Studies of metamaterial structures

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Dispersive effective material parameters for Maxwell's equations

We study how effective material parameters can be defined for Maxwell's equations when taking dispersion into account. The reasoning is based on the concept of dispersion relations, and is consequently primarily concerned with lossless media. We essentially require that the effective material parameters should produce the same dispersion relations as the heterogeneous problem, which implies the effective material is primarily connected to the phase velocity of the waves. Material parameters which exhibit temporal dispersion only, can be defined if the propagation direction is fixed

Time-domain wave splitting of Maxwell's equations

Wave splitting of the time dependent Maxwell's equations in three dimensions with and without dispersive terms in the constitutive equation is treated. The procedure is similar to the method developed for the scalar wave equation except as follows. The up-and down-going wave condition is expressed in terms of a linear relation between the tangential components of E and H. The resulting system of differential-integral equations for the up-and down-going waves is directly obtained from Maxwell's equations. This splitting (arising from the principal part of Maxwell's equations) is applied to the case where there is dispersion. A formal derivation of the imbedding equation for the reflection operator in a medium with no dispersion is obtained

Shielding and Radiation Characteristics of Cylindrical Layered Bianisotropic Structures

In this paper we propose an analytical study in the spectral domain of cylindrical layered structures filled with general bianisotropic media and fed by a 3D electric source. The integrated structure is characterized in terms of transmission matrices leading to an equivalent circuit representation of the whole multilayered structure. Within the framework of this two-port formalism, we present a new contribution to the computation of the Green's function arising in the analysis of multilayered conformal integrated antennas loaded with general bianisotropic materials. We also propose an analytical study of the shielding effectiveness of general bianisotropic materials located in multilayered, cylindrical configuration. The expression of the shielded fields sustained both by plane wave and arbitrary sources is obtained in a closed analytical form. Numerical results are also presented showing effects of electromagnetic parameters on radiation pattern, matching properties and radar cross section of the integrated structure

Transient electromagnetic scattering on anisotropic media

This dissertation treats the problem of transient scattering of obliquely incident electromagnetic plane waves on a stratified anisotropic dielectric slab. Scattering operators are derived for the reflective response of the medium. The internal fields are calculated. Wave splitting and invariant imbedding techniques are used. These techniques are first presented for fields normally incident on a stratified, isotropic dielectric medium. The techniques of wave splitting and invariant imbedding are applied to normally incident plane waves on an anisotropic medium. An integro-differential equation is derived for the reflective response and the direct and inverse scattering problems are discussed. These techniques are applied to the case of obliquely incident plane waves. The reflective response is derived and the direct and inverse problems discussed and compared to those for the normal incidence case. The internal fields are investigated for the oblique incidence via a Green\u27s function approach. A numerical scheme is presented to calculate the Green\u27s function. Finally, symmetry relations of the reflective response are discussed

An inverse electromagnetic scattering problem for a bi-periodic inhomogeneous layer on a perfectly conducting plate

This paper is concerned with uniqueness for reconstructing a periodic inhomogeneous medium covered on a perfectly conducting plate. We deal with the problem in the frame of time-harmonic Maxwell systems without TE or TM polarization. An orthogonal relation for two refractive indices is obtained, and then inspired by Kirsch's idea, the refractive index can be identified by utilizing the eigenvalues and eigenfunctions of a quasi-periodic Sturm-Liouville eigenvalue problem

Nonlinear optics

Nonlinear light-matter interactions have been drawing attention of physicists since the 1960's. Quantum mechanics played a significant role in their description and helped to derive important formulas showing the dependence on the intensity of the electromagnetic field. High intensity light is able to generate second and third harmonics which translates to generation of electromagnetic field with multiples of the original frequency. In comparison with the linear behaviour of light, the nonlinear interactions are smaller in scale. This makes perturbation methods well suited for obtaining solutions to equations in nonlinear optics. In particular, the method of multiple scales is deployed in paper 3, where it is used to solve nonlinear dispersive wave equations. The key difference in our multiple scale solution is the linearity of the amplitude equation and a complex valued frequency of the mode. Despite the potential ill-posedness of the amplitude equation, the multiple scale solution remained a valid approximation of the solution to the original model. The results showed great potential of this method and its promising wider applications. Other methods use pseudo-spectral methods which require an orthogonal set of eigenfunctions (modes) used to create a substitute for the usual Fourier transform. This mode transform is only useful if it succeeds to represent target functions well. Papers 1 and 2 deal with investigating such modes called resonant and leaky modes and their ability to construct a mode transform. The modes in the first paper are the eigenvalues for a quantum mechanical system where an external radiation field is used to excite an electron trapped in an electrical potential. The findings show that the resonant mode expansion converges inside the potential independently of its depth. Equivalently, leaky modes are obtained in paper 2 which are in close relation to resonant modes. Here, the modes emerge from a system where a channel is introduced with transparent boundaries for simulation of one-directional optical beam propagation. Artificial index material is introduced outside the channel which gives rise to leaky modes associated with such artificial structure. The study is showing that leaky modes are well suited for function representation and thus solving the nonlinear version of this problem. In addition, the transparent boundary method turns out to be useful for spectral propagators such as the unidirectional pulse propagation equation in contrast to a perfectly matched layer

Direct and inverse scattering of classical waves at oblique incidence to stratified media via invariant imbedding equations

Direct and inverse scattering problems in stratified media can be solved by first using invariant imbedding techniques to derive integro-differential equations and boundary conditions for the reflection kernels. These equations can be solved numerically to find the reflection kernels in the direct problem or the material parameter functions in the inverse problem. Previous work dealt with plane waves at normal incidence to stratified meda. This dissertation extends the method to the case of oblique incidence. Integro-differential equations are derived for lossless acoustic, electromagnetic, and elastic problems. Direct algorithms and complete inversion algorithms are given in each case. Numerical examples are provided. A final chapter gives examples of the use of Hamilton\u27s quaternion analysis to factor three-dimensional wave equations