Search

Metasurface anomalous reflectors can enhance future wireless communication systems due to their ability to redirect electromagnetic waves and establish metasurface-assisted communication links. However, metasurface reflectors typically suffer from chromatic aberrations with the reflected angle shifting as the frequency varies. Herein, we design achromatic metasurfaces for anomalous reflection by using an integral-equation framework that fully accounts for the frequency dispersion of the individual scatterers (unit cells). Rather than engineering the dispersion of each metasurface cell locally, we harness the emerging near-field interactions (evanescent waves) between the scatterers to realize anomalous reflection at a fixed angle over a wide frequency range. Three anomalous reflectors are designed and experimentally verified at 10GHz, demonstrating high performance metrics compared to traditional achromatic reflectors, while employing simple, low-profile unit cells. The presented results pave an effective way to realize achromatic wave functionalities, such as anomalous reflection, refraction or lensing, over a wide bandwidth with low-profile and highly efficient metasurfaces., Comment: 12 pages, 10 figures

An adaptive mesh refinement and error estimation method for numerically solving optimal control problems is developed using Legendre-Gauss-Radau direct collocation. In regions of the solution where the desired accuracy tolerance has not been met, the mesh is refined by either increasing the degree of the approximating polynomial in a mesh interval or dividing a mesh interval into subintervals. In regions of the solution where the desired accuracy tolerance has been met, the mesh size may be reduced by either merging adjacent mesh intervals or decreasing the degree of the approximating polynomial in a mesh interval. Coupled with the mesh refinement method described in this paper is a newly developed relative error estimate that is based on the differences between solutions obtained from the collocation method and those obtained by solving initial-value and terminal-value problems in each mesh interval using an interpolated control obtained from the collocation method. Because the error estimate is based on explicit simulation, the solution obtained via collocation is in close agreement with the solution obtained via explicit simulation using the control on the final mesh, which ensures that the control is an accurate approximation of the true optimal control. The method is demonstrated on three examples from the open literature, and the results obtained show an improvement in final mesh size when compared against previously developed mesh refinement methods., Comment: 32 pages; 9 figures; 4 tables

A comprehensive study on the Finite Difference Time Domain (FDTD) numerical modelling of space- and time-varying media is presented. We investigate the dynamic behavior of oblique incidence of both TM and TE electromagnetic fields on space-timemodulated gratings. In their general form, these media have electrical permittivity, magnetic permeability, and electrical conductivity modulated across both space and time. We provide the FDTDschemes, the Courant-Friedrichs-Lewy (CFL) stability condition and equations for both TM and TE wave illuminations of space-time-varying slabs, along with the boundary conditions for the FDTD scheme. Furthermore, with engaging illustrative examples, we showcase the versatility and applications of space-time-varying media.

The Robert Stobie Spectrograph (RSS) on the Southern African Large Telescope (SALT) offers multi-object spectroscopy over an 8' field-of-view at resolutions up to 3000. Reduction is typically conducted using RSSMOSPipeline, which performs basic data calibrations, sky subtraction, and wavelength calibration. However, flux calibration of SALT-RSS using spectrophotometric standard star observations is difficult due to variable primary mirror illumination. We describe a novel approach where stars with Sloan Digital Sky Survey spectra are included as alignment stars on RSS slitmasks and then used to perform flux calibration of the resulting data. RSS offers multiple settings that can be pieced together to cover the entire optical range, utilizing grating angle dithers to fill chip gaps. We introduce a non-linear reprojection routine that defines an exponential wavelength array spanning 3500-9500 Angstroms with gradually decreasing resolution and then reprojects several individual settings into a single 2D spectrum for each object. Our flux calibration and non-linear reprojection routines are released as part of the Calibration And Reprojection for RSS Pipeline (CARRSSPipeline; https://github.com/GeorgeTheGeorgian/CARRSSPipeline.git ), that enables the extraction of full-optical-coverage, flux-calibrated, medium-resolution one-dimensional spectra., Comment: 12 pages, 9 figures, and 4 tables. Submitted to PASP

