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There is today a growing need to accurately model the angular scattering response of metasurfaces for optical analog processing applications. However, the current metasurface modeling techniques are not well suited for such a task since they are limited to small angular spectrum transformations, as shall be demonstrated. The goal of this work is to overcome this limitation by improving the modeling accuracy of these techniques and, specifically, to provide a better description of the angular response of metasurfaces. This is achieved by extending the current methods, which are restricted to dipolar responses and weak spatially dispersive effects, so as to include quadrupolar responses and higher-order spatially dispersive components. The accuracy of the newly derived multipolar model is demonstrated by predicting the angular scattering of a dielectric metasurface placed in a vacuum. This results in a modeling accuracy that is substantially better than the standard dipolar model.

While metasurfaces (MSs) are constructed from deeply subwavelength unit cells, they are generally electrically large and full-wave simulations of the complete structure are computationally expensive. Thus, to reduce this high computational cost, nonuniform MSs can be modeled as zero-thickness boundaries, with sheets of electric and magnetic polarizations related to the fields by surface susceptibilities and the generalized sheet transition conditions (GSTCs). While these two-sided boundary conditions (BCs) have been extensively studied for single sheets of resonant particles, it has not been shown if they can correctly model structures where the two sides are electrically isolated, such as a fully reflective surface. In particular, we consider in this work whether the fields scattered from a fully reflective MS can be correctly predicted for arbitrary field illuminations, with the source placed on either side of the surface. In the process, we also show the mapping of a perfect electric conductor (PEC) sheet with a dielectric cover layer to bianisoptropic susceptibilities. Finally, we demonstrate the use of the susceptibilities as compact models for use in various simulation techniques, with an illustrative example of a parabolic reflector, for which the scattered fields are correctly computed using an integral-equation (IE)-based solver.

Optical metasurfaces rely on subwavelength scale nanostructures, which puts significant constraints on nanofabrication accuracies. These constraints are becoming increasingly important, as metasurfaces are maturing toward real applications that require the fabrication of very large area samples. Here, we focus on beam steering gradient metasurfaces and show that perfect nanofabrication does not necessarily equate with best performances: metasurfaces with missing elements can actually be more efficient than intact metasurfaces. Both plasmonic metasurfaces in reflection and dielectric metasurfaces in transmission are investigated. These findings are substantiated by experiments on purposely misfabricated metasurfaces and full-wave calculations. A very efficient quasi-analytical model is also introduced for the design and simulations of metasurfaces; it agrees very well with full-wave calculations. Our findings indicate that the substrate properties play a key role in the robustness of a metasurface and the smoothness of the approximated phase gradient controls the device efficiency.

Optical components interact with light through radiative channels, and as such they experience intrinsic losses, giving rise to complex-valued eigenfrequencies and singularities. Spatial inversion symmetry breaking -implemented herein by controlling the coupling efficiency between input and output radiative channels of metasurfaces- lifts the directional degeneracy of reflection zeros, and introduces a complex singularity with a positive imaginary part for full 2π-phase modulation of light. Our work establishes a general framework to predict and study the response of resonant systems in photonics and metaoptics.

We look beyond the standard time-average approach and investigate optical forces in the time domain. The formalism is developed for both the Abraham and Minkowski momenta, which appear to converge in the time domain. We unveil an extremely rich - and by far unexplored - physics associated with the dynamics of the optical forces, which can even attain negative values over short time intervals or produce low frequency dynamics that can excite mechanical oscillations in macroscopic objects under polychromatic illumination. The magnitude of this beating force is tightly linked to the average one. Implications of this work for transient optomechanics are discussed. (C) 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

We review three different approaches for the calculation of electromagnetic multipoles, namely, the Cartesian primitive multipoles, the Cartesian irreducible multipoles, and the spherical multipoles. We identify the latter as the best suited to describe the scattering of electromagnetic radiation, as exemplified for an amorphous silicon sphere. These multipoles are then used to calculate the optical force acting on semiconductor, dielectric or metallic particles in a wide wavelength range, from the dipolar regime down to the Mie regime.

