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 others1,2 lie in the possibility to study contemporaneously the three coupled components of the electric field (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 ) and letting the dielectric tensor εr = εm0I + Δε = (nm0I + Δn)2 (where nm0 = (no0 + ne0))/2 and Δnij≪nm0 is assumed), tensorial phase factor, corrector and propagator terms can be separated in the expression of 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 nmo, 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
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