Abstract

The beam-propagation method (BPM) is a widespread tool to model isotropic optical devices. Here, an extension of the BPM to study propagation in anisotropic media with nondiagonal dielectric permittivity tensor £ is proposed. The main features of the present approach compared with others^1,2 lie in the possibility to study contemporaneously the three coupled components of the electric field $\overline{E}$ (allowing application to nonaxial propagation) and to analyze structures with different ordinary and extraordinary index variations. Starting from the vector Helmholtz wave equation (i.e., assuming $\nabla \cdot \overline{E}=0$) and letting the dielectric tensor ε_r = ε_m0I + Δε = (n_m0I + Δn)² (where n_m0 = (n_o0 + n_e0))/2 and Δn_ij≪n_m0 is assumed), tensorial phase factor, corrector and propagator terms can be separated in the expression of $\overline{E}$ with the same formal procedure used in isotropic media.³ The field propagated over Δz in the unperturbed region is then corrected by exp(−jk₀ΔnΔz), which carries out the components coupling owing to both anisotropy and non-homogeneity. The choice of a constant and appropriate value n_mo, involving the assumption of an isotropic, homogeneous substrate, is necessary to fulfill matricial algebra requirements in separating tensorial propagator and corrector terms.

© 1991 Optical Society of America