A single shot coherent Ising machine based on a network of injection-locked multicore fiber lasers.

Combinatorial optimization problems over large and complex systems have many applications in social networks, image processing, artificial intelligence, computational biology and a variety of other areas. Finding the optimized solution for such problems in general are usually in non-deterministic polynomial time (NP)-hard complexity class. Some NP-hard problems can be easily mapped to minimizing an Ising energy function. Here, we present an analog all-optical implementation of a coherent Ising machine (CIM) based on a network of injection-locked multicore fiber (MCF) lasers. The Zeeman terms and the mutual couplings appearing in the Ising Hamiltonians are implemented using spatial light modulators (SLMs). As a proof-of-principle, we demonstrate the use of optics to solve several Ising Hamiltonians for up to thirteen nodes. Overall, the average accuracy of the CIM to find the ground state energy was ~90% for 120 trials. The fundamental bottlenecks for the scalability and programmability of the presented CIM are discussed as well.

Nonlinear optical components for all-optical probabilistic graphical model.

The probabilistic graphical models (PGMs) are tools that are used to compute probability distributions over large and complex interacting variables. They have applications in social networks, speech recognition, artificial intelligence, machine learning, and many more areas. Here, we present an all-optical implementation of a PGM through the sum-product message passing algorithm (SPMPA) governed by a wavelength multiplexing architecture. As a proof-of-concept, we demonstrate the use of optics to solve a two node graphical model governed by SPMPA and successfully map the message passing algorithm onto photonics operations. The essential mathematical functions required for this algorithm, including multiplication and division, are implemented using nonlinear optics in thin film materials. The multiplication and division are demonstrated through a logarithm-summation-exponentiation operation and a pump-probe saturation process, respectively. The fundamental bottlenecks for the scalability of the presented scheme are discussed as well.

Detection with polychromatic x-ray pencil beam illumination: information-theoretic bounds.

Non-destructive testing (NDT) by x-ray imaging is commonly used for finding manufacturing defects, cargo inspection, or security screening. These tasks can be regarded as examples of a detection problem where a target is either present or not. Task-specific information (TSI) [J. Opt. Soc. Am. A24, B25 (2007)JOAOD60740-323210.1364/JOSAA.24.000B25; Appl. Opt.47, 4457 (2008)APOPAI0003-693510.1364/AO.47.004457] bounds, an information-theoretic based metric, are presented for a threat detection task. A system using polychromatic x-ray pencil beam object illumination and energy-resolving detectors for both absorption and diffraction measurements is employed for this task. Water and diesel are two liquids chosen as non-threat and threat materials, respectively, for this study. Three different threat class configurations are examined: a homogeneous object with fixed thickness, a homogeneous object with stochastic thickness, and a dual-material object (i.e., representing a target and clutter) with stochastic thickness, where the threat material has a fixed thickness. We find for the threat class composed of a dual-material object that a minimum threat thickness of 4.5 cm is needed to achieve a desired TSI≥0.7 using a joint absorption and diffraction measurement.

Face recognition with non-greedy information-optimal adaptive compressive imaging.

Adaptive compressive measurements can offer significant system performance advantages due to online learning over non-adaptive or static compressive measurements for a variety of applications, such as image formation and target identification. However, such adaptive measurements tend to be sub-optimal due to their greedy design. Here, we propose a non-greedy adaptive compressive measurement design framework and analyze its performance for a face recognition task. While a greedy adaptive design aims to optimize the system performance on the next immediate measurement, a non-greedy adaptive design goes beyond that by strategically maximizing the system performance over all future measurements. Our non-greedy adaptive design pursues a joint optimization of measurement design and photon allocation within a rigorous information-theoretic framework. For a face recognition task, simulation studies demonstrate that the proposed non-greedy adaptive design achieves a nearly two to three fold lower probability of misclassification relative to the greedy adaptive and static designs. The simulation results are validated experimentally on a compressive optical imager testbed.

RF-subcarrier-assisted four-state continuous-variable QKD based on coherent detection.

We theoretically investigate and experimentally demonstrate a RF-assisted four-state continuous-variable quantum key distribution (CV-QKD) system. Classical coherent detection is implemented with a simple digital phase noise cancelation scheme. In the proposed system, there is no need for frequency and phase locking between the quantum signals and the local oscillator laser. Moreover, in principle, there is no residual phase noise, and a mean excess noise of 0.0115 (in shot-noise units) can be acquired experimentally. In addition, the minimum transmittance of 0.45 is reached experimentally for secure transmission with commercial photodetectors, and the maximum secret key rate (SKR) of >12 Mbit/s can be obtained. The proposed RF-assisted CV-QKD system opens the door of incorporating microwave photonics into a CV-QKD system and improving the SKR significantly.

