| Bent-straight waveguide couplers are one of the ingredients of the ``standard model'' of circular microresonators. Capitalizing on the availability of rigorous analytical modal solutions for 2-D bent waveguides, in this chapter these couplers are modeled using a frequency domain spatial coupled mode formalism, derived by means of a variational principle. Simulation results for the response of 2-D couplers for varying separation distances, radii, and different wavelengths are discussed. The resulting scattering matrices show reciprocity properties as expected according to the symmetry of the coupler structures. |
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).
Analysis of circular microresonators by means of the functional decomposition
elaborated in Section 1.4 involves bent-straight waveguide
couplers. The response of these couplers is characterized by scattering
matrices, which in turn determine the spectral response of the
resonators. Therefore it is essential to have a parameter free model of
bent-straight waveguide couplers.
In this chapter, we analyze the interaction between bent waveguides and straight waveguides in two dimensional settings, using spatial coupled mode theory. The formulation presented in Section 3.2 takes into account that multiple modes in each of the cores may turn out to be relevant for the functioning of the resonators. Section 3.3 discusses reciprocity of the scattering matrices, which also provides a useful means of assessing the reliability of the simulations. Having access to analytical 2-D bend modes proves useful for the numerical implementation of this model, which is outlined in Section 3.4. Sections 3.4.1, 3.4.2 discuss simulation results for monomode and multimode settings. Section 3.5 presents the conclusions of the present work on bent-straight waveguide couplers.