Exact theory of plasmon reflection and transmission in partially gated two-dimensional system

TL;DR

This paper presents an exact analytical theory for plasmon reflection and transmission at boundaries in two-dimensional electron systems, accounting for evanescent fields and radiative losses, with implications for terahertz devices.

Contribution

The authors develop a rigorous analytical framework for plasmon scattering at 2DES boundaries using the Wiener-Hopf technique, including evanescent and radiative effects.

Findings

Reflected plasmon dominates electric field in non-retarded limit

Radiative losses are negligible when plasmon scattering is considered

Reflection and transmission coefficients depend complexly on 2DES-gate separation and conductivity

Abstract

We develop an exact theory of plasmon scattering at the boundary between gated and ungated regions of a two-dimensional electron system (2DES). Using the Wiener-Hopf technique, we derive analytical expressions for the complex reflection and transmission coefficients of plasmons incident from both sides of the interface. The theory fully accounts for evanescent fields at the gate edge and radiative losses into free-space electromagnetic waves. In the non-retarded limit and for small gate-2DES separation, the reflected plasmon dominates the total electric field, while radiative losses are negligible when plasmon scattering. The amplitudes and phases of the reflection and transmission coefficients for plasmons incident from both sides have a complex dependence from 2DES-gate separation and conductivity of 2DES. Our results provide a rigorous foundation for modeling tunable plasmonic crystals based on 2DES for terahertz detection and modulation.