Experimental control of mode-competition dynamics in a chaotic multimode semiconductor laser for decision making.

Photonic computing is widely used to accelerate the computational performance in machine learning. Photonic decision making is a promising approach utilizing photonic computing technologies to solve the multi-armed bandit problems based on reinforcement learning. Photonic decision making using chaotic mode-competition dynamics has been proposed. However, the experimental conditions for achieving a superior decision-making performance have not yet been established. Herein, we experimentally investigate mode-competition dynamics in a chaotic multimode semiconductor laser in the presence of optical feedback and injection. We control the chaotic mode-competition dynamics via optical injection and observe that positive wavelength detuning results in an efficient mode concentration to one of the longitudinal modes with a small optical injection power. We experimentally investigate two-dimensional bifurcation diagram of the total intensity of the laser dynamics. Complex mixed dynamics are observed in the presence of optical feedback and injection. We experimentally conduct decision making to solve the bandit problem using chaotic mode-competition dynamics. A fast mode-concentration property is observed at positive wavelength detunings, resulting in fast convergence of the correct decision rate. Our findings could be useful in accelerating the decision-making performance in adaptive optical networks using reinforcement learning.

Asymmetric leader-laggard cluster synchronization for collective decision-making with laser network.

Photonic accelerators have recently attracted soaring interest, harnessing the ultimate nature of light for information processing. Collective decision-making with a laser network, employing the chaotic and synchronous dynamics of optically interconnected lasers to address the competitive multi-armed bandit (CMAB) problem, is a highly compelling approach due to its scalability and experimental feasibility. We investigated essential network structures for collective decision-making through quantitative stability analysis. Moreover, we demonstrated the asymmetric preferences of players in the CMAB problem, extending its functionality to more practical applications. Our study highlights the capability and significance of machine learning built upon chaotic lasers and photonic devices.

Single-image phase retrieval for off-the-shelf Zernike phase-contrast microscopes.

Quantitative phase imaging (QPI), such as digital holography, is considered a promising tool in the field of life science due to its noninvasive and quantitative visualization capabilities without the need for fluorescence labeling. However, the popularity of QPI systems is limited due to the cost and complexity of their hardware. In contrast, Zernike phase-contrast microscopy (ZPM) has been widely used in practical scenarios but has not been categorized as QPI, owing to halo and shade-off artifacts and the weak phase condition. Here, we present a single-image phase retrieval method for ZPM that addresses these issues without requiring hardware modifications. By employing a rigorous physical model of ZPM and a gradient descent algorithm for its inversion, we achieve single-shot QPI with an off-the-shelf ZPM system. Our approach is validated in simulations and experiments, demonstrating QPI of a polymer microbead and biological cells. The quantitative nature of our method for single-cell imaging is confirmed through comparisons with observations from an established QPI technique conducted through digital holography. This study paves the way for transforming non-QPI ZPM systems into QPI systems.

Computer-generated holography with ordinary display.

We propose a method of computer-generated holography (CGH) using incoherent light emitted from a mobile phone screen. In this method, we suppose a cascade of holograms in which the first hologram is a color image displayed on the mobile phone screen. The hologram cascade is synthesized by solving an inverse problem with respect to the propagation of incoherent light. We demonstrate a three-dimensional color image reproduction using a two-layered hologram cascade composed of an iPhone and a spatial light modulator.

Noninvasive holographic imaging through dynamically scattering media.

We present a noninvasive method for quantitative phase imaging through dynamically scattering media. A complex amplitude object, illuminated with coherent light, is captured through a dynamically scattering medium and a variable coded aperture, without the need for interferometric measurements or imaging optics. The complex amplitude of the object is computationally retrieved from intensity images that use multiple coded aperture patterns, employing a stochastic gradient descent algorithm. We demonstrate the proposed method both numerically and experimentally.

Incoherent diffractive optical elements for extendable field-of-view imaging.

We present a diffractive optics design for incoherent imaging with an extendable field-of-view. In our design method, multiple layers of diffractive optical elements (DOEs) are synthesized so that images on the input plane illuminated with spatially incoherent light are reproduced upright on the output plane. In addition, our method removes the need for an approximation of shift invariance, which has been assumed in conventional optical designs for incoherent imaging systems. Once the DOE cascade is calculated, the field-of-view can be extended by using an array of such DOEs without further calculation. We derive the optical condition to calculate the DOEs and numerically demonstrate the proposed method with the condition.

Double-sided computer-generated holography.

