Optical Signal Processing Research Articles

Custom CMOS Ising Machine Based on Relaxed Burer-Monteiro-Zhang Heuristic

Custom CMOS Ising Machine Based on Relaxed Burer-Monteiro-Zhang Heuristic

Efficient optimization with higher-order ising machines

A prominent approach to solving combinatorial optimization problems on parallel hardware is Ising machines, i.e., hardware implementations of networks of interacting binary spin variables. Most Ising machines leverage second-order interactions although important classes of optimization problems, such as satisfiability problems, map more seamlessly to Ising networks with higher-order interactions. Here, we demonstrate that higher-order Ising machines can solve satisfiability problems more resource-efficiently in terms of the number of spin variables and their connections when compared to traditional second-order Ising machines. Further, our results show on a benchmark dataset of Boolean k-satisfiability problems that higher-order Ising machines implemented with coupled oscillators rapidly find solutions that are better than second-order Ising machines, thus, improving the current state-of-the-art for Ising machines.

A quantum-inspired probabilistic prime factorization based on virtually connected Boltzmann machine and probabilistic annealing

Probabilistic computing has been introduced to operate functional networks using a probabilistic bit (p-bit), broadening the computational abilities in non-deterministic polynomial searching operations. However, previous developments have focused on emulating the operation of quantum computers similarly, implementing every p-bit with large weight-sum matrix multiplication blocks and requiring tens of times more p-bits than semiprime bits. In addition, operations based on a conventional simulated annealing scheme required a large number of sampling operations, which deteriorated the performance of the Ising machines. Here we introduce a prime factorization machine with a virtually connected Boltzmann machine and probabilistic annealing method, which are designed to reduce the hardware complexity and number of sampling operations. From 10-bit to 64-bit prime factorizations were performed, and the machine offers up to 1.2 × 108 times improvement in the number of sampling operations compared with previous factorization machines, with a 22-fold smaller hardware resource.

Effective implementation of text{L}{0}-regularised compressed sensing with chaotic-amplitude-controlled coherent Ising machines

Coherent Ising machine (CIM) is a network of optical parametric oscillators that can solve large-scale combinatorial optimisation problems by finding the ground state of an Ising Hamiltonian. As a practical application of CIM, Aonishi et al., proposed a quantum-classical hybrid system to solve optimisation problems of l_0-regularisation-based compressed sensing. In the hybrid system, the CIM was an open-loop system without an amplitude control feedback loop. In this case, the hybrid system is enhanced by using a closed-loop CIM to achieve chaotic behaviour around the target amplitude, which would enable escaping from local minima in the energy landscape. Both artificial and magnetic resonance image data were used for the testing of our proposed closed-loop system. Compared with the open-loop system, the results of this study demonstrate an improved degree of accuracy and a wider range of effectiveness.

Multivariable Analysis of Nonlinear Optical Loop Mirror Operating Parameters Using Jones Matrices and Three-Dimensional Renderings

Nonlinear optical loop mirrors (NOLMs) are used in modern fiber optic devices and optical communications. In this study, we present numerical analyses of the multiple variables involved in the operation of an NOLM in low- and high-power transmissions. The Jones matrix formalism was used to model linear and circular polarization inputs. We used three-dimensional (3D) plots to identify the characteristics required in the experimental operation of the NOLM. These characteristics, including the critical power, low- and high-power transmission, and dynamic range, depend on parameters such as the fiber loop length, input power, angle of retarder plate, and input polarization. A standard single-mode fiber (SMF-28) with high twist loop lengths of 100, 300, and 500 m and input powers of 0–100 W was simulated. Three-dimensional surface graphics provided a comprehensive view of the NOLM transmission and considerably enhanced the optimal transmission by manipulating adjustable device components including the power and polarization control plates. Optimal transmission facilitates its use in integrating ultrafast pulse generation, optical signal processing, optical communication systems, and photonic integrated circuit applications.

