We propose a rigorous approach for the inverse design of functional photonic structures by coupling the adjoint optimization method and the 2D generalized Mie theory (2D-GMT) for the multiple scattering problem of finite-sized arrays of dielectric nanocylinders optimized to display desired functions. We refer to these functional scattering structures as “photonic patches.” We briefly introduce the formalism of 2D-GMT and the critical steps necessary to implement the adjoint optimization algorithm to photonic patches with designed radiation properties. In particular, we showcase several examples of periodic and aperiodic photonic patches with optimal nanocylinder radii and arrangements for radiation shaping, wavefront focusing in the Fresnel zone, and for the enhancement of the local density of states (LDOS) at multiple wavelengths over micron-sized areas. Moreover, we systematically compare the performances of periodic and aperiodic patches with different sizes and find that optimized aperiodic Vogel spiral geometries feature significant advantages in achromatic focusing compared to their periodic counterparts. Our results show that adjoint optimization coupled to 2D-GMT is a robust methodology for the inverse design of compact photonic devices that operate in the multiple scattering regime with optimal desired functionalities. Without the need for spatial meshing, our approach provides efficient solutions at a strongly reduced computational burden compared to standard numerical optimization techniques and suggests compact device geometries for on-chip photonics and metamaterials technologies.
This content will become publicly available on June 1, 2024
Parameter Space Exploration of Cellular Mechanical Metamaterials Using Genetic Algorithms
Cellular materials widely exist in natural biologic systems such as honeycombs, bones, and woods. With advances in additive manufacturing, research on cellular metamaterials is emerging due to their unique mechanical performance. However, the design of on-demand cellular metamaterials usually requires solving a challenging inverse design problem for exploring complex structure–property relations of microstructured representative volume elements (RVEs) in the design domain. Here, we propose an experience-free and systematic methodology for exploring a parametrized system for microstructures of cellular mechanical metamaterials using a multiobjective genetic algorithm (GA). Globally, by considering the importance of the initial population selection for a population-based heuristic optimization method, we study the impact of the populations initialized by the different sampling methods on the optimal solutions. Locally, we develop our method by using a micro-GA with a new searching strategy, which requires the standard genetic algorithm to be conditionally run for a sufficient number of times with a small population size during the global searching process. We have applied our method to explore optimal solutions for applications mapped on two different parameter spaces of the cellular mechanical metamaterials with periodic and nonperiodic RVEs effectively and accurately.
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- Award ID(s):
- 2053840
- NSF-PAR ID:
- 10418301
- Date Published:
- Journal Name:
- AIAA Journal
- ISSN:
- 0001-1452
- Page Range / eLocation ID:
- 1 to 11
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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