arXiv subjects

Zoé-Lise Deck-Léger

Publications and source records attributed to Zoé-Lise Deck-Léger.

At least 19 recordsLinked to original sources

arXiv2024

Wave-Medium Interactions in Dynamic Matter and Modulation Systems

Space-time modulation systems have garnered significant attention due to their resemblance to moving-matter systems and promising applications. Unlike conventional moving-matter systems, modulation systems do not involve net motion of matter, and are therefore easier to implement and not restricted to subluminal velocities. However, canonical wave-medium interaction aspects, such as scattering and energy-momentum relations, have remained largely unexplored. In this paper, we address the aforementioned issues for three dynamic systems: moving-matter blocs, moving-perturbation interfaces and moving-perturbation periodic structures, and provide corresponding general formulations along with comparisons. Our investigation reveals the significant roles played by the "catch-up" effect between waves and interfaces. Even more interestingly, it reveals different energy and momentum exchanges between moving media and homogenized moving-perturbation structures as a result of conventional and reverse Fresnel-Fizeau drag effects.

physics.optics↗

arXiv2023

Generalized FDTD Scheme for Moving Electromagnetic Structures with Arbitrary Space-Time Configurations

We present a generalized FDTD scheme to simulate moving electromagnetic structures with arbitrary space-time configurations. This scheme is a local adaptation and 2+1-dimensional extension of the uniform and 1+1-dimensional scheme recently reported in [1]. The local adaptation, which is allowed by the inherently matched nature of the generalized Yee cell to the conventional Yee cell, extends the range of applicability of the scheme in [1] to moving structures that involve multiple and arbitrary velocity profiles while being fully compatible with conventional absorbing boundary conditions and standard treatments of medium dispersion. We show that a direct application of the conventional FDTD scheme predicts qualitatively correct spectral transitions but quantitatively erroneous scattering amplitudes, we infer from this observation generalized, hybrid-physical and auxiliary (non-physical) - fields that automatically satisfy moving boundary conditions in the laboratory frame, and accordingly establish local update equations based on the related Maxwell's equations and constitutive relations. We subsequently provide a detailed stability analysis with a generalization of the Courant criterion to the dynamic regime. We finally validate and illustrate the proposed method by several representative examples. The proposed scheme fills an important gap in the open literature on computational electromagnetics and offers an unprecedented, direct solution for moving structures in commercial software platforms.

cs.CE↗

arXiv2023

Space-Time Fresnel Prism

Space-time modulation-based metamaterials have recently spurred considerable interest, owing to the fundamental addition of the time dimension to the medium parameters, and resulting novel properties and potential applications. However, the implementation of most related structures -- e.g., involving step, slab or gradient discontinuities -- has been hindered by the impossible requirement of infinitely or prohibitively large device sizes. We provide here a solution to this issue, consisting in a space-time transposition of the conventional Fresnel prism, whereby a copy of the target modulation is periodically re-injected at the input of a Fresnel-reduced finite structure, so as to provide the same anharmonic and nonreciprocal frequency conversion as the target space-time interface in the case of a modulation step. This concept, which may readily extend to slab or gradient modulations, as well as accelerated profiles for space-time chirping operations, may pave the way for the practical development of a wide range of novel microwave and optical space-time systems.

physics.optics↗

arXiv2023

Orthogonal Analysis of Space-Time Crystals

This paper presents a space-time-wise orthogonal analysis of space-time crystals. This analysis provides a solution consisting of a pair of explicit parametric equations that result from a separate application of the Bloch-Floquet theorem in the (orthogonal) directions of space and time. Compared to previous approaches, this solution offers the benefits of greater simplicity, clearer emphasis on space-time duality and deeper physical insight.

physics.optics↗

arXiv2023

Generalized FDTD Scheme for the Simulation of Electromagnetic Scattering in Moving Structures

Electromagnetic scattering in moving structures is a fundamental topic in physics and engineering. Yet, no general numerical solution to related problems has been reported to date. We introduce here a generalized FDTD scheme to remedy this deficiency. That scheme is an extension of the FDTD standard Yee cell and stencil that includes not only the usual, physical fields, but also auxiliary, unphysical fields allowing a straightforward application of moving boundary conditions. The proposed scheme is illustrated by four examples -- a moving interface, a moving slab, a moving crystal and a moving gradient -- with systematic validation against exact solutions.

