Analysis of Gaussian beam propagation and diffraction by inhomogeneous wave tracking

Inhomogeneous waves behave locally like A(r) exp[ikS(r)], where A and S are spatially dependent complex amplitude and phase functions, and k is the (large) free-space wavenumber. A previously developed asymptotic theory for high-frequency propagation and scattering of such waves is here applied to the propagation and scattering of paraxial Gaussian beams. Attention is given to Gaussian beams in free space, to beams in a lens-like medium with parabolic variation of the refractive index, and to beam reflection by a cylindrical obstacle. In the latter instance, the obstacle size may be comparable to the incident beamwidth, thereby introducing substantial distortion into the reflected beam. The results obtained from the asymptotic theory are verified by comparison with rigorously derived solutions, thereby confirming the validity of the theory, which can also be applied to more general medium and obstacle configurations.