WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...

2. Design and fabrication
Silicon-on-insulator (SOI) is an excellent choice of material for a monolithic integration of
PhC-based PICs and electronic devices. We define the PhC structures in the top silicon layer
of a SOI material by utilizing e-beam lithography and standard anisotropic reactive-ion etch
[14]. The regular PhCs are defined as air holes arranged in a triangular lattice and the PhCWs
are carved out as W1 waveguides by removing one row of holes in the nearest-neighbor
direction of the crystal lattice. The lattice pitch is Λ≈400nm and the diameter of the holes
D≈275nm. This configuration gives rise to a broad PBG below the silica-line from Λ/0.3463-
Λ/0.2592 and allows TE-like single-mode propagation in the PhCW.
The optimization of the 60° PhCW bend has typically relied on attempts to smooth out the
bend by altering, displacing, and/or removing holes in the bend region. However, the useful
bandwidth (~30nm) of practical waveguide bends has usually been one order of magnitude
smaller than the bandgap [9, 10, 15, 16]. Thus, a careful design, tolerant to fabrication
deviations, is very important to utilize the full bandgap of the PhC.
Figure 1 shows schematics of PhCWs defined in a triangular lattice and containing two
consecutive 60° bends. The distance between the bends has been chosen arbitrarily, but
sufficiently long to achieve steady-state behavior of the PBG mode in the waveguide section
separating the bends so that these bends can be treated as separate components. The left image
illustrates a PhCW with two simple 60° bends. Such generic bends form severe discontinuities
in the PhCW and introduce large reflections and excite higher order modes, which are not
necessarily guided in the PhCW.
input
port
output
port
Fig. 1. Schematics of photonic crystal waveguides containing two consecutive 60° bends. Left:
Generic bend configuration. The red areas illustrate the chosen design domains in the topology
optimization procedure. Right: Topology-optimized bends. The green areas highlight the optimized
structures showing that a non-trivial smoothening has been applied to the bend.
We use the method of topology optimization (see e.g. [17]) to optimize the performance of the
component. This is done by changing the material distribution in the designated design
domains indicated by the two red areas in Fig. 1 (left). No geometrical restrictions are
enforced so the resulting design in these domains may consist of an arbitrary number of holes
of arbitrary sizes and shapes.
The optimization algorithm is based on a 2D finite-element frequency-domain solver,
which produces an accurate 2D field solution. The solver is used repeatedly in an iterative
scheme, in which the material distribution is updated every iteration based on analytical
sensitivity analysis and use of a mathematical programming tool [18]. On a standard 2.66GHz
PC with 1 GB RAM each iteration takes about 10s. More details about the general method can
be found in [17] and its application in optimization of photonic/phononic crystal structures in
[12, 19, 20].
For the 60° bends in Fig. 1 (left) we optimize the component by modifying the material
distribution so that the transmission through the waveguide is maximized. The transmission is
evaluated as the power flow at the output port. In order to create a broadband component the
#5520 - $15.00 US Received 19 October 2004; revised 12 November 2004; accepted 15 November 2004
(C) 2004 OSA 29 November 2004 / Vol. 12, No. 24 / OPTICS EXPRESS 5918