Accurate coupling coefficients for fiber couplers with weakly fused cross sections

For fused tapered fiber couplers with weakly fused cross sections, power coupling takes place between two touching tapered cladding cylinders embedded in the air, and the cylinders then become a strongly guiding structure. We provide accurate polarization-dependent coupling coefficients for such a structure, on the basis of a rigorous vectorial numerical calculation. Our results for the corresponding weakly guiding structure are compared with previous vector perturbation methods base on scalar fields. It is found that the scalar theories are not applicable to those cases with large normalized frequencies or with small fiber separations when the polarization-splitting effect is concerned.