Guided EM waves in anisotropic dielectric plates

Guided EM waves in an infinite dielectric plate with general crystal symmetry surrounded by free space are studied in terms of the three-dimensional Maxwell´s equations. To exhibit how the crystal symmetry affects the propagation and coupling of the waves, the study is divided into four cases: (I) β₁₁, β₂₂, β₃₃≠0; (II) β₁₁, β₂₂, β₃₃, β₁₂≠0; (III) β₁₁, β_2(inf) β₃₃, β ₂₃≠0; (IV) all β_ij≠0; where β_ij is the impermeability tensor referred to the rectangular axes x_i with the x₂ axis normal to the plate faces. For each case, closed-form solutions are obtained, and dispersion relations and modes are computed and studied. It is found that in case 1, solutions can be separated into the TE and TM waves. TE and TM waves can be further separated into the symmetric and antisymmetric waves. In case II, the solutions for the TE waves remain the same as those in case I. However, TM waves can not be separated into symmetric and antisymmetric waves. In case III, solutions cannot be separated into the TE and TM waves, but they can still be separated into the symmetric and antisymmetric waves. In case IV, solutions can neither be separated into the TE and TM waves nor into the symmetric and antisymmetric waves