Outlook

Now we would like to mention several interesting issues intimately related to the work carried out in this thesis, that deserve further attention. A few aspects are of more theoretical nature, while others are interesting from the application point of view.

The present analysis for the shifts of propagation constants due to changes in the cavity core refractive index (see Section 2.5) takes into account only the change in the real part of the propagation constants. Further investigation is necessary concerning more appropriate expressions, which give the changes in both the real and imaginary parts of the propagation constants.

Besides the present formulation, there exist other versions of coupled mode theory, e.g. spatial CMT with an ansatz for only the electric or the magnetic field, or time dependent CMT, that are applicable to the 2-D resonators as well. A comparative study of these different versions of CMT should be attempted.

For demonstrating the applicability and performance of the CMT method for the modeling of 2-D circular resonators, in the present work we restricted ourselves to unidirectional waves, and discussed configurations with adiabatic couplers and negligible backreflections only. For very small cavities the interaction between the straight waveguides and the cavity may not be adiabatic. To handle such cases, the present model should be extended to bidirectional waves.

Multiple coupled rings can improve the filter performance, when compared to a single resonator, by enhancing the resonance features in certain aspects [22]. The multiple cavities can be cascaded serially or in parallel. Modeling of such multicavity resonators requires the simulations of the coupling between two bent waveguides (or cavities). A CMT analysis for the interaction between two curved waveguides needs to be carried out.