Generic placeholder image

Current Nanoscience

Editor-in-Chief

ISSN (Print): 1573-4137
ISSN (Online): 1875-6786

Research Article

Deep Learning-based Inverse Design of the Complete Photonic Band Gap in Two-Dimensional Photonic Crystals

Author(s): Bole Ma, Ran Hao*, Haotian Yan, Huaqing Jiang, Jianwei Chen and Kaida Tang

Volume 19, Issue 3, 2023

Published on: 12 September, 2022

Page: [423 - 431] Pages: 9

DOI: 10.2174/1573413718666220701143205

Price: $65

Abstract

Background: With the continuous development of computer science, data-driven computing methods have shown their advantages in various fields. In the field of photonics, deep learning (DL) can be used to inversely design the structure of optical devices.

Objective: The two-dimensional (2D) photonic crystal (PCs) with adjustable structural parameters and a large complete photonic band gap (CPBG) are inversely designed in terms of DL neural network (NN) tagged to obtain a specified width of CPBG.

Methods: The new PCs structure is designed by combining multiple factors that produce a CPBG. Tandem networks are used to speed up the training of the NN and tackle the problem of nonuniqueness that arises in inverse design.

Results: After various attempts and improvements, the ideal PCs structure was obtained. It is found that the connecting channel between the primitives in the PCs unit cell has a dominate effect on the CPBG. The use of a tandem network enables better convergence of the network. Finally, suitable NN can be obtained, which can realize the forward prediction of the CPBG and the inverse design of the structure.

Conclusion: DL can realize forward prediction and inverse design of 2D PCs targeting the width of the CPBG, which broadens the application scope of DL in the field of PCs.

Keywords: Photonic crystal, complete photonic band gap, deep learning, neural network, machine learning, inverse design.

