Non-linear non-local molecular electrodynamics with nano-optical fields

TL;DR

This paper introduces a semi-classical, non-local response function framework for modeling non-linear molecular electrodynamics under nano-optical fields, capturing all multipole effects without relying on the dipole approximation.

Contribution

It develops a gauge-invariant, correlation-based approach to non-linear response functions using the minimal coupling Hamiltonian, advancing the theoretical modeling of nano-scale optical interactions.

Findings

Formulation of first, second, and third order non-local response functions

Expressing response functions in terms of charge and current density correlations

Provides a physically transparent alternative to multipole expansion

Abstract

The interaction of optical fields sculpted on the nano-scale with matter may not be described by the dipole approximation since the fields vary appreciably across the molecular length scale. Rather than incrementally adding higher multipoles it is advantageous and more physically transparent to describe the optical process using non-local response functions that intrinsically include all multipoles. We present a semi-classical approach to the non-linear response functions based on the minimal coupling Hamiltonian. The first, second and third order non-local response functions are expressed in terms of correlation functions of the charge and the current densities. This approach is based on the gauge invariant current rather than the polarization, and on the vector potential rather than the electric and magnetic fields.