A General Scaling Rule for Matched Bend Waveguides

A scaling rule is introduced for reducing the dimensions of a matched waveguide bend without inducing additional transition loss and applied to photonic integrated circuits employing high index contrast waveguides. Mathematical expressions describing the wave propagation in the bend are obtained via a combination of analytical analysis and numerical calculations. These expressions show that if the bend radius R shrinks discretely by n=(m₁/m₂)³ times, where m₁ and m₂ are the integer number of beat lengths in the original and scaled matched bends, respectively, and the effective width of the waveguide is reduced also by n^1/3 times, then the loss of the matched bend (straight-curved-straight waveguide) transition will remain constant.