Ising machines are novel computing devices for the energy minimization of Ising models. These combinatorial optimization problems are of paramount importance for science and technology, but remain difficult to tackle on large scale by conventional electronics. Recently, various photonics-based Ising machines demonstrated ultra-fast computing of Ising ground state by data processing through multiple temporal or spatial optical channels. Experimental noise acts as a detrimental effect in many of these devices. On the contrary, we here demonstrate that an optimal noise level enhances the performance of spatial-photonic Ising machines on frustrated spin problems. By controlling the error rate at the detection, we introduce a noisy-feedback mechanism in an Ising machine based on spatial light modulation. We investigate the device performance on systems with hundreds of individually-addressable spins with all-to-all couplings and we found an increased success probability at a specific noise level. The optimal noise amplitude depends on graph properties and size, thus indicating an additional tunable parameter helpful in exploring complex energy landscapes and in avoiding trapping into local minima. The result points out noise as a resource for optical computing. This concept, which also holds in different nanophotonic neural networks, may be crucial in developing novel hardware with optics-enabled parallel architecture for large-scale optimizations.
Combinatorial optimization problems are crucial for widespread applications but remain difficult to solve on a large scale with conventional hardware. Novel optical platforms, known as coherent or photonic Ising machines, are attracting considerable attention as accelerators on optimization tasks formulable as Ising models. Annealing is a well-known technique based on adiabatic evolution for finding optimal solutions in classical and quantum systems made by atoms, electrons, or photons. Although various Ising machines employ annealing in some form, adiabatic computing on optical settings has b…
Recently, spatial photonic Ising machines (SPIM) have been demonstrated to compute the minima of Hamiltonians for large-scale spin systems. Here we propose to implement an antiferromagnetic model through optoelectronic correlation computing with SPIM. Also we exploit the gauge transformation which enables encoding the spins and the interaction strengths in a single phase-only spatial light modulator. With a simple setup, we experimentally show the ground state search of an antiferromagnetic model with $40000$ spins in number-partitioning problem. Thus such an optoelectronic computing exhibits …
Statistical spin dynamics plays a key role to understand the working principle for novel optical Ising machines. Here we propose the gauge transformations for spatial photonic Ising machine, where a single spatial phase modulator simultaneously encodes spin configurations and programs interaction strengths. Thanks to gauge transformation, we experimentally evaluate the phase diagram of high-dimensional spin-glass equilibrium system with $100$ fully-connected spins. We observe the presence of paramagnetic, ferromagnetic as well as spin-glass phases and determine the critical temperature $T_c$ a…
Ising machines based on analog systems have the potential of acceleration in solving ubiquitous combinatorial optimization problems. Although some artificial spins to support large-scale Ising machine is reported, e.g. superconducting qubits in quantum annealers and short optical pulses in coherent Ising machines, the spin coherence is fragile due to the ultra-low equivalent temperature or optical phase sensitivity. In this paper, we propose to use short microwave pulses generated from an optoelectronic parametric oscillator as the spins to implement the Ising machine with large scale and also…
The mining in physics and biology for accelerating the hardcore algorithm to solve non-deterministic polynomial (NP) hard problems has inspired a great amount of special-purpose ma-chine models. Ising machine has become an efficient solver for various combinatorial optimizationproblems. As a computing accelerator, large-scale photonic spatial Ising machine have great advan-tages and potentials due to excellent scalability and compact system. However, current fundamentallimitation of photonic spatial Ising machine is the configuration flexibility of problem implementationin the accelerator mode…
Precision Hamiltonian Encoding in Full-Aperture Spatial Photonic Ising Machines
Westlake University（西湖大学）；FORTH-QuTech；University of Crete（克里特大学）；Sapienza University（罗马第一大学）；Institute for Complex Systems, National Research Council (ISC-CNR)（国家研究委员会复杂系统研究所）；QUBITECH；University of Cambridge（剑桥大学）
Incorporating rank-free coupling and external field via an incoherent modulated spatial photonic Ising machine
State Key Laboratory of Photonics and Communications（光子与通信国家重点实验室）；Institute for Quantum Sensing and Information Processing（量子传感与信息处理研究所）；Shanghai Jiao Tong University（上海交通大学）；Hefei National Laboratory（合肥国家实验室）；Shanghai Research Center for Quantum Sciences（上海量子科学研究中心）
Quantum and classical physics can be used for mathematical computations that are hard to tackle by conventional electronics. Very recently, optical Ising machines have been demonstrated for computing the minima of spin Hamiltonians, paving the way to new ultra-fast hardware for machine learning. However, the proposed systems are either tricky to scale or involve a limited number of spins. We design and experimentally demonstrate a large-scale optical Ising machine based on a simple setup with a spatial light modulator. By encoding the spin variables in a binary phase modulation of the field, w…