Efficient combinatorial optimization by quantum-inspired parallel annealing in analogue memristor crossbar

Combinatorial optimization problems are prevalent in various fields, but obtaining exact solutions remains challenging due to the combinatorial explosion with increasing problem size. Special-purpose hardware such as Ising machines, particularly memristor-based analog Ising machines, have emerged as promising solutions. However, existing simulate-annealing-based implementations have not fully exploited the inherent parallelism and analog storage/processing features of memristor crossbar arrays. This work proposes a quantum-inspired parallel annealing method that enables full parallelism and improves solution quality, resulting in significant speed and energy improvement when implemented in analog memristor crossbars. We experimentally solved tasks, including unweighted and weighted Max-Cut and traveling salesman problem, using our integrated memristor chip. The quantum-inspired parallel annealing method implemented in memristor-based hardware has demonstrated significant improvements in time- and energy-efficiency compared to previously reported simulated annealing and Ising machine implemented on other technologies. This is because our approach effectively exploits the natural parallelism, analog conductance states, and all-to-all connection provided by memristor technology, promising its potential for solving complex optimization problems with greater efficiency.

Improved error tolerance of programmable photonic integrated circuits for MNIST handwritten digit classification

Programmable photonic integrated circuits (PPICs) can realize linear optical unitary transformation between arbitrary multi-port input and multi-port output for optical computing and signal processing. With the scale increase of PPICs, the accumulation of manufacturing errors will lead to overall performance deviations. A symmetrical Mach-Zehnder interferometer (MZI) circuit with a shorter optical path and lower propagation loss has been proposed recently to replace the traditional asymmetrical MZI circuit. However, no systematic research on the error compensation of symmetrical MZI circuits has been reported yet. In this paper, the error tolerance characteristics of symmetrical MZI circuits and asymmetrical MZI circuits are analyzed and compared in detail. An effective strategy to compensate the 3 dB beam splitter error of a symmetrical MZI circuit is proposed. A deep learning task of the Modified National Institute of Standards and Technology (MNIST) handwritten digit dataset classification was carried out with two hidden layers, which are implemented by rectangular symmetrical MZI circuit structures. The recognition accuracy can be significantly improved with this error compensation method.

Investigating the impact of plasma nitriding on Ti6Al4V surface, structural, and mechanical properties and their simultaneous evaluation via laser opto-ultrasonic dual detection (LOUD) approach

Titanium alloys possess exceptional properties, but due to their poor surface characteristics, several engineering processes have been developed to modify surface properties. Surface modification methodologies such as plasma nitriding exhibit a favourable pathway to improve these properties. This study investigates the impact of plasma nitriding on surface properties and their evaluation via the laser opto-ultrasonic dual detection (LOUD) technique. The scanning electron microscope, X-ray diffraction, and tensile testing results showed that with the increase in nitride plasma power density from 1.42 to 10.0 × 102 W/cm2, a substantial variation in microstructure and phase transformation occurs, eventually refining the grain size, increasing the hardness from 310.83-HV5.0 to 745.50-HV5.0 and elastic modulus (E) from 115.26 to 128.35 GPa, respectively. Furthermore, these characteristics were assessed concurrently through ultrasonic and optical signal processing for LOUD detection. The results of G.S and E from the acoustic attenuation coefficient and longitudinal and shear wave velocities are reliable with the results of conventional optical microscopy and tensile testing with (R2 ≥ 0.996). Meanwhile, the optical spectral data were analyzed to determine the hardness. The results showed that the calibration curve of the intensity ratios (Ti-II/Ti-I) and plasma electron temperature exhibited a linear relationship with hardness (R2 ≥ 0.989), which showed a good approximation.

