Coupled-mode theory of optical waveguides

The coupled-mode theory of parallel waveguides is derived from a variational principle for the propagation constant of the waveguide-wave solution using a superposition of the uncoupled modes as a trial field. The nonorthogonality of modes as emphasized by Hardy and Streifer is part of this formalism as well. The coupling Coefficients agree with those of Hardy and Streifer derived for TE modes of loss-free guides. For TM modes the coupling coefficients differ slightly for the simpler trial solution and agree exactly for a different trial solution. The simpler trial solution gives results closer to the exact solution. Conventional coupled-mode theory emerges from orthonormalization.