Derivation of Coupled Power Equations

The modes of a multimode dielectric waveguide are coupled by imperfections of the waveguide structure. The propagation of the coupled modes is described by coupled wave equations involving the wave amplitudes. If the coupling functions are random variables the interaction between the modes can be described more easily by coupled power equations. The derivation of the coupled power equations from the coupled wave equations is accomplished with the help of perturbation theory.