WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...

Chapter 4
Optimization of photonic waveguides
Bandgap materials for optical waves are known as photonic crystals. Technological
applications have appeared in photonic crystal fibers for telecommunication
purposes, for example, but also for waveguides in planar photonic crystals which
are believed to have an important role in future integrated optical circuits. Thus,
there has been a large interest in optimizing the performance of such components
especially with respect to efficiency bottlenecks such as sharp waveguide bends.
Chapter 3 introduced a design methodology for phononic bandgap structures
using topology optimization based on FE analysis. Chapter 4 applies the same
methodology to the case of planar photonic waveguides. Although the two problems
relate to very different physical settings (and magnitude of physical dimensions),
the governing equations are similar so that the methodology can be adapted quite
easily. However, important differences exist. When photonic crystal waveguides are
concerned, the focusis often ondesigning only small parts of the structure where the
problemsoccurinsteadoftheentirestructure. Additionally, itisnecessary tomodify
theoptimizationformulationinseveral waysinordertoovercomenewproblemssuch
as the appearance of intermediate material properties in the optimized design.
Thesis papers [10]–[17]
Papers [10] and [11] present the first numerical results for the optimal design of
photonic crystal waveguide bends and junctions using topology optimization. The
material distribution in a 90-degree bend and in a T-junction of a waveguide are
optimized in order to maximize the power flow through the components. Both
examples use a two-dimensional model for E-polarized optical waves. Furthermore,
paper [11] proposes a method for efficient optimization of the performance in a
frequency range using Padé approximants. It also introduces a novel method for
eliminating intermediate material properties in the optimized designs by using an
artificial damping method.
In papers [12]–[15] a number of different photonic crystal waveguide components
are optimized, fabricated and tested experimentally 1 . The components form the
basic building blocks for photonic crystal waveguide devices in the form of a 120degree,
60-degree and a 90-degree bend and a wave splitter.
1 These papers are the result of a fruitful collaboration between the author, colleague Ole Sigmund,
andanumberofpeopleatthe PhotonicsdepartmentattheTechnicalUniversityofDenmark
(now DTU fotonik).
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