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Boris Gralak

Publications and source records attributed to Boris Gralak.

At least 19 recordsLinked to original sources

Robust Quasi-Bound States in the continuum: Accidental and Symmetry-Protected Variants in Dielectric Metasurfaces

Recently, man-made dielectric materials composed of finite-sized dielectric constituents have emerged as a promising platform for quasi-bound states in the continuum (QBICs). These states allow for an extraordinary confinement of light within regions smaller than the wavelength scale. Known for their exceptional quality factors, they have become crucial assets across a diverse array of applications. Given the circumstances, there is a compelling drive to find meta-designs that can possess multiple QBICs. Here, we demonstrate the existence of two different types of QBICs in silicon-based metasurfaces: accidental QBIC and symmetry-protected QBIC. The accidental QBIC evinces notable resilience to variations in geometrical parameters and symmetry, underscoring its capacity to adeptly navigate manufacturing tolerances while consistently upholding a distinguished quality factor of $10^5$. Conversely, the symmetry-protected QBIC inherently correlates with the disruption of unit cell symmetry. As a result, a phase delay yields an efficient channel for substantial energy transference to the continuum, endowing this variant with an exceedingly high quality factor, approaching $10^8$. Moreover, the manifestation of these QBICs stems from the intricate interplay among out-of-plane electric and magnetic dipoles, alongside in-plane quadrupoles exhibiting odd parities.

cond-mat.mtrl-sci

Dispersive Perfectly Matched Layer and high order Absorbing Boundary Conditions for the computation of Quasinormal modes of open electromagnetic structures

Resonances, also known as quasinormal modes (QNM) in the non-Hermitian case, play a ubiquitous role in all domains of physics ruled by wave phenomena, notably in continuum mechanics, acoustics, electrodynamics, and quantum theory. The non-Hermiticity arises from the system losses, whether they are material (Joule losses in electromagnetism) or linked to the openness of the problem (radiation losses). In this paper, we focus on the latter delicate matter when considering bounded computational domains mandatory when using e.g. Finite Elements. Dispersive perfectly matched layers and absorbing boundary conditions are studied.

physics.optics

Non-linear eigenvalue problems with GetDP and SLEPc: Eigenmode computations of frequency-dispersive photonic open structures

We present a framework to solve non-linear eigenvalue problems suitable for a Finite Element discretization. The implementation is based on the open-source finite element software GetDP and the open-source library SLEPc. As template examples, we propose and compare in detail different ways to address the numerical computation of the electromagnetic modes of frequency-dispersive objects. This is a non-linear eigenvalue problem involving a non-Hermitian operator. A classical finite element formulation is derived for five different solutions and solved using algorithms adapted to the large size of the resulting discrete problem. The proposed solutions are applied to the computation of the dispersion relation of a diffraction grating made of a Drude material. The important numerical consequences linked to the presence of sharp corners and sign-changing coefficients are carefully examined. For each method, the convergence of the eigenvalues with respect to the mesh refinement and the shape function order, as well as computation time and memory requirements are investigated. The open-source template model used to obtain the numerical results is provided. Details of the implementation of polynomial and rational eigenvalue problems in GetDP are given in appendix.

physics.comp-ph

Experimental demonstration of spectrally-broadband Huygens sources using low-index spheres

Manipulating the excitation of resonant electric and magnetic multipole moments in structured dielectric media has unlocked many sophisticated electromagnetic functionalities. This article demonstrates the experimental realization of a broadband Huygens' source. This Huygens' source consists of a spherical particle that exhibits a well-defined forward-scattering pattern across more than an octave-spanning spectral band at GHz frequencies, where the scattering in the entire backward hemisphere is suppressed. Two different low-index nonmagnetic spheres are studied that differ in their permittivity. This causes them to offer a different shape for the forward-scattering pattern. The theoretical understanding of this broadband feature is based on the approximate equality of the resonant electric and magnetic multipole moments in both amplitude and phase in low permittivity spheres. This is a key condition to approximate the electromagnetic duality symmetry which, together with the spherical symmetry, suppresses the backscattering. With such a configuration, broadband Huygens' sources can be designed even if magnetic materials are unavailable. This article provides guidelines for designing broadband Huygens' sources using low-index spheres that could be valuable to a plethora of applications.

physics.class-ph

Completeness and divergence-free behavior of the quasi-normal modes using causality principle

A fundamental feature of the quasi-normal modes (QNMs), which describe light interaction with open (leaky) systems like nanoparticles, lies in the question of the completeness of the QNMs representation and in the divergence of their field profile due to their leaky behavior and complex eigenfrequency. In this article, the QNMs expansion is obtained by taking into consideration the frequency dispersion and the causality principle. The derivation based on the complex analysis ensures the completeness of the QNMs expansion and prevents from any divergence of the field profile. The general derivation is tested in the case of a one-dimensional open resonator made of a homogeneous absorptive medium with frequency dispersion given by the Lorentz model. For a harmonic excitation, the result of the QNMs expansion perfectly matches the exact formula for the field distribution outside as well as inside the resonator.

