Analysis of Photonic Structures by the Multiple Multipole Program with Complex Origin Layered Geometry Green's Functions

An upgrade for the layered geometry Green's functions is introduced in order to analyze photonic structures in layered geometries by the Multiple Multipole Program (MMP) contained in the open-source simulation package OpenMaX. This upgrade uses the concept of complex origin for point sources in layered geometries, as in the case of complex origin multipole expansions in free space that produce beams. This technique makes it possible for the user to decide on the direction and the shape of the beam generated by a complex origin point source in a layered geometry. By using these point sources as expansions in the MMP, it is possible to decrease the total number of expansions and the solution time for the simulations, especially for long structures compared with the wavelength, built in or on a layered geometry. In this paper, the derivation of the complex origin layered geometry Green's functions will be discussed with a special emphasis on the physical meaning of the complex origin. Several numerical examples, showing the fields generated by the complex origin Green's functions and using them as expansions in MMP will be analyzed.