To scale up programmable photonic circuits, one must overcome challenges of size, power, and robustness to hardware imperfections. Considering linear multiport interferometers as a concrete example, we show how architectural choices can significantly improve the prospects for scalability. First, we review the field of photonic-circuit error correction, and show how 3-splitter MZI (3-MZI) architectures are more robust to errors than standard MZI architectures, even achieving asymptotic fault-tolerance to hardware imperfections. Second, we discuss the problem of economizing phase-shift, which is especially relevant for power-hungry thermo-optic platforms, and show how the 3-MZI architecture can reduce average phase shifts by a factor of 3-10x in near-term systems.
Within the last decade, research and development in the field of silicon microring resonators have been accelerated due to their potential in a wide range of applications. In this study, we experimentally characterize the selfpulsing dynamics in active silicon ring cavities under the effects of varying the optical power, detuning, and free-carrier lifetime. Self-pulsing is measured by coupling a single laser source into the microring resonator’s input port. The light collected from the output grating is fiber coupled and sent to a photodetector, oscilloscope, power meter, and optical spectrum analyzer (OSA) for both time and frequency domain measurement.
Existing photonic matrix processers are too small to tackle relevant problems. Here, I review our group’s recent work on scaling up analog photonic platforms. This work includes iterative advances to old approaches (accurate methods to calibrate MZI meshes), experimental demonstrations of recent proposals (a VCSEL array-based coherent detection ONN and a single-shot ONN based on reconfigurable free-space optical fan-out and weighting), and entirely new architectures (WDM-powered and RF-photonic fiber circuits for edge computing). The lessons learned from studying this diverse array of approaches helps inform the future development of photonic hardware for computation.
We demonstrated a large-scale space-time-multiplexed homodyne optical neural network (ONN) using arrays of high-speed (GHz) vertical-cavity surface-emitting lasers (VCSELs). Injection locking enables precise phase control over tens of VCSEL devices simultaneously, facilitating photoelectric-multiplication-based matrix operations and all-optical nonlinearity, operating at the quantum-noise limit. Our VCSEL transmitters exhibit ultra-high electro-optic conversion efficiency (Vπ=4 mV), allowing neural encoding at 5 attojoule/symbol. Three-dimensional neural connectivity allows parallel computing. The full-system energy efficiency reaches 7 fJ/operation, which is >100-fold better than the state-of-the-art digital microprocessors and other ONN demonstrations. Digit classification is achieved with an accuracy of 98% of the group truth.
We demonstrate both second harmonic generation (with a normalized efficiency of 0.20 %W−1 cm−2 ) and, to our knowledge, the first degenerate χ (2) optical parametric amplifier (with an estimated normalized gain of 0.6 dBW−1/2 cm−1 ) using silicon-on-insulator waveguides fabricated in a CMOS-compatible commercial foundry.
Subwavelength grating (SWG) metamaterial structures are excellent platforms for guided-wave nonlinear optics, but their design and optimization are challenging due to the large number of geometric degrees of freedom and the need for compute-intensive 3D simulations. Here, we demonstrate inverse design of χ(2) SWG waveguides using an efficient and accurate differentiable plane-wave expansion (PWE) eigensolver. Our solver, which incorporates sparse iterative algorithms and subpixel smoothing, enables efficient eigensolution and end-to-end differentiation from geometric parameters to the SWG figure of merit, which depends both on the eigenvalues (first-order perturbation theory) and the eigenvectors and group indices (second-order perturbation theory), both in forward- and reverse-mode. We apply this solver to the design and optimization of metamaterial waveguides for two types of backward SHG: idler-reversed and pump-reversed. This approach may find use in designing periodic structures more generally, including nanobeam cavities, slow-light modulators, and vertically coupled resonators.
Conventional multiport interferometers based on MZI meshes suffer from component imperfections, which limit their scaling. We introduce two new designs that overcome this limitation: a 3-splitter MZI for generic errors and a broadband MZI+Crossing design for more realistic correlated errors. These architectures, motivated by the correspondence between SU(2) and the Riemann sphere, are more error tolerant than the standard MZI mesh and support progressive self-configuration. Numerical simulations reveal orders-of-magnitude error reductions compared to the standard MZI mesh; moreover, the mesh is asymptotically perfect: the matrix error decreases with mesh size.
