Guided electromagnetic waves in anisotropic dielectric plates

Abstract

Guided electromagnetic 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 as how the crystal symmetry may affect the propagation, symmetry, 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,β22,β33,β23≠0; (IV) all βij≠0; where βij is the impermeability tensor referred to the rectangular axes xi with the x2 axis normal to the plate faces. Closed-form solutions are obtained and then the dispersion relations and modes are computed and studied for each case. It is found that in case I, solutions can be separated into the transverse-electric or TE waves and the transverse-magnetic or 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 the case I; however, TM waves cannot 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. In case the solutions are not separable, the resulting waves can always be expressed as the sum of symmetric and antisymmetric waves which differ by a phase angle of π/2. Numerical computations are made for singly and doubly rotated cuts of lithium niobate corresponding to the four cases of symmetry.