physics.optics

Electromagnetic waves in photonic crystals: laws of dispersion, causality and analytical properties

Photonic crystals are periodic structures which prevent light propagation along one or more directions in certain frequency intervals. Their band spectrum is usually analyzed using Floquet-Bloch decomposition. This spectrum is located on the real axis, and it enters the complex plane when absorption and dispersion is considered in the dielectric permittivity of material constituents. Here, we review fundamental definition and properties of dispersion law and group velocity in photonic crystals and we illustrate them with numerical examples.

physics.optics

Approached vectorial model for Fano resonances in guided mode resonance gratings

We propose a self-consistent vectorial method, based on a Green's function technique, to describe the Fano resonances that appear in guided mode resonance gratings. The model provides intuitive expressions of the reflectivity and transmittivity matrices of the structure, involving coupling integrals between the modes of a planar reference structure and radiative modes. These expressions are used to derive a physical analysis in configurations where the effect of the incident polarization is not trivial. We provide numerical validations of our model. On a technical point of view, we show how the Green's tensor of our planar reference structure can be expressed as two scalar Green's functions, and how to deal with the singularity of the Green's tensor.

physics.optics

Electromagnetic wave propagation through a slab of a dispersive medium

A method is proposed for the analysis of the propagation of electromagnetic waves through a homogeneous slab of a medium with Drude-Lorentz dispersion behavior, and excited by a causal sinusoidal source. An expression of the time dependent field, free from branch-cuts in the plane of complex frequencies, is established. This method provides the complete temporal response in both the steady-state and transient regimes in terms of discrete poles contributions. The Sommerfeld and Brillouin precursors are retrieved and the corresponding set of poles are identified. In addition, the contribution in the transient field of the resonance frequency in the Drude-Lorentz model is exhybited, and the effect of reflections resulting from the refractive index mismatch at the interfaces of the slab are analyzed.

physics.optics

Analytic properties of the electromagnetic Green's function

The electromagnetic Green's function is expressed from the inverse Helmholtz operator, where a second frequency has been introduced as a new degree of freedom. The first frequency results from the frequency decomposition of the electromagnetic field while the second frequency is associated with the dispersion of the dielectric permittivity. Then, it is shown that the electromagnetic Green's function is analytic with respect to these two complex frequencies as soon as they have positive imaginary part. Such analytic properties are also extended to complex wavevectors. Next, Kramers-Kronig expressions for the inverse Helmholtz operator and the electromagnetic Green's function are derived. In addition, these Kramers-Kronig expressions are shown to correspond to the classical eigengenmodes expansion of the Green's function established in simple situations. Finally, the second frequency introduced as a new degree of freedom is exploited to characterize non-dispersive systems.

math-ph

Finite Element Analysis of Electromagnetic Waves in Two-Dimensional Transformed Bianisotropic Media

We analyse wave propagation in two-dimensional bianisotropic media with the Finite Element Method (FEM). We start from the Maxwell-Tellegen's equations in bianisotropic media, and derive some system of coupled Partial Difference Equations (PDEs) for longitudinal electric and magnetic field components. Perfectly Matched Layers (PMLs) are discussed to model such unbounded media. We implement these PDEs and PMLs in a finite element software. We apply transformation optics in order to design some bianisotropic media with interesting functionalities, such as cloaks, concentrators and rotators. We propose a design of metamaterial with concentric layers made of homogeneous media with isotropic permittivity, permeability and magneto-electric parameters that mimic the required effective anisotropic tensors of a bianisotropic cloak in the long wavelength limit (homogenization approach). Our numerical results show that well-known metamaterials can be transposed to bianisotropic media.

physics.optics

Calculation and analysis of complex band structure in dispersive and dissipative two-dimensional photonic crystals

Numerical calculation of modes in dispersive and absorptive systems is performed using the finite element method. The dispersion is tackled in the frame of an extension of Maxwell's equations where auxiliary fields are added to the electromagnetic field. This method is applied to multi-domain cavities and photonic crystals including Drude and Drude-Lorentz metals. Numerical results are compared to analytical solutions for simple cavities and to previous results of the literature for photonic crystals, showing excellent agreement. The advantages of the developed method lie on the versatility of the finite element method regarding geometries, and in sparing the use of tedious complex poles research algorithm. Hence the complex spectrum of resonances of non-hermitian operators and dissipative systems, like two-dimensional photonic crystal made of absorbing Drude metal, can be investigated in detail. The method is used to reveal unexpected features of their complex band structures.

physics.optics

Analogies between optical propagation and heat diffusion: Applications to micro-cavities, gratings and cloaks

