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Accurate and efficient calculation of light propagation in one-dimensional inhomogeneous anisotropic media through extrapolation.

Berreman's 4 x 4 matrix approach has been generally applied to calculating light propagation in one-dimensional (1-D) inhomogeneous anisotropic media. In numerical calculations the propagator (propagation matrix) of whole 1-D inhomogeneous media is approximated by a stack of N homogeneous slab propagators. We analyze the error of the slab propagator in this slab approximation and show it is correct through the order 1/N(2). By using the extrapolation approach, we eliminate the leading error terms of the product (total propagator) of N homogeneous slab propagators successively. Numerical tests for a cholesteric liquid crystal show that the total propagator constructed through extrapolation is of higher accuracy and efficiency than Berreman's and Abdulhalim's or faster 4 x 4 total propagators.