Search

Imaging polarimetry plays an essential role in various fields since it imparts rich information that cannot be obtained through mere intensity and spectral measurements. To retrieve full Stokes parameters, at least four sensor pixels are required, each of which projects incident light to a different polarization state in the Stokes space. Conventional full-Stokes division-of-focal-plane (DoFP) cameras realize this function by integrating angled polarizers and retarders on top of image sensors. Due to the inevitable absorption at the polarizers, however, the maximum efficiency of these schemes is limited to 50% in theory. Instead of polarizers, three sets of lossless polarization beam splitters can be used to achieve higher-efficiency polarimetry, however, at the cost of reduced spatial resolution due to the need for six redundant sensor pixels. In this paper, we reveal, for the first time to our knowledge, that low-loss four-output polarization splitting (without filtering) is possible using a single-layer dielectric metasurface. Although these four states are not orthogonal to each other, our metasurface enables simultaneous sorting and focusing onto four sensor pixels with an efficiency exceeding 50\%, which is not feasible by a simple combination of space-optic components. The designed metasurface composed of silicon nanoposts is fabricated to experimentally demonstrate complete retrieval of full Stokes parameters at the near-infrared wavelength range from 1500 to 1600 nm with $-$2.28-dB efficiency. Finally, simple imaging polarimetry is demonstrated using a 3$\times$4 superpixel array.

We show that two independent elephant random walks on the integer lattice $\mathbb{Z}$ meet each other finitely often or infinitely often depends on whether the memory parameter $p$ is strictly larger than $3/4$ or not. Asymptotic results for the distance between them are also obtained., Comment: 4 pages

Gut and Stadm\"{u}ller (2021, 2022) initiated the study of the elephant random walk with limited memory. Aguech and El Machkouri (2024) published a paper in which they discuss an extension of results by Gut and Stadtm\"{u}ller (2022) for an "increasing memory" version of the elephant random walk without stops. Here we present a formal definition of the process which has been hinted at Eq. (2.2) in Gut and Stadtm\"{u}ller (2022). This definition is based on the triangular array setting. We give a positive answer to the open problem in Gut and Stadtm\"{u}ller (2022) for the elephant random walk, possibly with stops. We also obtain the CLT for the supercritical case of this model., Comment: 13 pages

In this paper, we propose a method for estimating the algebraic Riccati equation (ARE) with respect to an unknown discrete-time system from the system state and input observation. The inverse optimal control (IOC) problem asks, ``What objective function is optimized by a given control system?'' The inverse linear quadratic regulator (ILQR) problem is an IOC problem that assumes a linear system and quadratic objective function. The ILQR problem can be solved by solving a linear matrix inequality that contains the ARE. However, the system model is required to obtain the ARE, and it is often unknown in fields in which the IOC problem occurs, for example, biological system analysis. Our method directly estimates the ARE from the observation data without identifying the system. This feature enables us to economize the observation data using prior information about the objective function. We provide a data condition that is sufficient for our method to estimate the ARE. We conducted a numerical experiment to demonstrate that our method can estimate the ARE with less data than system identification if the prior information is sufficient.

For the standard elephant random walk, Laulin (2022) studied the case when the increment of the random walk is not uniformly distributed over the past history instead has a power law distribution. We study such a problem for the unidirectional elephant random walk introduced by Harbola, Kumar and Lindenberg (2014). Depending on the memory parameter $p$ and the power law exponent $\beta$, we obtain three distinct phases in one such phase the elephant travels only a finite distance almost surely, and the other two phases are distinguished by the speed at which the elephant travels., Comment: 18 pages

A vectorial optical mode converter that can transform an orthogonal set of multiple input vector beams into another orthogonal set of vector beams is attractive for a wide range of applications in optics and photonics. While multi-plane light conversion (MPLC) and metasurface (MS) technologies have been explored to individually address multiple spatial mode conversion and polarization mode manipulation, there has been no universal methodology to simultaneously convert a set of multiple vectorial modes, having non-uniform spatial distributions in both their complex amplitude and polarization, to another set of multiple vectorial modes. In this paper, we demonstrate versatile devices based on the MPLC concept incorporating multi-layer locally birefringent MSs and present a general design formalism for complete vectorial mode conversion in arbitrary cases. The effectiveness of our proposed method is confirmed experimentally by demonstrating a 6-mode (3 spatial modes $\times$ 2 polarization modes) multiplexer, fabricated on a compact chip with a ~0.65 mm$^2$ lateral size in a folded MS configuration. Additionally, we verify its applicability to more advanced functional devices through numerical demonstration of a mode-division-multiplexed dual-polarization coherent receiver and spatial-mode-multiplexed vectorial holography. The versatility of our protocol makes it suitable for designing a myriad of multi-input-multi-output devices, providing a powerful tool for realizing universal optical mode converters for a wide range of applications., Comment: 25 pages, 12 figures

