[en] Metasurfaces offer a flexible framework for the manipulation of light properties in the realm of thin-film optics. Specifically, the polarization of light can be effectively controlled through the use of thin phase plates. This study aims to introduce a surrogate optimization framework for these devices. The framework is applied to develop two kinds of vortex phase masks (VPMs) tailored for application in astronomical high-contrast imaging. Computational intelligence techniques are exploited to optimize the geometric features of these devices. The large design space and computational limitations necessitate the use of surrogate models like partial least-squares kriging, radial basis functions, or neural networks. However, we demonstrate the inadequacy of these methods in modeling the performance of VPMs. To address the shortcomings of these methods, a data-efficient evolutionary optimization setup using a deep neural network as a highly accurate and efficient surrogate model is proposed. The optimization process in this study employs a robust particle swarm evolutionary optimization scheme, which operates on explicit geometric parameters of the photonic device. Through this approach, optimal designs are developed for two design candidates. In the most complex case, evolutionary optimization enables optimization of the design that would otherwise be impractical (requiring too many simulations). In both cases, the surrogate model improves the reliability and efficiency of the procedure, effectively reducing the required number of simulations by up to 75% compared to conventional optimization techniques.
Research center :
STAR - Space sciences, Technologies and Astrophysics Research - ULiège [BE]
Disciplines :
Physics
Author, co-author :
Roy, Nicolas
König, Lorenzo ; Université de Liège - ULiège > Département d'astrophysique, géophysique et océanographie (AGO) > Planetary & Stellar systems Imaging Laboratory
Absil, Olivier ; Université de Liège - ULiège > Département d'astrophysique, géophysique et océanographie (AGO)
Beauthier, Charlotte
Mayer, Alexandre
Lobet, Michaël
Language :
English
Title :
Photonic-structure optimization using highly data-efficient deep learning: Application to nanofin and annular-groove phase masks
J. B. Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, Metasurface polarization optics: Independent phase control of arbitrary orthogonal states of polarization, Phys. Rev. Lett. 118, 113901 (2017) 0031-9007 10.1103/PhysRevLett.118.113901.
W. T. Chen, A. Y. Zhu, and F. Capasso, Flat optics with dispersion-engineered metasurfaces, Nat. Rev. Mater. 5, 604 (2020) 2058-8437 10.1038/s41578-020-0203-3.
W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, A broadband achromatic metalens for focusing and imaging in the visible, Nat. Nanotechnol. 13, 220 (2018) 1748-3387 10.1038/s41565-017-0034-6.
S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, and A. W. Rodriguez, Inverse design in nanophotonics, Nat. Photon. 12, 659 (2018) 1749-4885 10.1038/s41566-018-0246-9.
Z. Lin, R. Pestourie, C. Roques-Carmes, Z. Li, F. Capasso, M. Soljačić, and S. G. Johnson, End-to-end metasurface inverse design for single-shot multi-channel imaging, Opt. Express 30, 28358 (2022) 1094-4087 10.1364/OE.449985.
Z. Li, R. Pestourie, Z. Lin, S. G. Johnson, and F. Capasso, Empowering metasurfaces with inverse design: Principles and applications, ACS Photon. 9, 2178 (2022) 2330-4022 10.1021/acsphotonics.1c01850.
A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission, Nat. Nanotechnol. 10, 937 (2015) 1748-3387 10.1038/nnano.2015.186.
Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, Space-variant Pancharatnam-Berry phase optical elements with computer-generated subwavelength gratings, Opt. Lett. 27, 1141 (2002) 0146-9592 10.1364/OL.27.001141.
K. Koshelev and Y. Kivshar, Dielectric resonant metaphotonics, ACS Photon. 8, 102 (2021) 2330-4022 10.1021/acsphotonics.0c01315.
D. Mawet, P. Riaud, O. Absil, and J. Surdej, Annular groove phase mask coronagraph, Astrophys. J. 633, 1191 (2005) 0004-637X 10.1086/462409.
