Study on low-loss and small-size S-shaped bends in thermo-optic switch matrix

First, in order to get the low-loss and small-size 2-arc S-shaped bend, the lateral offset between waveguides with different curvature was optimized to reduce the mode mismatch. To get the smoother S-shaped bend, which also has the overall bending loss as small as possible, another S-shaped bend based on functional approximation theory of B-spline was put forward. By this means, the transition loss at the junctions can be completely eliminated and also make the pure bending loss as small as possible. A comparison among sine-generated, cosine-generated, 2-arc and numerical calculated S-shaped bends was also been conducted. Using Beam Propagation Method (BPM) and analytical method, the result was verified and good agreement was got.