arXiv subjects

Karim Achouri

Publications and source records attributed to Karim Achouri.

At least 19 recordsLinked to original sources

arXiv2026

Dipolar Modeling of Multipolar Metasurfaces

Multipolar decomposition is a powerful tool for analyzing and designing metasurfaces, but its practical application is often limited by the mathematical complexity that arises when a large number of multipole moments must be taken in to account. To minimize this modeling complexity without sacrificing accuracy, we present an efficient method that exploits the coordinates origin dependence of spherical multipole moments. We show that the optimal origins for minimizing higher-order contributions, such as quadrupoles and octupoles, depend strictly on the spatial parity of the electromagnetic response. This is achieved by modeling a metasurface response using multipolar generalized sheet transition conditions (GSTCs). By separating the GSTCs into independent even and odd parity components, we can evaluate the electric and magnetic discontinuities at distinct physical positions. This parity-splitting framework allows us to systematically suppress unwanted higher-order terms and reconstruct the complete scattering parameters using only the dipole moments. We validate our analytical approach using two numerical examples: vertically asymmetric dielectric cones on a substrate, and a horizontally symmetry-broken metasurface supporting a double quasi-bound state in the continuum resonance. In both cases, the retrieved scattering parameters show excellent agreement with full-wave simulations. This method provides a simple, physically intuitive framework that simplifies the modeling of geometrically complex and non-local metasurfaces down to a purely dipolar level.

physics.optics↗

arXiv2026

Generalized Invisibility in Metasurfaces

Electromagnetic invisibility, defined as reflectionless transmission with zero phase delay, imposes strict constraints on metasurface designs that go beyond conventional reflection suppression based on the Kerker effect. This condition can be viewed as a metasurface analogue of radiationless states such as anapole excitations. Here, we show that invisibility in metasurfaces embedded in identical media can only be achieved by introducing degrees of freedom, such as non-zero angle of incidence or higher-order multipolar responses. We demonstrate that, in dissimilar substrate and superstrate, achieving invisibility within a dipolar framework fundamentally requires pure bianisotropic coupling, while purely electric and magnetic responses are insufficient for lossless, passive and reciprocal systems. Using effective surface susceptibilities that account for the surrounding media and transverse wave vector, we derive closed-form conditions for both co- and cross-polarized invisibility. Importantly, we also demonstrate that the required bianisotropy does not need to be intrinsic, as an effective bianisotropic response may be achieved with anisotropic metasurface in dissimilar media leading to magnetoelectric coupling. Full-wave simulations of a metasurface at an air-dielectric interface confirm invisibility under oblique incidence. This work establishes a universal dipolar framework for invisible meta-optics in practically realistic scenarios.

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arXiv2026

Scattering Symmetries in Diffraction Gratings

Metasurfaces enable powerful control of electromagnetic waves using subwavelength planar structures, but their deeply subwavelength periodicity typically suppresses propagating diffraction orders, which limits the number of available scattering channels. Diffraction gratings and metagratings overcome this limitation by supporting multiple propagating diffraction orders, thus providing additional degrees of freedom for controlling wave propagation. However, when several diffraction channels are present, it becomes nontrivial to predict how spatial symmetries combined with reciprocity affect the overall scattering response. For this purpose, we develop a formalism to determine the scattering symmetries of diffraction gratings supporting multiple diffraction orders. The approach is based on constructing a global scattering matrix that connects all incident and scattered diffraction channels and on introducing matrix representations of spatial symmetry operations acting on the field amplitudes. From these representations, we derive an invariance condition that directly constrains the sub-scattering matrices associated with each pair of diffraction orders. This provides a rigorous approach for computing the grating scattering coefficients imposed by symmetry and reciprocity. We illustrate the application of this approach via several examples and show how metagratings may be used to achieve, for instance, angle-asymmetric transmission and extrinsic chiral effects.

