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.