S-parameters, non-Hermitian ports and the finite-element implementation in photonic devices with PT-symmetry

• Published in: Optics express 2019-06, Vol.27 (13), p.17648-17657
• Main Authors: Wu, Bei, Wang, Zhuoran, Chen, Weijin, Xiong, Zhongfei, Xu, Jing, Chen, Yuntian
• Format: Article
• Language: English
• ISSN: 1094-4087; 1094-4087
• DOI: 10.1364/OE.27.017648

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 PT-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 PT-symmetry.