An acceleration technique for computing fields from a periodic source above a layered medium

In this work we derive a time domain Green´s function for a periodic source distribution above a layered medium and a corresponding acceleration scheme. A representation using sums of complex exponentials allows closed form evaluation of the requisite integrals, leading to a fully closed form expression for the Green´s function. A separable expansion based on this expression is accelerated in space using the method of Accelerated Cartesian Expansions and in time with a block-FFT scheme. The resulting method scales as O(N_sN_t log² N_t) method, where N_s and N_t represent the number of spatial and temporal degrees of freedom.