We present an algorithm for synthesizing generalized cascaded Mach-Zehnder interferometer (GCMZI) lattice ﬁlters. The algorithm is then used to design a tenth-order ﬁlter using a GCMZI ﬁlter with eight stages.
Microring resonators are important elements in a wide variety of optical systems, ranging from optical switches and tunable filterbanks to optical sensors. In these structures, the resonant frequencies are normally controlled by tuning the effective index of refraction. In optical switches and filters, this has traditionally been achieved through electro-optic or thermo-optic effects. In sensors, the effective refractive index is changed by the presence of the measurand. Adding a mechanical degree of freedom to these optical systems allows additional evanescent frequency tuning. In particular, the presence of a cantilever in the near-field of the optical mode can tune the effective refractive index. A specific cantilever displacement can therefore induce a desired resonant frequency shift. Alternatively, a measured shift in the resonant frequency can be associated with a cantilever displacement, and be used for pressure or acceleration sensing. In this paper, we explore a geometry that can be used for controlling the resonant frequency of a microring resonator through evanescent field perturbation, using a cantilever defined in the same silicon layer as the optical waveguides, in a silicon-on-insulator platform. The effects of the lateral gap size between the optical waveguide and the cantilever, and the cantilever vertical displacement, on both the resonant frequency and quality factor of the resonator, are evaluated through finite-difference timedomain computations for wavelengths centered at 1550 nm. The presence of the cantilever in the near-field of the optical mode changes the effective refractive index, resulting in frequency tuning, but also lowers the quality factor due to additional coupling into the membrane.