Scattering by a periodic tube in R-3: part ii. A radiation condition

This second part of a pair of papers complements the first part (see Kirsch 2018 (35 104004)) but can be read independently. Scattering of time-harmonic waves from periodic structures at some fixed real-valued wave number becomes analytically difficult whenever there arise surface waves: These nonzero solutions to the homogeneous scattering problem physically correspond to modes propagating along the periodic structure and clearly imply nonuniqueness of any solution to the scattering problem. As in the first part we consider a medium described by a refractive index which is periodic along the axis of an infinite cylinder in R3 and constant outside of the cylinder. We formulate a proper radiation condition which allows the existence of traveling modes (and is motivated by the limiting absorption principle proven in the first part) and prove uniqueness and existence.