In order to effectively model, synthesize, and analyze a metasurface, we need to understand how it interacts with electromagnetic waves. This chapter introduces the conventional bianisotropic constitutive relations. It describes the temporal response of matter (temporal dispersion) and the mechanism responsible for resonances. The chapter presents the spatially dispersive nature of matter (spatial dispersion), which helps understanding the fundamental origin of bianisotropy. It derives the Lorentz reciprocity theorem and the Poynting theorem, respectively. Based on the Poynting theorem, the chapter then deduces energy conservation relations for lossless‐gainless systems both in terms of susceptibilities and scattering parameters. Finally, it classifies bianisotropic media according to their fundamental material properties.

This chapter discusses different methods to compute the fields scattered by a metasurface. The metasurface is synthesized to be reflectionless and to focalize the incident wave into a single point. The Finite‐Difference Frequency‐Domain (FDFD) method is a numerical technique to solve Maxwell equations in the frequency domain. The FDFD method uses a conventional computational domain composed of a total‐field (TF) region and a scattered‐field (SF) region separated by a TF–SF boundary. The chapter utilizes the Fourier‐based scattered‐field analysis technique. The Fourier‐based method leads to undesired effects, as evidenced by the difference in the back scattering and the overall amplitude of the fields. The Finite‐Difference Time‐Domain method numerically solves Maxwell equations in the time domain. The chapter provides a frequency‐domain computational method that may be used to compute the fields scattered by a metasurface by expressing the generalized sheet transition conditions in the spectral domain.

This repository contains python scripts used to create visualizations for the paper "Multipolar origin of shape birefringence inmetasurfaces", submitted to Optics Express. The output of this script is an interactive html file and/or static image in png format. You can select your preference by commenting out save_in_2D/3D function at the end of the script. To choose what multipoles you want to use for the visualization, please navigate to line 634 inget_E()function where you can select them by editing this line of code. Many examples are already present in the form of comments. The general formula is: total_E = total_E + get_E_p(element_position, dipole_px, pi) field of which multipole to calculate↑ ↑ select multipole orientation↑ ↑ always set "element position" ↑ select phase shift of multipole ↑ ,where pstands for electric dipole,mfor magnetic dipole,eqfor electric quadrupole andmqfor magnetic quadrupole.

While metasurfaces (MSs) are constructed from deeply-subwavelength unit cells, they are generally electrically large and full-wave simulations of the complete structure are computationally expensive. Thus, to reduce this high computational cost, non-uniform MSs can be modelled as zero-thickness boundaries, with sheets of electric and magnetic polarizations related to the fields by surface susceptibilities and the generalized sheet transition conditions (GSTCs). While these two-sided boundary conditions have been extensively studied for single sheets of resonant particles, it has not been shown if they can correctly model structures where the two sides are electrically isolated, such as a fully-reflective surface. In particular, we consider in this work whether the fields scattered from a fully reflective metasurface can be correctly predicted for arbitrary field illuminations, with the source placed on either side of the surface. In the process, we also show the mapping of a PEC sheet with a dielectric cover layer to bi-anisotropic susceptibilities. Finally, we demonstrate the use of the susceptibilities as compact models for use in various simulation techniques, with an illustrative example of a parabolic reflector, for which the scattered fields are correctly computed using a integral equation (IE) based solver., 8 pages, 5 figures

We propose to use metasurfaces as a means of controlling optical forces for increasing the range of motions in spacecraft solar sails. Specifically, we present a theoretical study of metasurface structures that allow one to achieve attractive, lateral, and rotational forces, in addition to the conventional repulsive force. Such solar “meta-sails” may facilitate future travels in the solar system and toward exoplanets.

We provide a self-consistent extension of the Lorentz reciprocity theorem and the Poynting theorem for media possessing electric and magnetic dipolar and quadrupolar responses related to electric and magnetic fields and field gradients thus corresponding to weak spatial dispersion. Using these two theorems, we respectively deduce the conditions of reciprocity and gainlessness and losslessness that apply to the various tensors mediating the interactions of these multipole moments and the associated fields and field gradients. We expect that these conditions will play an essential role in developing advanced metamaterial modeling techniques that include quadrupolar and spatially dispersive responses.

