Interaction Between Shaped Beams and an Infinite Cylinder,including a discussion of Gaussian beams

The theory of interaction between a shaped beam and an infinite cylinder arbitrarily located in it is presented. The same approach as for the generalized Lorenz-Mie theory is first used. In particular, variable separability is assumed in solving the wave equation. The special case of Gaussian beams, however, implies that, unexpectedly, a special class of non-separable scalar potentials is required for some kinds of beams.