Fluctuations of the Power of Coupled Modes

Using perturbation theory, an expression for the variance of the power of each mode of a multimode waveguide with randomly-coupled modes is derived. The variance builds up from zero to a constant value as a function of z (length along the waveguide). For most cases of interest, the variance is equal to the square of the average power. This means that the power of each mode of a system of randomly-coupled modes of a multimode waveguide fluctuates like the short-term time averaged power of a narrowband electrical signal the voltage of which is a random variable with Gaussian probability distribution.