Modal analysis of two-dimensional photonic-crystal waveguides formed by rectangular cylinders using an improved Fourier series method

A full-wave method for modal analysis of two-dimensional photonic-crystal waveguides consisting of layered arrays of rectangular cylinders is presented. The mode propagation constants and the mode field profiles can be derived by an improved Fourier series method, which is of very simple form, and is always suitable for all the arrays of arbitrary profiles, any depth, and any permittivity. The dispersion equation is expressed by using the generalized reflection matrices for space harmonic waves. The validity of the proposed method has been confirmed by comparison with other methods. Numerical examples of the dispersion characteristics and field distributions are presented for the lowest TE and TM modes of several waveguides in different structures. This method can analyze not only the propagation properties of waveguides, but also their loss natures.