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Karim Achouri

Publications and source records attributed to Karim Achouri.

At least 37 records · Page 2Linked to original sources
arXiv2021

Extension of Lorentz Reciprocity and Poynting Theorems for Spatially Dispersive Media with Quadrupolar Responses

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. 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.

physics.optics↗
arXiv2021

Surface Susceptibilities as Compact Full-Wave Simulation Models of Fully-Reflective Volumetric Metasurfaces

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.

physics.app-ph↗
arXiv2020

Reciprocal Metasurfaces for On-axis Reflective Optical Computing

Analog computing has emerged as a promising candidate for real-time and parallel continuous data processing. This paper presents a reciprocal way for realizing asymmetric optical transfer functions (OTFs) in the reflection side of the on-axis processing channels. It is rigorously demonstrated that the presence of Cross-polarization Exciting Normal Polarizabilities (CPENP) of a reciprocal metasurface circumvents the famous challenge of Green's function approach in implementation of on-axis reflective optical signal processing while providing dual computing channels under orthogonal polarizations. Following a comprehensive theoretical discussion and as a proof of concept, an all-dielectric optical metasurface is elaborately designed to exhibit the desired surface polarizabilities, thereby reflecting the first derivative and extracting the edges of images impinging from normal direction. The proposed study offers a flexible design method for on-axis metasurface-based optical signal processing and also, dramatically facilitates the experimental setup required for ultrafast analog computation and image processing.

physics.optics↗
arXiv2020

Fundamental Properties and Classification of Polarization Converting Bianisotropic Metasurfaces

We provide a detailed discussion on the electromagnetic modeling and classification of polarization converting bianisotropic metasurfaces. To do so, we first present a general approach to compute the scattering response of such metasurfaces, which relies on a generalized sheet transition conditions based susceptibility model. Then, we review how the fundamental properties of reciprocity, energy conservation, rotation invariance and matching may be expressed in terms of metasurface susceptibilities and scattering parameters, and show how these properties may affect and limit the polarization effects of metasurfaces. Finally, we connect together the metasurface susceptibility model to the structural symmetries of scattering particles and their associated polarization effects. This work thus provides a detailed understanding of the polarization conversion properties of metasurfaces and may prove to be of particular interest for their practical implementation.

physics.optics↗
arXiv2020

Multipolar Origin of the Unexpected Transverse Force Resulting from Two-Wave Interference

We propose a theoretical study on the electromagnetic forces resulting from the superposition of a TE and TM plane waves interacting with a sphere. Specifically, we first show that, under such an illumination condition, the sphere is subjected to a force transverse to the propagation direction of the waves. We then analyze the physical origin of this counter-intuitive behavior using a multipolar decomposition of the electromagnetic modes involved in that scattering process. This analysis reveals that interference effects, due to the two-wave illumination, lead to a Kerker-like asymmetric scattering behavior resulting in this peculiar transverse force.

physics.optics↗
arXiv2020

Metasurface Modeling by a Thin Slab

We investigate the possibility to model a metasurface, defined as a zero-thickness sheet of surface polarization currents, by a thin slab, characterized by a subwavelength thickness and usual voluminal medium parameters. First, we elaborate a general equivalence relation between the metasurface and the slab in terms of average electromagnetic fields. Then, we derive exact relations between the metasurface and slab susceptibilities and validate them by full-wave simulations. Finally, we discuss the simple and insightful Average Field Approximation (AFA) formula, illustrate its inappropriate for strong metasurface field transformations, and establish its range of validity. All of these developments are restricted to the simplest case of a uniform isotropic metasurface under normal plane wave incidence. We conclude from the complexity of the equivalence for this case, that a metasurface is generally best modeled in terms of Generalized Sheet Transition Conditions (GSTCs).

physics.app-ph↗
arXiv2018

Generalized Optical Signal Processing Based on Multi-Operator Metasurfaces Synthesized by Susceptibility Tensors

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.

physics.optics↗
arXiv2018

Influence of Reciprocity, Symmetry and Normal Polarizations on the Angular Scattering Properties of Bianisotropic Metasurfaces

This paper aims at studying the angular scattering properties of bianisotropic metasurfaces and at clarifying the different roles played by tangential and normal polarization densities. Different types of metasurfaces are considered for this study and are classified according to their symmetrical/asymmetrical and reciprocal/nonreciprocal angular scattering behavior. Finally, the paper presents the relationships between the symmetrical angular scattering properties of reciprocal metasurfaces and the structural symmetries of their scattering particles. This may prove to be practically useful for the implementation of metasurfaces with complex angular scattering characteristics.

physics.optics↗
arXiv2018

Surface-Wave Dispersion Retrieval Method and Synthesis Technique for Bianisotropic Metasurfaces

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.

physics.optics↗
arXiv2018

What is Nonreciprocity?

