication tolerance of the device is also analyzed numerically, as shown in Figs. 5. From Fig. 5(a) and 5(b), we can see that the ENOB is kept above 3.15 bit and the IL is below 0.5 dB by the deviation ΔW and ΔL of ± 20 nm and ± 800 nm, respectively, indicating that the device is robust to the variation of size and it is highly tolerant to the fabrication imperfections. Figure 5(c) shows the analysis of wavelength insensitivity in a range of 20 nm, where ENOB is still above 3.27 bit and the IL is below 0.45 dB.
Fig. 5 ENOB and insertion loss of CSS-MMI as a function of (a) width variation, (b) length variation, and (c) operation wavelength.
For general, a PSOQ scheme with K quantization channels quantize the signal to 2K levels, and a quantization precision of log2(2K) can be obtained. As the device mentioned above, to achieve a quantization precision of above 3 bit, the analog signal is quantized to 10 levels and expressed by 5 binary codes. However, the digit number can be reduced by a series of XOR operation during electric data processing. As shown in Fig. 6 and 8 levels are retained to quantize the analog signal, the binary codes from Ch-4 are chosen as bit 1 without any operation, while XOR operations are executed between Ch-1 and Ch-2, Ch-3 and Ch-5, to create bit 2 and bit 3, respectively. Thus, each level can be expressed by 3 binary codes, which means the length of codes is reduced into standard level.
3.2 Resolution enhancement
According to the principle of CSS-MMI, a higher quantization precision can be obtained by means of increasing the number of MMI2nd ’s output ports. Take the 5-bit quantization for an example, 17 output channels are utilized as the quantization channels. The size of MMI1st and gap between input ports or output channels (G1 and G2) are same to that of the 3-bit quantizer mentioned above. The width and length of MMI2nd are optimized as 25.5 μm and 137.68 μm, respectively.
The simulation results when the light Ep or Es is injected are shown in Figs. 7(a) and 7(b), respectively. The optical power is split into all 17 output channels equally in both cases. When the phase-modulated signal and reference signal are injected simultaneously, the interference curves as a function of ΔФsignal is shown in Fig. 7(c). Obviously, through a threshold decision, the phase difference relevant to the amplitude of the analog signal is quantized into 34 levels with Gary code, which means a quantization precision of above 5-bit quantization can be achieved. Moreover, the simulated insertion loss of CMMI is as low as around 0.13 dB.
Fig. 7 Optical field distribution when the light (a) Ep or (b) Es is injected into CSS-MMI, respectively. (c) Transmission characteristics of 17 outputs as a function of ΔФsignal and corresponding code table.
To reduce the digit number, XOR operation between output channels can be executed during data processing. Through choosing the channels for XOR operation appropriately, 17 binary waveforms with similar period can be converted into 5 waveforms with different period, as shown in Fig. 8. Hence, the amplitude of analog signal can be quantized to 32 levels and expressed by 5 binary codes.
The fabrication tolerance of the device is analyzed as shown in Fig. 9. Figures 9(a) and 9(b) show that the ENOBs and ILs can be kept above 4 bit and below 0.5 dB as the deviation ΔW and ΔL vary between ± 15 nm and ± 800 μm, respectively. Figure 9(c) shows the same analysis to wavelength sensitivity, where ENOB is kept above 4.68 bit and the IL is below 0.5 dB in a range of 10 nm.
Fig. 9 ENOB and insertion loss of CSS-MMI as a function of (a) width variation, (b) length variation, and (c) operation wavelength for 5-bit quantization.
Compare to the 3-bit quantizer mentioned above, the 5-bit quantizer is more sensitive to the variation of structure or the wavelength, because the coupling length of MMI2nd becomes more sensitive as the width increases, leading to a reduction of stability. To relieve this problem, applying multi-wavelength or parallel connection to quantizers with lower precision and higher stability can be considered as alternative proposal for the future enhance of quantization precision. However, the achievement of 5-bit quantization with such a compact footprint of less than 25.5 × 200 μm2 is still inspiring.
4. Conclusions
We have proposed a novel on-chip all-optical quantizer using cascade step-size MMI structure. By carefully designing the dimensions of CSS-MMI, a 3-bit and a 5-bit quantization are achieved with a quite compact size. To simplify the lengthy codes generated by this phase-shifted quantizer, the code reduction procedure is drawn up for the data processing module. This device is robust to the fabrication error and wavelength variation, which means that it can be fabricated through commercial fabrication process and the performance would be quite stable. The proposed quantizer is expected to have significant applications in photonic integratable optical communication links, optical interconnection networks, and real-time signal processing systems.
Funding
National Natural Science Foundation of China (NSFC) (61335009, 61505011, 61475022, 61331008); Program 863 (2015AA015503); Program 973 (2014CB340100).
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