Interpretable-machine-learning-enabled discretized antireflective multilayer design outperforms traditional...

Area of Science:

• Optics and Photonics
• Materials Science
• Machine Learning Applications

Background:

• Designing deep-ultraviolet (DUV) antireflective coatings is challenging due to limited material properties and sensitivity to thickness errors.
• Traditional multilayer coatings often struggle to meet stringent performance requirements in the DUV spectrum.

Purpose of the Study:

• To develop a novel discrete optimization framework for designing high-performance DUV antireflective coatings.
• To leverage machine learning, specifically active learning with second-order factorization machines, for inverse design.
• To improve robustness against fabrication imperfections compared to existing methods.

Main Methods:

• Treated antireflective coating design as a discrete optimization problem.
• Employed an active learning scheme with second-order factorization machines using binary, quaternary, and octal refractive index bases.
• Benchmarked discrete designs against analytical double/tri-layer and idealized graded-index coatings.
• Assessed fabrication tolerance using Monte Carlo simulations with layer thickness variations.

Main Results:

• The best quaternary design achieved a reflectance of 0.05% at 170 nm, outperforming ideal graded-index profiles.
• Discrete designs significantly outperformed analytical multilayer coatings.
• Octal designs demonstrated superior robustness to fabrication perturbations (±50% thickness variation) compared to binary designs, maintaining near 1% reflectance.
• Phasor-based interpretation explained the effectiveness of factorization machines in navigating the design space.

Conclusions:

• A discrete optimization framework using machine learning can surpass traditional analytical multilayer design rules for high-performance coatings.
• The proposed method enables fast, interpretable, and fabrication-tolerant inverse design of advanced optical coatings.
• Richer refractive index bases in discrete optimization enhance robustness to manufacturing tolerances.