Modification of the refractive index of the region common to intersecting waveguides (fractional doping) provides a mechanism, independent of intersection angle, for controlling the optical coupling characteristics of this geometry. We derive a pair of expressions based on a multiple scattering analysis of intersecting waveguides which predict the coupling behavior as a function of intersection angle and fractional doping for both polarizations. The expressions are in good agreement with experimental data from several different laboratories. The conditions for polarization-independent coupling and polarization splitting are demonstrated. © 1991 IEEE.