Dispersive Dielectrics Research Articles

Dielectric Mie voids: confining light in air

Manipulating light on the nanoscale has become a central challenge in metadevices, resonant surfaces, nanoscale optical sensors, and many more, and it is largely based on resonant light confinement in dispersive and lossy metals and dielectrics. Here, we experimentally implement a novel strategy for dielectric nanophotonics: Resonant subwavelength localized confinement of light in air. We demonstrate that voids created in high-index dielectric host materials support localized resonant modes with exceptional optical properties. Due to the confinement in air, the modes do not suffer from the loss and dispersion of the dielectric host medium. We experimentally realize these resonant Mie voids by focused ion beam milling into bulk silicon wafers and experimentally demonstrate resonant light confinement down to the UV spectral range at 265 nm (4.68 eV). Furthermore, we utilize the bright, intense, and naturalistic colours for nanoscale colour printing. Mie voids will thus push the operation of functional high-index metasurfaces into the blue and UV spectral range. The combination of resonant dielectric Mie voids with dielectric nanoparticles will more than double the parameter space for the future design of metasurfaces and other micro- and nanoscale optical elements. In particular, this extension will enable novel antenna and structure designs which benefit from the full access to the modal field inside the void as well as the nearly free choice of the high-index material for novel sensing and active manipulation strategies.

FDTD-Based Electromagnetic Modeling of Dielectric Materials with Fractional Dispersive Response

The use of fractional derivatives and integrals has been steadily increasing thanks to their ability to capture effects and describe several natural phenomena in a better and systematic manner. Considering that the study of fractional calculus theory opens the mind to new branches of thought, in this paper, we illustrate that such concepts can be successfully implemented in electromagnetic theory, leading to the generalizations of the Maxwell’s equations. We give a brief review of the fractional vector calculus including the generalization of fractional gradient, divergence, curl, and Laplacian operators, as well as the Green, Stokes, Gauss, and Helmholtz theorems. Then, we review the physical and mathematical aspects of dielectric relaxation processes exhibiting non-exponential decay in time, focusing the attention on the time-harmonic relative permittivity function based on a general fractional polynomial series approximation. The different topics pertaining to the incorporation of the power-law dielectric response in the FDTD algorithm are explained, too. In particular, we discuss in detail a home-made fractional calculus-based FDTD scheme, also considering key issues concerning the bounding of the computational domain and the numerical stability. Finally, some examples involving different dispersive dielectrics are presented with the aim to demonstrate the usefulness and reliability of the developed FDTD scheme.

Effects ofCPT-odd terms of dimensions three and five on electromagnetic propagation in continuous matter

In this work we study how CPT-odd Maxwell-Carroll-Field-Jackiw (MCFJ) electrodynamics as well as a dimension-5 extension of it affect the optical activity of continuous media. The starting point is dimension-3 MCFJ electrodynamics in matter whose modified Maxwell equations, permittivity tensor, and dispersion relations are recapitulated. Corresponding refractive indices are achieved in terms of the frequency and the vector-valued background field. For a purely timelike background, the refractive indices are real. Their associated propagation modes are circularly polarized and exhibit birefringence. For a purely spacelike background, one refractive index is always real and the other can be complex. The circularly polarized propagating modes may exhibit birefringence and dichroism (associated with absorption). Subsequently, we examine a dimension-five MCFJ-type electrodynamics, previously scrutinized in the literature, in a continuous medium. Following the same procedure, we find the refractive indices from a sixth-order dispersion equation. For a purely timelike background, three distinct refractive indices are obtained, one of them being real and two being complex. They are associated with two circularly polarized propagating modes that exhibit birefringence or dichroism, depending on the frequency range. Scenarios of propagation and absorption analogous to those found in dispersive dielectrics are also observed for spacelike background configurations. We conclude by comparing the dimension-three and five results and by emphasizing the richer phenomenology of the propagating modes in the higher-derivative model. Our results are applicable in the realm of Weyl semimetals.

