  Topology optimization of a waveguide-cavity structure in phononic crystals
for designing narrow band filters under the given operating frequencies is
presented in this paper. We show that it is possible to obtain an ultra-high-Q
filter by only optimizing the cavity topology without introducing any other
coupling medium. The optimized cavity with highly symmetric resonance can be
utilized as the multi-channel filter, raising filter and T-splitter. In
addition, most optimized high-Q filters have the Fano resonances near the
resonant frequencies. Furthermore, our filter optimization based on the
waveguide and cavity, and our simple illustration of a computational approach
to wave control in phononic crystals can be extended and applied to design
other acoustic devices or even opto-mechanical devices.
