Statistics of Group Delays in Multimode Fiber with Strong Mode Coupling

TL;DR

This paper analyzes the statistical distribution of group delays in multimode fibers with strong mode coupling, deriving analytical results for various mode counts and revealing a semicircle distribution for many modes.

Contribution

It provides the first analytical derivation of the GD probability density function for fibers with two to seven modes and extends the analysis to high mode numbers, linking delay spread to fiber length.

Findings

GDs follow eigenvalue distribution of zero-trace Gaussian unitary ensemble

For many modes, the GD distribution approaches a semicircle law

Delay spread scales with the square root of fiber length

Abstract

The modal group delays (GDs) are a key property governing the dispersion of signals propagating in a multimode fiber (MMF). A 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 (p.d.f.) of the GDs is the eigenvalue distribution of the ensemble. For fibers with two to seven modes, the marginal p.d.f. of the GDs is derived analytically. For fibers with a large number of modes, this p.d.f. 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. This revision also made clarification to the original paper, the group delay statistics is also extended to high number of modes.