We propose a new method to design low-loss Y-branch waveguides. Previous designing methods are as follows; The shape of branch comes first. Next, parameters describing details of the shape (for example, location, size, and refractive index of microprisms) are determined by ray optics and others. On the other hand, we take quite a different approach. According to the scolor Helmholtz equation, if one complex field distribution is given, the corresponding distribution ef refractive index of complex number is determined uniquely. First, we make up an ideal field distribution for dividing optical waves smoothly. Next, we calculate the refractive index associated with the ideal field. Finally, the imaginary part of the refractive index is set to be zero and its real part is descretized into several values from the practical viewpoint. Our design method gives extremely low loss Y-branch waveguides.
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