physics.comp-ph↗

arXiv2023

Electrodynamics of Accelerated-Modulation Space-Time Metamaterials

Space-time varying metamaterials based on uniform-velocity modulation have spurred considerable interest over the past decade. We present here the first extensive investigation of accelerated modulation space-time metamaterials. Using the tools of general relativity, we establish their electrodynamic principles and describe their fundamental phenomena, in comparison with the physics of moving-matter media. We show that an electromagnetic beam propagating in an accelerated modulation metamaterial is bent in its course, which reveals that such a medium curves space-time for light, similarly to gravitation. Finally, we illustrate the vast potential diversity of accelerated modulation metamaterial by demonstrating related Schwarzschild holes.

physics.optics↗

arXiv2022

Generalized Total Internal Reflection at Dynamic Interfaces

Recent research developments in the area of spacetime metamaterial structures and systems have raised new questions as to how the physics of fundamental phenomena is altered in the presence of spacetime modulation. In this context, we present a generalized and comparative description of the phenomenon of total internal reflection (TIR) at different dynamic interfaces. Such interfaces include, beyond the classical interfaces corresponding to the boundaries of moving bodies (moving interface -- moving matter systems), interfaces formed by a traveling-wave step modulation of an electromagnetic parameter (e.g., refractive index) (moving interface -- stationary matter systems) and fixed interfaces between moving-matter media (stationary interface -- moving matter systems). We first resolve the problem using the evanescence of the transmitted wave as the criterion for TIR and applying the conventional technique of relative frame hopping (between the laboratory and rest frames), which results in closed-form formulas for the relevant critical (incidence, reflection, phase refraction and power refraction) angles. We then introduce the concept of catch-up limit between the dynamic interface and the transmitted wave as an alternative criterion for the critical angle. We use this approach both to analytically verify the critical angle formulas, further validated by full-wave (FDTD) analysis, and to explain the related physics, using Fresnel-Fizeau drag and spacetime frequency transition considerations. These results might find various applications in ultra-fast optics, gravity analogs and quantum processing.

physics.optics↗

arXiv2022

Generalized Space-Time Engineered Modulation (GSTEM) Metamaterials

This article presents a global and generalized perspective of electrodynamic meta-materials formed by space and time engineered modulations, which we name Generalized Space-Time Engineered Modulation (GSTEM) Metamaterials, or GSTEMs. In this perspective, it describes metamaterials from a unified spacetime viewpoint and introduces accelerated metamaterials as an extra type of dynamic metamaterials. First, it positions GSTEMs in the even broader context of electrodynamic systems that include (non-modulated) moving sources in vacuum and moving bodies, explains the difference between the moving-matter nature of the latter and the moving-perturbation nature of GSTEMs, and enumerates the different types of GSTEMs considered, namely Space EMs (SEMs), Time EMs (TEMs), Uniform Space-Time EMs (USTEMs) and Accelerated Space-Time EMs (ASTEMs). Next, it establishes the physics of the related interfaces, which includes direct-spacetime scattering and inverse-spacetime transition transformations. Then, it exposes the physics of the GSTEM metamaterials formed by stacking these interfaces and homogenizing the resulting crystals; this includes an original explanation of light deflection by USTEMs as being a spacetime weighted averaging phenomenon and the demonstration of ASTEM light curving and black-hole light attraction. Finally, it discusses some future prospects. Useful complementary information and animations are provided in the Supplementary Material.

physics.optics↗

arXiv2021

Wave Scattering in Moving Media across the Subluminal-Interluminal Regimes

This paper extends current knowledge on electromagnetic wave scattering from bounded moving media in several regards. First, it complements the usual dispersion relation of moving media, $ω(θ_\mathbf{k})$ ($θ_\mathbf{k}$: phase velocity direction, associated with the wave vector, $\mathbf{k}$), with the equally important impedance relation, $η(θ_\mathbf{S})$ ($θ_\mathbf{S}$: group velocity direction, associated with the Poynting vector, $\mathbf{S}$). Second, it explains the interluminal-regime phenomenon of double-downstream wave transmission across a stationary interface between a regular medium and the moving medium, assuming motion perpendicular to the interface, and shows that the related waves are symmetric in terms of the energy refraction angle, while being asymmetric in terms of the phase refraction angle, with one of the waves subject to negative refraction, and shows that the wave impedances of the two transmitted waves are equal. Third, it generalizes the problem to the case where the medium moves obliquely with respect to the interface. Finally, it highlights the connection between this problem and a spacetime modulated medium.

