Level set methods for gradient-free optimization of metasurface arrays.
Journal
Scientific reports
ISSN: 2045-2322
Titre abrégé: Sci Rep
Pays: England
ID NLM: 101563288
Informations de publication
Date de publication:
19 Jul 2024
19 Jul 2024
Historique:
received:
09
08
2023
accepted:
08
07
2024
medline:
20
7
2024
pubmed:
20
7
2024
entrez:
19
7
2024
Statut:
epublish
Résumé
Global optimization techniques are increasingly preferred over human-driven methods in the design of electromagnetic structures such as metasurfaces, and careful construction and parameterization of the physical structure is critical in ensuring computational efficiency and convergence of the optimization algorithm to a globally optimal solution. While many design variables in physical systems take discrete values, optimization algorithms often benefit from a continuous design space. This work demonstrates the use of level set functions as a continuous basis for designing material distributions for metasurface arrays and introduces an improved parameterization which is termed the periodic level set function. We explore the use of alternate norms in the definition of the level set function and define a new pseudo-inverse technique for upsampling basis coefficients with these norms. The level set method is compared to the fragmented parameterization and shows improved electromagnetic responses for two dissimilar cost functions: a narrowband objective and a broadband objective. Finally, we manufacture an optimized level set metasurface and measure its scattering parameters to demonstrate real-world performance.
Identifiants
pubmed: 39030316
doi: 10.1038/s41598-024-67142-2
pii: 10.1038/s41598-024-67142-2
doi:
Types de publication
Journal Article
Langues
eng
Sous-ensembles de citation
IM
Pagination
16674Informations de copyright
© 2024. The Author(s).
Références
Dudley, R. A. & Fiddy, M. A. Meta-Atoms 39–65 (SPIE Press, 2017).
Vynck, K., Burresi, M., Riboli, F. & Wiersma, D. S. Photon management in two-dimensional disordered media. Nat. Mater. 11, 1017–1022. https://doi.org/10.1038/nmat3442 (2012).
doi: 10.1038/nmat3442
pubmed: 23042416
Kim, I. et al. Pixelated bifunctional metasurface-driven dynamic vectorial holographic color prints for photonic security platform. Nat. Commun. 12, 3614. https://doi.org/10.1038/s41467-021-23814-5 (2021).
doi: 10.1038/s41467-021-23814-5
pubmed: 34127669
pmcid: 8203667
So, S., Mun, J., Park, J. & Rho, J. Revisiting the design strategies for metasurfaces: Fundamental physics, optimization, and beyond. Adv. Mater. https://doi.org/10.1002/adma.202206399 (2023).
doi: 10.1002/adma.202206399
pubmed: 38016048
Chen, H.-T., Taylor, A. J. & Yu, N. A review of metasurfaces: Physics and applications. Rep. Prog. Phys. 79, 076401. https://doi.org/10.1088/0034-4885/79/7/076401 (2016).
doi: 10.1088/0034-4885/79/7/076401
pubmed: 27308726
Shelby, R. A., Smith, D. R., Nemat-Nasser, S. C. & Schultz, S. Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial. Appl. Phys. Lett. 78, 489–491. https://doi.org/10.1063/1.1343489 (2001).
doi: 10.1063/1.1343489
Rahmat-Samii, Y. & Mosallaei, H. Electromagnetic band-gap structures: classification, characterization, and applications. In 2001 Eleventh International Conference on Antennas and Propagation, (IEE Conf. Publ. No. 480), vol. 2, 560–564, https://doi.org/10.1049/cp:20010350 (2001).
Ali, A., Mitra, A. & Aïssa, B. Metamaterials and metasurfaces: A review from the perspectives of materials, mechanisms and advanced metadevices. Nanomaterials 12, 1027. https://doi.org/10.3390/nano12061027 (2022).
doi: 10.3390/nano12061027
pubmed: 35335837
pmcid: 8953484
Almeida, E., Bitton, O. & Prior, Y. Nonlinear metamaterials for holography. Nat. Commun. 7, 12533. https://doi.org/10.1038/ncomms12533 (2016).
doi: 10.1038/ncomms12533
pubmed: 27545581
pmcid: 4996937
Shi, J. et al. Dual-polarity metamaterial circular polarizer based on giant extrinsic chirality. Sci. Rep. 5, 1–7 (2015).
doi: 10.1038/srep16666
Islam, M. R. et al. Metamaterial sensor based on rectangular enclosed adjacent triple circle split ring resonator with good quality factor for microwave sensing application. Sci. Rep. 12, 6792. https://doi.org/10.1038/s41598-022-10729-4 (2022).
doi: 10.1038/s41598-022-10729-4
pubmed: 35474227
pmcid: 9042823
Kent, E. F., Doken, B. & Kartal, M. A new equivalent circuit based FSS design method by using genetic algorithm. In 2nd International Conference on Engineering Optimization, 1–4 (2010).