Electro-optical sampling of quantum vacuum fluctuations in dispersive dielectrics

Electro-optical sampling has been recently used to perform spectrally-resolved measurements of electromagnetic vacuum fluctuations. In order to understand which information on the ground state of an interacting system can be acquired thanks to this technique, in this paper we will develop the quantum theory of electro-optical sampling in arbitrary dispersive dielectrics. Our theory shows that a measure of the time correlations of the vacuum fluctuations effectively implements an ellipsometry measurement on the quantum vacuum, allowing to access the frequency-dependent dielectric function. We discuss consequences of these results on the possibility to use electro-optical sampling to probe the population of ground-state virtual photons in the ultrastrong light-matter coupling regime.

Permittivity measurement of cementitious materials and constituents with an open-ended coaxial probe: combination of experimental data, numerical modelling and a capacitive model

The study presents the development of a new two-dimensional FEM numerical model describing the operation of two large open-ended coaxial probes designed to investigate the permittivity of concrete, and its constituents. This numerical simulation, combined with a capacitive approach describing the behaviour of the probes, enabled to prove the suitability of such device to determine the permittivity of dispersive dielectrics. Finding back the permittivity of a specified material by calculation of the S parameters, change of the reference plane and use of the capacitive model is the key to the proof. Measurements performed onto different materials show good similarities with the numerical simulations. Special considerations are mentioned concerning the size of the probe and its ability to measure the permittivity of heterogeneous materials made of large inclusions. Combination of such numerical tool and measuring device can be used as a non-destructive testing technique to assess the near surface permittivity of concrete structures or as a calibration technique for GPR measurements.

Dispersion analysis of finite difference and discontinuous Galerkin schemes for Maxwell's equations in linear Lorentz media

In this paper, we consider Maxwell's equations in linear dispersive media described by a single-pole Lorentz model for electronic polarization. We study two classes of commonly used spatial discretizations: finite difference methods (FD) with arbitrary even order accuracy in space and high spatial order discontinuous Galerkin (DG) finite element methods. Both types of spatial discretizations are coupled with second order semi-implicit leap-frog and implicit trapezoidal temporal schemes. By performing detailed dispersion analysis for the semi-discrete and fully discrete schemes, we obtain rigorous quantification of the dispersion error for Lorentz dispersive dielectrics. In particular, comparisons of dispersion error can be made taking into account the model parameters, and mesh sizes in the design of the two types of schemes. This work is a continuation of our previous research on energy-stable numerical schemes for nonlinear dispersive optical media [6,7]. The results for the numerical dispersion analysis of the reduced linear model, considered in the present paper, can guide us in the optimal choice of discretization parameters for the more complicated and nonlinear models. The numerical dispersion analysis of the fully discrete FD and DG schemes, for the dispersive Maxwell model considered in this paper, clearly indicate the dependence of the numerical dispersion errors on spatial and temporal discretizations, their order of accuracy, mesh discretization parameters and model parameters. The results obtained here cannot be arrived at by considering discretizations of Maxwell's equations in free space. In particular, our results contrast the advantages and disadvantages of using high order FD or DG schemes and leap-frog or trapezoidal time integrators over different frequency ranges using a variety of measures of numerical dispersion errors. Finally, we highlight the limitations of the second order accurate temporal discretizations considered.

Fractional‐Calculus‐Based Electromagnetic Tool to Study Pulse Propagation in Arbitrary Dispersive Dielectrics

Fractional calculus is a fruitful field of research in science and engineering. The concept of fractional exponents is an outgrowth of exponents with integer value. In the same way, fractional order of integration is a generalization of the mathematical operations of differentiation and integration to arbitrary, general, noninteger order. Although it better models the higher complexity by nature, it is still fairly easy to physically represent its meaning. However, taking in consideration that the study of fractional calculus theory opens the mind to entirely new branches of thought, in this feature article the authors illustrate as such concept can be an interesting and useful tools in electromagnetic theory to solve specific electromagnetic problems regarding the wave propagation and radiation in arbitrary dispersive dielectric materials. In particular, time fractional Maxwell's equations for media with power‐law frequency dispersions are illustrated focusing the attention on the mathematical and computational topics. Moreover, practical examples highlighting their usefulness for understanding a variety of electromagnetic phenomena are provided.

