A ray expansion with matrix coefficients for sourcesin absorbing anisotropic media

A ray or quasi-optical approximation is developed, using complex rays. The ‘amplitude’ terms are matrices, rather than vectors that represent the wave polarization. Thus, the way the propagation resolves a source into various modes is described. The second term in the amplitude series is shown to include a type of inter-mode coupling. It is shown that initial values needed to integrate along the rays can be chosen so that the leading term of the approximation agrees with the far-field solution for localized sources in a homogeneous medium. By invoking the ‘canonical problem’ method, the result is extended to give an approximation for the Green's matrix in a slowly-varying medium.