Symmetric vector coupled-mode theory of dielectric waveguides

A new vector coupled-mode theory for an array of dielectric waveguides is presented. It generalizes our previous work and is based on the most general symmetric perturbative expansion of the total electro-magnetic field on the eigenstates of the individual channels of the waveguide array. Equations of motion for the expansion coefficients are derived that are consistent with the system of Maxwell's equations. As an example, our theory is applied to the investigation of evanescent coupling and supermodes of two circular microcores in an optical fiber. It was found that our symmetric approach solves the singular anomaly in the effective index of in-phase supermodes found in the earlier improved coupled-mode theory.