In this paper, we aim at unveiling the underlying physical mechanism for transversal optical forces, appearing due to the simultaneous illumination of a spherical object with two plane waves possessing different polarizations. The appearance of such a transversal force is quite counterintuitive since it seems to contradict the law of momentum conservation. We consider the cases of perfect electric conductor (PEC) and silver spheres illuminated by two orthogonally polarized plane waves propagating obliquely with respect to each other. Interestingly, the Poynting vector in these cases acquires a nonzero component transverse to the plane of propagation. Since the momentum transfer is related to the energy transfer, or equivalently, to non-negligible Poynting vector pointed in a particular direction, an arbitrary object placed in such external field is expected to experience a transversal force. To cast light upon this peculiar effect, we use a surface integral equation method and, along with the Maxwell stress tensor formalism, find the optical force acting on various spheres. We observe this effect for PEC spheres of different sizes and find that they are indeed subject to such transversal force. We find an explanation for this phenomenon via interference effects between selected multipoles excited in the structure. With recently developed methods, we expand the optical force into contributing pairs of selected multipoles and show that, depending on the phase between each multipole pair, the sign and direction of the force can be controlled. We also compare the results for silver and PEC spheres and find that the transversal force magnitude in silver has higher values for more limited range of sphere radii, as compared to PEC.

A novel approach is introduced to determine the time evolution of optical forces and torques on arbitrary shape nanostructures by combining Maxwell's stress tensor with the surface integral equation method (SIE). Conventional time averaging of Maxwell’s stress tensor allows obtaining an elegant form in terms of surface currents for the force exerted on nanostructures. Unfortunately, the information about the time dependence of the force – which can be very important in ultrafast photonics experiments and in nano-manipulation applications – is lost in such an approach. To overcome this, we have developed a time-domain method based on the inverse Fourier transform of the frequency-domain SIE. The calculations in the frequency domain allow accurately taking into account the dispersion of the permittivity function of the system and the use of surface currents enables the rigorous treatment of intricate geometries for the scatterer. Furthermore, the integration of Maxwell’s stress tensor directly on the scatterer’s boundary significantly reduces the required computation time and increases the accuracy of the method. We show quite unusual sum frequency-like terms in the dynamics of the force appearing in Maxwell’s stress tensor, which normally vanish for the time-averaged force. To illustrate this effect, we study how the pulse duration influences the dynamics of optical force in the case of a rectangular shape and Gaussian pulses illuminating thin film at normal incidence. In the framework of the developed numerical method, we study the influence of the sum-frequency-like terms on the dynamics of optical forces in the case of a spherical scatterer.

We investigate optical forces in the time domain, instead of using the time-average Maxwell stress tensor. We demonstrate first that a plane wave causes on a physical object an optical pressure that fluctuates at optical frequency in the time domain. The analytical formula for the optical force dynamics is presented for this case. The case for two-wave illumination with slightly different frequencies is considered next. It is shown that in this case the optical force acquires a component at the beating frequency. The analytical expression for the transient force is deduced and its relation with average force explained in detail.

Metasurfaces represent one of the most vibrant fields of modern science and technology. A metasurface is a complex electromagnetic structure, which is typically deeply subwavelength in thickness, electrically large in transverse size, and composed of subwavelength scattering particles with extremely small features; it may generally be bianisotropic, space-varying and time-varying, nonlinear, curved, and multiphysics. With such complexity, the design of a metasurface requires a holistic approach, involving synergistic synthesis and analysis operations, based on a solid model. The generalized sheet transition conditions (GSTCs), combined with bianisotropic surface susceptibility functions, provide such a model and allow now for the design of sophisticated metasurfaces, which still represented a major challenge a couple of years ago. This paper presents this problem, focusing on the computational analysis of metasurfaces via the GSTC-susceptibility approach. It shows that this analysis plays a crucial role in the holistic design of metasurfaces and overviews recently reported related frequency-domain (finite-difference frequency-domain, spectral-domain integral-equation, and finite-element method) and time-domain (finite-difference time-domain) computational techniques.