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arXiv2025

Electromagnetic Theory of Metasurface Perfect Magnetic Conductor (PMC)

Artificial magnetic conductors (AMCs) mimic the idealized boundary condition of a perfect magnetic conductor (PMC), which reflects electromagnetic waves with a preserved electric field and inverted magnetic field. Despite their usefulness, existing AMC implementations often rely on complex or impractical designs, and lack a clear electromagnetic theory explaining their behavior, especially under oblique or polarization-diverse incidence. This work addresses these limitations by presenting a rigorous electromagnetic framework for PMC metasurfaces based on dipolar and quadrupolar surface susceptibilities within the generalized sheet transition conditions (GSTCs) formalism. We show that achieving polarization- and angle-independent PMC behavior requires a specific set of heteroanisotropic (nonlocal) susceptibilities, and we derive closed-form expressions for angular scattering that include higher-order multipole contributions. A physically realizable, asymmetric metasurface structure is then designed to satisfy these theoretical conditions. Despite its geometric asymmetry, the proposed structure exhibits a isotropic PMC response at resonance, confirmed by full-wave simulations and multipolar susceptibility extraction. These results demonstrate how properly engineered surface multipoles can yield angularly independent magnetic boundary conditions using only thin, passive metallic layers. This work bridges the gap between AMC design and electromagnetic theory, and enables a new class of angle-independent metasurface reflectors for more accurate simulations, optimizations and innovative AMC designs.

physics.optics↗

arXiv2025

Metapinhole: Planar Fourier Optics Without Lenses

The 4f lens system is a standard Fourier-optics building block for angular control in optical platforms such as spatial light modulators, imaging systems, and data storage devices. This work presents the first nanoscale implementation of an equivalent system, achieving a five-orders-of-magnitude footprint reduction. By engineering the angular scattering response of metagratings, sharp-edge spatial filtering is realized through the interplay of angle-dependent two-dimensional dipolar resonances, Rayleigh anomalies, and Kerker-like dipolar cancellation. The metagrating functions as a high-efficiency low-pass and a controllable high-pass angular filter in transmission. In addition, diffraction-controllable angular invariance across the entire spatial Fourier space enables tunable band-pass filtering in reflection. This lens-free approach provides a compact, alignment-insensitive solution for spatial filtering in electromagnetic regimes where conventional lenses or pinholes are impractical or costly -- such as the terahertz or infrared ranges -- and facilitates spatial filtering for movable beams without complex mechanical adjustments. It also enables unprecedented single-shot multiplexing of diverse spatial filtering functions at distinct central wavelengths, and extends spatial filtering to signals with extremely low coherence lengths.

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arXiv2025

Multipolar Angular Scattering of Substrated Metasurfaces

Properly modeling and predicting the scattering response of a metasurface is a particularly challenging task. This has been shown to be especially difficult if the metasurface supports both local and nonlocal interactions, in the form of lattice coupling effects, multipolar contributions or bianisotropic responses. So far, existing methods to approach this problem have been restricted to normal incidence in a homogeneous background medium. We overcome these limitations by providing a rigorous and comprehensive formalism that accommodates both oblique incidence and the presence of different superstrate and substrate. This is achieved by extending our existing metasurface modeling framework to account for nonlocal and multipolar contributions up to the octupolar order and properly accounting for the scattering effects due to an inhomogeneous background medium. Additionally, our method is based on exact spherical multipole decomposition, which intrinsically accounts for toroidal contributions. We demonstrate the effectiveness of our approach by modeling the response of several dielectric and plasmonic metasurfaces that exhibit sharp spectral features including bound states in the continuum. Overall, our formalism yields excellent agreement with full-wave simulations.

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arXiv2025

A General Expression for Homogeneous Metasurface Scattering

The general approach in metasurface design is to find the unit-cell properties required to achieve a given functionality. This is usually done by modeling the metasurface as a combination of surface electric and magnetic polarization densities, whose parameters are determined by solving the generalized sheet transition conditions. This is a time consuming task, as the so-called boundary conditions needs to be solved per-case basis, depending on the source polarization, angle of incidence, and intended functionality. Evermore, the task complexity increases as factors such as different media around the metasurface and more than one illumination scenario are taken into account. In this work, we provide a general solution for a uniform metasurface homogenized in terms of susceptibilities. With this model, it is possible to obtain analytical expressions for the specular scattering produced by a metasurface illuminated with arbitrary illumination and angle of incidence. It is expected that the proposed model can ease the analysis and design of metasurfaces, by providing straight-forward expressions which can be simplified by exploiting the unit-cell symmetries.

