Efficient calculation of lattice sums for free-space periodic Green´s function

An efficient method to calculate the lattice sums is presented for a one-dimensional (1-D) periodic array of line sources. The method is based on the recurrence relations for Hankel functions and the Fourier integral representation of the zeroth-order Hankel function. The lattice sums of arbitrary high order are then expressed by an integral of elementary functions, which is easily computed using a simple scheme of numerical integration. The calculated lattice sums are used to evaluate the free-space periodic Green´s function. The numerical results show that the proposed method provides a highly accurate evaluation of the Green´s function with far less computation time, even when the observation point is located near the plane of the array