Coupled Mode Formalism for Guided Wave Interactions

Abstract

Consider two electromagnetic modes with, in general, different frequencies whose complex amplitudes are A and B. These are taken as the eigenmodes of the unperturbed medium so that they represent propagating disturbances

$$ \begin{gathered} a\left( {z,t} \right) = A{e^{i\left( {{\omega _a}t - {\beta _a}z} \right)}} \hfill \\ b\left( {z,t} \right) = B{e^{i\left( {{\omega _b}t \pm {\beta _b}z} \right)}} \hfill \\ \end{gathered} $$

((1))

with A and B constant.