We present a method for computer-generated holography (CGH) in which different images are reproduced on both sides of a hologram with a single illumination source. In the proposed method, we use a transmissive spatial light modulator (SLM) and a half mirror (HM) located downstream of the SLM. The light modulated by the SLM is partially reflected by the HM, and the reflected light is modulated again by the SLM for the double-sided image reproduction. We derive an algorithm for double-sided CGH and experimentally demonstrate it.

Extrapolated speckle-correlation imaging with an untrained deep neural network.

We present a method for speckle-correlation imaging with an extended field of view to observe spatially non-sparse objects. In speckle-correlation imaging, an object is recovered from a non-invasively captured image through a scattering medium by assuming shift-invariance of the optical process called the memory effect. The field of view of speckle-correlation imaging is limited by the size of the memory effect, and it can be extended by extrapolating the speckle correlation in the reconstruction process. However, spatially sparse objects are assumed in the inversion process because of its severe ill-posedness. To address this issue, we introduce a deep image prior, which regularizes the image statistics by using the structure of an untrained convolutional neural network, to speckle-correlation imaging. We experimentally demonstrated the proposed method and showed the possibility of extending the method to imaging through scattering media.

Effect of temporal resolution on the reproduction of chaotic dynamics via reservoir computing.

Reservoir computing is a machine learning paradigm that uses a structure called a reservoir, which has nonlinearities and short-term memory. In recent years, reservoir computing has expanded to new functions such as the autonomous generation of chaotic time series, as well as time series prediction and classification. Furthermore, novel possibilities have been demonstrated, such as inferring the existence of previously unseen attractors. Sampling, in contrast, has a strong influence on such functions. Sampling is indispensable in a physical reservoir computer that uses an existing physical system as a reservoir because the use of an external digital system for the data input is usually inevitable. This study analyzes the effect of sampling on the ability of reservoir computing to autonomously regenerate chaotic time series. We found, as expected, that excessively coarse sampling degrades the system performance, but also that excessively dense sampling is unsuitable. Based on quantitative indicators that capture the local and global characteristics of attractors, we identify a suitable window of the sampling frequency and discuss its underlying mechanisms.

Information-theoretical analysis of statistical measures for multiscale dynamics.

Multiscale entropy (MSE) has been widely used to examine nonlinear systems involving multiple time scales, such as biological and economic systems. Conversely, Allan variance has been used to evaluate the stability of oscillators, such as clocks and lasers, ranging from short to long time scales. Although these two statistical measures were developed independently for different purposes in different fields, their interest lies in examining the multiscale temporal structures of physical phenomena under study. We demonstrate that from an information-theoretical perspective, they share some foundations and exhibit similar tendencies. We experimentally confirmed that similar properties of the MSE and Allan variance can be observed in low-frequency fluctuations (LFF) in chaotic lasers and physiological heartbeat data. Furthermore, we calculated the condition under which this consistency between the MSE and Allan variance exists, which is related to certain conditional probabilities. Heuristically, natural physical systems including the aforementioned LFF and heartbeat data mostly satisfy this condition, and hence, the MSE and Allan variance demonstrate similar properties. As a counterexample, we demonstrate an artificially constructed random sequence, for which the MSE and Allan variance exhibit different trends.

Acceleration of Approximate Matrix Multiplications on GPUs.

Matrix multiplication is important in various information-processing applications, including the computation of eigenvalues and eigenvectors, and in combinatorial optimization algorithms. Therefore, reducing the computation time of matrix products is essential to speed up scientific and practical calculations. Several approaches have been proposed to speed up this process, including GPUs, fast matrix multiplication libraries, custom hardware, and efficient approximate matrix multiplication (AMM) algorithms. However, research to date has yet to focus on accelerating AMMs for general matrices on GPUs, despite the potential of GPUs to perform fast and accurate matrix product calculations. In this paper, we propose a method for improving Monte Carlo AMMs. We also give an analytical solution for the optimal values of the hyperparameters in the proposed method. The proposed method improves the approximation of the matrix product without increasing the computation time compared to the conventional AMMs. It is also designed to work well with parallel operations on GPUs and can be incorporated into various algorithms. Finally, the proposed method is applied to a power method used for eigenvalue computation. We demonstrate that, on an NVIDIA A100 GPU, the computation time can be halved compared to the conventional power method using cuBLAS.

Bandit Algorithm Driven by a Classical Random Walk and a Quantum Walk.

Quantum walks (QWs) have a property that classical random walks (RWs) do not possess-the coexistence of linear spreading and localization-and this property is utilized to implement various kinds of applications. This paper proposes RW- and QW-based algorithms for multi-armed-bandit (MAB) problems. We show that, under some settings, the QW-based model realizes higher performance than the corresponding RW-based one by associating the two operations that make MAB problems difficult-exploration and exploitation-with these two behaviors of QWs.