An active interior cloak is composed of a conformal array of radiating sources surrounding a target object. With proper configuration, this array radiates a field discontinuity which cancels out any scattering which occurs when the object is illuminated by an impinging electromagnetic wave. Unlike many other cloaking methods, an interior cloak can be completely constructed using conventional components while its active nature allows it to circumvent passivity-based constraints. This enables an interior cloak to hide an object of virtually any size, shape, and material composition as well as accommodate multiple frequencies and polarizations. Despite its potential, this approach has only been demonstrated on 2D and quasi-2D targets to date. As such, this paper presents the first 3D implementation of an interior cloak. Here, the design of a cloak array capable of hiding a conductive, circular cylinder in free-space is first presented. Cloaking performance is then validated via full-wave simulations and an experimental demonstration in which the device successfully suppresses scattering when the target is illuminated by a ridged horn antenna at 1.2 GHz.

When the underlying conditional density is known, conditional expectations can be computed analytically or numerically. When, however, such knowledge is not available and instead we are given a collection of training data, the goal of this work is to propose simple and purely data-driven means for estimating directly the desired conditional expectation. Because conditional expectations appear in the description of a number of stochastic optimization problems with the corresponding optimal solution satisfying a system of nonlinear equations, we extend our data-driven method to cover such cases as well. We test our methodology by applying it to Optimal Stopping and Optimal Action Policy in Reinforcement Learning., Comment: 20 pages, 6 figures

In the problem of quickest change detection, a change occurs at some unknown time in the distribution of a sequence of random vectors that are monitored in real time, and the goal is to detect this change as quickly as possible subject to a certain false alarm constraint. In this work we consider this problem in the presence of parametric uncertainty in the post-change regime and controlled sensing. That is, the post-change distribution contains an unknown parameter, and the distribution of each observation, before and after the change, is affected by a control action. In this context, in addition to a stopping rule that determines the time at which it is declared that the change has occurred, one also needs to determine a sequential control policy, which chooses the control action at each time based on the already collected observations. We formulate this problem mathematically using Lorden's minimax criterion, and assuming that there are finitely many possible actions and post-change parameter values. We then propose a specific procedure for this problem that employs an adaptive CuSum statistic in which (i) the estimate of the parameter is based on a fixed number of the more recent observations, and (ii) each action is selected to maximize the Kullback-Leibler divergence of the next observation based on the current parameter estimate, apart from a small number of exploration times. We show that this procedure, which we call the Windowed Chernoff-CuSum (WCC), is first-order asymptotically optimal under Lorden's minimax criterion, for every possible possible value of the unknown post-change parameter, as the mean time to false alarm goes to infinity. We also provide simulation results to illustrate the performance of the WCC procedure.

The Secretary problem is a classical sequential decision-making question that can be succinctly described as follows: a set of rank-ordered applicants are interviewed sequentially for a single position. Once an applicant is interviewed, an immediate and irrevocable decision is made if the person is to be offered the job or not and only applicants observed so far can be used in the decision process. The problem of interest is to identify the stopping rule that maximizes the probability of hiring the highest-ranked applicant. A multiple-choice version of the Secretary problem, known as the Dowry problem, assumes that one is given a fixed integer budget for the total number of selections allowed to choose the best applicant. It has been solved using tools from dynamic programming and optimal stopping theory. We provide the first combinatorial proof for a related new \emph{query-based model} for which we are allowed to solicit the response of an expert to determine if an applicant is optimal. Since the selection criteria differ from those of the Dowry problem we obtain nonidentical expected stopping times. Our result indicates that an optimal strategy is the $(a_s, a_{s-1}, \ldots, a_1)$-strategy, i.e., for the $i^{th}$ selection, where $1 \le i \le s$ and $1 \le j = s+1-i \le s$, we reject the first $a_j$ applicants, wait until the decision of the $(i-1)^{th}$ selection (if $i \ge 2$), and then accept the next applicant whose qualification is better than all previously appeared applicants. Furthermore, our optimal strategy is right-hand based, i.e., the optimal strategies for two models with $s_1$ and $s_2$ selections in total ($s_1 < s_2$) share the same sequence $a_1, a_2, \ldots, a_{s_1}$ when it is viewed from the right. When the total number of applicants tends to infinity, our result agrees with the thresholds obtained by Gilbert and Mosteller., Comment: 15 pages, 1 figure, 1 table. arXiv admin note: substantial text overlap with arXiv:2101.07250

