Nonlinear finite-difference time-domain method for exciton-polaritons: application to saltatory conduction in polariton neurons

• Main Authors: Dini, Kevin, Sigurðsson, H., Seet, Nathan Wei En, Walker, P. M., Liew, Timothy Chi Hin
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2024
• Subjects: Physics; Exciton polaritons; Finite-difference time-domain method; Semiconductor microcavities; First principles calculations
• Online Access: https://hdl.handle.net/10356/181502; https://doi.org/10.1103/PhysRevB.110.214303
• Institution: Nanyang Technological University

Recently emerging complex photonic structures exhibiting giant optical nonlinearity through strong light-matter coupling require new theoretical approaches to accurately capture the interplay of the photonic and interacting-matter degrees of freedom. Extending the finite-difference time-domain method, we develop an algorithm for solving the nonlinear Maxwell-Bloch equations. This allows first-principles modeling of exciton-polariton systems for arbitrarily complex photonic structures with photon-exciton coupling and frequency dependent nonlinear response included without approximations or phenomenological parameters. We first validate the algorithm by reproducing the bistable hysteresis cycle of polaritons in the nonlinear regime. We then give a key example of its utility by simulating polariton dynamics in integrated photonic circuitry composed of spatially localized bistable nodes connected by high speed waveguides. We propose a polariton circuit element inspired by saltatory conduction in biological neurons. This design supports faster polariton signal propagation than previous designs, however, requires a full account of the nonlinear field distributions in both propagation and growth directions to be calculated.