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# Ab initio multimode linewidth theory for arbitrary inhomogeneous laser cavities

## Author(s): Pick, A; Cerjan, A; Liu, D; Rodriguez, Alejandro W; Stone, AD; et al

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 Abstract: We present a multimode laser-linewidth theory for arbitrary cavity structures and geometries that contains nearly all previously known effects and also finds new nonlinear and multimode corrections, e.g., a correction to the α factor due to openness of the cavity and a multimode Schawlow-Townes relation (each linewidth is proportional to a sum of inverse powers of all lasing modes). Our theory produces a quantitatively accurate formula for the linewidth, with no free parameters, including the full spatial degrees of freedom of the system. Starting with the Maxwell-Bloch equations, we handle quantum and thermal noise by introducing random currents whose correlations are given by the fluctuation-dissipation theorem. We derive coupled-mode equations for the lasing-mode amplitudes and obtain a formula for the linewidths in terms of simple integrals over the steady-state lasing modes. Publication Date: 2015 Citation: Pick, A, Cerjan, A, Liu, D, Rodriguez, AW, Stone, AD, Chong, YD, Johnson, SG. (2015). Ab initio multimode linewidth theory for arbitrary inhomogeneous laser cavities. Physical Review A - Atomic, Molecular, and Optical Physics, 91 (10.1103/PhysRevA.91.063806 DOI: doi:10.1103/PhysRevA.91.063806 Type of Material: Journal Article Journal/Proceeding Title: Physical Review A - Atomic, Molecular, and Optical Physics Version: Author's manuscript

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