Coupled mode equations physical derivation

The coupled mode equations of the previous section can be derived intuitively. This also provides insight into the physical mechanism of the coupling process. Consider a differential section of the perturbed waveguide of length dz, as shown in Fig. 31-2, and its effect on the k th forward-propagating bound mode. The z dependence of the fields, hi(z) of Eq. (31-45), is expressible as... 

There are essentially two methods for deriving the equations satisfied by the bj(z). The more physical approach is to divide the fiber into a series of differential sections, one of which is shown in Fig. 31-2, and then consider the change in each modal amplitude across each section [1]. Details are given in Section 31-16. Alternatively, we substitute Eq. (28-1) into Maxwell s equations and use the orthogonality conditions for local modes to derive the set of coupled local-mode equations [2,3], This approach is presented in Section 31-14, and leads to Eq. (31-65)... 

Fields of z-dependent waveguides 31-14 Coupled local-mode equations 31-15 Alternative form of the coupling coeflScients 31-16 Physical derivation of the coupled equations... 

---