Wide-angle deep ultraviolet antireflective multilayers via discrete-to-continuous optimization.

Area of Science:

• Photonics and optical engineering
• Materials science
• Computational physics

Background:

• Designing complex photonic structures often requires advanced optimization techniques.
• Non-convex objective functions with multiple local optima pose challenges for traditional algorithms.
• Effective training datasets are crucial for guiding optimization processes in continuous parameter spaces.

Purpose of the Study:

• To develop and validate a novel discrete-to-continuous optimization algorithm for designing photonic structures.
• To apply the algorithm to create deep-ultraviolet (DUV) antireflective coatings with high performance.
• To demonstrate the algorithm's utility for fabricating and simulating optical multilayers.

Main Methods:

• A discrete-to-continuous optimization approach combining binary encoding with continuous refinement.
• Encoding multilayer structures into binary vectors, where each bit represents a specific material layer thickness.
• Utilizing factorization machines to formulate surrogate functions from binary-based training data for initial optimization.
• Employing continuous optimization methods, such as the interior-point method, for refining the figure of merit.

Main Results:

• Successful design and fabrication of Magnesium Fluoride (MgF₂)/Lanthanum Fluoride (LaF₃) multilayers for DUV applications.
• An optimized MgF₂/LaF₃ multilayer (ten bits, ~100 nm total thickness) achieved an average reflectance of 0.2% at 193 nm.
• Experimental results closely matched the optimized design, validating the algorithm's effectiveness.
• Simulations predicted 99.7% transmittance for a lens coated with the optimized multilayer.

Conclusions:

• The developed discrete-to-continuous optimization algorithm effectively designs high-performance photonic structures.
• The method is particularly suitable for multilayer optical coatings and can be extended to other binary-representable photonic devices like microwave metasurfaces.
• This approach offers a pathway to achieving unconventional optical performance in various nanophotonic applications.