LaGuerre-Gaussian periodically focusing beams in a quadratic index medium

The Hermite-Gaussian periodically focusing beam solutions of the scalar paraxial wave equation with quadratic index variation are appropriate for rectangular coordinates. One expects the solutions appropriate to cylindrical coordinates to be LaGuerre-Gaussian multifocusing beams. The phase shifts of these solutions appear not to be available in the published literature. In this note, we present an expression for these phase shifts together with a sketch of its derivation.