High-Q semiconductor microdisk resonators laterally coupled to optical waveguides serve as compact and robust components in wavelength-division-multiplexing systems. We present an efficient algorithm for the two-dimensional design of wavelength-selective filters based on waveguide-coupled whispering-gallery-mode (WGM) microresonators of arbitrary cross-sectional shape. A full-wave integral equation formulation enables us to accurately account for the coupling between the resonator and bus waveguide as well as for radiation and material losses. Furthermore, we apply this approach to the analysis of elliptic-resonator filters. Filter tuning by changing the resonator shape from circular to elliptic reduces the dependence of the coupling efficiency on the width of the air gap. Two alternative coupling designs are suggested for monolithic and hybrid integration technologies. One is based on increasing the coupling length, while the other exploits the field concentration at the increased-curvature portion of the deformed WGM resonator.
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