Delay-Spread Distribution for Multimode Fiber With Strong Mode Coupling

In the strong mode coupling regime, the delay spread of multimode fiber is statistically the same as the difference between the maximum and minimum eigenvalues of a Gaussian unitary ensemble. We study the delay-spread distribution using three methods: 1) numerical evaluation of the Fredholm determinant; 2) numerical integration based on the Andréief identity; and 3) approximation based on the Tracy-Widom distribution. Results obtained using the Fredholm determinant and the Andréief identity are virtually indistinguishable. The approximation based on the Tracy-Widom distribution is sufficiently accurate for most engineering purposes when the number of modes is at least 12. In a digital equalizer, a memory length of four to five times the group-delay standard deviation is sufficient to ensure that the delay spread will exceed the equalizer memory length with a probability of less than 10-4-10-6.