Multiple spatial modes based QKD over marine free-space optical channels in the presence of atmospheric turbulence.

We investigate a multiple spatial modes based quantum key distribution (QKD) scheme that employs multiple independent parallel beams through a marine free-space optical channel over open ocean. This approach provides the potential to increase secret key rate (SKR) linearly with the number of channels. To improve the SKR performance, we describe a back-propagation mode (BPM) method to mitigate the atmospheric turbulence effects. Our simulation results indicate that the secret key rate can be improved significantly by employing the proposed BPM-based multi-channel QKD scheme.

Experimental characterization of a 400 Gbit/s orbital angular momentum multiplexed free-space optical link over 120 m.

We experimentally demonstrate and characterize the performance of a 400-Gbit/s orbital angular momentum (OAM) multiplexed free-space optical link over 120 m on the roof of a building. Four OAM beams, each carrying a 100-Gbit/s quadrature-phase-shift-keyed channel are multiplexed and transmitted. We investigate the influence of channel impairments on the received power, intermodal crosstalk among channels, and system power penalties. Without laser tracking and compensation systems, the measured received power and crosstalk among OAM channels fluctuate by 4.5 dB and 5 dB, respectively, over 180 s. For a beam displacement of 2 mm that corresponds to a pointing error less than 16.7 µrad, the link bit error rates are below the forward error correction threshold of 3.8×10(-3) for all channels. Both experimental and simulation results show that power penalties increase rapidly when the displacement increases.

Capacity of electromagnetic communication modes in a noise-limited optical system.

We present capacity bounds of an optical system that communicates using electromagnetic waves between a transmitter and a receiver. The bounds are investigated in conjunction with a rigorous theory of degrees of freedom (DOF) in the presence of noise. By taking into account the different signal-to-noise ratio (SNR) levels, an optimal number of DOF that provides the maximum capacity is defined. We find that for moderate noise levels, the DOF estimate of the number of active modes is approximately equal to the optimum number of channels obtained by a more rigorous water-filling procedure. On the other hand, for very low- or high-SNR regions, the maximum capacity can be obtained using less or more channels compared to the number of communicating modes given by the DOF theory. In general, the capacity is shown to increase with increasing size of the transmitting and receiving volumes, whereas it decreases with an increase in the separation between volumes. Under the practical channel constraints of noise and finite available power, the capacity upper bound can be estimated by the well-known iterative water-filling solution to determine the optimal power allocation into the subchannels corresponding to the set of singular values when channel state information is known at the transmitter.

Turbulence compensation of an orbital angular momentum and polarization-multiplexed link using a data-carrying beacon on a separate wavelength.

We investigate the sensing of a data-carrying Gaussian beacon on a separate wavelength as a means to provide the information necessary to compensate for the effects of atmospheric turbulence on orbital angular momentum (OAM) and polarization-multiplexed beams in a free-space optical link. The influence of the Gaussian beacon's wavelength on the compensation of the OAM beams at 1560 nm is experimentally studied. It is found that the compensation performance degrades slowly with the increase in the beacon's wavelength offset, in the 1520-1590 nm band, from the OAM beams. Using this scheme, we experimentally demonstrate a 1 Tbit/s OAM and polarization-multiplexed link through emulated dynamic turbulence with a data-carrying beacon at 1550 nm. The experimental results show that the turbulence effects on all 10 data channels, each carrying a 100 Gbit/s signal, are mitigated efficiently, and the power penalties after compensation are below 5.9 dB for all channels. The results of our work might be helpful for the future implementation of a high-capacity OAM, polarization and wavelength-multiplexed free-space optical link that is affected by atmospheric turbulence.

Crosstalk mitigation in a free-space orbital angular momentum multiplexed communication link using 4×4 MIMO equalization.

We demonstrate crosstalk mitigation using 4×4 multiple-input-multiple-output (MIMO) equalization on an orbital angular momentum (OAM) multiplexed free-space data link with heterodyne detection. Four multiplexed OAM beams, each carrying a 20 Gbit/s quadrature phase-shift keying signal, propagate through weak turbulence. The turbulence induces inter-channel crosstalk among each beam and degrades the signal performance. Experimental results demonstrate that with the assistance of MIMO processing, the signal quality and the bit-error-rate (BER) performance can be improved. The power penalty can be reduced by >4 dB at a BER of 3.8×10-3.

Adaptive optics compensation of multiple orbital angular momentum beams propagating through emulated atmospheric turbulence.

