Intensity fluctuations and cross correlations in coupled-mode optical systems

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Abstract
In nonlinear multimode optical systems, stochastic fluctuations of the intensities of the competing modes have signatures (characteristic moments, cumulants, and cross correlations) that depend on the number of modes and on any constraints on the total intensity. For the cases of maximum entropy fluctuations within a constant total intensity and within a fluctuating total intensity, we derive the intensity probability distribution functions and calculate the moments, cumulants, and cross correlation. The latter two are shown to be sensitive indicators of the number of interacting modes. When the modes are statistically equivalent, particular relations between the variance of one mode and the cross correlation of any two modes can indicate the type of mode coupling independent of their number. The predictions of these models are compared to recent experimental measurements on a multimode source of amplified spontaneous emission. Statistical results for a system that randomly jumps among single-mode states while maintaining constant total intensity are also calculated and are compared with the statistics of a (deterministic) two-mode bidirectional ring-laser simulation. The results are widely applicable to other coupled-mode systems including multimode lasers.

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