Pairing Optimization via Statistics: Algebraic Structure in Pairing Problems and Its Application to Performance Enhancement.

Fully pairing all elements of a set while attempting to maximize the total benefit is a combinatorically difficult problem. Such pairing problems naturally appear in various situations in science, technology, economics, and other fields. In our previous study, we proposed an efficient method to infer the underlying compatibilities among the entities, under the constraint that only the total compatibility is observable. Furthermore, by transforming the pairing problem into a traveling salesman problem with a multi-layer architecture, a pairing optimization algorithm was successfully demonstrated to derive a high-total-compatibility pairing. However, there is substantial room for further performance enhancement by further exploiting the underlying mathematical properties. In this study, we prove the existence of algebraic structures in the pairing problem. We transform the initially estimated compatibility information into an equivalent form where the variance of the individual compatibilities is minimized. We then demonstrate that the total compatibility obtained when using the heuristic pairing algorithm on the transformed problem is significantly higher compared to the previous method. With this improved perspective on the pairing problem using fundamental mathematical properties, we can contribute to practical applications such as wireless communications beyond 5G, where efficient pairing is of critical importance. As the pairing problem is a special case of the maximum weighted matching problem, our findings may also have implications for other algorithms on fully connected graphs.

Incoherent computer-generated holography: publisher's note.

This publisher's note contains a correction to Opt. Lett.47, 3844 (2022)10.1364/OL.464454.

Incoherent computer-generated holography.

We present a method for computer-generated holography (CGH) using spatially and temporally incoherent light. The proposed method synthesizes a hologram cascade by solving an inverse problem for the propagation of incoherent light. The spatial incoherence removes speckle noise in CGH, and the temporal incoherence simplifies the optical setup, including the light source. We demonstrate two- and three-dimensional color image reproductions by a two-layer grayscale hologram cascade with a chip-on-board white light-emitting diode.

Compressive propagation with coherence.

In this Letter, we present wave propagation models of spatially partially coherent (or spatially incoherent) light to compress the computational load of forward and back propagations in inverse problems. In our model, partially coherent light is approximated as a set of random or plane wavefronts passing through spatial bandpass filters, which corresponds to an illumination pupil, and each wave coherently propagates onto a sensor plane through object space. We show that our models reduce the number of coherent propagations in inverse problems, which are essential in optical control and sensing, such as computer-generated holography (CGH) and quantitative phase imaging. We verify the proposed models by numerical and experimental demonstrations of CGH incorporating spatially partially coherent light.

Single-shot blind deconvolution with coded aperture.

In this paper, we present a method for single-shot blind deconvolution incorporating a coded aperture (CA). In this method, we utilize the CA, inserted on the pupil plane, as support constraints in blind deconvolution. Not only an object is estimated, but also a point spread function of turbulence from a single captured image by a reconstruction algorithm with CA support. The proposed method is demonstrated by simulation and an experiment in which point sources are recovered under severe turbulence.

Incoherent optical phase conjugation.

Optical phase conjugation is a known technique for optically reproducing an object behind a scattering medium. Here we present digital optical phase conjugation through scattering media with spatially and temporally incoherent light. This enables us to eliminate the inevitable light coherence and the need for interferometric measurement for optical phase conjugation. Moreover, we show a method for suppressing background noise, which is critical in incoherent optical phase conjugation. We numerically and experimentally demonstrate the proposed method with background suppression.

Fast dynamics of low-frequency fluctuations in a quantum-dot laser with optical feedback.

We experimentally investigate the complex dynamics of a multi-mode quantum-dot semiconductor laser with time-delayed optical feedback. We examine a two-dimensional bifurcation diagram of the quantum-dot laser as a comprehensive dynamical map by changing the injection current and feedback strength. We found that the bifurcation diagram contains two different parameter regions of low-frequency fluctuations. The power-dropout dynamics of the low-frequency fluctuations are observed in the sub-GHz region, which is considerably faster than the conventional low-frequency fluctuations in the MHz region. Comparing the dynamics of quantum-dot laser with those of single- and multi-mode quantum-well semiconductor lasers reveals that the fast low-frequency fluctuation dynamics are unique characteristics of quantum-dot lasers with time-delayed optical feedback.

Spectral speckle-correlation imaging.

We present a method for single-shot spectrally resolved imaging through scattering media by using the spectral memory effect of speckles. In our method, a single speckle pattern from a multi-colored object is captured through scattering media with a monochrome image sensor. The color object is recovered by correlation of the captured speckle and a three-dimensional phase retrieval process. The proposed method was experimentally demonstrated by using point sources with different emission spectra located between diffusers. This study paves the way for non-invasive and low-cost spectral imaging through scattering media.