Coupling of Nearly Degenerate Modes in Parallel Asymmetric Dielectric Waveguides

The coupling of modes in two parallel dielectric waveguides is studied. The individual waveguides are assumed to be asymmetric and unlike each other. If the individual waveguides support modes with nearly equal propagation constants β2and β4= β2+ 2Δ, then the double waveguide system will support two new modes with propagation constants β_ = β2− Δbar; and β+= β4+ Δbar;. The shift Δbar; is related to Δ and to the shift Δ which would occur if the original modes were degenerate; Δ is expressed in terms of the parameters describing the asymmetric double waveguide system. The field distributions of the new modes are approximately even and odd combinations of those of the original modes in the isolated waveguides; the relative amplitudes with which they are combined depend upon the amount of mismatching Δ. As the modes travel down the waveguide system, they partially cancel and add, thus transferring power. A power transfer ratio F is defined and is shown to decrease rapidly as Δ/Δ increases. The beat length L depends upon both Δ and Δ/Δ it also decreases as Δ/Δ increases. A numerical example is given to illustrate the effects of mismatching and to demonstrate the feasibility of constructing a mode-coupling device. Possibilities of tuning the device to reduce mismatching are discussed.