D. Mawet, P. Riaud, J. Surdej, and J. Baudrand, Subwavelength surface-relief gratings for stellar coronagraphy, Appl. Opt. 44, 7313 (2005) 0003-6935 10.1364/AO.44.007313.
M. G. Moharam and T. K. Gaylord, Rigorous coupled-wave analysis of planar-grating diffraction, J. Opt. Soc. Am. 71, 811 (1981) 0030-3941 10.1364/JOSA.71.000811.
L. König, O. Absil, M. Lobet, C. Delacroix, M. Karlsson, G. O. de Xivry, and J. Loicq, Optimal design of the annular groove phase mask central region, Opt. Express 30, 27048 (2022) 1094-4087 10.1364/OE.461047.
B. Settles, Active learning literature survey, University of Wisconsin-Madison Department of Computer Sciences 2009 Technical Report Nr. 1648, https://minds.wisconsin.edu/handle/1793/60660.
Z. Bodó, Z. Minier, and L. Csató, in Active Learning and Experimental Design Workshop, in conjunction with AISTATS 2010, Sardinia, 2010, edited by I. Guyon, G. Cawley, G. Dror, V. Lemaire, and A. Statnikov [JMLR 16, 127 (2011)].
O. Ronneberger, P. Fischer, and T. Brox, in Medical Image Computing and Computer-Assisted Intervention-MICCAI 2015, edited by N. Navab, J. Hornegger, W. Wells, and A. Frangi, Lecture Notes in Computer Science Vol. 9351 (Springer, Cham, 2015), pp. 234-241.
M. Chen, R. Lupoiu, C. Mao, D.-H. Huang, J. Jiang, P. Lalanne, and J. A. Fan, in High Contrast Metastructures XI, edited by C. J. Chang-Hasnain, J. A. Fan, and W. Zhou, SPIE Proc. Vol. 12011 (SPIE, Bellingham, 2022), p. 120110C.
https://github.com/Kaeryv/Keever.
https://github.com/Kaeryv/PRA23Suppl.
D. Weile and E. Michielssen, Genetic algorithm optimization applied to electromagnetics: A review, IEEE Trans. Antennas Propag. 45, 343 (1997) 0018926X 10.1109/8.558650.
R. Eberhart and J. Kennedy, Proceedings of the IEEE International Conference on Neural Networks, Perth, 1995 (IEEE, Piscataway, 1995), Vol. 4, pp. 1942-1948.
J. H. Holland, Genetic algorithms and the optimal allocation of trials, SIAM J. Comput. 2, 88 (1973) 0097-5397 10.1137/0202009.
A. Mayer, H. Bi, S. Griesse-Nascimento, B. Hackens, J. Loicq, E. Mazur, O. Deparis, and M. Lobet, Genetic-algorithm-aided ultra-broadband perfect absorbers using plasmonic metamaterials, Opt. Express 30, 1167 (2022) 1094-4087 10.1364/OE.442405.
M. A. Bouhlel, J. T. Hwang, N. Bartoli, R. Lafage, J. Morlier, and J. R. R. A. Martins, A python surrogate modeling framework with derivatives, Adv. Eng. Softw. 135, 102662 (2019) 0965-9978 10.1016/j.advengsoft.2019.03.005.
H. Wang, Y. Jin, and J. Doherty, Committee-based active learning for surrogate-assisted particle swarm optimization of expensive problems, IEEE Trans. Cybern. 47, 2664 (2017) 2168-2267 10.1109/TCYB.2017.2710978.
A. I. Forrester and A. J. Keane, Recent advances in surrogate-based optimization, Prog. Aeronaut. Sci. 45, 50 (2009) 0376-0421 10.1016/j.paerosci.2008.11.001.
Y.-S. Ong, Z. Zhou, and D. Lim, in Proceedings of the IEEE International Conference on Evolutionary Computation, Vancouver, 2006 (IEEE Computational Intelligence Society, Piscataway, 2006), pp. 2928-2935.
