Parametrized non-hermitian Laplacian eigenvalue problem for solution of the laser equations

Alfred Stone
Yale University

Starting from coupled non-linear Maxwell-Bloch equations of a laser, we
derive a new self-consistent equation which determines the stationary
states of a laser in the multi-mode regime. This equation is based on
the well-controlled approximation of stationary inversion and treats the
non-linear interactions between lasing modes to infinite order. The
equation is efficiently solved iteratively by expressing the solution in
a basis determined by a non-hermitian Laplacian eigenvalue problem
parametrized by the unknown lasing frequencies. This time-independent
approach is much more computationally efficient than direct solution of
the MB equations, and is shown to give good agreement with such direct
numerical solutions. The approach provides a link between linear
wave-chaotic eigenfunctions and non-linear steady state laser modes, and can even treat random lasers with no long-lived resonant states.

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