Photon shot noise

TL;DR

This paper reviews a theory relating optical shot noise in random media to the scattering matrix, highlighting how absorption and amplification influence noise levels and drawing analogies with electronic shot noise phenomena.

Contribution

It introduces a theoretical framework connecting optical shot noise to the scattering matrix, extending Buttiker's electronic shot noise formula to optical systems with absorption and amplification.

Findings

Absorption increases the Fano factor to a universal limit of 1+3f/2.

Scattering alone does not affect the Fano factor, which remains Poissonian.

The Fano factor diverges at the laser threshold in amplifying media.

Abstract

A recent theory is reviewed for the shot noise of coherent radiation propagating through a random medium. The Fano factor P/I (the ratio of the noise power and the mean transmitted current) is related to the scattering matrix of the medium. This is the optical analogue of Buttiker's formula for electronic shot noise. Scattering by itself has no effect on the Fano factor, which remains equal to 1 (as for a Poisson process). Absorption and amplification both increase the Fano factor above the Poisson value. For strong absorption P/I has the universal limit 1+3f/2 with f the Bose-Einstein function at the frequency of the incident radiation. This is the optical analogue of the one-third reduction factor of electronic shot noise in diffusive conductors. In the amplifying case the Fano factor diverges at the laser threshold, while the signal-to-noise ratio I^2/P reaches a finite, universal limit.