Graphical Abstract
[1]
Yablonovitch, E. Inhibited spontaneous emis-sion in solid-state physics and electronics. Phys. Rev. Lett., 1987, 58(20), 2059-2062.
[http://dx.doi.org/10.1103/PhysRevLett.58.2059] [PMID: 10034639]
[2]
John, S. Strong localization of photons in cer-tain disordered dielectric superlattices. Phys. Rev. Lett., 1987, 58(23), 2486-2489.
[http://dx.doi.org/10.1103/PhysRevLett.58.2486] [PMID: 10034761]
[3]
Alipour-Banaei, H.; Mehdizadeh, F. A proposal for anti-uvb filter based on one-dimensional pho-tonic crystal structure. Dig. J. Nanomater. Biostruct., 2012, 7(1), 367-371.
[4]
Alipour-Banaei, H.; Mehdizadeh, F. Significant role of photonic crystal resonant cavities in WDM and DWDM communication tunable filters. Optik (Stuttg.), 2013, 124(17), 2639-2644.
[http://dx.doi.org/10.1016/j.ijleo.2012.07.029]
[5]
Alipour-Banaei, H.; Mehdizadeh, F.; Hassangholizadeh-Kashtiban, M. Important effect of defect parameters on the characteristics of thue-morse photonic crystal filters. Adv. Optoelectron., 2013, 2013, 1-5.
[http://dx.doi.org/10.1155/2013/856148]
[6]
Robinson, S.; Nakkeeran, R. Investigation on two dimensional photonic crystal resonant cavity based bandpass filter. Optik (Stuttg.), 2012, 123(5), 451-457.
[http://dx.doi.org/10.1016/j.ijleo.2011.05.004]
[7]
Mahmoud, M.Y.; Bassou, G.; Taalbi, A.; Che-kroun, Z.M. Optical channel drop filters based on photonic crystal ring resonators. Opt. Commun., 2012, 285(3), 368-372.
[http://dx.doi.org/10.1016/j.optcom.2011.09.068]
[8]
Li, H.; Ma, B. Research development on fabri-cation and optical properties of nonlinear photonic crystals. Front Optoelectron., 2020, 13(1), 35-49.
[http://dx.doi.org/10.1007/s12200-019-0946-x]
[9]
Adhikary, M.; Uppu, R.; Harteveld, C.A.M.; Grishina, D.A.; Vos, W.L. Experimental probe of a complete 3D photonic band gap. Opt. Express, 2020, 28(3), 2683-2698.
[http://dx.doi.org/10.1364/OE.28.002683] [PMID: 32121951]
[10]
Men, H.; Nguyen, N.C.; Freund, R.M.; Par-rilo, P.A.; Peraire, J. Bandgap optimization of two-dimensional photonic crystals using semidefinite programming and subspace methods. J. Comput. Phys., 2010, 229(10), 3706-3725.
[http://dx.doi.org/10.1016/j.jcp.2010.01.023]
[11]
Li, H.; Djaoued, H.; Robichaud, J.; Djaoued, Y. A pleasant blue-green colored 2D vanadium dioxide inverse opal monolayer: Large area fabrica-tion and its thermochromic application. J. Mater. Chem. C Mater. Opt. Electron. Devices, 2020, 8(33), 11572-11580.
[http://dx.doi.org/10.1039/D0TC02427A]
[12]
Rose, M.A.; Vinod, T.P.; Morin, S.A. Mi-croscale screen printing of large-area arrays of mi-croparticles for the fabrication of photonic struc-tures and for optical sorting. J. Mater. Chem. C Mater. Opt. Electron. Devices, 2018, 6(44), 12031-12037.
[http://dx.doi.org/10.1039/C8TC02978D]
[13]
Turduev, M.; Giden, I.H.; Kurt, H. Modified annular photonic crystals with enhanced dispersion relations: Polarization insensitive self-collimation and nanophotonic wire waveguide designs. J. Opt. Soc. Am. B, 2012, 29(7), 1589-1598.
[http://dx.doi.org/10.1364/JOSAB.29.001589]
[14]
Deghdak, R.; Bouchemat, M.; Lahoubi, M.; Pu, S.; Bouchemat, T.; Otmani, H. Sensitive mag-netic field sensor using 2D magnetic photonic crys-tal slab waveguide based on BIG/GGG structure. J. Comput. Electron., 2017, 16(2), 392-400.
[http://dx.doi.org/10.1007/s10825-017-0965-z]
[15]
Hou, J.; Citrin, D.S.; Cao, Z.; Yang, C.; Zhong, Z.; Chen, S. Slow light in square-lattice chalcogenide photonic crystal holey fibers. IEEE J. Sel. Top. Quantum Electron., 2016, 22(2), 271-278.
[http://dx.doi.org/10.1109/JSTQE.2015.2422997]
[16]
Oskooi, A.F.; Joannopoulos, J.D.; Johnson, S.G. Zero-group-velocity modes in chalcogenide holey photonic-crystal fibers. Opt. Express, 2009, 17(12), 10082-10090.
[http://dx.doi.org/10.1364/OE.17.010082] [PMID: 19506660]
[17]
Russell, P. Photonic crystal fibers. Science, 2003, 299(5605), 358-362.
[http://dx.doi.org/10.1126/science.1079280] [PMID: 12532007]
