Theory of the photocount statistics for multi-mode multi-frequency radiation fields

TL;DR

This paper develops a quantum optics framework to analyze photocount uncertainties in multi-mode, multi-frequency radiation fields, accounting for quantum correlations, spectral effects, and speckle phenomena.

Contribution

It introduces a quantum-optical expression for photocount uncertainty that incorporates mode structure, frequency spectrum, and speckle effects, linking them through a new phase space volume definition.

Findings

Quantifies the impact of quantum correlations on photocount uncertainty.

Describes how frequency spectrum causes dynamic laser speckle.

Explains how static speckle arises from mode structure disturbances.

Abstract

We derive on the level of quantum optics expressions for the uncertainty of the photocount in a multi-mode multi-frequency setup. The result depends on the quantum correlations of the individual modes and the frequency spectrum of the radiation, the latter leading to a frequency beating sometimes referred to as dynamic laser speckle. When the mode structure of the radiation field is disturbed between source and detector, another contribution to the photocount uncertainty referred to as static speckle appears. To predict the size of this effect, we present a suitable definition of the etendue (or phase space volume) that links the number of modes of a radiation field to macroscopic quantities.