Optimization of a Photonic Crystal Nanocavity Using Covariance Matrix Adaptation Evolution Strategy

Abstract

H0-type photonic crystal nanocavities hold high quality factors <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> and quite small cavity mode volumes. This study finds their ultrahigh <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> structures, which allow stable operation as a nanolaser even with fabrication-induced disordering. Previously, we generated a neural network model for predicting <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> s, searched for a high- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> structure and its slotted version, and found those showing <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> = 1,140,000 and 91,600, respectively. These values were an order of magnitude higher than those obtained by manual optimizations. However, further improvement above these values was saturated because of the insufficient accuracy of the neural network model at the high <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> regime. Instead of applying the model, we repeated directly calculating <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> s, implementing a covariance matrix adaptation evolution strategy algorithm to search structures in this study. Consequently, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> values were increased up to 14,500,000 and 741,000 while consuming shorter calculation time. We also confirmed that these structures significantly improve robustness against structural disordering.