Normal mode coupling and Bloch states in elliptically birefringent 1D photonic crystals

A number of publications have discussed the propagation of electromagnetic waves in onedimensional birefringent stratified media [1, 2]. Of particular interest is the formulation pioneered by P. Yeh that employs a translation matrix approach for periodic structures. The propagation of light across a single period is analyzed in conjunction with Floquet’s theorem to determine the dispersion relation and Bloch waves for the system. This approach has been used to study the properties of layered media where the optic axes are rotated from one layer to the next [2]. Numerical solutions have been found for normal incidence of the light for identical birefringent plates with alternating azimuth angles and layer thicknesses [1]. More recently the present authors have used this technique to study elliptically birefringent media [3], where elliptically polarized normal modes characterize the system locally. Analytic solutions were found for light normally incident into stratified media consisting of alternating magneto-optic layers with different gyration vectors [4] and birefringence levels [3]. Adjacent layers were assumed to have their anisotropy axes aligned to each other. This model captures some important features of one-dimensional magnetophotonic crystal waveguides, particularly the presence of magneto-optical gyrotropy and alternating birefringence levels. Such systems are presently being studied for use in integrated fast optical switches and ultra-small optical isolators [5–7]. Work on these systems extends prior theoretical and experimental efforts on magnetophotonic crystals in order to encompass distinctive properties of planar structures [8–10].