Microwave engineering filter synthesis technique for coupled ridge resonator filters.

Wavelength filters are among the most important building blocks required for integrated optical circuits. However, existing filter building blocks provide only basic functionality with limited options for controlling the filter function unless sophisticated filter design techniques are employed. Conversely, in the microwave regime, elegant and powerful filter synthesis techniques exist which use coupled resonators. As waveguide ring resonators have emerged, researchers in the optical domain have sought to translate these techniques but the multi-wavelength spacing required to couple optical ring resonator structures severely limits the types of filters that can be realized. In this paper we show how recently reported ridge resonance structures can be arranged as coupled resonators with very close spacing and thus can be harnessed to achieved many of the filter functionalities available in the field of microwave engineering. Our filter is comprised of multiple parallel ridges on a common silicon slab, with each resonator exhibiting a resonant frequency and quality factor which can be controlled through engineering the geometry of the ridge. It is thus possible to choose appropriate combinations of ridge geometries to satisfy the conditions required by filter synthesis prototype. We demonstrate through rigorous simulation how our approach can be used to achieve high order optical bandpass filters at 1.55 µm center wavelength with Butterworth or Chebychev responses and analyse the impact of non-ideal behaviours on filter performance.