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arXiv2024

Angle-Invariant Scattering in Metasurfaces

Metasurfaces are efficient and versatile electromagnetic structures that have already enabled the implementation of a wide range of microwave and photonic wave shaping applications. Despite the extensive research into metasurfaces, a rigorous and comprehensive understanding of their angular dispersion remains vastly under-explored. Here, we use the generalized sheet transition conditions (GSTCs) to model and analyze the angular dispersive properties of metasurfaces. Based on this theoretical framework, we demonstrate that a metasurface may exhibit either partial or complete co- and cross-polarized transmission and reflection coefficients that are angle-invariant, meaning that their amplitude, phase, or both remain unchanged with varying incidence angles. We show that these angle-independent responses exist only when specific conditions, given in terms of the metasurface effective susceptibilities, are met. Using the GSTCs formalism, we derive several of these conditions and illustrate their scattering properties. Among other findings, this analysis reveals that, contrary to common assumptions, nonlocality (spatial dispersion) does not only increase the angular dispersion of a metasurface, but may also be used to achieve complete angle-invariant scattering. Additionally, this work demonstrates that fully efficient extrinsic chirality is possible with a pseudochiral metasurface in a partially angle-invariant fashion. We expect our work to provide a general strategy for eliminating, or at least reducing, angular-dependent scattering responses of metasurfaces, which may prove instrumental for applications that are highly sensitive to the detrimental effects of angular dispersion.

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arXiv2024

Step Function in Momentum Space by a Metagrating

Metasurface research has shown significant potential for controlling the polarization, amplitude, phase and propagation direction of light. Nevertheless, control over the angular response of incident light still remains a long-standing problem. In this work, we show the potential of diffractive systems for obtaining a step function in momentum space where the mirror symmetry of the angular transmittance is broken. By engineering the scattering response of an asymmetric particles in a metagrating, we could obtain such a step function in a passive, reciprocal, and lossless fashion. More specifically, the metagrating performs filtering in the momentum space with an abrupt switching from reflection to transmission for an incident electromagnetic wave with an arbitrary spatial profile. This metagrating may find diverse applications in the context of optical spatial analog computing. Moreover, it paves the way for exploring the capabilities of diffractive systems for gaining full control over the angular response of light using arbitrary momentum transfer functions.

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arXiv2024

T-matrix representation of optical scattering response: Suggestion for a data format

The transition matrix, frequently abbreviated as T-matrix, contains the complete information in a linear approximation of how a spatially localized object scatters an incident field. The T-matrix is used to study the scattering response of an isolated object and describes the optical response of complex photonic materials made from ensembles of individual objects. T-matrices of certain common structures, potentially, have been repeatedly calculated all over the world again and again. This is not necessary and constitutes a major challenge for various reasons. First, the resources spent on their computation represent an unsustainable financial and ecological burden. Second, with the onset of machine learning, data is the gold of our era, and it should be freely available to everybody to address novel scientific challenges. Finally, the possibility of reproducing simulations could tremendously improve if the considered T-matrices could be shared. To address these challenges, we found it important to agree on a common data format for T-matrices and to enable their collection from different sources and distribution. This document aims to develop the specifications for storing T-matrices and associated metadata. The specifications should allow maximum freedom to accommodate as many use cases as possible without introducing any ambiguity in the stored data. The common format will assist in setting up a public database of T-matrices.

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arXiv2023

The art of finding the optimal scattering center(s)

The efficient use of a multipole expansion of the far field for rapid numerical modeling and optimization of the optical response from ordered and disordered arrays of various structural elements is complicated by the ambiguity in choosing the ultimate expansion centers for individual scatterers. Since the multipolar decomposition depends on the position of the expansion center, the sets of multipoles are not unique. They may require constrained optimization to get the compact and most efficient spatial spectrum for each scatterer. We address this problem by finding {\em the optimal scattering centers} for which the spatial multipolar spectra become unique. We separately derive these optimal positions for the electric and magnetic parts by minimizing the norm of the poloidal electric and magnetic quadrupoles. Employing the long-wave approximation (LWA) ansatz, we verify the approach with the theoretical discrete models and realistic scatterers. We show that the optimal electric and magnetic scattering centers, in all cases, are not co-local with the centers of mass. The optimal multipoles, including the toroidal terms, are calculated for several structurally distinct scattering cases, and their utility for low-cost numerical schemes, including the generalized T-matrix approach, is discussed. Expansion of the work beyond the LWA is possible, with a promise for faster and universal numerical schemes.