This paper presents the experimental demonstration of a dual-input/dual-output reflective impedance metasurface. The design of the metasurface relies on the Method of Moments and leverages auxiliary surface waves to achieve anomalous reflection of two impinging plane waves with controlled sidelobe levels. The two beams are chosen independently compared to those in a conventional phase-gradient metasurface where the design presents a single slope to achieve a certain reflection and all other incident beams would depend on that slope. A prototype that ensures maximum directivity at two prescribed reflection angles for the two input waves is then fabricated on a Rogers RO3003 printed-circuit board using 42 metawires loaded with printed capacitors. The proposed metasurface is capable of reflecting an incident beam from $-20^\circ$ to $-55^\circ$ and a second from $+10^\circ$ to $50^\circ$ at 9.93 GHz. The metasurface is experimentally characterized and an illumination efficiency of at least 89% is calculated for each of the reflected waves, indicating a high multiplexing efficacy.

This paper presents an end-to-end design method for the synthesis of dielectric metasurfaces with modulated thickness that are able to realize desired radiation patterns in the far-field with high precision. The method relies on integral equations and the Method of Moments to calculate the induced surface and volumetric current densities throughout the metasurface upon a given incident illumination. By avoiding homogenization of the dielectric layer and calculating directly the scattered fields through the Method of Moments, the near-field and far-field response of the metasurface can be accurately predicted and optimized. In particular, a design example of a modulated dielectric metasurface, fed by a single embedded line source, is presented for the realization of a Chebyshev array pattern with -20 dB sidelobe level. Moreover, an externally-fed dielectric metasurface performing beam splitting of a normally-incident plane wave is designed, 3-D printed and measured, showing two reflected beams at +-30 degrees, high suppression of specular reflections (> 14 dB) and satisfactory agreement with the simulated and desired radiation patterns. The proposed design method for beamforming with dielectric metasurfaces can find application in higher frequencies where the use of copper may be problematic due to higher ohmic losses and fabrication challenges., Comment: 14 pages, 13 figures

Scattering of refracting Huygens' metasurfaces is revisited. A new analytical closed-form solution is obtained for the two-dimensional problem under transverse electric (TE) plane-wave incidence -- a solution which gives the scattering for any (in-plane) angle of incidence and frequency. In the process of obtaining the solution, interesting mathematical concepts are considered -- such as solving and enforcing uniqueness upon an infinite system of equations. The obtained solution uncovers two previously unknown functionalities of refracting Huygens' metasurfaces -- namely reflectionless refraction and oblique absorption.

Over the past decades, many radome designs to extend the angular scan range of phased-array antennas have been devised by utilizing dielectric materials and metamaterials. More recently, metasurface technology such as planar lenses and beam deflectors have been applied to phased arrays, enabling scan-angle enhancers to have a low profile. In this work, a physical Huygens' metasurface (HMS) two-lens system for scanangle doubling of a phased array is presented. For the HMS unit cells, the wire-loop topology is deployed to achieve high transmission for the required phase-angle shift. The proposed two-lens system is analyzed by full-wave simulations and experiments. The simulation results demonstrate that the scan angle doubles when the incident angle is below 15{\deg} in accordance to the design specification. Furthermore, the directivity degradation of the refracted beams by the two-HMS lenses is in good agreement with theory. Finally, a fabricated two-lens system with two 15{\lambda} long by 15{\lambda} wide metasurface lenses and a 16{\times}16-element patch antenna array as a source is experimentally verified at 10 GHz. The experimental results are in good agreement with the simulated results by showing angle-doubling performance with {\pm}2{\deg} scan errors.

