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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 withdoi:10.1109/3.81367 fatcat:jkrnehirtrehtcuozlb2kpi2um