| Circular integrated optical microresonators are increasingly employed as compact and versatile wavelength filters. In this chapter, we investigate an ab-initio 2-D frequency domain model for these devices. The resonators are functionally represented in terms of two couplers with appropriate connections using bent and straight waveguides. The abstract scattering matrices of these couplers and the propagation constants of the cavity bends allow to compute the spectral responses of the resonators. These parameters are calculated by means of the rigorous analytical model of bent waveguides, and the spatial coupled mode theory model of the constituent bent-straight waveguide couplers. We present results for the spectral response and field examples for microresonators with mono- and multi-modal cavities for TE and TM polarizations. Comparisons with finite difference time domain simulations show very good overall agreement. Effect of the separation distances on the spectral response is investigated. Also examples for the effect of slight changes of the core refractive index on the resonator spectra, evaluated by perturbational expressions, are presented. |
Parts of this chapter are adapted from:
K. R. Hiremath, R. Stoffer, M. Hammer. Modeling of circular integrated
optical microresonators by 2-D frequency domain coupled mode theory.
Optics Communications. (accepted).
In Section 1.4 we discussed the ``standard resonator model''
for structures with monomodal waveguides. Knowing the propagation constants of
the cavity segments and the scattering matrices of the bent-straight waveguide
couplers, one can compute the throughput power and the dropped power for the
entire resonator devices. As explained in Chapter 2, the required
propagation constants of bent waveguides can be calculated analytically. With
the coupled mode theory model of bent-straight waveguide couplers, as
presented in Chapter 3, one can reckon the required scattering
matrices. Thus, given the geometrical and material parameters of a resonator,
the spectral response can be computed. Preliminary results of this approach
are contained in Refs. [34,71].
In this chapter, we generalize the above resonator model to the multimodal setting. The chapter is organized as follows. Section 4.1 introduces the schematic microresonator model, formulated directly for configurations with multimode cavities. Section 4.3 outlines how to compute the spectral response of the resonators. Section 4.4 provides a series of example simulations, including the benchmarking against independent rigorous numerical calculations. A detailed study of effect of the separation distances on the resonator spectral response is presented in Section 4.5. Tuning of resonators is investigated in Section 4.6.