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Optical Computing on Silicon-on-Insulator-Based Photonic Integrated Circuits Zheng Zhao1, Zheng Wang2, Zhoufeng Ying1, Shounak Dhar1, Ray T. Chen1; 2, and David Z. Pan1 1Department of Electrical and Computer Engineering, University of Texas at Austin 2Department of Materials Science and Engineering, University of Texas at Austin [email protected], [email protected], [email protected], [email protected], [email protected] [email protected] ABSTRACT ing paradigms, logic functions and matrix multiplication, The advancement of photonic integrated circuits (PICs) both of which can be realized in SOI-based PIC. The ad- brings the possibility to accomplish on-chip optical in- vantages and limitations are also studied. The paper is terconnects and computations. Optical computing, as a concluded in Section4. promising alternative to traditional CMOS computing, has great potential advantages of ultra-high speed and low- 2. OPTICAL COMPUTING COMPONENTS power in information processing and communications. In In this section, we introduce the common SOI-based op- this paper, we survey the current research efforts on opti- tical components that demonstrate computing capabilities cal computing demonstrated on silicon-on-insulator-based as well as their working principles. PICs. The advantages, limitations, and possible research directions for further investigation are discussed. 2.1 Mach-Zehnder Interferometer The Mach-Zehnder interferometer (MZI) is a common 1. INTRODUCTION integrated photonic device used as electro-optic modula- tors and switches. In the 2 × 2 MZI in Figure 1a, the Optical computing is to use optical systems to perform lights from input ports a, b go into a splitter, traveling numerical computations [1]. The idea is to leverage the for some distance, then are combined to the output a0, b0. properties of speed, parallelism and ultra-low power trans- MZI demonstrates constructive/destructive interference in mission of light in order to process information at a high- the combiner depending on the phase difference ∆φ of the data rate. The information can be in the form of an op- two paths and leads to a frequency-dependent response in tical signal sourced by optical lasers and detected by pho- the amplitude of the output. The phase difference can be todetectors. In terms of computing, the advantages of the expressed as ∆φ = 2π/λ · ∆N · L, where λ is the oper- optics include but are not limited to: (1) significant reduc- eff ating wavelength, N is the effective refractive index of tion of signal transfer latency, (2) ultra-low energy con- eff propagating mode of the waveguide, L is the length of the sumption, and (3) simplified layout architecture for many sensitive arm. complex computation structures [2,3]. When the phase ∆φ is set to π such that the combined In the early days of optical computing, research efforts lights have opposite phase difference and there is no light at had focused on free-space optical applications, which in- the output port. If this phase shift ∆φ is controlled by an cludes Fourier transform and pattern recognition [4,5]. electrical signal (by changing N ), the MZI implements However, these implementations require free space as the eff an electrical-optical (EO) switch. medium between transceivers and involve large devices such as lenses, slits or mirrors, which prevent the scaling a Δϕ a’ coupling and integration of free-space applications. region With Moore's law approaching the limits, photonic inte- b Splitter Combiner grated circuits (PICs) have received increasing attention. b’ Among all platforms of PICs, silicon-on-insulator (SOI) is the most promising due to the CMOS-compatible process (a) (b) enabled low-cost and large-volume manufacturing and the Figure 1: (a) Mach-Zehnder Interferometer. (b) 2 × 2 Direc- ability of monolithic integration of electronics and photon- tional coupler. ics. As the footprint of the SOI waveguides and optical de- vices decreases, nanophotonics also promises the scaling for 2.2 Microresonators photonics, similar to the shrinking of CMOS devices [6{9]. Like MZIs, microresonators, such as microrings and mi- Optical logic gates and synthesis have been studied to crodisks can also be used to realize modulation and switch- exploit the aforementioned advantages. Although nonlin- ing. Figure 2a shows a schematic of a typical 2 × 2 micro- ear optical devices that directly use light to control light resonator-based optical switch/modulator using microrings, have not been able to meet the low power goals [10], gen- which has a light input and two outputs: the through out- eral architectures based on binary decision diagram to al- put and drop output. When a continuous wave (CW) light low electrical signals to control light [11, 12] have shown is fed into the switch from the