KEYWORDS: Wavelength division multiplexing, Neural networks, Integrated optics, Modulators, Computer programming, Modulation, Analog electronics, Time-frequency analysis, Signal to noise ratio
We introduce an optical neural-network architecture for edge computing that takes advantage of wavelength multiplexing, high-bandwidth modulation, and integration detection. Our protocol consists of a server and a client, which divide the task of neural-network inference into two steps: (1) a difficult step of optical weight distribution, performed at the server and (2) an easy step of modulation and integration detection, performed at the edge device. This arrangement allows for large-scale neural networks to be run on low-power edge devices accessible by an optical link. We perform simulations to estimate the speed and energy limits of this scheme.
Optical approaches to machine learning rely heavily on programmable linear photonic circuits. Since the performance and energy efficiency scale with size, a major challenge is overcoming scaling roadblocks to the photonic technology. Recently, we proposed an optical neural network architecture based on coherent detection. This architecture has several scaling advantages over competing approaches, including linear (rather than quadratic) chip-area scaling and constant circuit depth. We review the fundamental and technological limits to the energy consumption in this architecture, which shed light on the quantum limits to analog computing, which are distinct from the thermodynamic (e.g. Landauer) limits to digital computing. Lastly, we highlight a recent "digital" implementation of our architecture, which sheds light on the scaling challenges associated with controlling aberrations in the free-space optical propagation.
Storing, processing, and learning from data is a central task in both industrial practice and modern science. Recent advances in modern statistical learning, particularly Deep Neural Networks (DNNs), have given record breaking performance on tasks in game playing,1, 2 natural language processing,3 computer vision,4 computational biology,5, 6 and many others. The rapid growth of the field has been driven by an increase in the amount of public datasets,7 improvements to algorithms,8 and a substantial growth in computing power.9 In order to perform well on these tasks networks have had to grow in size, learning more complicated statistical features. The training and deployment of these large neural networks has spurred the creation of many neural network accelerators to aid in the computation of these networks.10-12
Existing general purpose computing devices such as CPUs and GPUs are limited both by thermal dissipation per unit area and yield associated with large chips.13, 14 The design of Application Specific Integrated circuits (ASICs) has aided in decreasing the energy consumption per workload substantially by limiting the supported operations on chip. An example of this is the first generation tensor processing unit (TPU)15 which is able to perform the inference of large convolutional neural networks in datacenter in <10ms with an idle power of 28W and an workload power of 40W. It may seen counterintuitive then that the limiting factor for the implementation of DNNs is not computation, but rather the energy and bandwidth associated with reading and writing data from memory as well as the energy cost of moving data inside of the ASIC.15, 16 Several emerging technologies, such as in-memory computing,17 memristive crossbar arrays18 promise increased performance, but these emerging architectures suffer from calibration issues and limited accuracy.19
Photonics as a field has had tremendous success in improving the energy efficiency of data interconnects.20 This has motivated the creation of optical neural networks (ONNs) based on 3D-printed diffractive elements,21 spiking neural networks utilizing ring-resonators,22 reservoir computing23 and nanophotonic circuits.24 However, these architectures have several issues. 3D-printed diffractive networks and schemes requiring spatial light modulators are non-programmable, meaning that they are unable to perform the task of training. Nanophotonic circuits allow for an O(N2) array of interferometers to be programmed, providing passive matrix-vector multiplication. However, the large (≈1mm2) size of on chip electro-optic interferometers means that scaling to an array of 100x100 would require 10; 000mm2 of silicon, demonstrating the limitations of scaling this architecture. To date no architecture has demonstrated high-speed (GHz) speed computation with more than N ≥ 10; 000 neurons.
Here we present an architecture that is scalable to N ≥ 106 neurons. The key mechanism of this architecture is balanced homodyne detection. By scaling the architecture to such a large size we show that we can decimate energy costs per operation associated with the optical component of this architecture, reaching a bound set by shot noise on the receiving photodetectors which leads to classification error. We call this bound a standard quantum limit (SQL) which reaches 100zJ/MAC on problems such as MNIST. We also analyze the energy consumption using existing technologies and show that sub-fJ/MAC energy consumption should be possible.
This paper is organized as follows: In section 1 we will discuss the function of this architecture as a matrixmatrix processor. In section 2 we will analyze the energy consumption of the architecture. In section 3 we will discuss methods for training and extending the accelerator to a broader scope of problems, namely convolutionally neural networks (CNNs).
