WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...

J. S. Jensen and O. Sigmund Vol. 22, No. 6/June 2005/J. Opt. Soc. Am. B 1197
Fig. 9. Design optimized for frequency range ˜ =0.32–0.44 with
an enlarged design domain. The field is computed for ˜ =0.38.
Fig. 10. Transmission spectra for the design optimized for the
entire frequency range ˜ =0.32–0.44. Shown also is the spectrum
for the design optimized for ˜ =0.38.
tion of material in a design domain near the junction. By
maximizing the power transmission through the two
waveguide output ports, we obtain designs with vanishing
reflection at the junction.
We obtained a high transmission locally by performing
the optimization for single frequencies. To get a larger
bandwidth with high transmission, we introduced an
active-set strategy in which the transmission is maximized
for several frequencies simultaneously and in
which these target frequencies are repeatedly updated
with fast frequency sweeps to identify the most critical
frequencies with lowest transmission. It was shown that,
by increasing the design domain, we obtained a better
performance in a larger frequency range, approaching full
transmission for the entire frequency range under consideration.
To avoid local maxima based on local resonance effects,
we applied a continuation method by convexifying the object
and response functions with artificial damping. Additionally,
we introduced a scheme to avoid values of the
continuous design variable between 0 and 1, correspond-
ing to intermediate material. This was done by penalizing
these intermediate values with extra artificial damping.
The algorithm appears to be a robust and efficient design
tool for PhC components. Although based on a 2D
model, recent experience with manufactured structures 5
indicates that good performance of the actual devices can
be expected, and the optimization scheme can directly be
implemented with a three-dimensional computational
model to address the important issue of out-of-plane scattering.
Additionally, the objective function can easily be
modified to deal with other functionalities.
ACKNOWLEDGMENTS
The authors thank Martin P. Bendsøe for valuable comments
and suggestions. The work was supported by the
Danish Technical Research Council through the grant
“Designing bandgap materials and structures with optimized
dynamic properties.”
J. S. Jensen, the corresponding author, can be reached
by e-mail at jsj@mek.dtu.dk.
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