Eigenmodes of the waveguide formed in a 2D photonic crystal composed of metal cylinders

Eigenmodes of the waveguide in a photonic crystal formed from circular metal cylinders are considered. The method of compensating sources is used to solve a boundary value problem for a guiding channel in a photonic crystal formed by removing an infinite row of cylinders from the crystal. Eigenvectors for amplitudes of compensating sources are found and the dispersion relation for determining the eigenmode propagation constants is derived. The eigenvectors for amplitudes of compensating sources are used to obtain expressions for electromagnetic fields of waveguide eigenmodes. The operating frequency range of the photonic-crystal waveguide is determined. The influence of losses on attenuation of the fundamental waveguide mode is investigated. Methods of compensating sources and eigenmode expansion are used to solve the excitation problem for waveguide eigenmodes. A simple expression is derived for the power carried by the fundamental mode.