Spontaneous emission in non-Hermitian optical systems: distributed-feedback semiconductor lasers

A method is presented for calculating the fluctuation spectrum of laser resonators both below and above threshold. The method is applied to 1-D laser models, but the formalism is completely general. The laser field is written as the superposition of a left- and a right-order partial differential equations. This eventually allows the search for a complete set of biorthogonal eigenfunctions in which the field can be expanded. Below threshold the eigenfunction expansion method and the Green's function method give the same results, but the latter cannot be used above threshold as such because the problem becomes nonlinear. It is found that for a single-mode laser well above threshold the fluctuations in the main mode amplitude are practically uncorrelated with the fluctuations of the other (below threshold) modes. The mode method described is shown to be more flexible and physically transparent than the Green's function method.