Inverse design of optical elements based on arrays of dielectric spheres
Open accessAbstract
Arrays of wavelength scale scatterers are a promising platform for designing optical elements with a compact footprint. The large number of degrees of freedom in this system allows for unique and plentiful functionalities. However, the many variables also create a complex design problem. While intuitive forward design methods work for simple optical elements, they often fail to produce complicated elements, especially those involving multiple elements. We present an inverse design methodology for large arrays of wavelength scale spheres based on both adjoint optimization or sensitivity analysis and generalized multi-sphere Mie theory as a solution to the design problem. We validate our methodology by designing two sets of optical elements with scatterers on sub-wavelength and super-wavelength periodic grids. Both sets consist of a singlet and a doublet lens with one and two layers of spheres respectively designed for 1550 nm. The designed NA is ∼0.33 (∼0.5) for the sub-wavelength (super-wavelength) periodic structure. We find that with the sub-wavelength periodicity, the full width at half-maximum of the focal spot produced by the singlet and doublet is smaller than that produced by an ideal lens with the same geometric parameters. Finally, we simulate a realistic experimental scenario for the doublet, where the spheres are placed on a substrate with the same refractive index. We find the performance is similar, but with lower intensity at the focal spot and larger spot size. The method described here will simplify the design procedure for complicated multi-functional optical elements and or scatterer array-based volume optics based on a specified figure of merit.
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Topology optimization has been used to design photonic crystals, integrated photonics devices, and metamaterials with superior performance metrics than those based on conventional designs.
“This technique has been used to design photonic crystals [15], integrated photonics devices [16,17], and metamaterials [18–24] with superior performance metrics than those based on conventional designs.”
From Robust design of topology-optimized metasurfaces (2019) · cites this paper as [23]
The Introduction (p. 2) describes gradient-based inverse design of dielectric-sphere arrays by optimizing sphere radii, supporting the metamaterial-related design example to which this citation is attached. It does not describe the method as topology optimization or establish superior performance metrics relative to conventional designs. The paper does not address the separately cited photonic-crystal and integrated-photonics examples. (LLM, conf=0.78)
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Inverse design and flexible parameterization of meta-optics using algorithmic differentiationPreprint
Colburn, S., & Majumdar, A. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2011.03626
Self-citation
- Authors
- Zhan, A., Fryett, T. K., Colburn, S., & Majumdar, A.
- Affiliations
- University of Washington (US)
- Corresponding author
- Zhan, Alan
- Fryett, Taylor K.
- Colburn, Shane
- Majumdar, Arka
- Venue
- Applied Optics
- Publisher
- Optica Publishing Group
- Published
- 2018-02-16
- Volume
- 57
- Issue
- 6
- Pages
- 1437
- ISSN
- 0003-6935 (ISSN-L)
- 1559-128X
- 2155-3165
- OpenAlex
- W2789174688
- Cited by
- 43
- References
- 54
- Citations by year
- 2026: 1 · 2025: 2 · 2024: 2 · 2023: 3 · 2022: 4 · 2021: 10 · 2020: 4 · 2019: 14 · 2018: 3
- FWCI
- 2.32
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Applied Optics (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Figshare (submittedVersion, cc-by)
- arXiv (Cornell University)
- Funders
- University of Washington (UW), Seattle
- Topics
- Physical Sciences › Materials Science › Electronic, Optical and Magnetic Materials › Metamaterials and Metasurfaces Applications
- Physical Sciences › Engineering › Biomedical Engineering › Advanced optical system design
- Physical Sciences › Engineering › Biomedical Engineering › Plasmonic and Surface Plasmon Research
- Keywords
- inverse design, adjoint-based optimization, sensitivity analysis, singlet lens, doublet lens, numerical aperture, focal spot size, 1550 nm
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