Monavar, F. M. & Komjani, N. Bandwidth enhancement of microstrip patch antenna using Jerusalem cross-shaped frequency selective surfaces by invasive weed optimization approach. Prog. Electromagn. Res. 121, 103–120 (2011).
doi: 10.2528/PIER11051305
Arbabi, A. & Faraon, A. Fundamental limits of ultrathin metasurfaces. Sci. Rep. 7, 1–9 (2017).
doi: 10.1038/srep43722
Molesky, S. et al. Inverse design in nanophotonics. Nat. Photonics 12, 659–670. https://doi.org/10.1038/s41566-018-0246-9 (2018).
doi: 10.1038/s41566-018-0246-9
Friederich, P. et al. A New Class of Broadband Planar Apertures. In Proceedings of the 2001 Antenna Application Symposium - Volume II Monticello, IL, (2001).
Cui, T. J., Qi, M. Q., Wan, X., Zhao, J. & Cheng, Q. Coding metamaterials, digital metamaterials and programmable metamaterials. Light Sci. Appl. 3, e218. https://doi.org/10.1038/lsa.2014.99 (2014).
doi: 10.1038/lsa.2014.99
Rockafellar, R. T. Lagrange multipliers and optimality. SIAM Rev. 35, 183–238. https://doi.org/10.1137/1035044 (1993).
doi: 10.1137/1035044
Boyd, S. P. & Vandenberghe, L. Convex Optimization (Cambridge University Press, 2004).
doi: 10.1017/CBO9780511804441
Rios, L. M. & Sahinidis, N. V. Derivative-free optimization: A review of algorithms and comparison of software implementations. J. Glob. Optim. 56, 1247–1293. https://doi.org/10.1007/s10898-012-9951-y (2012).
doi: 10.1007/s10898-012-9951-y
Allen, K. W., Dykes, D. J. P., Reid, D. R. & Lee, R. T. Multi-objective genetic algorithm optimization of frequency selective metasurfaces to engineer ku-passband filter responses. Prog. Electromagn. Res. 167, 19–30. https://doi.org/10.2528/PIER19112609 (2020).
doi: 10.2528/PIER19112609
Zhang, J., Wang, G., Wang, T. & Li, F. Genetic algorithms to automate the design of metasurfaces for absorption bandwidth broadening. ACS Appl. Mater. Interfaces 13, 7792–7800. https://doi.org/10.1021/acsami.0c21984 (2021).
doi: 10.1021/acsami.0c21984
pubmed: 33533610
Rahmat-Samii, Y., Kovitz, J. M. & Rajagopalan, H. Nature-inspired optimization techniques in communication antenna designs. Proceedings of the IEEE 100, 2132–2144. https://doi.org/10.1109/JPROC.2012.2188489 (2012).
doi: 10.1109/JPROC.2012.2188489
Zhu, D. Z., Werner, P. L. & Werner, D. H. Design and optimization of 3-D frequency-selective surfaces based on a multiobjective lazy ant colony optimization algorithm. IEEE Trans. Antennas Propag 65, 7137–7149 (2017).
doi: 10.1109/TAP.2017.2766660
Bayraktar, Z., Komurcu, M. & Werner, D. H. Wind driven optimization (WDO): A novel nature-inspired optimization algorithm and its application to electromagnetics. In 2010 IEEE Antennas and Propagation Society International Symposium, 1–4 (IEEE, 2010).
Hou, F., Zhao, Y., Zhang, S. & Li, L. Compression mapping based bayesian optimization for the design of frequency selective surface. In 2021 Photonics & Electromagnetics Research Symposium (PIERS), 1768–1775. (IEEE, 2021). https://doi.org/10.1109/PIERS53385.2021.9694821 .
Elsharabasy, A., Bakr, M. & Deen, M. J. Wide-angle, wide-band, polarization-insensitive metamaterial absorber for thermal energy harvesting. Sci. Rep. 10, 16215. https://doi.org/10.1038/s41598-020-73368-7 (2020).
doi: 10.1038/s41598-020-73368-7
pubmed: 33004962
pmcid: 7529747
Hammond, A. M. et al. High-performance hybrid time/frequency-domain topology optimization for large-scale photonics inverse design. Opt. Express 30, 4467. https://doi.org/10.1364/OE.442074 (2022).
doi: 10.1364/OE.442074
pubmed: 35209683
Schubert, M. F., Cheung, A. K. C., Williamson, I. A. D., Spyra, A. & Alexander, D. H. Inverse design of photonic devices with strict foundry fabrication constraints. ACS Photonics https://doi.org/10.1021/acsphotonics.2c00313 (2022).