Free-space electro-optic (EO) modulators operating at gigahertz and beyond are attractive for a wide range of emerging applications, including high-speed imaging, free-space optical communication, microwave photonics, and diffractive computing. Here we experimentally demonstrate a high-speed plasmonic metasurface EO modulator operating at a near-infrared wavelength range with a gigahertz modulation bandwidth. To achieve efficient intensity modulation of reflected light from an ultrathin metasurface layer, we utilize the bimodal plasmonic resonance inside a subwavelength metal-insulator-metal grating, which is precisely tuned to satisfy the critical coupling condition. As a result, perfect absorption of -27 dB (99.8%) and a high quality (Q) factor of 113 are obtained at a resonant wavelength of 1650 nm. By incorporating an EO polymer inside the grating, we achieve a modulation depth of up to 9.5 dB under an applied voltage of $\pm$30 V. The 3-dB modulation bandwidth is confirmed to be 1.25 GHz, which is primarily limited by the undesired contact resistance. Owing to the high electrical conductivity of metallic gratings and a compact device structure with a minimal parasitic capacitance, the demonstrated device can potentially operate at several tens of gigahertz, which opens up exciting opportunities for ultrahigh-speed active metasurface devices in various applications., Comment: Main text: 18 pages, 3 figures, 39 references Supplementary material: 3 pages, 2 figures

Programmable linear optical processors (LOPs) can have widespread applications in computing and information processing due to their capabilities to implement reconfigurable on-chip linear transformations. A conventional LOP that uses a mesh of Mach-Zehnder interferometers (MZIs) requires $2N+3$ stages of phase shifters for $N \times N$ matrices. However, it is beneficial to reduce the number of phase shifter stages to realize a more compact and lower-loss LOP, especially when long and lossy electro-optic phase shifters are used. In this work, we propose a novel structure for LOPs that can implement arbitrary matrices as long as they can be realized by previous MZI-based schemes. Through numerical analysis, we further show that the number of phase shifter stages in the proposed structure can be reduced to $N+2$ and $N+3$ for a large number of random dense matrices and sparse matrices, respectively. This work contributes to the realization of compact, low-loss, and energy-efficient programmable LOPs.

Programmable unitary photonic devices are emerging as promising tools to implement unitary transformation for quantum information processing, machine learning, and optical communication. These devices typically use a rectangular mesh of Mach-Zehnder interferometers (MZIs), which has a clear mathematical structure and can be configured deterministically. However, this mesh architecture is sensitive to fabrication errors, and the correction techniques are still under investigation. In contrast, the multi-plane light conversion (MPLC) architecture is more robust against fabrication errors, but a deterministic method for configuring the converter has not yet been developed due to its complex mathematical structure. In this work, we propose a fast iterative configuration method for MPLC, following the mathematical review of the matrix distance and proposal of a new norm. We show through numerical simulations that adding a few redundant layers significantly improves the convergence of the MPLC architecture, making it a practical and attractive option. We also consider the effects of finite resolution and crosstalk in phase shifters in our simulations. In addition, we propose a phase-insensitive distance suited for applications using only intensity detections. Our method demonstrates orders of magnitude better accuracy and a 20-fold speed-up compared to previous approaches.

The polarimetric self-coherent system using a direct-detection-based Stokes-vector receiver (SVR) is a promising technology to meet both the cost and capacity requirements of the short-reach optical interconnects. However, conventional SVRs require a number of optical components to detect the state of polarization at high speed, resulting in substantially more complicated receiver configurations compared with the current intensity-modulation-direct-detection (IMDD) counterparts. Here, we demonstrate a simple and compact polarimetric self-coherent receiver based on a thin dielectric metasurface and a photodetector array (PDA). With a single 1.05-$\mu$m-thick metasurface device fabricated on a compact silicon-on-quartz chip, we implement functionalities of all the necessary passive components: a 1$\times$3 splitter, three polarization beam splitters with different polarization bases, and six focusing lenses. Combined with a high-speed PDA, we demonstrate self-coherent transmission of 20-GBd 16-ary quadrature amplitude modulation (16QAM) and 50-GBd quadrature phase-shift keying (QPSK) signals over a 25-km single-mode fiber. Owing to the surface-normal configuration, it can easily be scaled to receive spatially multiplexed channels from a multicore fiber or a fiber bundle, enabling compact and low-cost receiver modules for the future highly parallelized self-coherent systems., Comment: 10 pages, 6 figures (main manuscript) + 2 pages, 2 figures (supplementary info)

A coherent receiver that can demodulate high-speed in-phase and quadrature signals of light is an essential component for optical communication, interconnects, imaging, and computing. Conventional waveguide-based coherent receivers, however, exhibit large footprints, difficulty in coupling a large number of spatial channels efficiently, and limited operating bandwidth imposed by the waveguide-based optical hybrid. Here, we present a surface-normal coherent receiver with nanometallic-grating-based polarizers integrated directly on top of photodetectors without the need for an optical hybrid circuit. Using a fabricated device with the active section occupying a 70-{\mu}m-square footprint, we demonstrate demodulation of high-speed (up to 64 Gbaud) coherent signals in various formats. Moreover, ultra-broadband operation from 1260 nm to 1630 nm is demonstrated, thanks to the wavelength-insensitive nanometallic polarizers. To our knowledge, this is the first demonstration of a surface-normal homodyne optical receiver, which can easily be scaled to a compact two-dimensional arrayed device to receive highly parallelized coherent signals., Comment: 23 pages, 4 figures (main manuscript) + 4 pages, 2 figures (supporting info)