We propose a surface-wave dispersion retrieval method and synthesis technique that applies to bianisotropic metasurfaces that are embedded in symmetric or asymmetric environments. Specifically, we use general zero-thickness sheet transition conditions to relate the propagation constants of surface-wave modes to the bianisotropic susceptibility components of the metasurface, which can themselves be directly related to its scattering parameters. It is then possible to either obtain the metasurface dispersion diagram from its known susceptibilities or, alternatively, compute the susceptibilities required to achieve a desired surface-wave propagation. The validity of the method is demonstrated by comparing its results to those obtained with exact dispersion relations of well known structures such as the propagation of surface plasmons on thin metallic films. In particular, this work reveals that it is possible to achieve surface-wave propagation only on one side of the metasurface either by superposition of symmetric and asymmetric modes in the case of anisotropic metasurfaces or by completely forbidding the existence of the surface wave on one side of the structure using bianisotropic metasurfaces.

We introduce the concept of a metasurface system able to route space waves via surface waves. This concept may be used to laterally shift or modulate the beam width of scattered waves. The system is synthesized based on a momentum transfer approach using phase-gradient metasurfaces. The concept is experimentally verified in an "electromagnetic periscope". Additionally, we propose two other potential applications namely a beam expander and a multi-wave refractor.

We present an initial study of the angular spectrum of a bianisotropic refractive metasurface at an interface between two dielectric media. In this study, we report on the existence of three distinct angular regions: a) a rotated transmission cone, b) a modified total internal reflection region, and c) a new total retro-reflection region.

This paper theoretically proposes a multichannel functional metasurface computer characterized by Generalized Sheet Transition Conditions (GSTCs) and surface susceptibility tensors. The study explores a polarization- and angle-multiplexed metasurfaces enabling multiple and independent parallel analog spatial computations when illuminated by differently polarized incident beams from different directions. The proposed synthesis overcomes substantial restrictions imposed by previous designs such as large architectures arising from the need of additional subblocks, slow responses, and most importantly, supporting only the even reflection symmetry operations for normal incidences, working for a certain incident angle or polarization, and executing only single mathematical operation. The versatility of the design is demonstrated in a way that an ultra-compact, integrable and planar metasurface-assisted platform can execute a variety of optical signal processing operations such as spatial differentiation and integration. It is demonstrated that a metasurface featuring non-reciprocal property can be thought of as a new paradigm to break the even symmetry of reflection and perform both even- and odd-symmetry mathematical operations at normal incidences. Numerical simulations also illustrate different aspects of multichannel edge detection scheme through projecting multiple images on the metasurface from different directions. Such appealing findings not only circumvent the major potential drawbacks of previous designs but also may offer an efficient, easy-to-fabricate, and flexible approach in wave-based signal processing, edge detection, image contrast enhancement, hidden object detection, and equation solving without any Fourier lens., Comment: 13 pages, 8 figures

We aim at providing a global perspective on electromagnetic nonreciprocity and clarifying confusions that arose in recent developments of the field. We provide a general definition of nonreciprocity and classify nonreciprocal systems according to their linear time-invariant (LTI), linear time-variant (LTV), or nonlinear natures. The theory of nonreciprocal systems is established on the foundation formed by the concepts of time reversal, time-reversal symmetry, time-reversal symmetry breaking, and related Onsager-Casimir relations. Special attention is given to LTI systems, the most-common nonreciprocal systems, for which a generalized form of the Lorentz reciprocity theorem is derived. The delicate issue of loss in nonreciprocal systems is demystified and the so-called thermodynamics paradox is resolved from energy-conservation considerations. An overview of the fundamental characteristics and applications of LTI, LTV, and nonlinear nonreciprocal systems is given with the help of pedagogical examples. Finally, asymmetric structures with fallacious nonreciprocal appearances are debunked.

