The Entropy Flow of a Laser Beam

TL;DR

This paper analyzes the entropy flow of an ideal laser beam with phase diffusion, deriving a simple formula for entropy flow based on photon number and phase diffusion rate, and compares it to thermal beams.

Contribution

It introduces a novel analysis of laser beam entropy considering phase diffusion, revealing an extensive entropy and a simple formula for entropy flow.

Findings

Entropy flow of laser beam: $oxed{ ext{~} extstyle rac{dS}{dt} = k_B extstyle rac{ ext{d}N}{ ext{d}t} imes extstyle rac{ ext{d}t}{ ext{d}S} = k_B rac{ ext{d}N}{ ext{d}t} rac{1}{ ext{d}S/ ext{d}N}$

Entropy flow is proportional to the square root of photon number flow and phase diffusion rate: $oxed{ ext{~} ext{entropy flow} = k_B imes ext{sqrt}( ext{d}N/ ext{d}t imes ext{diffusion rate})}$

Comparison of laser beam entropy flow to thermal beam shows distinct behaviors.

Abstract

A laser beam is often modelled by a pure coherent state. In fact its state is mixed, even if it has coherent-state photon-number statistics (Poissonian), because the phase must vary. We consider such an ideal laser beam, with phase diffusion rate $\ell$, equal to its (Lorentzian) spectral width. We show that the beam entropy is extensive, with an entropy flow of $\dot{S} = k_B \sqrt{\dot{N}\ell}$, where $\dot{N}$ is the number flow. We give an intuitive explanation for this remarkably simple result, and compare it to a unidirectional thermal beam's.