Light-by-light polarization control using Stimulated Brillouin Scattering with retardance spectrum shaping

The spectral broadening of a nonlinear polarization retarder based on the polarization dependent interactions of Stimulated Brillouin Scattering is proposed and demonstrated. Through phase-to-retardance conversion, it is shown that polarization can not only be controlled in a bandwidth wider than the natural Brillouin response, but it can also be tailored to provide a certain retardance profile. Broadening is achieved through the engineering of Brillouin phase frequency response via feedback pump regulation, unlike previous schemes based on amplitude and time delay control. Retardance broadening from 51 MHz (natural SBS interaction) to 0.9 GHz along with retardance flattening is demonstrated. This technique contributes to expand optical signal processing tools and opens new possibilities in all-optical switching and routing of data signals as well as in the field of microwave photonics.

Power-efficient polarization-insensitive tunable microring filter on a multi-layer Si3N4-on-SOI platform.

We develop and demonstrate a non-duplicate polarization-diversity tunable bandpass optical filter by leveraging the bi-directional transmission of add-drop dual-coupled microring resonators (MRRs) on a multi-layer Si3N4-on-silicon-on-insulator (SOI) platform. By using Euler-bends, we implement compact and low-loss Si3N4 MRRs with an equivalent bending radius of ∼38 µm. Fiber-to-fiber (on-chip) insertion loss of 4.3 dB (1.7 dB) with a low polarization-dependent loss of <0.5 dB and low differential group delay of <2.5 ps is achieved. The extinction ratio is more than 30 dB. The thermo-optic tuning efficiency of the Si3N4 MRRs is improved with a suspended micro-heater design. As a result, a wavelength tuning range of ∼2 nm and a 3-dB bandwidth tuning range of 20 GHz are experimentally demonstrated. The tuning efficiency is 33 pm/mW, which is ∼7.5 times higher than the previous design. This reconfigurable polarization-insensitive filter, with low loss, low cross talk, and high power efficiency, is highly promising for practical applications in optical communication and signal processing.

In-sensor reservoir computing based on optoelectronic synaptic devices

Artificial neural networks built with optoelectronic synaptic devices have been proven to process visual information effectively. However, it takes great latency time and energy consumption, especially facing dynamic visual information, due to the separated optical sensor, memory, and process unit. Reservoir computing (RC) based on optoelectronic synaptic devices provides an in-sensor RC for processing temporal information efficiently. It achieves efficient computation by sensing and processing optical signals directly with optoelectronic synaptic devices. Optoelectronic synaptic devices shine in visual information processing, whose application in visual sensing and processing will provide a viable hardware solution for in-sensor computing. Therefore, the application of optoelectronic synaptic devices in reservoir computing has prompted increasing attention. Herein, for promoting the application of physical reservoir computing (PRC) with optoelectrical synapses in machine vision, synaptic plasticity will be introduced first in this work and then illustrate the basic functions of optoelectronic synapses as well as their application in reservoir computing further, and provide a perspective on PRC with optoelectronic synapses in the final.

Evanescent coupling of nonlinear integrated cavities for all-optical reservoir computing

We consider theoretically a network of evanescently coupled optical microcavities to implement a space-multiplexed optical neural network in an integrated nanophotonic circuit. Nonlinear photonic network integrations based on evanescent coupling ensure a highly dense integration, reducing the chip footprint by several orders of magnitude compared to commonly used designs based on long waveguide connections while allowing the processing of optical signals with bandwidth in a practical range. Different nonlinear effects inherent to such microcavities are studied for realizing an all-optical autonomous computing substrate based on the reservoir computing concept, and their contribution to computing performance is demonstrated. We provide an in-depth analysis of the impact of basic microcavity parameters on the computational metrics of the system, namely, the dimensionality and the consistency. Importantly, we find that differences between frequencies and bandwidths of supermodes formed by the evanescent coupling are the determining factor of the reservoir’s dimensionality and scalability. The network’s dimensionality can be improved with frequency-shifting nonlinear effects such as the Kerr effect, while two-photon absorption has the opposite effect. Finally, we demonstrate in simulation that the proposed reservoir is capable of solving the Mackey–Glass prediction and the optical signal recovery tasks at gigahertz timescale.

