Constraining Continuous Topology Optimizations to Discrete Solutions for Photonic Applications

Area of Science:

• Photonics
• Computational Electromagnetics
• Materials Science

Background:

• Photonic topology optimization designs devices by determining permittivity distribution.
• Common methods include continuous density-based and discrete level-set optimizations.
• Existing methods can struggle with binarization requirements and hyperparameter tuning.

Purpose of the Study:

• To develop a constrained continuous optimization method for photonic devices.
• To guarantee convergence to a discrete solution in topology optimization.
• To offer a more robust and user-friendly approach for photonic device design.

Main Methods:

• Introduced a constrained suboptimization within a gradient-based framework.
• Implemented a single hyperparameter to control binarization aggressiveness.
• Validated through computational examples and analysis of hyperparameter behavior.

Main Results:

• The method guarantees convergence to discrete solutions.
• Demonstrated compatibility with projection filters.
• Showcased utility as a precursor for level-set optimization.
• Introduced an additional hyperparameter for material/void fraction control.

Conclusions:

• The developed technique effectively constrains continuous optimization to discrete outcomes.
• This method is particularly beneficial for electromagnetic figures-of-merit sensitive to binarization.
• It simplifies hyperparameter selection compared to existing photonic topology optimization techniques.