Conventional computing architectures have no known efficient algorithms for combinatorial optimization tasks, which are encountered in fundamental areas and real-world practical problems including logistics, social networks, and cryptography. Physical machines have recently been proposed and implemented as an alternative to conventional exact and heuristic solvers for the Ising problem, one such optimization task that requires finding the ground state spin configuration of an arbitrary Ising graph. However, these physical approaches usually suffer from decreased ground state convergence probab…
The inability of conventional electronic architectures to efficiently solve large combinatorial problems motivates the development of novel computational hardware. There has been much effort recently toward developing novel, application-specific hardware, across many different fields of engineering, such as integrated circuits, memristors, and photonics. However, unleashing the true potential of such novel architectures requires the development of featured algorithms which optimally exploit their fundamental properties. We here present the Photonic Recurrent Ising Sampler (PRIS), a heuristic m…
We evaluate the performance of different algorithms in minimizing the Hamiltonian of a spatial-photonic Ising machine (SPIM). We then encode the number-partitioning problem on the SPIM and adiabatically arrive at good solutions for the problem for over 16000 spins, with a time complexity that only scales linearly with problem size. Finally, we benchmark our machine performance against the classical solver, Gurobi, and also a D-Wave 5000+ quantum annealer. With just one spatial light modulator, and and adiabatic evolution scheme for the phase, our results surpass current state-of-the-art SPIMs.…
Optical Implementation of Equilibrium Propagation Using Spatial Photonic Ising Machines
Laboratoire d’Information Quantique, Université Libre de Bruxelles (ULB)（量子信息实验室，布鲁塞尔自由大学）；Dipartimento di Fisica, Sapienza Università di Roma（物理学系，萨皮恩扎罗马大学）
Accelerating ground state search of spatial photonic Ising machines with genetic-simulated annealing hybrid algorithm
Institute for Quantum Sensing and Information Processing（量子传感与信息处理研究所）；State Key Laboratory of Photonics and Communications（光子与通信国家重点实验室）；Global College（全球学院）；Shanghai Research Center for Quantum Sciences（上海量子科学研究中心）；Hefei National Laboratory（合肥国家实验室）；Shanghai Quantum Intelligence Sensing Technology Co., Ltd（上海量子智能感知技术有限公司）
Efficient Computation Using Spatial-Photonic Ising Machines: Utilizing Low-Rank and Circulant Matrix Constraints
University of Cambridge（剑桥大学）；Weizmann Institute of Science（魏茨曼科学研究所）；QUBITECH（QUBITECH公司）；UBITECH ltd（UBITECH有限公司）；University Sapienza（萨皮恩扎大学）；Research Center Enrico Fermi（恩里科·费米研究中心）；Institute for Complex Systems, National Research Council (ISC-CNR)（国家研究委员会复杂系统研究所）
The need for solving optimization problems is prevalent in a wide range of physical applications, including neuroscience, network design, biological systems, socio-economics, and chemical reactions. Many of these are classified as non-deterministic polynomial-time (NP) hard and thus become intractable to solve as the system scales to a large number of elements. Recent research advances in photonics have sparked interest in using a network of coupled degenerate optical parametric oscillators (DOPO's) to effectively find the ground state of the Ising Hamiltonian, which can be used to solve other…
We demonstrate a two-dimensional photonic hypercrystal that shows enhanced spontaneous emission from its metamaterial component and light extraction through its photonic crystal property. Spontaneous decay rate is enhanced by a factor of 19.5 and light extraction from the HMM is enhanced by a factor of ~100.
Periodic or gradient subwavelength structures are basic configurations of photonic crystals and metamaterials. While the numerical simulations predict trivial loss, but the fabricated photonic crystal waveguides by E-beam lithography and standard dry etching shows unacceptable loss beyond 10 dB. Nanofabrication variation introduced geometric inhomogeneity is considered as the primary cause of the deleterious performance. The deep UV photolithography in CMOS foundry is a large-scale parallel processing, which can significantly suppress the fabrication-related inhomogeneous offsets and thus the …
Electro-optic signal modulation provides a key functionality in modern technology and information networks. Photonic integration has enabled not only miniaturizing photonic components, but also provided performance improvements due to co-design addressing both electrical and optical device rules. However, the millimeter-to-centimeter large footprint of many foundry-ready photonic electro-optic modulators significantly limits on-chip scaling density. To address these limitations, here we experimentally demonstrate a coupling-enhanced electro-absorption modulator by heterogeneously integrating a…
We report on the experimental observation of the beaming effect in photonic crystals enhanced via surface modes. We experimentally map the spatial field distribution of energy emitted from a subwavelength photonic crystal waveguide into free-space, rendering with crisp clarity the diffractionless beaming of energy. Our experimental data agree well with our numerical studies of the beaming enhancement in photonic crystals with modulated surfaces. Without loss of generality, we study the beaming effect in a photonic crystal scaled to microwave frequencies and demonstrate the technological capaci…
We reveal that slow-light enhanced optical forces between side-coupled photonic-crystal nanowire waveguides can be flexibly controlled by introducing a relative longitudinal shift. We predict that close to the photonic band-edge, where the group velocity is reduced, the transverse force can be tuned from repulse to attractive, and the force is suppressed for a particular shift value. Additionally the shift leads to symmetry breaking that can facilitate longitudinal forces acting on the waveguides, in contrast to unshifted structures where such forces vanish.
