Why Do Field-Based Methods Fail to Model Plasmonics?

Abstract

The paper studies plasmonics modeling issues and examines the reasons behind the failure of the field-based methods relying on Pade approximations widely used in the analysis of photonic devices based on dielectric materials. Through a study of evanescent, radiation, guided, and surface modes of a plasmonic structure where the failure appears clearly, we demonstrate the physical explanation of this failure and suggest some remedies. We developed a Bidirectional Beam Propagation Method (BiBPM) by adopting a Blocked Schur (BS) algorithm to introduce an unconditionally stable method for plasmonic structures with strong discontinuities. Central to BiBPMs is the accurate calculation of the square root operators that is very widely performed using Pade approximations. However, recent reports demonstrate convergence of Pade that is too slow to lend itself a stable solver in plasmonics [1] . Moreover, Pade approximations completely fail in handling such a strong discontinuity between dielectric and plasmonic waveguides, where a very-wide spectrum of modes could be excited. Alternatively, we propose calculating these operators by the twice faster BS algorithm. Beyond the computational speed, our suggested approach overbears the Pade-based BiBPMs instability and accuracy problems, thanks to the proper physical treatment of surface and evanescent waves: the notorious sources of instability. Through the plasmonic discontinuity problems, the superiority of BS approach has been determined numerically and explained physically.