Contour of the attenuated length of an evanescent wave at constant frequency within a band gap of photonic crystal

The plane wave method is normally applied to determine the eigenfrequency of a two-dimensional (2D) photonic crystal. A slight change to this eigenvalue equation makes the wave number its eigenvalue providing a direct means to determine the attenuated length of the evanescent modes at the frequency within the photonic band gap. The contour of the length of attenuation of the evanescent modes in a square lattice can be determined using the proposed wave number eigenvalue equation. The wave number eigenvalue equation for the two-dimensional (3D) photonic crystal can also be obtained using a derivation similar to that for the 2D photonic crystal. Possible applications of the proposed calculation-method are presented.