Photonics Research, 2017, 5 (6): 06000B20, Published Online: Dec. 7, 2017
Constructing the scattering matrix for optical microcavities as a nonlocal boundary value problem Download: 741次
Abstract
We develop a numerical scheme to construct the scattering (S) matrix for optical microcavities, including the special cases with parity-time and other non-Hermitian symmetries. This scheme incorporates the explicit form of a nonlocal boundary condition, with the incident light represented by an inhomogeneous term. This approach resolves the artifact of a discontinuous normal derivative typically found in the R-matrix method. In addition, we show that, by excluding the aforementioned inhomogeneous term, the non-Hermitian Hamiltonian in our approach also determines the Periels–Kapur states, and it constitutes an alternative approach to derive the standard R-matrix result in this basis. Therefore, our scheme provides a convenient framework to explore the benefits of both approaches. We illustrate this boundary value problem using 1D and 2D scalar Helmholtz equations. The eigenvalues and poles of the S matrix calculated using our approach show good agreement with results obtained by other means.
Li Ge. Constructing the scattering matrix for optical microcavities as a nonlocal boundary value problem[J]. Photonics Research, 2017, 5(6): 06000B20.