A multiscale method for computing effective parameters of composite electromagnetic materials with memory effects

We consider the problem of computing (macroscopic) effective properties of composite materials that are mixtures of complex dispersive dielectrics described by polarization and magnetization laws. We assume that the micro-structure of the composite material is described by spatially periodic and deterministic parameters. Mathematically, the problem is to homogenize Maxwell’s equations along with constitutive laws that describe the material response of the micro-structure comprising the mixture, to obtain an equivalent effective model for the composite material with constant effective parameters. The novel contribution of this paper is the homogenization of a hybrid model consisting of the Maxwell partial differential equations along with ordinary (auxiliary) differential equations modeling the evolution of the polarization and magnetization, as a model for the complex dielectric material. This is in contrast to our previous work (2006) in which we employed a convolution in time of a susceptibility kernel with the electric field to model the delayed polarization effects in the dispersive material. In this paper, we describe the auxiliary differential equation approach to modeling material responses in the composite material and use the periodic unfolding method to construct a homogenized model.

Fractional-Calculus-Based FDTD Algorithm for Ultrawideband Electromagnetic Characterization of Arbitrary Dispersive Dielectric Materials

A novel finite-difference time-domain algorithm for modeling ultrawideband electromagnetic pulse propagation in arbitrary multirelaxed dispersive media is presented. The proposed scheme is based on a general, yet computationally efficient, series representation of the fractional derivative operators associated with the permittivity functions describing the frequency dispersion properties of a given dielectric material. Dedicated uniaxial perfectly matched layer boundary conditions are derived and implemented in combination with the basic time-marching scheme. Moreover, a total field/scattered field formulation is adopted in order to analyze the material response under plane-wave excitation. Compared with alternative numerical methodologies available in the scientific literature, the proposed technique features a significantly enhanced accuracy in the solution of complex electromagnetic propagation problems involving higher order dispersive dielectrics, such as the ones typically encountered in geoscience and bioengineering applications.

Design of Antireflection Grading Using Magneto-Dielectric Materials

A number of practical application areas would benefit from the development of thin wideband antireflective (AR) surfaces. Here, we incorporate magnetic materials into AR gradings using two approaches. 1) We use the analytic approach demonstrated in a recent paper that details an optimal wideband AR design using a continuous one-dimensional (1-D) grading of dispersive dielectrics [1] . We extend the dispersive nonmagnetic equations in [1] to design perfect AR magneto-dielectric gradings. 2) We derive a spatial-coordinate transformation (SCT) approach that transforms the nonmagnetics solution to achieve a perfect AR magneto-dielectric grading. We find, in general, that the SCT method enables more realizable and flexible solutions. We detail a practical approach for realizing the magneto-dielectric gradings using subwavelength texturing (i.e., motheye method). Several numerical examples demonstrate the utility of this approach in realizing very thin, yet broadband, and AR designs.

Unified position-dependent photon-number quantization in layered structures

We have recently developed a position-dependent quantization scheme for describing the ladder and effective photon-number operators associated with the electric field to analyze quantum optical energy transfer in lossy and dispersive dielectrics [Phys. Rev. A, 89, 033831 (2014)]. While having a simple connection to the thermal balance of the system, these operators only described the electric field and its coupling to lossy dielectric bodies. Here we extend this field quantization scheme to include the magnetic field and thus to enable description of the total electromagnetic field and discuss conceptual measurement schemes to verify the predictions. In addition to conveniently describing the formation of thermal balance, the generalized approach allows modeling of the electromagnetic pressure and Casimir forces. We apply the formalism to study the local steady state field temperature distributions and electromagnetic force density in cavities with cavity walls at different temperatures. The calculated local electric and magnetic field temperatures exhibit oscillations that depend on the position as well as the photon energy. However, the effective photon number and field temperature associated with the total electromagnetic field is always position-independent in lossless media. Furthermore, we show that the direction of the electromagnetic force varies as a function of frequency, position, and material thickness.

