Calculation of Guided Modes and Leaky Modes in Photonic Crystal Slabs

The scattering matrix S describing photonic crystal slabs is formulated. A new method is introduced to solve the eigenfrequency ω for a given Bloch wave vector K from the equation det S^-1 ( ω ,K)=0. Using this method, we can obtain not only guided modes but also leaky modes in photonic crystal slabs with a higher-frequency resolution than that of the FDTD method.