Coupled Line Equations with Random Coupling

We consider the coupled line equations for two modes traveling in the forward direction, 1 ^ + ^ + r07,,(z) r,/,(z) = jc(z)it(z), (1) = jc(z)h(z), subject to the initial conditions /o(0) = i0 , /i(0) = t, . (2) The time dependence exp (2irjft) has been suppressed. Here c(z) is the real coupling coefficient, which we take to be a random function of z, and the loss and phase constants are T,, = a 0 + j/3,, , T, = a, + 301 . (3)