Electromagnetic Modeling of Dielectric Mixtures

Electromagnetic modeling of dielectric materials allows us to study the effects of electromagnetic wave propagation and how such electromagnetic fields influence and interact with them. Dielectric materials are composites or mixtures, which often are made up of at least two constituents or phases. Modelling the electromagnetic behaviour of dielectric mixtures is crucial to understand how geometrical factors (shape and concentration), electromagnetic properties of inclusions and background medium, influence the permittivity of the overall material. The aim of this work is to develop new analytical models for dielectric mixtures, in order to describe their electromagnetic behaviour and design them with desired electromagnetic properties, for specific required applications. In particular, in this paper a new general expression for the effective permittivity of dielectric mixture is presented. The mixtures consist of inclusions, with arbitrary shapes, embedded in a surrounding dielectric environment. We consider the hosting environment and the hosted material as real dielectrics, both of them as dispersive dielectrics. The proposed analytical models simplify practical design tasks for dielectric mixtures and allow us to understand their physical phenomena and electromagnetic behaviours.

A Systematic Electromagnetic-Circuit Method for EMI Analysis of Coupled Interconnects on Dispersive Dielectrics

This paper presents a systematic electromagnetic-circuit method for efficient simulation of coupled interconnects on dispersive dielectrics in the presence of electromagnetic interference. The dispersive substrate of coupled interconnects is characterized by the multiterm Debye or Lorentz formula. According to the differential equations derived from the equivalent circuit modeling of dispersive media, the full-wave finite-difference time-domain algorithm is utilized to capture accurate field in a dispersive substrate. The effects of incident field, under the quasi-TEM assumption, are then represented by the distributed sources along transmission lines. An efficient algorithm based on the waveform relaxation with transverse partitioning (WR-TP) is employed for fast simulation of coupled transmission lines. A simple and clear derivation of the relaxation sources in WR-TP is described and the compact results are given. The impact of dispersive dielectrics on the incident field, and thus to the transient response of interconnects, is investigated by comparison with conventional techniques. Several numerical examples are given to illustrate the accuracy and efficiency of the proposed method.

Equivalence of the Abraham momentum and the Minkowski momentum of photons in media

The century-long debate on the momentum of light in a medium involves two rival forms of momentum, namely those of Abraham and Minkowksi. In this Letter, we analyze this dilemma from the view of the quantum theory of light, the result of which can be easily extended to the classical level. It is found that the Abraham momentum of one polariton mode in linear and dispersive dielectrics differs from its Minkowski momentum, by a considerable factor. However, after taking all branches into consideration, we find the two lead to the same end, which unifies the two rival forms of momentum. The sum rule is traditional, but our conclusion provides a new perspective on the Abraham–Minkowski dilemma, and is consistent with existing experiments including a recent measurement of recoil momentum of atoms using an atom interferometer with Bose–Einstein Condensates [G. K. Campbell et al. Phys. Rev. Lett. 94, 170403 (2005).] , the Cerenkov effect, the Doppler effect and the phase matching conditions in nonlinear optical processes.

Dispersive dielectrics and time reversal: Free energies, orthogonal spectra, and parity in dissipative media

Free energies of dissipative media are reviewed. Then we use free-energy-optimal excitation and de-excitation fields to generate a dielectric's time-reversal spectrum, with several properties: a) The spectrum generalizes the time-reversal parity from "even" and "odd" of conservative systems to an interval [-1,+1] of "time-reversal eigenvalues" λ in dissipative media. b) It yields eigenmodes that are complete: any state of the medium is optimally excitable or de-excitable by them. c) These excitations are orthogonal with respect to the work function of the medium and, so, d) characterize field excitations for the given medium that, when superimposed, only do work on the medium, not on each other via the medium-field interaction mechanism. Notions of en masse potential and kinetic energy in the dissipative medium arise through even (λ=+1) and odd (λ=-1) parity, but also other energy notions via alternative parity (|λ|<1) under time reversal.

On the Accuracy and Stability of Several Widely Used FDTD Approaches for Modeling Lorentz Dielectrics

A rigorous and comparative study on the approximation accuracy and stability limits of several widely used finite-difference time-domain (FDTD) approaches, namely the auxiliary differential equation (ADE) approach, the bilinear transform (BT) approach, the Z-transform approach (ZT) and the piecewise linear recursive convolution (PLRC) approach, for modeling dispersive Lorentz dielectrics is presented following the given updating equations between the electric flux density and the electric field intensity. We find the ZT approach with modified material parameters is much more accurate than the original ZT approach and the other three approaches for modeling Lorentz dielectrics. The stability limits of the ADE, ZT and PLRC approaches in simulating Lorentz dielectrics are also shown to be a bit more stringent than that of BT approach which preserves the Courant stability limit as previously reported.

