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An error analysis of trigonometric integrators (or exponential integrators) applied to spatial semi-discretizations of semilinear wave equations with periodic boundary conditions in one space dimension is given. In particular, optimal…
Micromechanically exfoliated mono- and multilayers of molybdenum disulfide (MoS2) are investigated by spectroscopic imaging ellipsometry. In combination with knife edge illumination, MoS2 flakes can be detected and classified on arbitrary…
Mueller polarized bi-directional scattering distribution functions (pBSDFs) are 4x4 matrix-valued functions which depend on acquisition geometry. The most popular pBSDF is a weighted sum between a Fresnel matrix and an ideal depolarizer.…
This thesis is divided into two parts. In the first part we study completely integrable systems, and their underlying structures, in detail. We study their deformation theory and the different equivalence relations surrounding it. We…
This paper presents a general approach to designing the isotropic spherical media with complex spatial structure that provide different types of imaging for different light rays. It is based on equivalence of the spherical medium and the…
This paper explores the mechanical behaviour of the composite materials used in modern lithium-ion battery electrodes. These contain relatively high modulus active particle inclusions within a two-component matrix of liquid electrolyte…
Fourier-based optical computing operations, such as spatial differentiation, have recently been realized in compact form factors using flat optics. Experimental demonstrations, however, have been limited to coherent light requiring laser…
Relating the electromagnetic scattering and absorption properties of an individual particle to the reflection and transmission coefficients of a two-dimensional material composed of these particles is a crucial concept that has driven both…
A random mixture of two isotropic dielectric materials, one composed of oriented spheroidal particles of relative permittivity $\epsilon_a$ and the other composed of oriented spheroidal particles of relative permittivity $\epsilon_b$, was…
In this paper an asymptotic homogenization method for the analysis of composite materials with periodic microstructure in presence of thermodiffusion is described. Appropriate down-scaling relations correlating the microscopic fields to the…
We show that the optical properties of an oblique layered system with two kinds of isotropic materials can be described using the concept of transformation media as long as the thickness of the layers is much smaller than the wavelength.…
The boundary element method (BEM) enables the efficient electromagnetic modelling of lossy conductors with a surface-based discretization. Existing BEM techniques for conductor modelling require either expensive dual basis functions or the…
This paper introduces a high-order accurate surface integral equation method for solving 3D electromagnetic scattering for dielectric objects with uniaxially anisotropic permittivity tensors. The N-M\"uller formulation is leveraged…
We perform a thorough theoretical analysis of resonance effects when an arbitrarily polarized plane monochromatic wave is incident onto a double periodically modulated metal film sandwiched by two different transparent media. The proposed…
This paper investigates a computational strategy for studying the interactions between multiple through-the-width delaminations and global or local buckling in composite laminates taking into account possible contact between the delaminated…
We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…
We have developed a nonlinear differential effective dipole approximation (NDEDA), in an attempt to investigate the effective linear and third-order nonlinear susceptibility of composite media in which graded spherical inclusions with weak…
We used numerical simulations based on the finite element method (FEM) to calculate both the amplitude and phase information of the scattered electric field from random rough surfaces, which can be directly compared to ellipsometric…
Nonlinear optics is essential for many recent photonic technologies. Here, we introduce a novel multi-scale approach to simulate the nonlinear optical response of molecular nanomaterials combining ab initio quantum-chemical and classical…
Classical theory of crystals states that a medium to be considered homogeneous must satisfy the following requirements: a) the dimension of the elementary cell must be much smaller than the incident wavelength; b) the sample must contain a…