## 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.

Original language | American English |
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Article number | 063806 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 91 |

Issue number | 6 |

DOIs | |

State | Published - 4 Jun 2015 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2015 American Physical Society.