5,145 research outputs found
Lorenz-Mie theory for 2D scattering and resonance calculations
This PhD tutorial is concerned with a description of the two-dimensional
generalized Lorenz-Mie theory (2D-GLMT), a well-established numerical method
used to compute the interaction of light with arrays of cylindrical scatterers.
This theory is based on the method of separation of variables and the
application of an addition theorem for cylindrical functions. The purpose of
this tutorial is to assemble the practical tools necessary to implement the
2D-GLMT method for the computation of scattering by passive scatterers or of
resonances in optically active media. The first part contains a derivation of
the vector and scalar Helmholtz equations for 2D geometries, starting from
Maxwell's equations. Optically active media are included in 2D-GLMT using a
recent stationary formulation of the Maxwell-Bloch equations called
steady-state ab initio laser theory (SALT), which introduces new classes of
solutions useful for resonance computations. Following these preliminaries, a
detailed description of 2D-GLMT is presented. The emphasis is placed on the
derivation of beam-shape coefficients for scattering computations, as well as
the computation of resonant modes using a combination of 2D-GLMT and SALT. The
final section contains several numerical examples illustrating the full
potential of 2D-GLMT for scattering and resonance computations. These examples,
drawn from the literature, include the design of integrated polarization
filters and the computation of optical modes of photonic crystal cavities and
random lasers.Comment: This is an author-created, un-copyedited version of an article
published in Journal of Optics. IOP Publishing Ltd is not responsible for any
errors or omissions in this version of the manuscript or any version derived
from i
Finite bending and pattern evolution of the associated instability for a dielectric elastomer slab
We investigate the finite bending and the associated bending instability of
an incompressible dielectric slab subject to a combination of applied voltage
and axial compression, using nonlinear electro-elasticity theory and its
incremental version. We first study the static finite bending deformation of
the slab. We then derive the three-dimensional equations for the onset of
small-amplitude wrinkles superimposed upon the finite bending. We use the
surface impedance matrix method to build a robust numerical procedure for
solving the resulting dispersion equations and determining the wrinkled shape
of the slab at the onset of buckling. Our analysis is valid for dielectrics
modeled by a general free energy function. We then present illustrative
numerical calculations for ideal neo-Hookean dielectrics. In that case, we
provide an explicit treatment of the boundary value problem of the finite
bending and derive closed-form expressions for the stresses and electric field
in the body. For the incremental deformations, we validate our analysis by
recovering existing results in more specialized contexts. We show that the
applied voltage has a destabilizing effect on the bending instability of the
slab, while the effect of the axial load is more complex: when the voltage is
applied, changing the axial loading will influence the true electric field in
the body, and induce competitive effects between the circumferential
instability due to the voltage and the axial instability due to the axial
compression. We even find circumstances where both instabilities cohabit to
create two-dimensional patterns on the inner face of the bent sector
The homogenisation of Maxwell's equations with applications to photonic crystals and localised waveforms on metafilms
An asymptotic theory is developed to generate equations that model the global
behaviour of electromagnetic waves in periodic photonic structures when the
wavelength is not necessarily long relative to the periodic cell dimensions;
potentially highly-oscillatory short-scale detail is encapsulated through
integrated quantities.
The theory we develop is then applied to two topical examples, the first
being the case of aligned dielectric cylinders, which has great importance in
the modelling of photonic crystal fibres. We then consider the propagation of
waves in a structured metafilm, here chosen to be a planar array of dielectric
spheres. At certain frequencies strongly directional dynamic anisotropy is
observed, and the asymptotic theory is shown to capture the effect, giving
highly accurate qualitative and quantitative results as well as providing
interpretation for the underlying change from elliptic to hyperbolic behaviour
A note on stress-driven anisotropic diffusion and its role in active deformable media
We propose a new model to describe diffusion processes within active
deformable media. Our general theoretical framework is based on physical and
mathematical considerations, and it suggests to use diffusion tensors directly
coupled to mechanical stress. A proof-of-concept experiment and the proposed
generalised reaction-diffusion-mechanics model reveal that initially isotropic
and homogeneous diffusion tensors turn into inhomogeneous and anisotropic
quantities due to the intrinsic structure of the nonlinear coupling. We study
the physical properties leading to these effects, and investigate mathematical
conditions for its occurrence. Together, the experiment, the model, and the
numerical results obtained using a mixed-primal finite element method, clearly
support relevant consequences of stress-assisted diffusion into anisotropy
patterns, drifting, and conduction velocity of the resulting excitation waves.
Our findings also indicate the applicability of this novel approach in the
description of mechano-electrical feedback in actively deforming bio-materials
such as the heart
Linear and nonlinear optical excitations in spatially-inhomogeneous semiconductor systems
Gegenstand der vorliegenden Arbeit ist die
Licht-Materie-Wechselwirkung in raeumlich inhomogenen Halbleiterstrukturen.
In den Kapiteln 2, 3 und 4 werden grundlegende Eigenschaften herausgearbeitet, die
dadurch entstehen, dass die untersuchten Systeme von dreidimensionaler
raeumlicher Homogenitaet abweichen. Darunter ist zu verstehen, dass
sowohl das (anregende) Lichtfeld inhomogen verteilt
(Kap 2 und 3) als auch die intrinsischen
Materialeigenschaften des Halbleiters raeumlich strukturiert sein
koennen (Kap. 2 und 4).
In Kapitel 2 wird eine Theorie entwickelt, die es
ermoeglicht, Halbleiterstrukturen zu beschreiben, die sich in der
Naehe eines photonischen Kristalls befinden.
Lineare und nichtlineare optische Eigenschaften von verschiedenen
Silizium-Halbleiteroberflaechen werden in Kapitel 4
behandelt
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