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Area of Science:

  • Quantum optics
  • Nanophotonics
  • Computational chemistry

Background:

  • Dipole approximation fails for nanoscale optical fields due to spatial variations.
  • Higher multipole expansions are cumbersome and less physically transparent.
  • Need for a unified approach to describe optical interactions at the nanoscale.

Purpose of the Study:

  • To develop a semi-classical method for calculating non-local optical response functions.
  • To provide a physically transparent and accurate description of light-matter interactions at the nanoscale.
  • To express response functions using gauge-invariant quantities.

Main Methods:

  • Utilizing a minimal coupling Hamiltonian in a semi-classical framework.
  • Calculating first, second, and third order response functions.
  • Expressing response functions via correlation functions of charge and current densities.

Main Results:

  • Developed a method to compute non-local response functions.
  • Formulated response functions based on gauge-invariant current and vector potential.
  • Demonstrated an intrinsically multipolar description of optical processes.

Conclusions:

  • The non-local response function approach offers a more accurate and transparent description of nanoscale optical interactions.
  • This method overcomes limitations of the dipole approximation.
  • The use of gauge-invariant current and vector potential provides a robust theoretical framework.