We consider sums over the square lattice which depend only on radial distance, and provide formulas which enable sums of functions with Neumann series to be reexpressed as combinations of hypergeometric series. We ...

Three-dimensional photonic band gap structures are the ultimate goal for photonic crystals as, unlike one and two-dimensional crystals, they provide for total confinement. One such configuration is the woodpile structure, ...

We give analytical results pertaining to the distributions of zeros of a class of sums which involve complex powers of the distance to points in a two-dimensional square lattice and trigonometric functions of their angle. ...