Level Set Reinitialization in Device Boundary Evolution Based on Inverse Design

We propose a level set reinitialization algorithm in the inverse design framework to avoid numerical errors in boundary evolution caused by kinks, which lead to stagnation in structural optimization. When applied to a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1\times 2$</tex> wavelength demultiplexer, this method reduces the number of kinks detected by the kink detection algorithm from 1873 to 1745, resulting in continued performance improvement. Moreover, the algorithm demonstrates good generalizability across different devices. We validate this approach by applying it to another <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1\times 2$</tex> power splitter and a 6-channel spatial light receiver.