Y. Augenstein, T. Repän, and C. Rockstuhl, Neural operator-based surrogate solver for free-form electromagnetic inverse design, ACS Photon. 10, 1547 (2023) 10.1021/acsphotonics.3c00156.
A. M. Hammond, A. Oskooi, M. Chen, Z. Lin, S. G. Johnson, and S. E. Ralph, High-performance hybrid time/frequency-domain topology optimization for large-scale photonics inverse design, Opt. Express 30, 4467 (2022) 1094-4087 10.1364/OE.442074.
M. J. D. Powell, in Advances in Numerical Analysis: Wavelets, Subdivision Algorithms, and Radial Basis Functions, edited by W. Light (Oxford University Press, Oxford, 1992), Vol. 11, Chap. 3, pp. 105-210.
M. A. Bouhlel, N. Bartoli, A. Otsmane, and J. Morlier, Improving kriging surrogates of high-dimensional design models by partial least squares dimension reduction, Struct. Multidiscip. Optim. 53, 935 (2016) 1615-147X 10.1007/s00158-015-1395-9.
R. O. L. Breiman, J. Friedman, and C. Stone, Classification and Regression Trees (Wadsworth, Belmont, 1988).
T. Chen and C. Guestrin, in Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, 2016 (ACM, New York, 2016), pp. 785-794.
G. Sun and S. Wang, A review of the artificial neural network surrogate modeling in aerodynamic design, Proc. Inst. Mech. Eng. G 233, 5863 (2019) 0954-4100 10.1177/0954410019864485.
D. Kochkov, J. A. Smith, A. Alieva, Q. Wang, M. P. Brenner, and S. Hoyer, Machine learning-accelerated computational fluid dynamics, Proc. Natl. Acad. Sci. USA 118, e2101784118 (2021) 0027-8424 10.1073/pnas.2101784118.
M. Chen, R. Lupoiu, C. Mao, D.-H. Huang, J. Jiang, P. Lalanne, and J. A. Fan, High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning, ACS Photon. 9, 3110 (2022) 2330-4022 10.1021/acsphotonics.2c00876.
G. Cybenko, Approximation by superpositions of a sigmoidal function, Math. Control Signal Syst. 2, 303 (1989) 0932-4194 10.1007/BF02551274.
Y. Lu and J. Lu, in Advances in Neural Information Processing Systems 33, edited by H. Larochelle, M. Ranzato, R. Hadsell, M. F. Balcan, and H. Lin (Curran, Red Hook, 2020), pp. 3094-3105.
A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga, A. Desmaison, A. Kopf, E. Yang, Z. DeVito, M. Raison, A. Tejani, S. Chilamkurthy, B. Steiner, L. Fang, J. Bai, in Advances in Neural Information Processing Systems 32, edited by H. Wallach, H. Larochelle, A. Beygelzimer, F. d'Alché-Buc, E. Fox, and R. Garnett (Curran, Red Hook, 2019), pp. 8024-8035.
D. M. Hawkins, The problem of overfitting, J. Chem. Inf. Comput. Sci. 44, 1 (2004) 0095-2338 10.1021/ci0342472.
Ö. Çiçek, A. Abdulkadir, S. S. Lienkamp, T. Brox, and O. Ronneberger, in Medical Image Computing and Computer-Assisted Intervention-MICCAI 2016, edited by S. Ourselin, L. Joskowicz, M. R. Sabuncu, G. Unal, and W. Wells (Springer, Cham, 2016), pp. 424-432.
J. Masci, U. Meier, D. Cireşan, and J. Schmidhuber, in Artificial Neural Networks and Machine Learning-ICANN 2011, edited by T. Honkela, W. Duch, M. Girolami, and S. Kaski (Springer, Berlin, 2011), pp. 52-59.
