Open AccessS-parameters, non-Hermitian ports and the finite-element implementation in photonic devices with đť’«đť’Ż-symmetry
Author(s) -
Bei Wu,
Zhuoran Wang,
Weijin Chen,
Zhongfei Xiong,
Jing Xu,
Yuntian Chen
Publication year - 2019
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.27.017648
Subject(s) - hermitian matrix , physics , orthogonality , coupled mode theory , photonics , optics , hermitian function , waveguide , finite element method , modal , photonic crystal , quantum mechanics , mathematics , geometry , materials science , refractive index , polymer chemistry , thermodynamics
In Hermitian photonic devices, S-parameters, i.e., the elements of a scattering matrix based on integrated power flux and Hermitian modal orthogonality, are used to account for the transmission or reflection of light from one port to another. The definition of S-parameters in Hermitian settings becomes inappropriate in the non-Hermitian optical environment. Here we revisit the fundamental problems associated with extracting the S-parameters of light in photonic -symmetric devices, i.e., waveguides or coupled waveguide-cavity systems, wherein the waveguide ports themselves may also be non-Hermitian. We first use the bi-orthogonal inner product that restores the modal orthogonality on the waveguide ports containing balanced gain and losses to quantify the modal overlapping instead of Hermitian inner product. Secondly, a finite element implementation is proposed and realized to extract the S-parameters on non-Hermitian ports. Lastly, we illustrate our approach of calculating the S-parameters on non-Hermitian ports via two waveguide-lattice structures. The numerical results of S-parameters are validated against the constraints imposed by reciprocity and -symmetry.