Cavity modes in one-dimensional photonic crystal slabs

A theoretical study of cavity modes in one-dimensional photonic crystal slabs embedded in Silicon-on-Insulator structures is reported. Three different methods are employed, namely a guided-mode expansion in which the coupling to radiative modes is treated by perturbation theory, a grating or scattering-matrix method for calculating the surface reflectance, and a Fourier modal expansion for in-plane transmission calculations. It is shown that all methods lead to the same values for the quality factors of cavity modes for both first- and second-order Bragg mirrors. We conclude that the quality factor of a cavity mode can be determined with optical reflectance from the surface of the slab.