We propose an adaptive optics compensation scheme to simultaneously compensate multiple orbital angular momentum (OAM) beams propagating through atmospheric turbulence. A Gaussian beam on one polarization is used to probe the turbulence-induced wavefront distortions and derive the correction pattern for compensating the OAM beams on the orthogonal polarization. By using this scheme, we experimentally demonstrate simultaneous compensation of multiple OAM beams, each carrying a 100 Gbit/s data channel through emulated atmospheric turbulence. The experimental results indicate that the correction pattern obtained from the Gaussian probe beam could be used to simultaneously compensate multiple turbulence-distorted OAM beams with different orders. It is found that the turbulence-induced crosstalk effects on neighboring modes are efficiently reduced by 12.5 dB, and the system power penalty is improved by 11 dB after compensation.

Information optimal compressive sensing: static measurement design.

The compressive sensing paradigm exploits the inherent sparsity/compressibility of signals to reduce the number of measurements required for reliable reconstruction/recovery. In many applications additional prior information beyond signal sparsity, such as structure in sparsity, is available, and current efforts are mainly limited to exploiting that information exclusively in the signal reconstruction problem. In this work, we describe an information-theoretic framework that incorporates the additional prior information as well as appropriate measurement constraints in the design of compressive measurements. Using a Gaussian binomial mixture prior we design and analyze the performance of optimized projections relative to random projections under two specific design constraints and different operating measurement signal-to-noise ratio (SNR) regimes. We find that the information-optimized designs yield significant, in some cases nearly an order of magnitude, improvements in the reconstruction performance with respect to the random projections. These improvements are especially notable in the low measurement SNR regime where the energy-efficient design of optimized projections is most advantageous. In such cases, the optimized projection design departs significantly from random projections in terms of their incoherence with the representation basis. In fact, we find that the maximizing incoherence of projections with the representation basis is not necessarily optimal in the presence of additional prior information and finite measurement noise/error. We also apply the information-optimized projections to the compressive image formation problem for natural scenes, and the improved visual quality of reconstructed images with respect to random projections and other compressive measurement design affirms the overall effectiveness of the information-theoretic design framework.

Space-time compressive imaging.

Compressive imaging systems typically exploit the spatial correlation of the scene to facilitate a lower dimensional measurement relative to a conventional imaging system. In natural time-varying scenes there is a high degree of temporal correlation that may also be exploited to further reduce the number of measurements. In this work we analyze space-time compressive imaging using Karhunen-Loève (KL) projections for the read-noise-limited measurement case. Based on a comprehensive simulation study, we show that a KL-based space-time compressive imager offers higher compression relative to space-only compressive imaging. For a relative noise strength of 10% and reconstruction error of 10%, we find that space-time compressive imaging with 8×8×16 spatiotemporal blocks yields about 292× compression compared to a conventional imager, while space-only compressive imaging provides only 32× compression. Additionally, under high read-noise conditions, a space-time compressive imaging system yields lower reconstruction error than a conventional imaging system due to the multiplexing advantage. We also discuss three electro-optic space-time compressive imaging architecture classes, including charge-domain processing by a smart focal plane array (FPA). Space-time compressive imaging using a smart FPA provides an alternative method to capture the nonredundant portions of time-varying scenes.

Feature-specific difference imaging.

Difference images quantify changes in the object scene over time. In this paper, we use the feature-specific imaging paradigm to present methods for estimating a sequence of difference images from a sequence of compressive measurements of the object scene. Our goal is twofold. First is to design, where possible, the optimal sensing matrix for taking compressive measurements. In scenarios where such sensing matrices are not tractable, we consider plausible candidate sensing matrices that either use the available a priori information or are nonadaptive. Second, we develop closed-form and iterative techniques for estimating the difference images. We specifically look at l(2)- and l(1)-based methods. We show that l(2)-based techniques can directly estimate the difference image from the measurements without first reconstructing the object scene. This direct estimation exploits the spatial and temporal correlations between the object scene at two consecutive time instants. We further develop a method to estimate a generalized difference image from multiple measurements and use it to estimate the sequence of difference images. For l(1)-based estimation, we consider modified forms of the total-variation method and basis pursuit denoising. We also look at a third method that directly exploits the sparsity of the difference image. We present results to show the efficacy of these techniques and discuss the advantages of each.

Information-theoretic analysis of a stimulated-Brillouin-scattering-based slow-light system.