physics.optics↗

arXiv2019

Uniform-Velocity Spacetime Crystals

We perform a comprehensive analysis of uniform-velocity bilayer spacetime crystals, combining concepts of conventional photonic crystallography and special relativity. Given that a spacetime crystal consists of a sequence of spacetime discontinuities, we do this by solving the following sequence of problems: 1) the spacetime interface, 2) the double spacetime interface, or spacetime slab, 3) the unbounded crystal, and 4) the truncated crystal. For these problems, we present the following respective new results: 1) an extension of the Stokes principle to spacetime interfaces, 2) an interference-based analysis of the interference phenomenology, 3) a quick linear approximation of the dispersion diagrams, a description of simultaneous wavenumber and frequency bandgaps, and 4) the explanation of the effects of different types of spacetime crystal truncations, and the corresponding scattering coefficients. This work may constitute the foundation for a virtually unlimited number of novel canonical spacetime media and metamaterial problems.

physics.optics↗

arXiv2019

Spacetime Metamaterials

This paper presents the authors' vision of the emerging field of spacetime metamaterials in a cohesive and pedagogical perspective. For this purpose, it systematically builds up the physics, modeling and applications of these media upon the foundation of their pure-space and pure-time counterparts.

physics.optics↗

arXiv2019

Scattering at Interluminal Interface

Interest for spacetime structures has recently been revived, following developments in metamaterials and ultrafast optics. Such structures essentially consist of successions of space-time interfaces for which the theory is still incomplete, in particular in the regime where the interface velocity lies between the wave velocities in the two media involved. This paper addresses this `interluminal' regime, providing exact scattering solutions for both approaching and receding interfaces. The solutions are verified to be consistent with the transmission matrix perspective and to be continuous at the limits of the subluminal and superluminal regimes.

physics.optics↗

arXiv2018

Microwave Hilbert Transformer and its Applications in Real-time Analog Processing (RAP)

A microwave Hilbert transformer is introduced as a new component for Real-time Analog Processing (RAP). In contrast to its optical counterpart, that resort to optical fiber gratings, this Hilbert transformer is based on the combination of a branch-line coupler and a loop resonator. The transfer function of the transformer is derived using signal flow graphs, and two figures of merits are introduced to effectively characterize the device: the rotated phase and the transition bandwidth. Moreover, a detailed physical explanation of its physical operation is given, using both a steady-state regime perspective and a transient regime perspective. The microwave RAP Hilbert transformer is demonstrated experimentally, and demonstrated in three applications: edge detection, peak suppression and single sideband modulation.

eess.SP↗

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

Wave Deflection and Shifted Refocusing in a Medium Modulated by a Superluminal Rectangular Pulse

We explore the problem of scattering in a medium modulated by a superluminal rectangular pulse, with the pulse modulation realized through transverse excitations. We solve this problem in the moving frame where the modulation appears purely temporal, since the solution to a purely temporal modulation is known. Upon this basis, we use a graphical approach to find the angle and frequency of the wave scattered by the modulation under oblique incidence. This study reveals that superluminal modulations deflect plane waves retro-directively, and refocus cylindrical waves to a shifted point of space with respect to the original source.

physics.class-ph↗

arXiv2017

New Electromagnetic Modes in Space-Time Modulated Dispersion-Engineered Media

We report on new electromagnetic modes in space-time modulated dispersion-engineered media. These modes exhibit unusual dispersion relation, field profile and scattering properties. They are generated by coupled codirectional space-time harmonic pairs, and occur in space-time periodic media whose constituent materials exhibit specific dispersion. Excitation of a slab of such a medium with subluminal modulation results in periodic transfer of energy between the incident frequency and a frequency shifted by a multiple of the modulation frequency, whereas superluminal modulation generates exponentially growing frequencies. These modes may find applications in optical mixers, terahertz sources and other optical devices.

physics.optics↗

arXiv2017

Optical Isolation based on Space-time Engineered Asymmetric Photonic Bandgaps

Nonreciprocal electromagnetic devices play an important role in modern optical and microwave technologies. Conventional methods for realizing such systems are incompatible with integrated circuits. With recent advances in integrated photonics, the need for efficient on-chip magnetless nonreciprocal devices is more urgent than ever. This paper leverages space-time engineered asymmetric photonic bandgaps to generate optical isolation. It is shown that a properly designed space-time modulated slab is highly reflective/transparent for opposite directions of propagation. The proposed method requires a low modulation frequency, is magnetless and can achieve very high isolation levels. Experimental proof of concept at microwave frequencies is provided.

physics.optics↗