doi: 10.1021/acsphotonics.2c00313
pubmed: 35434182
pmcid: 9007562
Pestourie, R., Mroueh, Y., Nguyen, T. V., Das, P. & Johnson, S. G. Active learning of deep surrogates for PDEs: Application to metasurface design. npj Comput. Mater. 6, 164. https://doi.org/10.1038/s41524-020-00431-2 (2020).
doi: 10.1038/s41524-020-00431-2
Alizadeh, R., Allen, J. K. & Mistree, F. Managing computational complexity using surrogate models: A critical review. Res. Eng. Des. 31, 275–298. https://doi.org/10.1007/s00163-020-00336-7 (2020).
doi: 10.1007/s00163-020-00336-7
Kim, Y. S., Byun, J. K. & Park, I. H. A level set method for shape optimization of electromagnetic systems. IEEE Trans. Magn. 45, 1466–1469. https://doi.org/10.1109/TMAG.2009.2012681 (2009).
doi: 10.1109/TMAG.2009.2012681
Zhou, S., Li, W. & Li, Q. Level-set based topology optimization for electromagnetic dipole antenna design. J. Comput. Phys. 229, 6915–6930. https://doi.org/10.1016/j.jcp.2010.05.030 (2010).
doi: 10.1016/j.jcp.2010.05.030
Noguchi, Y. & Yamada, T. Level set-based topology optimization for graded acoustic metasurfaces using two-scale homogenization. Finite Elem. Anal. Des. 196, 103606. https://doi.org/10.1016/j.finel.2021.103606 (2021).
doi: 10.1016/j.finel.2021.103606
Guo, J., Fang, Y., Qu, R. & Zhang, X. Development and progress in acoustic phase-gradient metamaterials for wavefront modulation. Mater. Today 66, 321–338. https://doi.org/10.1016/j.mattod.2023.04.004 (2023).
doi: 10.1016/j.mattod.2023.04.004
Vercruysse, D., Sapra, N. V., Su, L., Trivedi, R. & Vučković, J. Analytical level set fabrication constraints for inverse design. Sci. Rep. 9, 8999. https://doi.org/10.1038/s41598-019-45026-0 (2019).
doi: 10.1038/s41598-019-45026-0
pubmed: 31227721
pmcid: 6588594
Murai, N., Noguchi, Y., Matsushima, K. & Yamada, T. Multiscale topology optimization of electromagnetic metamaterials using a high-contrast homogenization method. Comput. Methods Appl. Mech. Eng. 403, 115728. https://doi.org/10.1016/j.cma.2022.115728 (2023).
doi: 10.1016/j.cma.2022.115728
Mansouree, M. & Arbabi, A. Metasurface design using level-set and gradient descent optimization techniques. In 2019 International Applied Computational Electromagnetics Society Symposium (ACES), 1–2 (2019).
Townsend, S. M., Zhou, S. W. & Li, Q. Sensitivity analysis in the level set method for electromagnetic problems. In Proceedings of the 10th World Congress on Structural and Multidisciplinary Optimization (2013).
Otomori, M., Yamada, T., Izui, K., Nishiwaki, S. & Andkjær, J. A topology optimization method based on the level set method for the design of negative permeability dielectric metamaterials. Comput. Methods Appl. Mech. Eng. 237–240, 192–211. https://doi.org/10.1016/j.cma.2012.04.022 (2012).
doi: 10.1016/j.cma.2012.04.022
Dong, L. et al. Quasi-continuous metasurface for high-efficiency beam deflection based on multi-objective level-set optimization. Opt. Mater. Express 12, 3667–3678. https://doi.org/10.1364/OME.470765 (2022).
doi: 10.1364/OME.470765
Guirguis, D. & Aly, M. F. A derivative-free level-set method for topology optimization. Finite Elem. Anal. Des. 120, 41–56. https://doi.org/10.1016/j.finel.2016.06.002 (2016).
doi: 10.1016/j.finel.2016.06.002
Guirguis, D., Melek, W. W. & Aly, M. F. High-resolution non-gradient topology optimization. J. Comput. Phys. 372, 107–125. https://doi.org/10.1016/j.jcp.2018.06.025 (2018).
doi: 10.1016/j.jcp.2018.06.025
Giddens, H. & Hao, Y. Multibeam graded dielectric lens antenna from multimaterial 3-D printing. IEEE Trans. Antennas Propag. 68, 6832–6837. https://doi.org/10.1109/TAP.2020.2978949 (2020).
doi: 10.1109/TAP.2020.2978949
Feng, T.-X. & Zhu, L. Ultra-wideband 3-D microwave absorbers with composite slotlines and microstrip lines: Synthetic design and implementation. IEEE Open J. Antennas Propag. 4, 303–311. https://doi.org/10.1109/OJAP.2023.3252676 (2023).
doi: 10.1109/OJAP.2023.3252676
Howard, C. T., Allen, K. W. & Hunt, W. D. A loss tangent measurement surface for free space focused beam characterization of low-loss dielectrics. In 2022 Antenna Measurement Techniques Association Symposium (AMTA), 1–6, https://doi.org/10.23919/AMTA55213.2022.9954958 IEEE, (2022).