Electro-optic tunable optical filter based on long-period waveguide grating in lithium niobate on insulator with absorption ribbons.

We propose an electro-optic tunable optical filter based on sidewall long period waveguide grating (LPWG) in lithium niobate on insolator (LNOI). The operation of our proposed filter is based on the mode coupling, filtering, and absorption achieved, respectively, with two corrugated sidewall LPWGs, a tapered waveguide, and two metal ribbons. Our typical fabricated devices achieved a 16.32-dB rejection band and an EO tuning efficiency of ∼0.344 nm/V. Our proposed LPWG and filter are compact and could be integrated with other LNOI waveguide devices to realize more sophisticated functions for on-chip optical signal processing.

Physics-Inspired Optimization in the QUBO Framework: Key Concepts and Approaches

Quantum computing promises to have a tremendous advantage over its classical counterpart for solving computationally hard problems, yet remains in a relatively early stage for practical applications owing to the limited capabilities of today’s quantum computers. The approach to the special purposes of quantum computers by exploiting the special-purpose physics-inspired or quantum-inspired computers is emerging as a novel alternative to its quantum counterpart in tackling hard problems in high-performance computing. Inspired by physics, the Ising machine — a type of special-purpose computer that implements or emulates physics or quantum effects of the Ising model to speed up finding solutions to optimization problems — has recently become an active research area in the field of combinatorial optimization. This paper is to address the key enabling software and hardware technology underlying physics-inspired optimization using Ising machines in the unified quadratic unconstrained binary optimization (QUBO) framework for modeling and solving computationally hard combinatorial optimization problems, and with an aim to shed some light on the challenges and opportunities associated with the ever-growing landscape of this novel high-performance computing.

A spinwave Ising machine

Time-multiplexed Coherent Ising Machines (CIMs) have demonstrated promising results in rapidly solving large-scale combinatorial problems. However, CIMs remain relatively large and power-demanding. Here, we demonstrate a spinwave-based Ising machine (SWIM) that due to the low spinwave group velocity allows for sufficient miniaturization and reduced power consumption. The SWIM is implemented using a 10-mm-long 5-μm-thick Yttrium Iron Garnet film with off-the-shelf microwave components and can support an 8-spin MAX-CUT problem and solve it in less than 4 μs consuming only 7 μJ. As the SWIM minimizes its energy, we observe that the spin states can demonstrate both uniform and domain-propagation-like switching. The developed SWIM has the potential for substantial further miniaturization with reduction of power consumption, scalability in the number of supported spins, increase of operational speed, and may become a versatile platform for commercially feasible high-performance solvers of combinatorial optimization problems.

High Q-factor reconfigurable microresonators induced in side-coupled optical fibres

High Q-factor monolithic optical microresonators found numerous applications in classical and quantum optical signal processing, microwave photonics, ultraprecise sensing, as well as fundamental optical and physical sciences. However, due to the solid structure of these microresonators, attaining the free spectral range tunability of most of them, critical for several of these applications, was, so far, unfeasible. To address this problem, here we experimentally demonstrate that the side-coupling of coplanar bent optical fibres can induce a high Q-factor whispering gallery mode optical microresonator. By changing the curvature radius of fibres from the centimetre order to the millimetre order, we demonstrate fully mechanically reconfigurable optical microresonators with dimensions varying from the millimetre order to 100-micron order and free spectral range varying from a picometre to ten picometre order. The developed theory describes the formation of the discovered microresonators and their major properties in a reasonable agreement with the experimental data. The new microresonators may find applications in cavity QED, microresonator optomechanics, frequency comb generation with tuneable repetition rate, tuneable lasing, and tuneable processing and delay of optical pulses.

