Efficient computation of the periodic Green´s function in layered dielectric media

A technique for the efficient computation of the periodic Green´s function in layered dielectric media is presented. The technique is based on expanding the spectral Green´s function into a finite number of inverse-transformable complex exponential functions. This enables the use of Poisson´s summation formula to express the periodic Green´s function as a combined sum of spectral terms and spatial terms, each set of which is rapidly convergent. Numerical results are obtained for the on-plane case, in which the direct summation of the series converges extremely slowly. Using the accelerated summation formula of this study, a computation time reduction of 160-fold is obtained. The technique can be applied to a wide class of problems in which periodic structures are to be modeled