A Fourier-Bessel (FB) basis is used to solve two-dimensional (2D) cylindrical Maxwell's equations for localized states within dielectric structures that possess rotational symmetry. The technique is used to determine the wavelengths and profiles of the stationary states supported by the structure and identify the bandgaps. 12-fold quasi-crystals for the TE and TM polarizations are analyzed. Since the FB approach with 2D photonic crystals in this fashion is new, the accuracy of the results is confirmed using finite-difference time-domain simulations.
The effect of adding a thin high index dielectric overlay layer onto a 3-layer slab waveguide demonstrates several interesting features that can be exploited in integrated optical device configurations. A simple modal analysis is employed to examine the behavior of guided light launched from a 3-layer waveguide structure then coupled and propagated in the 4-layer overlay region. Modal properties typically overlooked in conventional slab waveguides are made use of in the design and theoretical analysis of an MMI device and optical index of refraction sensor. The optical structure presented here can form the backdrop waveguide design for more complex and active devices.
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