C. Delacroix, P. Forsberg, M. Karlsson, D. Mawet, O. Absil, C. Hanot, J. Surdej, and S. Habraken, Design, manufacturing, and performance analysis of mid-infrared achromatic half-wave plates with diamond subwavelength gratings, Appl. Opt. 51, 5897 (2012) 1559-128X 10.1364/AO.51.005897.
C. Delacroix, O. Absil, D. Mawet, C. Hanot, M. Karlsson, P. Forsberg, E. Pantin, J. Surdej, and S. Habraken, A diamond AGPM coronagraph for VISIR, Proc. SPIE 8446, 84468K (2012) 0277786X 10.1117/12.926494.
D. Mawet, O. Absil, C. Delacroix, J. H. Girard, J. Milli, J. O'Neal, P. Baudoz, A. Boccaletti, P. Bourget, V. Christiaens, P. Forsberg, F. Gonte, S. Habraken, C. Hanot, M. Karlsson, M. Kasper, J. L. Lizon, K. Muzic, R. Olivier, E. Peña, (Equation presented)-band AGPM vector vortex coronagraph's first light on VLT/NACO: Discovery of a late-type companion at two beamwidths from an F0V star, Astron. Astrophys. 552, L13 (2013) 0004-6361 10.1051/0004-6361/201321315.
D. Defrère, O. Absil, P. Hinz, J. Kuhn, D. Mawet, B. Mennesson, A. Skemer, K. Wallace, V. Bailey, E. Downey, C. Delacroix, O. Durney, P. Forsberg, C. Gomez Gonzales, S. Habraken, W. F. Hoffmann, M. Karlsson, M. Kenworthy, J. Leisenring, M. Montoya, (Equation presented)-band AGPM vector vortex coronagraph's first light on LBTI/LMIRCam, Proc. SPIE 9148, 91483X (2014) 0277786X 10.1117/12.2057205.
E. Serabyn, E. Huby, K. Matthews, D. Mawet, O. Absil, B. Femenia, P. Wizinowich, M. Karlsson, M. Bottom, R. Campbell, B. Carlomagno, D. Defrère, C. Delacroix, P. Forsberg, C. Gomez Gonzalez, S. Habraken, A. Jolivet, K. Liewer, S. Lilley, P. Piron, The W. M. Keck Observatory infrared vortex coronagraph and a first image of HIP 79124 B, Astron. J. 153, 43 (2017) 1538-3881 10.3847/1538-3881/153/1/43.
A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method, Comput. Phys. Commun. 181, 687 (2010) 0010-4655 10.1016/j.cpc.2009.11.008.
See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevA.109.013514 for dielectric and leakage profiles for some of the best designs (S1), details for the reproducibility of the surrogate optimization procedure (S2), details for the reproducibility of the FDTD simulations (S3), and visualization of the evolution of U-Net accuracy during the surrogate optimization procedure (S4).
H.-M. Gutmann, A radial basis function method for global optimization, J. Global Optim. 19, 201 (2001) 0925-5001 10.1023/A:1011255519438.
N. Roy, C. Beauthier, and A. Mayer, Proceedings of the 2022 IEEE Congress on Evolutionary Computation, Padua, 2022 (IEEE, Piscataway, 2022), pp. 1-8.
J. A. Hartigan and M. A. Wong, A (Equation presented)-means clustering algorithm, Appl. Stat. 28, 100 (1979) 0035-9254 10.2307/2346830.
SPSS tutorials: Pearson correlation, https://libguides.library.kent.edu/SPSS/PearsonCorr (Kent State University, Kent, 2023).
S. M. Lundberg and S.-I. Lee, in Advances in Neural Information Processing Systems 30, Long Beach, 2017, edited by I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett (Curran, Red Hook, 2017).
C. Shorten and T. M. Khoshgoftaar, A survey on image data augmentation for deep learning, J. Big Data 6, 60 (2019) 2196-1115 10.1186/s40537-019-0197-0.
