Concluding remarks

A two dimensional frequency domain model of circular integrated optical microresonators based on spatial coupled mode theory has been investigated. Representing a direct implementation of the most common notions found in discussions of optical microring resonators, the present approach provides a thorough quantitative basis for the resonator design. It turns out that only a few most relevant basis fields are required to construct approximate solutions to the scattering problems that are sufficient for purposes of practical resonator design. The CMT results agree well with rigorous FDTD simulations; the computational effort for the CMT analysis is significantly lower. Hence the approach qualifies for a generalization to three spatial dimensions [69], where hardly any alternative, practically applicable tools are available.

The numerical examples included single- and multimode microring and -disk structures, with relatively small cavity diameters and substantial refractive index contrasts, which represent rather worst-case configurations for the CMT analysis. Beyond the optical power transmission characteristics, the CMT procedures permit the direct examination of the local amplitudes of all included basis modes, and the inspection of all components of the local optical electromagnetic field. By means of adequately interpolated bend mode propagation constants and coupler scattering matrices, the spectral properties of the resonators can be evaluated in a highly efficient way. A systematic analysis of effect of the separation distances on the resonator spectral response shows that for the identical couplers setting, at resonance the drop power is maximum and the through power is minimum. It is also verified that the constrain of invariance of the drop power for interchanging the gaps is satisfied by the present CMT simulations. A perturbational analysis permits to compute reliably shifts in the resonances due to small changes of the core refractive index.