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Multimode laser-linewidth theory for complex wavelength-scale laser cavities


  A. Pick [1]  ,  A. Cerjan [2]  ,  D. Liu [3]  ,  A. W. Rodriguez [4]  ,  A. D. Stone [2]  ,  Y. D. Chong [5]  ,  S. G. Johnson [6]  
 [1] Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
[2] Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
[3] Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
[4] Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
[5] Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
[6] Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

We present a multimode laser-linewidth formula that generalizes previous linewidth theories, including correction factors for cavity losses, nonlinear gain, amplitude–phase coupling and dispersion, but is derived in a much more general setting and is therefore applicable to complex wavelength-scale laser cavities. 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. We show that the multimode amplitude–phase coupling enhancement factor is a matrix generalization of the single-mode Henry α factor. Moreover, we relax the standard assumption that atomic populations follow the field adiabatically and, surprisingly, we find that the linewidths are independent of the population-inversion relaxation rate.