Efficient computation of the Green's function for multilayer structures with periodic dielectric gratings

Adanır, Süleyman
Numerical analysis of periodic structures in layered media is usually accomplished by using Method of Moments which requires the formation of the impedance matrix of the structure. The construction of this impedance matrix requires the evaluation of the periodic Green’s function in layered media which is expressed as an infinite series in terms of the spectral domain Green’s function. The slow converging nature of this series make these kinds of analysis computationally expensive. Although some papers have proposed methods to accelerate the computation of these series successfully for a single frequency point, it is still very computation intensive to obtain the frequency response of the structure over a band of frequencies. In this thesis, Discrete Complex Image Method (DCIM) is utilized for the efficient computation of the periodic Green’s function. First, the spectral domain Green’s function in layered media is approximated by complex exponentials through the use of DCIM. During the application of the DCIM, three-level approximation scheme is employed to improve accuracy. Then, Ewald’s transformation is applied to accelerate the computation of the infinite series involved in the periodic Green’s functions. The accuracy and the efficiency of the method is demonstrated through numerical examples.