Maria Bayard Dühring - Solid Mechanics

Chapter 1
Introduction
1.1 Aim of the thesis
The study of elastic and optical waves has obtained great importance during the
last century. Waves with different kinds of properties have been discovered, which
combined with an intense research in materials and fabrication techniques have
allowed for the fabrication of structures down to nano scale, resulting in a range of
important applications from sonar, ultrasound scanning over lasers, optical fibers
and integrated optics. The field of research is continuously expanding and opening
up for new and promising applications. It has therefore become essential to simulate
and understand wave propagation in order to design wave devices.
The aim of this thesis is to study propagating elastic and optical waves, which
are described on a time-harmonic form, and to optimize wave devices either by
varying different geometry parameters or by topology optimization. The method
of topology optimization is a gradient based optimization method that has proven
efficient for optimizing static and dynamic problems in engineering and is here extended
to three new wave propagation problems with increasing complexity. First
acoustic waves that are propagating in air are studied and topology optimization is
employed to design sound barriers such that the noise is reduced behind the barrier.
Then optical waves are simulated in photonic-crystal fibers and the energy flow
through the core is maximized by designing the cross section of the fiber by use of
topology optimization. Finally, surface acoustic waves are simulated in piezoelectric
materials and their interaction with optical waves in channel waveguides is investigated.
This study is both based on a parametric investigation of the geometry as
well as topology optimization in order to improve the acousto-optical interaction.
The different wave problems are all governed by second order differential equations
that can be discretized and solved in a similar way by the finite element program
Comsol Multiphysics with Matlab.
1.2 Structure of the thesis
This thesis is a common introduction to the work done during the Ph.D. study. It
gives an overview of the results presented in the seven publications [P1]-[P7] together
with a few additional results related to the three different wave propagation problems
that are simulated and optimized by parameter studies and topology optimization.
The three wave problems are connected to each other through the two introductory
chapters 2 and 3. Chapter 2 is a general introduction to elastic and optical
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