PEEC Modeling of Dispersive and Lossy Dielectrics

In this paper a general formulation is presented for the time-domain partial element equivalent circuit method in a general dispersive medium. The formulation is based on Debye and Lorentz models where the resulting model is passive. The incorporation of such models into a partial element equivalent circuit solver is described by both convolution techniques and equivalent circuits. The new circuit models can be applied in the frequency as well as the time domain. Numerical examples are given to validate the proposed formulation and to show that the proposed method is accurately capturing the physics of dispersive and lossy dielectrics.

QED theory for excitons with microscopic nonlocality

AbstractWe have constructed QED theory for excitons with microscopic nonlocality or nonlocal susceptibility originating from their center‐of‐mass motion. The nonlocality must be properly considered in excitons' weak (center‐of‐mass) confinement regime where the long wavelength approximation is breakdown. This theory keeps good correspondences with its underlying theories, the QED theory for dispersive and absorptive local dielectrics and the microscopic nonlocal theory developed in the semiclassical framework. Our theory provides correlation functions of excitons, which renormalize radiative shift, transition between exciton states via electromagnetic fields, radiative and nonradiative relaxation processes. By using these functions, we can systematically study various nonlinear, dephasing, and emission processes of excitons in weak‐confinement to bulk‐like systems

Band structure of two-dimensional photonic crystals that include dispersive left-handed materials and dielectrics in the unit cell

We determine the band structure of two-dimensional photonic crystals that are composed of left-handed materials and dielectrics, based on the numerical solution of the Helmholtz equation by using integral equations. It is found that plasmonic resonances appear constituting a band that is independent of the filling fraction. Wide bandgaps are present where the penetration depth of the electromagnetic field inside the photonic crystal is quite short compared to purely dielectric photonic crystals.

PEEC capacitance extraction of 3-D interconnects

As feature size of electronic devices decreases, fast and accurate capacitance extraction has become increasingly critical for verification and analysis as regard as electromagnetic compat- ibility and signal integrity issues. The partial element equivalent circuit method is implemented for three-dimensional capacitance extraction of interconnects and very large-scale integration circuits with multiple dielectrics. The electric field coupling due to free and bound charges are analysed and modelled separately thus allowing to distinguish their contribution. The proposed approach provides physical insight, totally compatible fast methods for accelerating matrix-vector products, allows an easy treatment of lossy and dispersive dielectrics and is well suited for applying model order reduction techniques. Modern electronic design is surely extremely challenging. It is known that power distribution and management, digital computing and radio frequency wireless communication have very different bandwidths, as well as voltage and current levels. In addition, today's mobile devices share the same printed circuit board and/or packaging substrate in a very dense design. The consequence of this fact is that parasitics and interference poses significant design challenges and deserves a special attention to electromag- netic compatibility (EMC) engineers to meet design requirements. Parasitics may compromise the signal fidelity and/or level and dominate the coupling in the case of elec- tromagnetic interference and immunity. Typically, coupling takes place through the electric field (capacitive coupling), magnetic field (inductive coupling) or through a common current return path. It is understood that design meeting EMC criteria has a critical need for methodologies and computer-aided design tools, which allow to predict para- sitic effects and capture coupling physics. Also it is extre- mely desirable to extract parasitic lumped element circuit models from a layout geometry. As the feature size of electronics in mobile devices has dramatically decreased, the interconnect is becoming a dominant factor in system delay and signal integrity (SI). An accurate and efficient electromagnetic modelling of three-dimensional (3-D) high speed interconnects and very large-scale integration (VLSI) circuits embedded in mul- tiple dielectrics is extremely important for the design and verification of nowadays systems on package and systems on-chip for communication systems. Circuit performances such as SI, EMC, delay, radiation, power consumption, reliability are strongly influenced by the electrical charac- teristics of interconnects. Among the other effects, timing verification requires accurate interconnect modelling of parasitic parameters especially as regard as the parasitic