Quasiguided modes and optical properties of photonic crystal slabs

We formulate a scattering-matrix-based numerical method to calculate the optical transmission properties and quasiguided eigenmodes in a two-dimensionally periodic photonic crystal slab (PCS) of finite thickness. The square symmetry (point group $C_{4v})$ is taken for the illustration of the method, but it is quite general and works for any point group symmetry for one-dimensional (1D) and 2D PCS’s. We show that the appearance of well-pronounced dips in the transmission spectra of a PCS is due to the interaction with resonant waveguide eigenmodes in the slab. The energy position and width of the dips in transmission provide information on the frequency and inverse radiative lifetime of the quasiguided eigenmodes. We calculate the energies, linewidths, and electromagnetic fields of such quasiguided eigenmodes, and analyze their symmetry and optical activity. The electromagnetic field in such modes is resonantly enhanced, which opens possibilities for use in creating resonant enhancement of different nonlinear effects.