Why the laser linewidth is so narrow: A modern perspective

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.

17 pages, 9 figures, invited contribution to Physica Scripta's focus issue on Quantum Optics in the International Year of Light

References in corpus (11)

• Strong Interactions in Multimode Random Lasers
• Supporting Online Material for "Strong Interactions in Multimode Random Lasers"
• Self-consistent multi-mode lasing theory for complex or random lasing media
• Random lasing in weakly scattering systems
• Theory of the spatial structure of non-linear lasing modes
• Quantitative Verification of Ab Initio Self-consistent Laser Theory
• Ab-initio multimode linewidth theory for arbitrary inhomogeneous laser cavities
• General linewidth formula for steady-state multimode lasing in arbitrary cavities
• Steady-state ab initio laser theory for complex gain media
• Quantitative test of general theories of the intrinsic laser linewidth
• Generalized Sub-Schawlow-Townes Laser Linewidths Via Material Dispersion

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• Exceptional points as lasing pre-thresholds in open-cavity lasers
• Amplified and directional spontaneous emission from arbitrary composite bodies: self-consistent treatment of Purcell effect below threshold
• Electromagnetic Eigenvalue Problems and Nonhermitian Effects in Linear and Saturable Scattering