input, part of the light is greater potential. Some recent works have also explored coupled into the microresonator, and then coupled back to the possibility of using optics in specific types of compu- the two bus waveguides with certain phase shifts. This re- tation such as neural networks, graphical models, Ising sults in a wavelength selective behavior shown in the black models, etc [9, 13, 14]. curves of Figure 2b. One could apply an electrical signal This paper surveys the emerging representative develop- to shift the resonance peaks to switch the light, which is ment in optical computing using SOI-based PIC. Section2 illustrated with the red and blue curves. By using both introduces the common SOI-based optical devices used in the through and drop ports of the switch, one can build optical computing. Section3 discusses two optical comput- optical switches controlled by electrical signals. The light passes or terminates depending on the controlling electrical a boolean function is implemented by a VG. While the signal. concept of such virtual gates is worthwhile for functional cascading, the proposed method usually generate a large 1.0 thru (0V) number of optical components, such as VGs and splitters. 0.8 drop (0V) thru (-1V) 0.6 drop (-1V) A straightforward binary decision diagram (BDD)-based λ through thru (1V) 0.4 drop (1V) synthesis method [11] is shown in Figure3. BDD [23] is a Normalized 0.2 transmission widely used data structure for logic synthesis and verifica- 0.0 tion. Each decision node in a BDD has a function of a 1×2 drop 1550 1555 1560 1565 1570 1575 1580 1585 Wavelength(nm) crossbar switch, which is controlled by a decision variable. (a) (b) The switch can be implemented with either MZIs or mi- Figure 2: (a) Schematic diagram of a microresonator (b) 2 × croresonators. In optical synthesis, the 1-terminal node of 1 and 1 × 1 switch notations (c) Optical transmission spectra a BDD is connected to a photo-detector, corresponding to measured at through and drop ports under various bias. a logic 1 of the function evaluation, as shown in Figure 3a. Table1 shows a comparison of EO switches using MZI, As shown in Figure 3c, the light (λ) from a laser source microring and microdisk [15{17]. Compared with MZIs (or from the output of the previous optical network) is used in the previous work, microresonators such as mi- streamed from the BDD top node to the 1-terminal, where crorings and microdisks, have much a smaller footprint. a photo-detector (PD) (or optical amplifier to the next The microresonators are used in microresonator-based op- computation stage) is located. The synthesis replaces each tical switches that could be driven by a CMOS-compatible BDD node by an optical switch (S), some with a termi- voltage (< 1V pp) with much lower energy consumption(< nator at one output (ST), each controlled by an electrical 50fJ=bit). primary input. Waveguides and combiners are used to con- Table 1: Comparison of EO switches. nect the crossbars. When there are multiple inputs to a MZI Microring Microdisk crossbar, optical combiners (CB) are used to merge the in- Footprint ∼ 2000 × 500um2 ∼ 10 × 10um2 ∼ 5 × 5um2 puts. From this configuration, we can see that the output Insertion loss ∼2.2 dB ∼2.8 dB ∼0.9 dB of the optical network is a logical 1, if the PD can detect Extinction ratio ∼4.1 dB ∼6.6 dB ∼7.8 dB some light at the 1-terminal, otherwise it is a logical 0. Energy ∼750 fJ/bit ∼50 fJ/bit ∼1 fJ/bit b f f 1 2.3 Directional Coupler a S 0 a a The directional optical coupler (Figure 1b) is a guided 1 c CB PD λ S 0 wave component for combining/ splitting lights with a con- b b CB ST1 trollable combining/splitting ratio, which is decided by the c c1 c2 1x2 1x1 S ST PD photo- coupling efficiency. Coupling occurs when two waveguides optical optical CB combiner detector are brought within close proximity to each other such that 1 1 switch switch the electromagnetic fields in one waveguide extend over the (a) (b) (c) other waveguide and vice versa, causing energy to cross Figure 3: (a) 1-terminal BDD (b) Combiner elimination (c) over between one waveguide to the other, as a function of BDD-based synthesis [11]. coupling length. The coupling efficiency is adjustable in the range of 0 The limitation of both synthesis works [11, 22] is that to 100% by adjusting the coupling length, which provides they contain a great number of optical splitters or com- further computational capabilities compared with plain Y- biners, each resulting in a 3dB optical power loss, and the branch combiner/splitters. An N × 1 coupler can be ob- loss cascaded inevitably leads to an extremely weak output tained by cascading (N-1) 2×1 couplers, with an arbitrary signal indistinguishable from noises. [12] proposes to mit- coupling efficiency to each input.

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