We propose an extensive discussion on the homogenization and scattering analysis of the second-order nonlinear metasurfaces. Our developments are based on the generalized sheet transition conditions (GSTCs) that are used to model the electromagnetic responses of nonlinear metasurfaces. The GSTCs are solved both in the frequency domain, assuming an undepleted pump regime, and in the time domain, assuming dispersionless material properties but a possible depleted pump regime. Based on these two modeling approaches, we derive the general second-harmonic reflectionless and transmissionless conditions as well as the conditions of asymmetric reflection and transmission. We also discuss and clarify the concept of nonreciprocal scattering pertaining to nonlinear metasurfaces.

The paper overviews our recent work on the synthesis of metasurfaces and related concepts and applications. The synthesis is based on generalized sheet transition conditions (GSTCs) with a bianisotropic surface susceptibility tensor model of the metasurface structure. We first place metasurfaces in a proper historical context and describe the GSTC technique with some fundamental susceptibility tensor considerations. On this basis, we next provide an in-depth development of our susceptibility-GSTC synthesis technique. Finally, we present five recent metasurface concepts and applications, which cover the topics of birefringent transformations, bianisotropic refraction, light emission enhancement, remote spatial processing, and nonlinear second-harmonic generation.

A general method, based on susceptibility tensors, is proposed for the synthesis of metasurfaces transforming arbitrary incident waves into arbitrary reflected and transmitted waves. The proposed method exhibits two advantages: 1)it is inherently vectorial, and therefore better suited for full vectorial (beyond paraxial) electromagnetic problems, 2) it provides closed-form solutions, and is therefore extremely fast. Incidentally, the method reveals that a metasurface is fundamentally capable to transform up to four independent wave triplets (incident, reflected and refracted waves). In addition, the paper provides the closed-form expressions relating the synthesized susceptibilities and the scattering parameters simulated within periodic boundary conditions, which allows one to design the scattering particles realizing the desired susceptibilities. The versatility of the method is illustrated by examples of metasurfaces achieving the following transformations: generalized refraction, reciprocal and non-reciprocal polarization rotation, Bessel vortex beam generation, and orbital angular momentum multiplexing.

We propose a discussion on the synthesis and scattering analysis of nonlinear metasurfaces. For simplicity, we investigate the case of a second-order nonlinear isotropic metasurface possessing both electric and magnetic linear and nonlinear susceptibility components. We next find the synthesis expressions relating the susceptibilities to the specified fields, which leads to the definition of the nonlinear metasurface conditions for no reflection, themselves revealing the nonreciprocal nature of such structures. Finally, we provide the approximate expressions of the scattered fields based on perturbation theory and compare the corresponding results to finite-difference time-domain simulations.

We discuss our most recent developments in the synthesis and the analysis of metasurfaces as well as their potential applications. We present a list of selected topics which includes the electromagnetic synthesis of metasurfaces and the applications of birefringence and bianisotropy. Several applications are discussed, among which, are the light emission enhancement of single photon source, metasur-face with controllable angular scattering and metasurface solar sail for the control of radiation pressure.

We present a closed-form analysis of electromagnetic scattering from a nonlinear metasurface. For simplicity, we restrict our attention to the case of an isotropic second-order nonlinear metasurface. We derive the reflectionless conditions for such a nonlinear metasurface, and show that those conditions depend on the direction of wave propagation, which reveals the nonreciprocal nature of the structure. Next, we provide approximate transmitted field expressions obtained by perturbation theory, and we shall present FDTD validations at the conference.

We propose the concept of a bianisotropic metasurface with controllable angular scattering. We illustrate this concept with the synthesis and the analysis of a metasurface exhibiting controllable absorption and transmission phase as function of the incidence angle.

Solar sails are spatial sails using radiation pressure as a spacecraft propulsion method. This technology is so far limited to repulsive forces. We propose a metasurface solar sail system that is able to produce not only repulsive forces but also attractive, lateral and rotational forces. The forces acting on the metasurface sail are produced by the light of a star or may be controlled by changing the polarization or wavelength of a laser beam. Here, we only present the field configurations corresponding to those four different forces. The design of the metasurfaces will be discussed at the conference.

