Photon shot noise

A recent theory is reviewed for the shot noise of coherent radiation propagating through a random medium. The Fano factor P/(I) over bar (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) over bar has the universal limit 1 + 3/2 f, 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) over bar(2)/P reaches a finite, universal limit.