Rapidly convergent Green's function representation for a linear periodic array near layered media

We have presented rapidly hybrid spectral-spatial techniques for the rapid calculation of 3D Green's functions of a linear periodic array residing in near a layered medium. The techniques are based on spectral field expansion over the transverse (to the array's axis) spectral parameter, extraction any singular field components, and efficient integration rules. The techniques are efficient for any complex phase shifts, a wide range of array's periodicities, as well as a wide range of observation locations including those on the array's axis. Numerical examples demonstrate the efficiency of the method.