Ab initio multimode linewidth theory for arbitrary inhomogeneous laser cavities

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Ab initio multimode linewidth theory for arbitrary inhomogeneous laser cavities

A. Pick, A. Cerjan, D. Liu, A. W. Rodriguez, A. D. Stone, Y. D. Chong, and S. G. Johnson

Phys. Rev. A 91, 063806 – Published 4 June 2015

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.

Received 24 February 2015

DOI:https://doi.org/10.1103/PhysRevA.91.063806

Authors & Affiliations

A. Pick^1,*, A. Cerjan², D. Liu³, A. W. Rodriguez⁴, A. D. Stone², Y. D. Chong⁵, and S. G. Johnson^6,†

¹Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
²Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
³Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
⁴Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
⁵Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
⁶Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

^*adipick@harvard.physics.edu
^†stevenj@math.mit.edu

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Vol. 91, Iss. 6 — June 2015

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