Compact high-Q filters based on one-dimensional photonic crystals containing single-negative materials

A mechanism to design compact high-Q filters is proposed in this paper, based on the properties of a defect mode in a one-dimensional (1D) photonic crystal composed of alternating layers of negative-permeability material and negative-permittivity material. The eigenfrequency equation for the defect mode is derived by means of the transfer-matrix method, and then, the dependence of the eigenfrequency on the thicknesses of the two host layers and the defect layer is calculated. In contrast to the case for a filter based on a conventional 1D photonic crystal (with positive refractive indices), we find that the quality factor Q of the filter involved in this paper can be boosted noticeably while the volume of the filter decreases.