A novel equivalent waveguide theory based on the conformal mapping method is employed to investigate the tapered waveguide with curved phase fronts, By using the theory, the curved phase fronts of a tapered waveguide would be transformed into the planar ones of its equivalent straight-liked structure, Therefore, the paraxial beam propagation method can be used to analyze the equivalent structures of tapered waveguides (even for wide-angle tapers), Two kinds of popular tapered waveguides, including the cross-sectional dimension tapering and the constant V-number tapering, are used to analyze by our combination of conformal mapping method and beam propagation method (BPM).
