Modes in a sequence of thick astigmatic lens-like focusers

Maxwell's equations are solved for a periodic sequence of lens-like focusers separated by gaps. Each focuser consists of an arbitrarily thick slab of dielectric in which the dielectric constant tapers off radially with different quadratic laws in two perpendicular directions. Since there are no limitations on the thickness of the slabs, the solutions cover the complete gamut from a sequence of infinitely thin lenses with astigmatism to a continuous dielectric waveguide, and from spherical to cylindrical lenses. The field configurations of the modes and their propagation constants, as well as the transmission and cutoff bands, are calculated. Any arbitrary input field distribution can then be expanded in terms of the normal modes, and the expansion determines the field everywhere. Formulas derived for sequences of weak lenses turn out to give very good results even for lenses whose thickness and separation are equal to the focal length.