Wave Manipulation by Topology Optimization - Solid Mechanics

Chapter 1
Introduction
1.1 Motivation and goal
With the rapid advancement in the areas of material science, nano-photonics, acoustics
and scientific computing, many interesting new optical and acoustic devices have
emerged in the recent years. The majority of these devices work by manipulating
wave propagation inside the device in order to enhance certain desirable physical
properties. The wave manipulation characteristics are a result of the spatial placement
and distribution of materials in the device. Hence control of the material
distribution inside the device enables manipulation of wave propagation for various
purposes.
The aim of this thesis is to study wave manipulation of acoustic and electromagnetic
waves by topology optimization. Topology optimization is a gradient based
optimization method that work by means of varying the distribution of materials
within a bounded design domain. The wave manipulation problems studied here
falls within three different class of problems. The first problem concerns minimization
of the scattered field in all directions or a specified angular range leading to
cloak designs for electromagnetic or acoustic waves. Optimization of grating couplers
for efficient in and out-coupling of electromagnetic surface waves propagating
at a metal-dielectric interface is considered in the second class of problems. Finally
planar Fresnel zone plate lenses are optimized for energy focusing. The physics for
the problems treated in this thesis are all governed by the same second order scalar
differential equation. The boundary value problems are either solved by the finite
element method or by analytic means.
1.2 Structure of the thesis
This thesis is a summary of the work done during the Ph.D. study. It gives an
overview of the main results presented in the six publications [P1]-[P6].
Chapter 2 presents a general introduction to acoustic and electromagnetic waves.
It is shown how the two types of waves are governed by the same scalar second order
differential equation in the special case of in-plane electromagnetic wave propagation.
The topology optimization method is introduced in chapter 3. Two different
design parametrizations in the realm of topology optimization are employed in this
thesis. Furthermore, the topology optimization algorithm, objective functions and
corresponding sensitivity analysis are described.
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