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

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.

Monitoring Spontaneous Charge-Density Fluctuations by Single-Molecule Diffraction of Quantum Light

“…Off-resonant diffraction is described by the minimal coupling matter/field interaction Hamiltonian [24,25],…”

Current vs Charge Density Contributions to Nonlinear X-ray Spectroscopy

“…13,14 Indices i, ii, iii will be used to denote the first, second and third order contribution in L int respectively. The third order non-local response function is given by :…”

“…The nonlocal response formalism 13,14 starts with the minimal coupling field-matter interaction Hamiltonian 15 :…”

Translational and rotational averaging of nonlocal response tensors for nano-shaped light

“…Here, r y ( ) † and r y ( ) are the electron field Fermion creation and annihilation operators at position r. j r ( ) is a purely material current density operator and is gauge non-invariant [12]. Using this Hamiltonian, we can express optical signals as correlation functions of charge and current densities of matter [12]. The response functions are nonlocal in space and time.…”