On the paraxial approximation in quantum optics II: Henochromatic modes of a Maxwell field

TL;DR

This paper extends the concept of henochromatic modes from scalar fields to Maxwell fields, emphasizing unitarity and addressing polarization-spatial degree intertwining in single-photon states within the paraxial approximation.

Contribution

It generalizes the henochromatic mode framework to Maxwell fields, incorporating polarization effects and maintaining unitarity in mode-state associations.

Findings

Extension of henochromatic modes to Maxwell fields.

Analysis of polarization and spatial degree intertwining.

Emphasis on unitarity in mode-state correspondence.

Abstract

A companion paper has argued that the best way to associate single-particle quantum states of a scalar field to the modes of a narrowly collimated beam of classical radiation modeled in the paraxial approximation uses the ``henochromatic'' states previously introduced by Sudarshan, Simon and Mukunda. This paper extends that result to Maxwell fields, again emphasizing the central role of unitarity in defining the association. The principal new technical element in the present discussion has to do with the intertwining of polarization and spatial degrees of freedom in the resulting single-photon states.