Slow-light enhanced optical detection in liquid-infiltrated photonic crystals is theoretically studied. Using a scattering-matrix approach and the Wigner-Smith delay time concept, we show that optical absorbance benefits both from slow-light phenomena as well as a high filling factor of the energy residing in the liquid. Utilizing strongly dispersive photonic crystal structures, we numerically demonstrate how liquid-infiltrated photonic crystals facilitate enhanced light-matter interactions, by potentially up to an order of magnitude. The proposed concept provides strong opportunities for impr…
We present a general framework for the design of thin-film photovoltaics based on a partially-disordered photonic crystal that has both enhanced absorption for light trapping and reduced sensitivity to the angle and polarization of incident radiation. The absorption characteristics of different lattice structures are investigated as an initial periodic structure is gradually perturbed. We find that an optimal amount of disorder controllably introduced into a multi-lattice photonic crystal causes the characteristic narrow-band, resonant peaks to be broadened resulting in a device with enhanced …
We demonstrate the generation of quantum-correlated photon pairs from a Si photonic-crystal coupled-resonator optical waveguide. A slow-light supermode realized by the collective resonance of high-Q and small-mode-volume photonic-crystal cavities successfully enhanced the efficiency of the spontaneous four-wave mixing process. The generation rate of photon pairs was improved by two orders of magnitude compared with that of a photonic-crystal line defect waveguide without a slow-light effect.
The unique properties of the emerging photonic materials - conducting nitrides and oxides - especially their tailorability, large damage thresholds, and the so-called epsilon-near-zero (ENZ) behavior, have enabled novel photonic phenomena spanning optical circuitry, tunable metasurfaces, and nonlinear optical devices. This work explores direct control of the optical properties of polycrystalline titanium nitride (TiN) and aluminum-doped zinc oxide (AZO) by tailoring the film thickness, and their potential for ENZ-enhanced photonic applications. We demonstrate that TiN-AZO bilayers act as Ferre…
We theoretically analyse photonic-plasmonic coupling between a high Q whispering gallery mode (WGM) resonator and a core-shell nanoparticle. Blue and red shifts of WGM resonances are shown to arise from crossing of the photonic and plasmonic modes. Level repulsion in the hybrid system is further seen to enable sensitivity enhancements in WGM sensors: maximal when the two resonators are detuned by half the plasmon linewidth. Approximate bounds are given to quantify possible enhancements. Criteria for reactive vs. resistive coupling are also established.
Since thin-film silicon solar cells have limited optical absorption, we explore the effect of a nanostructured back reflector to recycle the unabsorbed light. As a back reflector we investigate a 3D photonic band gap crystal made from silicon that is readily integrated with the thin films. We numerically obtain the optical properties by solving the 3D time-harmonic Maxwell equations using the finite-element method, and model silicon with experimentally determined optical constants. The absorption enhancement relevant for photovoltaics is obtained by weighting the absorption spectra with the AM…
We demonstrate a new mode of operation for the Time Stretched A/D converter. The technique is superior to the sampling scope in that it permits the capture of non periodic events such as clustered noise.
Plasmonic nanoparticles (NPs) hold tremendous promise for catalyzing light-driven chemical reactions. The conventionally assumed detrimental absorption loss from plasmon damping can now be harvested to drive chemical transformations of the NP adsorbent, through the excitation and transfer of energetic "hot" carriers. The rate and selectivity of plasmonic photocatalysis are dependent on the characteristics of the incident light. By engineering the strength and wavelength of the light harvesting of a NP, it is possible to achieve more efficient and predictive photocatalysts. We report a plasmoni…
Because of surface structural constraint and thermal management requirement, visible - infrared compatible camouflage is still a great challenge. In this study, we introduce a 2D periodic aperture array into ZnO/Ag/ZnO film to realize visible-infrared compatible camouflage with a performance of thermal management by utilizing the extraordinary optical transmission in a dielectric/metal/dielectric (D/M/D) structure. Because of the high visible transmittance of the D/M/D structure, when applied on a visible camouflage coating, the beneath coating can be observed, realizing arbitrary visible camo…
A coherent coupling among different energy photons provided by nonlinear optical interaction is regarded as a photonic version of the Rabi oscillation. Cavity enhancement of the nonlinearity reduces energy requirement significantly and pushes the scalability of the frequency-encoded photonic circuit based on the photonic Rabi oscillation. However, confinement of the photons in the cavity severely limits the number of interactable frequency modes. Here we demonstrate a wide-bandwidth and efficient photonic Rabi oscillation achieving full-cycle oscillation based on a cavity-enhanced nonlinear op…
We present the use of linearly down-tapered gas-filled hollow-core photonic crystal fiber in a single-stage, pumped with pulses from a compact infrared laser source, to generate a supercontinuum carrying significant spectral power in the deep ultraviolet (200 - 300 nm). The generated supercontinuum extends from the near infrared down to around 213 nm with up to 0.83 mW/nm in the deep ultraviolet.
