Quasi-optical description of wave beams in smoothly inhomogeneous anisotropic media

The quasi-optical description of wave beams is extended to smoothly inhomogeneous anisotropic and/or gyrotropic media. A method of deriving quasi-optical equations for a slow-varied scalar beam amplitude from Maxwellian equations is proposed. Transversal localization of the beam near the central ray allows one to separate and sequentially derive the refractional, focusing (or defocusing) and aberrational terms. The correct relationship between the scalar beam amplitude and the vector electric field is conserved for every order. For simplicity, a cold collisionless magnetized plasma is considered. However, all basic results are valid, with minor amendments, for media with spatial dispersion. The aberration-free parabolic-like equation for a complex beam envelope is considered in detail. Its physical properties are investigated and a general solution is found