Application of the multiple-scattering method to analysis of systems with semi-infinite photonic waveguides

Abstract

We propose a technique of compensating the spurious reflections implied by the multiple-scattering (MS) method, commonly used for analyzing finite photonic crystal (PC) systems, to obtain exact values of characteristic parameters, such as reflection and transmission coefficients, of PC functional elements. Rather than a modification of the MS computational algorithm, our approach involves postprocessing of results obtained by the MS method. We derive analytical formulas for the fields excited in a finite system, taking explicitly into account the spurious reflections occurring at the artificial system boundaries. The intrinsic parameters of the investigated functional element are found by fitting the results of MS simulations to those obtained from the formulas derived. Devices linked with one and two semi-infinite waveguides are analyzed explicitly; possible extensions of the formalism to more complex circuits are discussed as well. The accuracy of the proposed method is tested in a number of systems. The results of our calculations prove to be in good agreement with those obtained independently by other authors.