WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...

Y-splitter
W1 waveguide
60-degree bend
120-degree bend
90-degree bends
photonic crystal
Figure 1: Schematic overview of a photonic circuit made from a photonic crystal with circular air holes
in a dielectric including W1 waveguides and various bends and splitters.
due to a large out-of-plane loss of light, these structures seem to be less efficient than structures that
are based on photonic crystals with air holes drilled in a periodic pattern in a dielectric material.
Figure 1 shows a schematic photonic circuit created from a PhC base material consisting of circular
air holes in a triangular pattern in the dielectric. With a sufficiently high refractive index of the dielectric
and sufficiently large diameter of holes this configuration gives rise to a large band gap for plane TEpolarized
waves. The basic circuit component in the PhC is the waveguide, exemplified in the figure
in form of so-called W1-waveguides. This means that the waveguide is created by removing a single
row of air holes. The behavior of PhC waveguides is intricate [10], but most importantly the W1
waveguide with this PhC configuration supports wave propagation in a certain frequency interval within
the band gap range. However, dealing only with straight waveguides is not enough to enable sufficient
manipulation of the light in a circuit and additional building blocks like bends and splitters are needed.
In Figure 1 examples of bends (60-, 90-, and 120-degree) as well as a Y-splitter are shown. Without
modification of the straightforward material distribution shown in the figure, these bends and splitters
display huge excess losses due wave reflection at the discontinuities. This difficulty has been tried solved
by introducing various geometry modifications, such as changed radius and displacement of holes near
the highly reflective bend regions - however, with limited success [11].
In recent publications ([2], [12], [13], [14]) it has been shown how the excess loss of such building blocks
can be minimized by using topology optimization to redistribute the material in the critical regions. The
topology optimized designs have odd-shaped holes and are qualitatively very different looking than the
usual designs, but they nevertheless display a very good performance also for the actual fabricated
structures.
Here, we demonstrate the design of a complicated photonic crystal circuit that possesses many of
the basic building blocks that can be encountered in real circuits; bends, splittes and crossings - the PP
component ∗ .
4.1. The PP component (dedicated to Professor Pauli Pedersen)
Figure 2 illustrates the desired functionality for the PP component. A single mode wave is sent into the
component at the lower portion of the left boundary. The energy flow direction inside the structure is
∗ The PP component was designed (and later fabricated) in honor of Professor Pauli Pedersen’s retirement from the
Department of Mechanical Engineering, Technical University of Denmark in April 2005. The PP symbolizes Pauli’s initials.
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