The coherent Ising machine (CIM) is a network of optical parametric oscillators (OPOs) that solves for the ground state of Ising problems through OPO bifurcation dynamics. Here, we present experimental results comparing the performance of the CIM to quantum annealers (QAs) on two classes of NP-hard optimization problems: ground state calculation of the Sherrington-Kirkpatrick (SK) model and MAX-CUT. While the two machines perform comparably on sparsely-connected problems such as cubic MAX-CUT, on problems with dense connectivity, the QA shows an exponential performance penalty relative to CIMs. We attribute this to the embedding overhead required to map dense problems onto the sparse hardware architecture of the QA, a problem that can be overcome in photonic architectures such as the CIM.
KEYWORDS: Sum-frequency generation, Frequency conversion, Current controlled current source, Optical parametric oscillators, Mid-IR, Frequency combs, Femtosecond phenomena, Nonlinear dynamics, Harmonic generation, Femtosecond frequency combs
Half-harmonic generation is the reverse of second harmonic generation that happens in optical parametric oscillators (OPOs) at degeneracy. It is an intrinsically phase-locked down-conversion process, which can be used to efficiently transfer well-developed near-IR frequency combs to the mid-IR.
We overview recent experimental progress in cascading multiple stages of half-harmonic generation of femtosecond frequency combs starting from a 1-μm pump. We have achieved stable operation with efficiencies as high as ~64%, pulses as short as three optical cycles at 4 μm, and output powers as high as 2.6 W at 2 μm. Our recent numerical and analytical studies of nonlinear dynamics and different operation regimes of femtosecond OPOs indicate a path toward achieving even higher efficiencies and shorter pulses.
We theoretically study the nonlinear dynamics of silicon ring cavities with active carrier removal. In this system, linear dispersion, Kerr nonlinearity, two-photon absorption, and free-carrier dispersion / absorption play a key role in the dynamics and the steady-state behavior of the device. Placing the cavity inside a reverse-biased p-i-n junction allows one to reach a regime where both optical bistability and limit-cycle oscillations are accessible. Based on these phenomena, we propose and simulate a free-carrier based random number generator and an "Ising machine", consisting of interconnected ring cavities, which searches for the ground state of the NP-hard Ising XY problem.
We describe a large-scale degenerate optical parametric oscillator (DOPO) network for a coherent Ising machine that solves combinatorial optimization problems. By pumping a fiber-based phase-sensitive amplifier placed in a 1-km fiber cavity at a 2-GHz repetition frequency, we generated more than 10,000 DOPOs multiplexed in the time domain. We confirmed that the DOPO phases were discretized to {0, π} indicating that they could be used as stable artificial spins. We also implemented a one-dimensional Ising model by optically coupling adjacent DOPOs, and confirmed that the DOPOs well simulated the behavior of low-temperature spins.
In this paper, we analytically describe the parametric amplification in ring resonators using silicon and silicon nitride waveguides. Achievable gain and bandwidth of the ring-based amplifiers are studied taking into account the Kerr nonlinearity for silicon nitride and Kerr nonlinearity as well as two photon absorption and free carrier absorption for silicon waveguides. Both telecom and 2-μm wavelengths are investigated in case of silicon. An approach for obtaining the optimum amplifier design without initiating the comb generation has been introduced. It is shown that there is a trade-off between the input pump and amplifier bandwidth. It is estimated that using optimum designs an amplifier with a gain and bandwidth of 10 dB and 10 GHz could be feasible with silicon ring resonators in 2 μm.
Due to their strong light confinement, waveguides with optical nonlinearities may be a promising platform for energy-efficient optical computing. Slow light can enhance a waveguide’s effective nonlinearity, which could result in devices that operate in low-power regimes where quantum fluctuations are important, and may also have quantum applications including squeezing and entanglement generation. In this manuscript, slow-light structures based on the Kerr (χ(3)) nonlinearity are analyzed using a semi-classical model to account for the quantum noise. We develop a hybrid split-step / Runge-Kutta numerical model to compute the mean field and squeezing spectrum for pulses propagating down a waveguide, and use this model to study squeezing produced in optical waveguides. Scaling relations are explored, and the benefits and limitations of slow light are discussed in the context of squeezing.
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