[18]
Grgić, J.; Xiao, S.; Mørk, J.; Jauho, A.P.; Mortensen, N.A. Slow-light enhanced absorption in a hollow-core fiber. Opt. Express, 2010, 18(13), 14270-14279.
[http://dx.doi.org/10.1364/OE.18.014270] [PMID: 20588562]
[19]
Matsushita, S.; Suavet, O.; Hashiba, H. Full-photonic-bandgap structures for prospective dye-sensitized solar cells. Electrochim. Acta, 2010, 55(7), 2398-2403.
[http://dx.doi.org/10.1016/j.electacta.2009.11.105]
[20]
Kalra, Y.; Sinha, R.K. Design of ultra com-pact polarization splitter based on the complete photonic band gap. Opt. Quantum Electron., 2005, 37(9), 889-895.
[http://dx.doi.org/10.1007/s11082-005-1122-7]
[21]
Li, X.; Shen, H.; Li, T.; Liu, J.; Huang, X. T-shaped polarization beam splitter based on two-dimensional photonic crystal waveguide structures. Opt. Rev., 2016, 23(6), 950-954.
[http://dx.doi.org/10.1007/s10043-016-0277-8]
[22]
Zhang, H.; Scalari, G.; Faist, J.; Dunbar, L.A.; Houdre, R. Design and fabrication technology for high performance electrical pumped terahertz pho-tonic crystal band edge lasers with complete pho-tonic band gap. J. Appl. Phys., 2010, 108(9), 093104.
[http://dx.doi.org/10.1063/1.3476565]
[23]
Goodfellow, I.; Bengio, Y.; Courville, A. Deep learning; MIT Press: USA, 2016. ww.deeplearningbook.org
[24]
LeCun, Y.; Bengio, Y.; Hinton, G. Deep learning. Nature, 2015, 521(7553), 436-444.
[http://dx.doi.org/10.1038/nature14539] [PMID: 26017442]
[25]
Krizhevsky, A.; Sutskever, I.; Hinton, G.E. Imagenet classification with deep convolutional neural networks. Adv. Neural Inf. Process. Syst., 2012, 25, 1097-1105.
[26]
He, K.; Zhang, X.; Ren, S.; Sun, J. Deep residual learning for image recognition. arXiv, 2016, 2016, 1512.03385.
[http://dx.doi.org/10.1109/CVPR.2016.90]
[27]
Girshick, R. Fast r-cnn. IEEE International Conference on Computer Vision (ICCV), 07-13 December 2015, Santiago, Chile.
[http://dx.doi.org/10.1109/ICCV.2015.169]
[28]
Shen, D.; Wu, G.; Suk, H-I. Deep learning in medical image analysis. Annu. Rev. Biomed. Eng., 2017, 19(1), 221-248.
[http://dx.doi.org/10.1146/annurev-bioeng-071516-044442] [PMID: 28301734]
[29]
Graves, A.; Mohamed, A.-R.; Hinton, G. Speech recognition with deep recurrent neural networks. arXiv, 2013, 2013, 1303.5778.
[http://dx.doi.org/10.1109/ICASSP.2013.6638947]
[30]
Vinyals, O.; Toshev, A.; Bengio, S.; Erhan, D. Show and tell: A neural image caption generator. arXiv, 2015, 2015, 7298935
[http://dx.doi.org/10.1109/CVPR.2015.7298935]
[31]
Cho, K.; Van Merrienboer, B.; Gulcehre, C.; Bahdanau, D.; Bougares, F.; Schwenk, H.; Bengio, Y. The 2014 Conference on Empirical Methods In Natural Language Processing. EMNLP, October 25- 29, 2014, Doha, Qatar.
[http://dx.doi.org/10.3115/v1/D14-1179]
[32]
Devlin, J.; Chang, M.-W.; Lee, K.; Toutanova, K. BERT: Pretraining of deep bidirectional transformers for language understanding. arXiv preprint arXiv 2019, 2019, 1810-04805.
[33]
Silver, D.; Huang, A.; Maddison, C.J.; Guez, A.; Sifre, L.; van den Driessche, G.; Schrittwieser, J.; Antonoglou, I.; Panneershelvam, V.; Lanctot, M. Mastering the game of Go with deep neural networks and tree search. Nature, 2016, 529(7587), 484.
[http://dx.doi.org/10.1038/nature16961]
[34]
Volodymyr, M.; Kavukcuoglu, K.; Silver, D.; Rusu, A. Human-level control through deep rein-forcement learning. Nature, 2015, 518(7540), 529-533.
[35]
Peurifoy, J.; Shen, Y.; Jing, L.; Yang, Y.; Ca-no-Renteria, F.; DeLacy, B.G.; Joannopoulos, J.D.; Tegmark, M.; Soljačić, M. Nanophotonic particle simulation and inverse design using artificial neural networks. Sci. Adv., 2018, 4(6), eaar4206.
[http://dx.doi.org/10.1126/sciadv.aar4206] [PMID: 29868640]
[36]
Liu, D.; Tan, Y.; Khoram, E.; Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics, 2018, 5(4), 1365-1369.
[http://dx.doi.org/10.1021/acsphotonics.7b01377]
[37]
