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

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

Adaptive Wavelet Collocation Method for Simulation of Time Dependent Maxwell's Equations

This paper investigates an adaptive wavelet collocation time domain method for the numerical solution of Maxwell's equations. In this method a computational grid is dynamically adapted at each time step by using the wavelet decomposition of the field at that time instant. In the regions where the fields are highly localized, the method assigns more grid points; and in the regions where the fields are sparse, there will be less grid points. On the adapted grid, update schemes with high spatial order and explicit time stepping are formulated. The method has high compression rate, which substantially reduces the computational cost allowing efficient use of computational resources. This adaptive wavelet collocation method is especially suitable for simulation of guided-wave optical devices