Abstract
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=(m<sub>1</sub>/m<sub>2</sub>)<sup>3</sup> times, where m<sub>1</sub> and
m<sub>2</sub> 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<sup>1/3</sup> times, then the loss of the matched bend (straight-curved-straight
waveguide) transition will remain constant.
© 2011 IEEE
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