So, S.; Mun, J.; Rho, J. Simultaneous inverse design of materials and structures via deep learn-ing: Demonstration of dipole resonance engineer-ing using core-shell nanoparticles. ACS Appl. Mater. Interfaces, 2019, 11(27), 24264-24268.
[http://dx.doi.org/10.1021/acsami.9b05857] [PMID: 31199610]
[38]
Zhou, Y.; Chen, R.; Chen, W.; Chen, R.P.; Ma, Y. Optical analog computing devices designed by deep neural network. Opt. Commun., 2020, 458, 124674.
[http://dx.doi.org/10.1016/j.optcom.2019.124674]
[39]
Ma, W.; Cheng, F.; Xu, Y.; Wen, Q.; Liu, Y. Probabilistic representation and inverse design of metamaterials based on a deep generative model with semi-supervised learning strategy. Adv. Mater., 2019, 31(35), e1901111.
[http://dx.doi.org/10.1002/adma.201901111] [PMID: 31259443]
[40]
Tahersima, M.H.; Kojima, K.; Koike-Akino, T.; Jha, D.; Wang, B.; Lin, C.; Parsons, K. Deep neural network inverse design of integrated pho-tonic power splitters. Sci. Rep., 2019, 9(1), 1368.
[http://dx.doi.org/10.1038/s41598-018-37952-2] [PMID: 30718661]
[41]
Malkiel, I.; Mrejen, M.; Nagler, A.; Arieli, U.; Wolf, L.; Suchowski, H. Plasmonic nanostructure design and characterization via deep learning. Light Sci. Appl., 2018, 7(1), 60.
[http://dx.doi.org/10.1038/s41377-018-0060-7] [PMID: 30863544]
[42]
Li, X.; Ning, S.; Liu, Z.; Yan, Z.; Luo, C.; Zhuang, Z. Designing phononic crystal with antic-ipated band gap through a deep learning based da-ta-driven method. Comput. Methods Appl. Mech. Eng., 2020, 361, 112737.
[http://dx.doi.org/10.1016/j.cma.2019.112737]
[43]
Cassagne, D.; Jouanin, C.; Bertho, D. Hexag-onal photonic-band-gap structures. Phys. Rev. B Condens. Matter, 1996, 53(11), 7134-7142.
[http://dx.doi.org/10.1103/PhysRevB.53.7134] [PMID: 9982159]
[44]
Rezaei, B.; Kalafi, M. Engineering absolute band gap in anisotropic hexagonal photonic crys-tals. Opt. Commun., 2006, 266(1), 159-163.
[http://dx.doi.org/10.1016/j.optcom.2006.04.035]
[45]
Alipour-Banaei, H.; Serajmohammadi, S.; Mehdizadeh, F.; Andalib, A. Band gap properties of two-dimensional photonic crystal structures with rectangular lattice. J. Optical Communicat., 2015, 36(2), 49.
[http://dx.doi.org/10.1515/joc-2014-0049]
[46]
Qiu, M.; He, S. Large complete band gap in two-dimensional photonic crystals with elliptic air holes. Phys. Rev. B Condens. Matter, 1999, 60(15), 67088-10612.
[http://dx.doi.org/10.1103/PhysRevB.60.10610]
[47]
Kaliteevski, M.A.; Martinez, J.M.; Cassagne, D.; Albert, J.P. Disorder-induced modification of the attenuation of light in a two-dimensional pho-tonic crystal with complete band gap. Phys. Status Solidi, A Appl. Res., 2003, 195(3), 612-617.
[http://dx.doi.org/10.1002/pssa.200306161]
[48]
Li, H.; Jiang, L.; Jia, W.; Qiang, H.; Li, X. Genetic optimization of two-dimensional photonic crystals for large absolute band-gap. Opt. Commun., 2009, 282(14), 3012-3017.
[http://dx.doi.org/10.1016/j.optcom.2009.03.071]
[49]
Wang, D.; Yu, Z.; Liu, Y.; Lu, P.; Han, L.; Feng, H.; Guo, X.; Ye, H. The optimal structure of two dimensional photonic crystals with the large absolute band gap. Opt. Express, 2011, 19(20), 19346-19353.
[http://dx.doi.org/10.1364/OE.19.019346] [PMID: 21996875]
[50]
Shen, L.; Ye, Z.; He, S. Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm. Phys. Rev. B Condens. Matter, 2003, 68(3), 204-213.
[http://dx.doi.org/10.1103/PhysRevB.68.035109]
[51]
Rezaei, B.; Khalkhali, T.F.; Vala, A.S.; Kalafi, M. Absolute band gap properties in two-dimensional photonic crystals composed of air rings in anisotropic tellurium background. Opt. Commun., 2009, 282(14), 2861-2869.
[http://dx.doi.org/10.1016/j.optcom.2009.04.048]
[52]
Khalkhali, T.F.; Rezaei, B.; Kalafi, M. En-largement of absolute photonic band gap in modi-fied 2D anisotropic annular photonic crystals. Opt. Commun., 2011, 284(13), 3315-3322.
[http://dx.doi.org/10.1016/j.optcom.2011.03.006]
[53]
Liu, D.; Gao, Y.; Tong, A.; Hu, S. Absolute photonic band gap in 2D honeycomb annular pho-tonic crystals. Phys. Lett. A, 2015, 379(3), 214-217.