Gregory, A. P. Q-factor measurement by using a Vector Network Analyser. Tech. Rep., National Physical Laboratory (2022). https://doi.org/10.47120/npl.MAT58 .
Rapin, J. & Teytaud, O. Nevergrad—A Gradient-Free Optimization Platform. https://GitHub.com/FacebookResearch/Nevergrad (2018).
Hansen, N., Müller, S. D. & Koumoutsakos, P. Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). Evol. Computat. 11, 1–18. https://doi.org/10.1162/106365603321828970 (2003).
doi: 10.1162/106365603321828970
Gregory, M. D., Bayraktar, Z. & Werner, D. H. Fast optimization of electromagnetic design problems using the covariance matrix adaptation evolutionary strategy. IEEE Trans. Antennas Propag. 59, 1275–1285. https://doi.org/10.1109/TAP.2011.2109350 (2011).
doi: 10.1109/TAP.2011.2109350
Liu, J. et al. Versatile black-box optimization. In Proceedings of the 2020 Genetic and Evolutionary Computation Conference, GECCO ’20, 620–628, https://doi.org/10.1145/3377930.3389838 Association for Computing Machinery, New York, NY, USA, (2020).
Deb, K., Pratap, A., Agarwal, S. & Meyarivan, T. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6, 182–197. https://doi.org/10.1109/4235.996017 (2002).
doi: 10.1109/4235.996017
Haupt, R. L. & Haupt, S. E. Practical Genetic Algorithms 2nd edn. (Wiley, 2004).
Shi, Z. et al. Super-resolution orbital angular momentum holography. Nat. Commun. 14, 1869. https://doi.org/10.1038/s41467-023-37594-7 (2023).
doi: 10.1038/s41467-023-37594-7
pubmed: 37015931
pmcid: 10073211
Huang, Y. et al. A direct laser-synthesized magnetic metamaterial for low-frequency wideband passive microwave absorption. Int. J. Extreme Manuf. 5, 035503. https://doi.org/10.1088/2631-7990/acdb0c (2023).
doi: 10.1088/2631-7990/acdb0c
Mair, D., Renzler, M., Unterladstaetter, M. & Ussmueller, T. Performance analysis of pixelated antennas employing shifted cross-shaped elements. IET Microw. Antennas Propag. https://doi.org/10.1049/mia2.12378 (2023).
doi: 10.1049/mia2.12378
Hong, Y.-P., Hwang, I.-J., Yun, D.-J., Lee, D.-J. & Lee, I.-H. Design of single-layer metasurface filter by conformational space annealing algorithm for 5G mm-wave communications. IEEE Access 9, 29764–29774 (2021).
doi: 10.1109/ACCESS.2021.3059019
Genovesi, S., Mittra, R., Monorchio, A. & Manara, G. Particle swarm optimization for the design of frequency selective surfaces. IEEE Antennas Wirel. Propag. Lett. 5, 277–279 (2006).
doi: 10.1109/LAWP.2006.875900
Oskooi, A. F. et al. MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method. Comput. Phys. Commun. 181, 687–702. https://doi.org/10.1016/j.cpc.2009.11.008 (2010).
doi: 10.1016/j.cpc.2009.11.008
Howard, C. & Saad-Falcon, A. topherocity/lsf-mwe: v0.1.0. Zenodo, https://doi.org/10.5281/zenodo.12602604 (2024).
Rogers Corporation. RO3000® Series Circuit Materials: RO3003™, RO3006™, RO3010™ and RO3035™ High Frequency Laminates. Tech. Rep. 92-130, Rogers Corporation, Chandler, AZ (2022).
Ko, W. & Mittra, R. A combination of FD-TD and Prony’s methods for analyzing microwave integrated circuits. IEEE Trans. Microw. Theory Tech. 39, 2176–2181. https://doi.org/10.1109/22.106561 (1991).
doi: 10.1109/22.106561
Hansen, N. et al. CMA-ES/pycma: r3.3.0, https://doi.org/10.5281/ZENODO.2559634 (2023).
Bartley, P. & Begley, S. Improved free-space S-parameter calibration. In 2005 IEEE Instrumentation and Measurement Technology Conference Proceedings, vol. 1, 372–375, https://doi.org/10.1109/IMTC.2005.1604138 (2005).