Light-Matter Interactions Beyond the Dipole Approximation in Extended Systems Without Multipole Expansion

TL;DR

This paper develops a comprehensive theoretical framework to accurately model light-matter interactions beyond the electric-dipole approximation, especially for extended systems interacting with complex electric fields, enabling more precise simulations in nanophotonics and quantum materials.

Contribution

It introduces a general approach based on the PZW Hamiltonian and MLWFs to go beyond the dipole approximation without multipolar expansion, improving accuracy and computational efficiency.

Findings

The dipole approximation is robust for 1D/2D materials with perpendicular illumination.

Breakdown of EDA occurs in 3D materials or non-perpendicular illumination when wavelength is comparable to system size.

The proposed method captures beyond-dipole effects efficiently at standard computational cost.

Abstract

We present a general theoretical framework to capture light-matter interactions beyond the electric-dipole approximation (EDA), applicable to extended nano- and microscale materials interacting with spatially structured electric fields without truncation at finite multipolar order. The approach is based on the Power-Zienau-Woolley (PZW) Hamiltonian for light-matter interactions and a representation of the material's Hamiltonian in a basis of maximally localized Wannier functions (MLWFs), obtainable from first-principles calculations. We utilize this approach to clarify the limitations of the ubiquitous dipole approximation. We consider electric fields with both uniform and non-uniform intensities and a range of ratios of system size to the wavelength of light. Through this analysis, we identify the conditions under which the EDA breaks down, leading to significant errors in the light-induced dynamics. Contrary to conventional belief, we find that the EDA is remarkably robust for uniformly illuminated 1-D or 2-D materials when light propagates perpendicular to the material. For 3-D materials or non-perpendicular illumination of lower-dimensional materials, conventional wisdom holds and the EDA begins to break down when the wavelength becomes comparable to the system size. Furthermore, the EDA fails when the material is illuminated partially or non-uniformly. For slowly varying field intensities this failure can be corrected by finite-order multipolar corrections. However, for fields that vary substantially, correcting via multipolar terms becomes computationally impractical. In contrast, our approach captures beyond-dipole light-matter interactions at the computational cost of a standard dipole calculation. This efficiency enables accurate first-principles simulations of spatially structured light-matter dynamics in nanoscale devices, quantum materials, and interfaces.