Application of Madelung Hydrodynamics to Plasmonics and Nonlinear Optics in Two-Dimensional Materials

TL;DR

This paper applies Madelung hydrodynamic models to two-dimensional materials to analyze nonlocal plasmonics and nonlinear optics, deriving spectra and exploring nonlinear phenomena like second-harmonic generation and self-modulation.

Contribution

It introduces a hydrodynamic approach to study nonlocal and nonlinear optical effects in 2D materials, providing analytic expressions for spectra and insights into plasmon renormalization.

Findings

Madelung equations effectively model 2D plasmonic spectra.

Nonlinearity enhances nonlocal effects in plasmonics.

Analytic expression for renormalized plasmon spectra derived.

Abstract

This paper explores the application of Madelung hydrodynamic models to study two-dimensional electron gases, with a focus on nonlocal plasmonics and nonlinear optics. We begin by reviewing the derivation of the Madelung equations. Using the Madelung equations in conjunction with Poisson's equation, we calculate the spectrum of magnetoplasmons and the magneto-optical conductivity in the electrostatic regime, incorporating nonlocal corrections due to the Fermi pressure. In the absence of a magnetic field, we analyze nonlinear and nonlocal second-harmonic generation, demonstrating how plasmon excitation enhances this process. We further discuss the emergence of self-modulation phenomena driven by nonlinearity, leading to the renormalization of the plasmon dispersion. Notably, we show that nonlinearity amplifies nonlocal effects and, leveraging the hydrodynamic formalism, derive a simple analytic expression for the renormalized spectra.