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arXiv2023

Multipolar Pseudochirality Induced Optical Torque

It has been observed that achiral nano-particles, such as flat helices, may be subjected to an optical torque even when illuminated by normally incident linearly polarized light. However, the origin of this fascinating phenomenon has so far remained mostly unexplained. We therefore propose an exhaustive discussion that provides a clear and rigorous explanation for the existence of such a torque. Using multipolar theory, and taking into account nonlocal interactions, we find that this torque stems from multipolar pseudochiral responses that generate both spin and orbital angular momenta. We also show that the nature of these peculiar responses makes them particularly dependent on the asymmetry of the particles. By elucidating the origin of this type of torque, this work may prove instrumental for the design of high-performance nano-rotors.

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arXiv2023

Quadrupolar susceptibility modeling of substrated metasurfaces with application to the generalized Brewster effect

We derive generalized sheet transition conditions (GSTCs) including dipoles and quadrupoles, using generalized functions (distributions). This derivation verifies that the GSTCs are valid for metasurfaces in non-homogeneous environments, such as for practical metasurfaces fabricated on a substrate. The inclusion of quadrupoles and modeling of spatial dispersion provides additional hyper-susceptibility components which serve as degrees of freedom for wave transformations. We leverage them to demonstrate a generalized Brewster effect with multiple angles of incidence at which reflection is suppressed, along with an ``anti-Brewster'' effect where transmission is suppressed.

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arXiv2023

Demonstration of a plasmonic nonlinear pseudo-diode

We demonstrate a nonlinear plasmonic metasurface that exhibits strongly asymmetric second-harmonic generation: nonlinear scattering is efficient upon excitation in one direction and it is substantially suppressed when the excitation direction is reversed, thus enabling a diode-like functionality. A significant (approximately 10 dB) extinction ratio of SHG upon opposite excitations is measured experimentally and those findings are substantiated with full-wave simulations. The combination of two commonly used metals - aluminium and silver - produces a material composition asymmetry that results into a bianisotropic response of the system, as confirmed by performing homogenization analysis and extracting an effective susceptibility tensor. Finally, we discuss the implications of our results from the more fundamental perspectives of reciprocity and time-reversal asymmetry.

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arXiv2022

Spatial Symmetries in Multipolar Metasurfaces: From Asymmetric Angular Transmittance to Multipolar Extrinsic Chirality

We propose a framework that connects the spatial symmetries of a metasurface to its material parameter tensors and its scattering matrix. This provides a simple yet effective way to effortlessly determine properties of a metasurface scattering response, such as chirality or asymmetric transmission, and which of its effective material parameters should be taken into account in the prospect of a homogenization procedure. In contrast to existing techniques, this approach does not require any a priori knowledge of group theory or complicated numerical simulation schemes, hence making it fast, easy to use and accessible. Its working principle consists in recursively solving symmetry-invariance conditions that apply to dipolar and quadrupolar material parameters, which include nonlocal interactions, as well as the metasurface scattering matrix. The overall process thus only requires listing the spatial symmetries of the metasurface. Using the proposed framework, we demonstrate the existence of multipolar extrinsic chirality, which is a form of chiral response that is achieved in geometrically achiral structures sensitive to field gradients even at normal incidence.

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arXiv2022

Multipolar expansions for scattering and optical force calculations beyond the long wavelength approximation

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 down to the Mie regimes.

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arXiv2022

Crossing of the branch cut: the topological origin of a universal 2π-phase retardation in non-Hermitian metasurfaces

Full wavefront control by photonic components requires that the spatial phase modulation on an incoming optical beam ranges from 0 to 2π. Because of their radiative coupling to the environment, all optical components are intrinsically non-Hermitian systems, often described by reflection and transmission matrices with complex eigenfrequencies. Here, we show that Parity-Time symmetry breaking -- either explicit or spontaneous -- moves the position of Zero singularities of the reflection or transmission matrices from the real axis to the upper part of the complex frequency plane. A universal 0 to 2π-phase gradient of an output channel as a function of the real frequency excitation is thus realized whenever the discontinuity branch bridging a Zero and a Pole, i.e a pair of singularities, is crossing the real axis. This basic understanding is applied to engineer electromagnetic fields at interfaces, including, but not limited to, metasurfaces. Non-Hermitian topological features associated with exceptional degeneracies or branch cut crossing are shown to play a surprisingly pivotal role in the design of resonant photonic systems.

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arXiv2021

Multipolar Modeling of Spatially Dispersive Metasurfaces

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. This results in a modeling accuracy that is at least two times better than the standard dipolar model.

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