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In this paper we develop applications of the spectral moments method to the study of the propagation of sound waves and electromagnetic waves in heterogeneous systems with or without energy dissipation.Ln these systems the matrices are often asymmetric. We show that the moments method can be very useful for determining the Green functions of such systems. For a matrix with real eigenvalues the method requires only the introduction of a ID auxiliary density function while for a matrix with complex eigenvalues it needs the introduction of a ZD density function. These functions can be calculated by the moments technique and lead to computation of the Green functions.For systems involving slightly asymmetric matrices, we found thd the method is particularly stable while, for strongly asymmetric matrices, it is better to calculate directly a response function which is a bilinear combination of Green functions.

This paper presents a first attempt at using the spectral moments method (SMM) to solve Maxwell's equations in twisted anisotropic media in the presence of defects. This numerical method, previously developed in condensed matter physics, allows computation of Green functions for very large systems. The dynamic matrix of the discretized system is built from the medium parameters. Green functions, calculated for a given source, representing a point source at infinity and given receiver, are developed as a continued fraction whose coefficients are related to the moments and directly computed from the dynamic matrix. In this study we compute the light transmitted through thin surface-stabilized ferroelectric liquid crystal cells with a chevron structure and a twisted director distribution. The efficiency and accuracy of the method are analysed by comparing the results obtained by SMM with the analytical solution obtained using the Jones matrix formalism. Finally, we apply SMM to compute the transmitted light with different director configurations. We show, by comparisons with experimental data, that the simplest director configuration is certainly the most probable.

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