Abstract

For conditions in which the radiation losses can be neglected, multiple scattering analysis^1,2 predicts that the fraction of coupled optical power between intersecting waveguides is where K^ev corresponds to the single-Δn geometry (i.e., the guiding index is constant throughout the intersecting waveguide geometry) and K^fd, the contribution from the additional doping (see Fig. 1) of the intersection region, is given by Here β, 2a, α, and γ are the propagation constant, guide film thickness, and the magnitudes of the transverse components of the wave vectors in the film and substrate [determined from the dispersion relation, γ = αtan(αa)], respectively. The change in permittivity in the intersection region, Δε_fd, above that in a waveguide, ε_f, is related to the fractional doping thickness of Ti, Δτ/τ_o by Δε_fd ≅ (ε_f-ε_s Δτ/ε_o.

© 1991 Optical Society of America