Coupled-mode theory of optical waveguides

TLDR

The formalism incorporates mode nonorthogonality, as noted by Hardy and Streifer, and reduces to conventional coupled‑mode theory under orthonormalization. The theory is derived via a variational principle that treats the propagation constant of the coupled waveguide system as a superposition of uncoupled modes. The coupling coefficients for TE modes agree with Hardy and Streifer; for TM modes they differ slightly with the simpler trial solution but match exactly with a different trial solution, and the simpler trial solution yields results closer to the exact solution.

Abstract

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.