Local geometry of electromagnetic fields and its role in molecular multipole transitions

TL;DR

This paper develops a systematic framework to analyze how complex electromagnetic fields interact with molecules, enabling targeted excitation of multipole transitions and advancing molecular spectroscopy and optical control techniques.

Contribution

It introduces a set of local electromagnetic quantities coupled to specific multipole transitions, and demonstrates how superpositions of plane waves can generate field configurations for molecular excitation.

Findings

Allowed field configurations can be generated by superpositions of plane waves.

Local electromagnetic quantities can be large in certain superpositions, enabling multipole transitions.

Framework facilitates designing experiments for molecular structure analysis and optical control.

Abstract

Electromagnetic fields with complex spatial variation routinely arise in Nature. We study the response of a small molecule to monochromatic fields of arbitrary three-dimensional geometry. First, we consider the allowed configurations of the fields and field gradients at a single point in space. Many configurations cannot be generated from a single plane wave, regardless of polarization, but any allowed configuration can be generated by superposition of multiple plane waves. There is no local configuration of the fields and gradients that requires near-field effects. Second, we derive a set of local electromagnetic quantities, where each couples to a particular multipole transition. These quantities are small or zero in plane waves, but can be large in regions of certain superpositions of plane waves. Our findings provide a systematic framework for designing far-field and near-field experiments to drive multipole transitions. The proposed experiments provide information on molecular structure that is inaccessible to other spectroscopic techniques, and open the possibility for new types of optical control of molecules.