We investigate for the first time the enhancement of the stimulated Raman scattering in slow-light Silicon-on-Insulator (SOI) photonic crystal line defect waveguides. By applying the Bloch-Floquet formalism to the guided modes in a planar photonic crystal, we develop a formalism that relates the intensity of the down-shifted Stokes signal to the pump intensity and the modal group velocities. The formalism is then applied to two prospective schemes for enhanced stimulated Raman generation in slow-light photonic crystal waveguides. The results demonstrate a maximum factor of 10^4 (66,000) enhanc…
We study the configuration of efficient nonlinear Cerenkov diffraction generated from a one-dimensional nonlinear photonic crystal surface, which underlies the incorporation of both quasi-phase-matching and total internal reflection by the crystal surface. Multidirectional radiation spots with different Cerenkov angles are demonstrated experimentally, which results from different orders of reciprocal vectors. At specific angles, the incident light and total internal reflect light associating with quasi-phase-matching format completely phase-matching scheme, leading to great enhancement of harm…
Slow light is a fascinating physical effect, raising fundamental questions related to our understanding of light-matter interactions as well as offering new possibilities for photonic devices. From the first demonstrations of slow light propagation in ultra-cold atomic gasses, solid-state Ruby and photonic crystal structures, focus has shifted to applications, with slow light offering the ability to enhance and control light-matter interactions. The demonstration of tuneable delay lines, enhanced nonlinearities and spontaneous emission, enlarged spectral sensitivity and increased phase shifts …
Nano-resonator integrated with two-dimensional materials (e.g. transition metal dichalcogenides) have recently emerged as a promising nano-optoelectronic platform. Here we demonstrate resonatorenhanced second-harmonic generation (SHG) in tungsten diselenide using a silicon photonic crystal cavity. By pumping the device with the ultrafast laser pulses near the cavity mode at the telecommunication wavelength, we observe a near visible SHG with a narrow linewidth and near unity linear polarization, originated from the coupling of the pump photon to the cavity mode. The observed SHG is enhanced by…
Multimode hollow microcavities in three-dimensional (3D) photonic crystals (PhCs) are designed for achieving enhanced coherent anti-Stokes Raman scattering, which requires a cavity to have three high quality-factor (Q) modes with equally spaced resonant frequencies. Cavities in 3D PhCs allows more flexibility in design and tuning than their 2D slab counterparts, since radiation loss that degrades Q can be suppressed by the 3D photonic band gap. We first tune all the mode frequencies simultaneously by changing the material and geometry of the cavity based on perturbation theory. Spectral spacin…
We theoretically and experimentally investigate the optical absorption properties of heterostructures composed of graphene films and truncated photonic crystals (PCs) in the visible range. The experimental results show that the absorption of the heterostructure is enhanced greatly in the whole forbidden gap of PCs compared with that of graphene alone. The absorption is enhanced over a wide angle of incidence for both transverse electric (TE) and transverse magnetic (TM) polarizations. The enhanced absorption band broadens for TE polarization but narrows for TM polarization as the incident angl…
Systems with coupled cavities and waveguides have been demonstrated as optical switches and optical sensors. To optimize the functionalities of these optical devices, Fano resonance with asymmetric and steep spectral line shape has been used. We theoretically propose a coupled photonic crystal cavity-waveguide structure to achieve Fano resonance by placing partially reflecting elements in waveguide. To enhance Fano resonance, optical gain material is introduced into the cavity. As the gain increases, the transmission line shape becomes steepened and the transmissivity can be six times enhanced…
The iso-frequency contours of a photonic crystal are important for predicting and understanding exotic optical phenomena that are not apparent from high-symmetry band structure visualizations. Here, we demonstrate a method to directly visualize the iso-frequency contours of high-quality photonic crystal slabs that shows quantitatively good agreement with numerical results throughout the visible spectrum. Our technique relies on resonance-enhanced photon scattering from generic fabrication disorder and surface roughness, so it can be applied to general photonic and plasmonic crystals, or even q…
