Coupling of Modes

Abstract

In waveguides whose refractive index profiles are independent of the z-coordinate, the energy of a mode remains constant over the whole length. The superposition of two propagating modes a and b of the same frequency can be written as

$$ E = (x,y,z) = A exp\{ \mp i{\beta _a}z\} {\hat E_a}(x,y) + B exp\{ \mp i{\beta _b}z\} {\hat E_b}(x,y), $$

(5.1)

where A and B are complex amplitudes, and the plus and minus signs denote backward and forward travelling waves. If the waveguide has perturbations which lead to a refractive index profile dependent on z, there is scattering of energy from the mode.