This paper aims at providing a global perspective on electromagnetic nonreciprocity and clarifying confusions that arose in the recent developments of the field. It provides a general definition of nonreciprocity and classifies nonreciprocal systems according to their linear time-invariant (LTI), linear time-variant (LTV) or nonlinear nonreciprocal natures. The theory of nonlinear systems is established on the foundation of the concepts of time reversal, time-reversal symmetry, time-reversal symmetry breaking and related Onsager- Casimir relations. Special attention is given to LTI systems, as 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. The fundamental characteristics and applications of LTI, LTV and nonlinear nonreciprocal systems are overviewed with the help of pedagogical examples. Finally, asymmetric structures with fallacious nonreciprocal appearances are debunked.

physics.optics↗
arXiv2018

What is Nonreciprocity? Part II

This paper is the second part of a two-part paper on \emph{Electromagnetic (EM) Nonreciprocity (NR)}. Part~I has defined NR, pointed out that linear NR is a stronger form of NR than nonlinear (NL) NR, explained EM Time-Reversal (TR) Symmetry (TRS) Breaking (TRS-B), described linear Time-Invariant (TI) NR media, generalized the Lorentz reciprocity theorem for NR, and provided a physical interpretation of the resulting Onsager-Casimir relations~\cite{Caloz_AWPL_NR_I_2018}. This part first explains the TR specificity of lossy and open systems. Next, it proposes an extended version of the S-parameters for \emph{all NR} systems. Then, it presents the fundamentals of linear-TI (LTI) NR, linear Time-Variant (LTV) Space-Time (ST) modulated NR and NL NR systems. Finally, it addresses confusions between with systems.

physics.optics↗
arXiv2018

Homogenization and Scattering Analysis of Second-Harmonic Generation in Nonlinear Metasurfaces

We propose an extensive discussion on the homogenization and scattering analysis of second-order nonlinear metasurfaces. Our developments are based on the generalized sheet transition conditions (GSTCs) which 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.

physics.optics↗
arXiv2017

Design, Concepts and Applications of Electromagnetic 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. Upon 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.

physics.optics↗
arXiv2017

Computational Analysis of Metasurfaces

Metasurfaces represent one of the most vibrant fields of modern science and technology. A metasurface is a complex electromagnetic structure, that 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, spacevarying 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 problematic, 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 (FDFD, SD-IE, FEM) and time-domain (FDTD) computational techniques.

physics.optics↗
arXiv2017

Metasurface Solar Sail for flexible Radiation Pressure Control

We propose to use metasurfaces as a mean of controlling radiation pressure for increasing the range of motions of spacecraft solar sails. Specifically, we present a theoretical study of different electromagnetic field configurations, and corresponding metasurface structures, that allow one to achieve repulsive, attractive, lateral and rotational forces.

physics.optics↗
arXiv2017

Refracting Metasurfaces without Spurious Diffraction

Refraction represents one of the most fundamental operations that may be performed by a metasurface. However, simple phasegradient metasurface designs suffer from restricted angular deflection due to spurious diffraction orders. It has been recently shown, using a circuit-based approach, that refraction without spurious diffraction, or diffraction-free, can fortunately be achieved by a transverse metasurface exhibiting either loss-gain or bianisotropy. Here, we rederive these conditions using a medium-based - and hence more insightfull - approach based on Generalized Sheet Transition Conditions (GSTCs) and surface susceptibility tensors, and experimentally demonstrate two diffraction-free refractive metasurfaces that are essentially lossless, passive, bianisotropic and reciprocal.

physics.class-ph↗
arXiv2017

Perfectly Refractive Metasurface using Bianisotropy

A passive and reciprocal perfectly refractive metasurface 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.

physics.class-ph↗