Level set methods for gradient-free optimization of metasurface arrays

Area of Science:

• Electromagnetics
• Materials Science
• Computational Physics

Background:

• Global optimization is preferred for designing electromagnetic structures like metasurfaces.
• Efficient parameterization is crucial for optimization convergence and computational efficiency.
• Continuous design spaces benefit optimization algorithms, though physical variables are often discrete.

Purpose of the Study:

• To demonstrate level set functions for continuous material distribution design in metasurface arrays.
• To introduce an improved parameterization: the periodic level set function.
• To compare the level set method with fragmented parameterization for electromagnetic responses.

Main Methods:

• Utilized level set functions for continuous basis in material distribution design.
• Introduced and explored the periodic level set function parameterization.
• Investigated alternate norms and a new pseudo-inverse technique for upsampling basis coefficients.
• Compared level set method against fragmented parameterization for narrowband and broadband objectives.
• Manufactured an optimized level set metasurface for experimental validation.

Main Results:

• The periodic level set function demonstrated improved electromagnetic responses compared to fragmented parameterization.
• The method showed effectiveness for both narrowband and broadband electromagnetic objectives.
• Experimental measurements of the manufactured metasurface validated the simulated performance.

Conclusions:

• Level set functions offer a robust and efficient continuous basis for metasurface design.
• The periodic level set function parameterization enhances optimization and performance.
• The developed method is validated through experimental manufacturing and measurement, confirming its practical applicability.