Why the laser linewidth is so narrow: A modern perspective

TL;DR

This paper presents a modern perspective on laser linewidth, using SALT and N-SALT theories to unify lasing and amplification, providing a comprehensive and analytic understanding of linewidth including quantum noise effects.

Contribution

It introduces N-SALT, a generalized SALT framework that incorporates quantum noise, resulting in a more accurate and analytically tractable linewidth formula.

Findings

N-SALT provides a more general linewidth formula than previous models.

Lasing modes are described as solutions to a non-linear scattering problem.

Quantum fluctuations, especially in the gain medium polarization, dominate linewidth control.

Abstract

We review and interpret a modern approach to laser theory, steady-state ab initio laser theory (SALT), which treats lasing and amplification in a unified manner as a non-unitary scattering problem described by a non-linear scattering matrix. Within the semiclassical version of the theory the laser line has zero width as the lasing mode corresponds to the existence of an eigenvector of the S-matrix with diverging eigenvalue due to the occurrence of a pole of the scattering matrix on the real axis. In this approach the system is infinite from the outset and no distinction is made between cavity modes and modes of the universe; lasing modes exist both in the cavity and in the external region as solutions satisfying Sommerfeld radiation boundary conditions. We discuss how such solutions can be obtained by a limiting procedure in a finite box with damping according to the limiting absorption principle. When the electromagnetic and matter fields are treated as operators, quantum fluctuations enter the relevant correlation functions and a finite linewidth is obtained, via a generalization of SALT to include noise (N-SALT). N-SALT leads to an analytic formula for the linewidth that is more general than all previous corrected versions of the Schawlow-Townes formula, and can be evaluated simply from knowledge of the semiclassical SALT modes. We derive a simpler version of this formula which emphasizes that the noise is dominated by the fluctuations in the polarization of the gain medium and is controlled by the rate of spontaneous emission.