Statistics of Group Delays in Multimode Fiber With Strong Mode Coupling

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Abstract
The modal group delays (GDs) are a key property governing the dispersion of signals propagating in a multimode fiber (MMF). An MMF is in the strong-coupling regime when the total length of the MMF is much greater than the correlation length over which local principal modes can be considered constant. In this regime, the GDs can be described as the eigenvalues of zero-trace Gaussian unitary ensemble, and the probability density function (pdf) of the GDs is the eigenvalue distribution of the ensemble. For fibers with two to seven modes, the marginal pdf of the GDs is derived analytically. For fibers with a large number of modes, this pdf is shown to approach a semicircle distribution. In the strong-coupling regime, the delay spread is proportional to the square root of the number of independent sections, or the square root of the overall fiber length.