Two Derivations of the Time-Dependent Coupled-Power Equations

Suppose a multimode fiber guide with random mode coupling is excited by an optical source at one end at time t = 0. This input excitation will produce, at time t, a response of optical power in each mode v at a position z from the input end given by sv(t, z). Marcuse 2 has suggested from intuitive arguments t h a t sv(t, z) should satisfy the following differential equation £ «.(*, z)) + ·,(«, z)> = £ K^F{Sll{t, z)) CLlK^mis^z)), M (1)