We use an information-theoretic method developed by Neifeld and Lee [J. Opt. Soc. Am. A 25, C31 (2008)] to analyze the performance of a slow-light system. Slow-light is realized in this system via stimulated Brillouin scattering in a 2 km-long, room-temperature, highly nonlinear fiber pumped by a laser whose spectrum is tailored and broadened to 5 GHz. We compute the information throughput (IT), which quantifies the fraction of information transferred from the source to the receiver and the information delay (ID), which quantifies the delay of a data stream at which the information transfer is largest, for a range of experimental parameters. We also measure the eye-opening (EO) and signal-to-noise ratio (SNR) of the transmitted data stream and find that they scale in a similar fashion to the information-theoretic method. Our experimental findings are compared to a model of the slow-light system that accounts for all pertinent noise sources in the system as well as data-pulse distortion due to the filtering effect of the SBS process. The agreement between our observations and the predictions of our model is very good. Furthermore, we compare measurements of the IT for an optimal flattop gain profile and for a Gaussian-shaped gain profile. For a given pump-beam power, we find that the optimal profile gives a 36% larger ID and somewhat higher IT compared to the Gaussian profile. Specifically, the optimal (Gaussian) profile produces a fractional slow-light ID of 0.94 (0.69) and an IT of 0.86 (0.86) at a pump-beam power of 450 mW and a data rate of 2.5 Gbps. Thus, the optimal profile better utilizes the available pump-beam power, which is often a valuable resource in a system design.

Compressive imaging: hybrid measurement basis design.

The inherent redundancy in natural scenes forms the basis of compressive imaging where the number of measurements is less than the dimensionality of the scene. The compressed sensing theory has shown that a purely random measurement basis can yield good reconstructions of sparse objects with relatively few measurements. However, additional prior knowledge about object statistics that is typically available is not exploited in the design of the random basis. In this work, we describe a hybrid measurement basis design that exploits the power spectral density statistics of natural scenes to minimize the reconstruction error by employing an optimal combination of a nonrandom basis and a purely random basis. Using simulation studies, we quantify the reconstruction error improvement achievable with the hybrid basis for a diverse set of natural images. We find that the hybrid basis can reduce the reconstruction error up to 77% or equivalently requires fewer measurements to achieve a desired reconstruction error compared to the purely random basis. It is also robust to varying levels of object sparsity and yields as much as 40% lower reconstruction error compared to the random basis in the presence of measurement noise.

High-fidelity, broadband stimulated-Brillouin-scattering-based slow light using fast noise modulation.

We demonstrate a 5-GHz-broadband tunable slow-light device based on stimulated Brillouin scattering in a standard highly-nonlinear optical fiber pumped by a noise-current-modulated laser beam. The noisemodulation waveform uses an optimized pseudo-random distribution of the laser drive voltage to obtain an optimal flat-topped gain profile, which minimizes the pulse distortion and maximizes pulse delay for a given pump power. In comparison with a previous slow-modulation method, eye-diagram and signal-to-noise ratio (SNR) analysis show that this broadband slow-light technique significantly increases the fidelity of a delayed data sequence, while maintaining the delay performance. A fractional delay of 0.81 with a SNR of 5.2 is achieved at the pump power of 350 mW using a 2-km-long highly nonlinear fiber with the fast noise-modulation method, demonstrating a 50% increase in eye-opening and a 36% increase in SNR in the comparison.

Object reconstruction from adaptive compressive measurements in feature-specific imaging.

Static feature-specific imaging (SFSI), where the measurement basis remains fixed/static during the data measurement process, has been shown to be superior to conventional imaging for reconstruction tasks. Here, we describe an adaptive approach that utilizes past measurements to inform the choice of measurement basis for future measurements in an FSI system, with the goal of maximizing the reconstruction fidelity while employing the fewest measurements. An algorithm to implement this adaptive approach is developed for FSI systems, and the resulting systems are referred to as adaptive FSI (AFSI) systems. A simulation study is used to analyze the performance of the AFSI system for two choices of measurement basis: principal component (PC) and Hadamard. Here, the root mean squared error (RMSE) metric is employed to quantify the reconstruction fidelity. We observe that an AFSI system achieves as much as 30% lower RMSE compared to an SFSI system. The performance improvement of the AFSI systems is verified using an experimental setup employed using a digital micromirror device (DMD) array.

Increased field of view through optical multiplexing.

Traditional approaches to wide field of view (FoV) imager design usually lead to overly complex optics with high optical mass and/or pan-tilt mechanisms that incur significant mechanical/weight penalties, which limit their applications, especially on mobile platforms such as unmanned aerial vehicles (UAVs).We describe a compact wide FoV imager design based on superposition imaging that employs thin film shutters and multiple beamsplitters to reduce system weight and eliminate mechanical pointing. The performance of the superposition wide FoV imager is quantified using a simulation study and is experimentally demonstrated. Here, a threefold increase in the FoV relative to the narrow FoV imaging optics employed imager design is realized. The performance of a superposition wide FoV imager is analyzed relative to a traditional wide FoV imager and we find that it can offer comparable performance.