Modeling of tuning of microresonator filters by perturbational evaluation of cavity mode phase shifts

Microresonator filters, realized by evanescent coupling of circular cavities with two parallel bus waveguides, are promising candidates for applications in dense wavelength division multiplexing. Tunability of these filters is an essential feature for their successful deployment. In this paper we present a framework for modeling of tuning of the microresonators by changes of their cavity core refractive index. Using a reciprocity theorem, a perturbational expression for changes in the cavity propagation constants due to slight modifications of the cavity core refractive index is derived. This expression permits to analytically calculate shifts in spectral response of the 2D resonators. Comparisons of the resultant shifts and spectra with direct simulations based on coupled mode theory show satisfactory agreement

Comparison of coupled mode theory and FDTD simulations of coupling between bent and straight optical waveguides

Analysis of integrated optical cylindrical microresonators involves the coupling between a straight waveguide and a bent waveguide. Our (2D) variant of coupled mode theory is based on analytically represented mode profiles. With the bend modes expressed in Cartesian coordinates, coupled mode equations can be derived in a classical way and solved by numerical integration. Proper manipulation of the propagation matrix leads to stable results even in parameter domains of compact and/or radiative structures, which seemed unsuitable for a perturbational approach due to oscillations of the matrix elements along the propagation. Comparisons with FDTD calculations show convincing agreement

Multimode circular integrated optical microresonators: Coupled mode theory modeling

A frequency domain model of multimode circular microresonators for filter applications in integrated optics is investigated. Analytical basis modes of 2D bent waveguides or curved interfaces are combined with modes of straight channels in a spatial coupled mode theory framework. Free of fitting parameters, the model allows to predict quite efficiently the spectral response of the microresonators. It turns out to be sufficient to take only a few dominant cavity modes into account. Comparisons of these simulations with computationally more expensive rigorous numerical calculations show a satisfactory agreement