A Novel Silicon Forward-Biased PIN Mach-Zehnder Modulator with Two Operating States.

In this paper, we demonstrate a silicon forward-biased positive intrinsic negative (PIN) Mach-Zehnder modulator (MZM), which has two operating states of high efficiency and high speed. The two operating states are switched by changing the position where the electric signal is loaded. The modulator incorporates a PIN phase shifter integrated with the passive resistance and capacitance (RC) equalizer (PIN-RC), which expands the electro-optic (E-O) bandwidth by equalizing it with modulation efficiency. The fabricated modulator exhibits a low insertion loss of 1.29 dB in two operating states and a compact design with a phase shifter length of 500 μm. The modulation efficiencies are 0.0088 V·cm and 1.43 V·cm, and the corresponding 3 dB E-O bandwidths are 200 MHz and 7 GHz, respectively. The high-speed modulation performance of the modulator is confirmed by non-return-to-zero (NRZ) modulation with a data rate of 15 Gbps without any pre-emphasis or post-processing. The presented modulator shows functional flexibility, low insertion loss, and a compact footprint, and it can be suitable for applications like optical switch arrays and analog signal processing.

On-chip optical matrix-vector multiplier based on mode division multiplexing

A matrix-vector multiplication (MVM) optical signal processor based on mode division multiplexing (MDM) was proposed and demonstrated in the current work, which is composed of a mode multiplexer, a multimode beam splitter, a mode demultiplexer, a modulator array and combiners. In addition, the characteristics of MDM obviate the need for multiple wavelengths and therefore multiple laser light sources are unneeded, which greatly reduces the complexity and cost. A 4 × 4 MDM-MVM was realized on a standard silicon-on-insulator (SOI) platform. Combined with the off-chip light source and photodetectors (PDs), 4-level modulation has been demonstrated, and each level of the output signal could represent 2 bits of information.

Engineering the electro-optic effect in HfO2 and ZrO2 through strain and polarization control

The ability to control the optical properties of a material with an electric field has led to optical memory devices, communication systems, optical signal processing, or quantum cryptography. Understanding electro-optic effects, especially in thin films, would improve the efficiency of these applications. In particular, the influence of epitaxial strains is of prime importance. In addition, the active control of these effects would be of great interest to tailor the material to the desired performance. Here, we demonstrate through first-principle calculations that the linear electro-optic response (Pockels effect) of two silicon-compatible ferroelectrics is stable with respect to bi-axial strain and that the electro-optic response can be strongly enhanced through the electrical control of the polarization. We attribute the former to the lack of optical phonon softening and a weak elasto-optic response and the latter to the externally induced softening of a phonon of symmetry A1. Our results are readily applicable to other polar materials and show that the electro-optic effect can be efficiently engineered to meet the performance criteria of future technologies.

Low-Rank Combinatorial Optimization and Statistical Learning by Spatial Photonic Ising Machine.

The spatial photonic Ising machine (SPIM) [13D. Pierangeli et al., Large-Scale Photonic Ising Machine by Spatial Light Modulation, Phys. Rev. Lett. 122, 213902 (2019).PRLTAO0031-900710.1103/PhysRevLett.122.213902] is a promising optical architecture utilizing spatial light modulation for solving large-scale combinatorial optimization problems efficiently. The primitive version of the SPIM, however, can accommodate Ising problems with only rank-one interaction matrices. In this Letter, we propose a new computing model for the SPIM that can accommodate any Ising problem without changing its optical implementation. The proposed model is particularly efficient for Ising problems with low-rank interaction matrices, such as knapsack problems. Moreover, it acquires the learning ability of Boltzmann machines. We demonstrate that learning, classification, and sampling of the MNIST handwritten digit images are achieved efficiently using the model with low-rank interactions. Thus, the proposed model exhibits higher practical applicability to various problems of combinatorial optimization and statistical learning, without losing the scalability inherent in the SPIM architecture.