We propose and numerically demonstrate two novel double-metasurface cavities for light manipulation, a Partially-Reflecting Metasurface Cavity (PRMC) for simultaneously enhanced light extraction efficiency, spontaneous emission rate and far-field directivity, and an Anisotropic Reflecting Metasurface Cavity (ARMC) for tuning the spontaneous emission and achieving strong quantum interference.

The enhancement of the power conversion efficiency (PCE), and subsequent reduction of cost, of light emitting diodes (LEDs) is of crucial importance in the current lightening market. For this reason, we propose here a PCE-enhanced LED architecture, based on a partially reflecting metasurface cavity (PRMC) structure. This structure simultaneously enhances the light extraction efficiency (LEE) and the spontaneous emission rate (SER) of the LED by enforcing the emitted light to radiate perpendicularly to the device, so as to suppress wave trapping and enhance field confinement near the emitter, while ensuring cavity resonance matching and maximal constructive field interference. The PRMC structure is designed using a recent surface susceptibility metasurface synthesis technique. A PRMC blue LED design is presented and demonstrated by full-wave simulation to provide LEE and SER enhancements by factors 4.0 and 1.9, respectively, which correspond to PCE enhancement factors of 6.2, 5.2 and 4.5 for IQEs of 0.25, 0.5 and 0.75, respectively, suggesting that the PRMC concept has a promising potential in LED technology.

A passive and reciprocal perfectly refractive meta-surface is designed using a general susceptiblity synthesis method. The metasurface uses weak spatial dispersion in the form of bianisotropy to achieve perfect refraction. Its operation is validated using a full-wave simulation of the metasurface implemented with cascaded metallic layers separated by dielectric.

The paper presents an overview of the recent research on metasurfaces performed in the author's group. This covers the introduction of bianistropic Sheet Transition Conditions (STCs), the subsequent elaboration of a general synthesis technique based on surface susceptibility tensors, the complementary elaboration of Finite Difference (FD) and Finite Element (FE) computational schemes for analysis, and, based upon this solid foundation, the development of a host of novel applications across the whole microwave to optical range of the electromagnetic spectrum.

We present a spectral-domain (SD) technique for the efficient analysis of metasurfaces. The metasurface is modeled by generalized sheet transition conditions (GSTCs) as a zero-thickness sheet creating a discontinuity in the electromagnetic field. The SD expression of these GSTCs for a specified incident field leads to a system of four surface integral equations for the reflected and transmitted fields, which are solved using the method of moments in the spectral domain. Compared to the finite-difference and finite-element techniques that require meshing the entire computational domain, the proposed technique reduces the problem to the surface of the metasurface, hence eliminating one dimension and providing substantial benefits in terms of memory and speed. A monochromatic generalized-refractive metasurface and a polychromatic focusing metasurface are presented as illustrative examples.

We introduce the concept of a metasurface system able to route space wave via surface waves. This concept may be used to laterally shift or modulate the beam width of scattered waves. We propose two corresponding synthesis techniques, one that is exact but leads to practically challenging material parameters and one that is approximate but leads to simpler material parameters. The concept is experimentally verified in an electromagnetic periscope. Additionally, we propose two other potential applications namely a beam expander and a multi-wave refractor.

A metasurface routing electromagnetic beams via surface waves from one point to another point of space is introduced. This metasurface is transparent and may simultaneously support generalized refraction for another orthogonal beam (birefringence). The metasurface is designed by the general surface susceptibility synthesis method and its operation is validated by finite difference analysis, both being based on generalized sheet boundary conditions.

The generalized sheet transition conditions (GSTCs) have been recently leveraged for synthesizing metasurfaces transforming specified monochromatic incident waves in arbitrary fashions. This paper extends the technique to general polychromatic designs. The resulting polychromatic metasurfaces provide unprecedented control on the temporal and spatial frequency components of incident pulsed electromagnetic waves. They may find applications in spatial filters, spatial phasers, real-time Fourier transformers and real-time spectrum analyzers.