New design method for low-loss Y-branch waveguides

We propose a new method to design low-loss Y-branch waveguides. In conventional design methods, a specific geometry of branching structure is given first, and then structural parameters describing the details of the proposed geometry (for example, location, sizes, and refractive index of microprisms or phase-adjusting elements) are determined by ray optics or other means. In this paper, we take quite a different approach. Given a complex field distribution, one complex refractive index distribution that supports it is determined uniquely, according to the scalar Helmholtz equation. Using this relation, we first make up an ideal field distribution for dividing optical waves smoothly in the branching region. Next, we calculate the refractive index distribution corresponding to the ideal field. Finally, the imaginary part of the refractive index is set to be zero and its real part is discretized into three levels from the practical viewpoint. Numerical simulations show that the present design method offers extremely low-loss Y-branch waveguides.