[http://dx.doi.org/10.1016/j.physleta.2014.11.030]
[54]
Wen, F.; David, S.; Checoury, X.; El Kurdi, M.; Boucaud, P. Two-dimensional photonic crys-tals with large complete photonic band gaps in both TE and TM polarizations. Opt. Express, 2008, 16(16), 12278-12289.
[http://dx.doi.org/10.1364/OE.16.012278] [PMID: 18679505]
[55]
Takayama, S.I.; Kitagawa, H.; Tanaka, Y.; Asano, T.; Noda, S. Experimental demonstration of complete photonic band gap in two-dimensional photonic crystal slabs. Appl. Phys. Lett., 2005, 87(6), 608.
[http://dx.doi.org/10.1063/1.2009060]
[56]
Marsal, L.F.; Trifonov, T. Rodrı, x; Guez, A.; Pallarés, J; Alcubilla, R. Larger absolute photonic band gap in two-dimensional air–silicon structures. Phys. E, 2003, 16(3), 580-585.
[http://dx.doi.org/10.1016/S1386-9477(02)00650-1]
[57]
Qiu, M.; Sailing, H. Optimal design of a two-dimensional photonic crystal of square lattice with a large complete two-dimensional bandgap. J. Opt. Soc. Am. B, 2000, 17, 6.
[58]
Hou, J.; Yang, C.; Li, X.; Cao, Z.; Chen, S. Enhanced complete photonic bandgap in a moder-ate refractive index contrast chalcogenideair sys-tem with connected-annular-rods photonic crystals. Photon. Res., 2018, 6(4), 282-289.
[http://dx.doi.org/10.1364/PRJ.6.000282]
[59]
Chau, Y.F.; Wu, F.L.; Jiang, Z.H.; Li, H.Y. Evolution of the complete photonic bandgap of two-dimensional photonic crystal. Opt. Express, 2011, 19(6), 4862-4867.
[http://dx.doi.org/10.1364/OE.19.004862] [PMID: 21445122]
[60]
Liu, W.L.; Yang, T.J. Photonic band gaps in a two-dimensional photonic crystal with open veins. Solid State Commun., 2006, 140(3), 144-148.
[http://dx.doi.org/10.1016/j.ssc.2006.08.011]
[61]
Kalra, Y.; Sinha, R.K. Modelling and design of complete photonic band gaps in two-dimensional photonic crystals. Pramana, 2008, 70(1), 153-161.
[http://dx.doi.org/10.1007/s12043-008-0013-4]
[62]
Li, X.J.; Yang, Y.B.; Han, P.D.; Wang, S.F.; Wang, Y.C.; Liang, W. Numerical simulation of absolute photonic band gaps for two-dimensional photonic crystals with the rotational square lattice. Optoelectron. Lett., 2010, 6(5), 359-362.
[http://dx.doi.org/10.1007/s11801-010-9255-8]
[63]
Zhang, S.K.; Bian, L.H.; Zhang, Y.Y. High-accuracy inverse optical design by combining ma-chine learning and knowledge-depended optimiza-tion. J. Opt., 2020, 22(10), 105802.
[http://dx.doi.org/10.1088/2040-8986/abb1ce]
[64]
Qiu, C.; Wu, X.; Luo, Z.; Yang, H.; Wang, G.; Liu, N.; Huang, B. Simultaneous inverse de-sign continuous and discrete parameters of nano-photonic structures via back-propagation inverse neural network. Opt. Commun., 2021, 483, 126641.
[http://dx.doi.org/10.1016/j.optcom.2020.126641]
[65]
Pilozzi, L.; Farrelly, F.A.; Marcucci, G.; Conti, C. Topological nanophotonics and artificial neural networks. Nanotechnology, 2021, 32(14), 142001.
[http://dx.doi.org/10.1088/1361-6528/abd508] [PMID: 33339006]
[66]
Singh, R.; Agarwal, A.W.; Anthony, B. Map-ping the design space of photonic topological states via deep learning. Opt. Express, 2020, 28(19), 27893-27902.
[http://dx.doi.org/10.1364/OE.398926] [PMID: 32988072]
[67]
Christensen, T.; Loh, C.; Picek, S.; Jing, L.; Fisher, S.; Ceperic, V.; Joannopoulos, J.D.; Soljacic, M.; Jakobovic, D. Predictive and genera-tive machine learning models for photonic crystals. Nanophotonics, 2020, 9(13), 4183-4192.
[http://dx.doi.org/10.1515/nanoph-2020-0197]
[68]
Du, L.L.; Liu, Y.H.; Zhou, X.; Tao, L.Y.; Li, M.Z.; Ren, H.L.; Ji, R.N.; Song, K.; Zhao, X.P.; Navarro-Cia, M. Dual-band all-dielectric chiral photonic crystal. J. Phys. D Appl. Phys., 2022, 55(16), 165303.
[http://dx.doi.org/10.1088/1361-6463/ac4768]
[69]
Zhi, W.Q.; Fei, H.M.; Han, Y.H.; Wu, M.; Zhang, M.D.; Liu, X.; Cao, B.Z.; Yang, Y.B. Uni-directional transmission of funnel-shaped wave-guide with complete bandgap. Wuli Xuebao, 2022, 71(3), 038501.
[http://dx.doi.org/10.7498/aps.71.20211299]

Rights & Permissions Print Cite
© 2024 Bentham Science Publishers | Privacy Policy