A new analogy between optical propagation and heat diffusion in heterogeneous anisotropic media has been proposed recently [S. Guenneau, C. Amra, and D. Veynante, Optics Express Vol. 20, 8207-8218 (2012)]. A detailed derivation of this unconventional correspondence is presented and developed. In time harmonic regime, all thermal parameters are related to optical ones in artificial metallic media, thus making possible to use numerical codes developed for optics. Then the optical admittance formalism is extended to heat conduction in multilayered structures. The concepts of planar micro-cavities, diffraction gratings, and planar transformation optics for heat conduction are addressed. Results and limitations of the analogy are emphasized.

physics.optics

Phase retrieval of reflection and transmission coefficients from Kramers-Kronig relations

Analytic and passivity properties of reflection and transmission coefficients of thin-film multilayered stacks are investigated. Using a rigorous formalism based on the inverse Helmholtz operator, properties associated to causality principle and passivity are established when both temporal frequency and spatial wavevector are continued in the complex plane. This result extends the range of situations where the Kramers-Kronig relations can be used to deduce the phase from the intensity. In particular, it is rigorously shown that Kramers-Kronig relations for reflection and transmission coefficients remain valid at a fixed angle of incidence. Possibilities to exploit the new relationships are discussed.

physics.optics

Finite frequency external cloaking with complementary bianisotropic media

We investigate the twofold functionality of a cylindrical shell consisting of a negatively refracting heterogeneous bianisotropic (NRHB) medium deduced from geometric transforms. The numerical simulations indicate that the shell enhances their scattering by a perfect electric conducting (PEC) core, whereas it considerably reduces the scattering of electromagnetic waves by closely located dipoles when the shell surrounds a bianisotropic core. The former can be attributed to a homeopathic effect, whereby a small PEC object scatters like a large one as confirmed by numerics, while the latter can be attributed to space cancelation of complementary bianisotropic media underpinning anomalous resonances counteracting the field emitted by small objects (external cloaking). Space cancellation is further used to cloak a NRHB finite size object located nearby a slab of NRHB with a hole of same shape and opposite refracting index. Such a finite frequency external cloaking is also achieved with a NRHB cylindrical lens. Finally, we investigate an ostrich effect whereby the scattering of NRHB slab and cylindrical lenses with simplified parameters hide the presence of dipoles in the quasi-static limit.

physics.optics

Optical properties of multilayer optics including negative index materials

Negative indices are revisited through the thin-film admittance formalism. Effective indices and phase delay associated with wave propagation through negative index layers are carefully defined and computational rules easily implementable in standard thin-film software are derived from this approach. This admittance formalism is then used to recover the main features of the perfect lens and to highlight the benefit of such negative index materials to improve the performances of quarter-wavelength Bragg mirrors and Fabry-Perot band-pass filters.

physics.optics

Negative Index Materials: The Key to "White" Multilayer Fabry-Perot

The use of negative index materials is highly efficient for tayloring the spectral dispersion properties of a quarter-wavelength Bragg mirror and for obtaining a resonant behavior of a multilayer Fabry-Perot cavity over a very large spectral range. An optimization method is proposed and validated on some first promising devices.

physics.optics

Artificial magnetism and magnetoelectric coupling from dielectric layers

We investigate a high-order homogenization (HOH) algorithm for periodic multilayered stacks. The mathematical tool of choice is a transfer matrix method. Expressions for effective permeability, permittivity and magnetoelectric coupling are explored by frequency power expansions. On the physical side, this high-order homogenization uncovers a magnetoelectric coupling effect (odd order approximation) and artificial magnetism (even order approximation) in moderate contrast photonic crystals. Comparing the effective parameters' expressions of a stack with three layers against that of a stack with two layers, we note that the magnetoelectric coupling effect vanishes while the artificial magnetism can still be achieved in a center symmetric periodic structure. Furthermore, we numerically check the effective parameters through the dispersion law and transmission curves of a stack with two dielectric layers against that of an effective bianisotropic medium: they present a good agreement in the low frequency (acoustic) band until the first stop band, where the analyticity of the logarithm function of transfer matrix ($\log\{T\}$) breaks down.

cond-mat.mes-hall

A route to all frequency homogenization of periodic structures

We start from a one-dimensional periodic multilayered stack in order to define a frequency power expansion of effective permittivity, permeability and bianisotropic parameters. It is shown from the first order that a simple dielectric multilayer can display a magnetoelectric coupling effect and, from the second order, that artificial magnetism can be obtained with arbitrary low contrast. However, this frequency power expansion is found to diverge at the first band gap edge. Thus, an alternative set of effective parameters, made of the propagation index and the surface impedance, is proposed. It is established that these effective parameters, as functions of the complex frequency, possess all the analytic properties required by the causality principle and passivity. Finally, we provide arguments to extend these results to the three-dimensional and frequency-dispersive case.

physics.optics