Recently, nonreciprocal phase shifters have attracted a surge of interest thanks to the advent of nonreciprocal electromagnetic systems, such as nonreciprocal metasurfaces, nonreciprocal-beam antennas, and invisibility cloaks. To overcome the limitations associated with conventional technologies for realizing nonreciprocal phase shifters and gyrators, here we propose a low-noise, lightweight, low-profile, and linear magnetless nonreciprocal phase shifter formed by two temporal loops. The proposed temporal apparatus operates based on the generation of time-harmonic signals and destructive and constructive interferences for the undesired and desired time harmonics, respectively, at different locations of the structure. An external time-harmonic modulation signal injects an effective electronic angular momentum to the system to control the phase and frequency of the two loops. Such a temporal nonreciprocal phase shifter offers low insertion loss, and a large return loss (input matching) of greater than 28.1 dB. Additionally, this nonreciprocal phase shifter possesses a reconfigurable architecture and can be directly embedded in integrated circuit (IC) technology to create high power handling and linear IC-based nonreciprocal phase shifters., Comment: arXiv admin note: text overlap with arXiv:2107.09788

We study the parametric online changepoint detection problem, where the underlying distribution of the streaming data changes from a known distribution to an alternative that is of a known parametric form but with unknown parameters. We propose a joint detection/estimation scheme, which we call Window-Limited CUSUM, that combines the cumulative sum (CUSUM) test with a sliding window-based consistent estimate of the post-change parameters. We characterize the optimal choice of the window size and show that the Window-Limited CUSUM enjoys first-order asymptotic optimality as average run length approaches infinity under the optimal choice of window length. Compared to existing schemes with similar asymptotic optimality properties, our test can be much faster computed because it can recursively update the CUSUM statistic by employing the estimate of the post-change parameters. A parallel variant is also proposed that facilitates the practical implementation of the test. Numerical simulations corroborate our theoretical findings., Comment: 28 pages, 4 figures

Optimum parameter estimation methods require knowledge of a parametric probability density that statistically describes the available observations. In this work we examine Bayesian and non-Bayesian parameter estimation problems under a data-driven formulation where the necessary parametric probability density is replaced by available data. We present various data-driven versions that either result in neural network approximations of the optimum estimators or in well defined optimization problems that can be solved numerically. In particular, for the data-driven equivalent of non-Bayesian estimation we end up with optimization problems similar to the ones encountered for the design of generative networks.

We present the end-to-end design of compact passive and lossless metasurface (MTS) antennas with integrated feeds. The complete low-profile system consists of a single-layered reactive impedance MTS printed on top of a grounded dielectric substrate, and is fed by sources which are embedded inside the substrate. An accurate and efficient volume-surface integral equation-based model of the device is developed, and used as the basis for the rapid optimization of its performance. The optimized designs leverage tailored auxiliary surface waves supported by the impedance MTS to distribute the localized source power across their apertures. This facilitates the realization of extreme field transformations such as wide-angle beam-forming or shared-aperture beam-forming, with nearly 100% aperture efficiencies. The procedure also allows for arbitrary beam-shaping with complete main beam and side lobe control. We also derive several feasibility-related constraints, which can significantly enhance the power efficiency as well as the bandwidth of the MTS antennas when they are implemented in practice. Full-wave numerical simulations confirm the effectiveness of the presented approach, as well as the extreme field transformation capabilities of the synthesized designs.

We present a highly efficient metagrating-assisted antenna (MGA) architecture with a simple integrated feed. Power from a localized line source is distributed throughout the arbitrarily large antenna aperture with the help of a passive and lossless electromagnetic metagrating (MG). With appropriately designed meta-wire loading, the omnidirectional source field can be efficiently transformed into directive radiation. To aid the design process, a 2-dimensional volume-surface integral equation framework which accurately predicts the radiation pattern of the MGA is developed. Through constrained optimization, the directivity of the MGA in the desired direction is maximized. In this way, extreme-angle beam steering is demonstrated.