[1] Y. Chen, Y. Cheng, R. Zhu, F. Wang, H. Cheng, Z. Liu, C. Fan, Y. Xue, Z. Yu, J. Zhu, X. Hu, Q. Gong. Nanoscale all-optical logic devices. Sci. Chin. Phys. Mech., 62, 44201(2019).

[2] K. Yao, R. Unni, Y. Zheng. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics, 8, 339(2019).

[3] S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vucković, A. W. Rodriguez. Inverse design in nanophotonics. Nat. Photonics, 12, 659(2018).

[4] N. Palumbo. 525.770 – Intelligent algorithms.

[5] M. S. Kumar, S. Menabde, S. Yu, N. Park. Directional emission from photonic crystal waveguide terminations using particle swarm optimization. J. Opt. Soc. Am. B, 27, 343(2010).

[6] M. D. Huntington, L. J. Lauhon, T. W. Odom. Subwavelength lattice optics by evolutionary design. Nano Lett., 14, 7195(2014).

[7] Z. Liu, X. Liu, Z. Xiao, C. Lu, H. Wang, Y. Wu, X. Hu, Y. Liu, H. Zhang, X. Zhang. Integrated nanophotonic wavelength router based on an intelligent algorithm. Optica, 6, 1367(2019).

[8] C. Lu, Z. Liu, Y. Wu, Z. Xiao, D. Yu, H. Zhang, C. Wang, X. Hu, Y. C. Liu, X. Liu, X. Zhang. Nanophotonic polarization routers based on an intelligent algorithm. Adv. Opt. Mater., 8, 1902018(2020).

[9] S. R. Granter, A. H. Beck, D. J. Papke. AlphaGo, deep learning, and the future of the human microscopist. Arch. Pathol. Lab. Med., 141, 619(2017).

[10] G. E. Hinton, R. R. Salakhutdinov. Reducing the dimensionality of data with neural networks. Science., 313, 504(2006).

[11] Y. LeCun, Y. Bengio, G. Hinton. Deep learning. Nature, 521, 436(2015).

[12] A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson. Meep: a flexible free-software package for electromagnetic simulations by the FDTD method. Comput. Phys. Commun., 181, 687(2010).

[13] I. Malkiel, M. Mrejen, A. Nagler, U. Arieli, L. Wolf, H. Suchowski. Plasmonic nanostructure design and characterization via deep learning. Light Sci. Appl., 7, 555(2018).

[14] D. Liu, Y. Tan, E. Khoram, Z. Yu. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photon., 5, 1365(2018).

[15] L. Xu, M. Rahmani, Y. Ma, D. A. Smirnova, K. Z. Kamali, F. Deng, Y. K. Chiang, L. Huang, H. Zhang, S. Gould, D. N. Neshev, A. E. Miroshnichenkoa. Enhanced light-matter interactions in dielectric nanostructures via machine-learning approach. Adv. Photon., 2, 026003(2020).

[16] M. H. Tahersima, K. Kojima, T. Koike-Akino, D. Jha, B. Wang, C. Lin, K. Parsons. Deep neural network inverse design of integrated photonic power splitters. Sci. Rep., 9, 1368(2019).

[17] W. Ma, F. Cheng, Y. Liu. Deep-learning-enabled on-demand design of chiral metamaterials. ACS Nano., 12, 6326(2018).

[18] B. Wu, K. Ding, C. T. Chan, Y. Chen. Machine prediction of topological transitions in photonic crystals(2017).

[19] J. Zhao, Y. S. H. Zhu, Z. Zhu, J. E. Antonio-Lopez, R. A. Correa, S. Pang, A. Schulzgen. Deep-learning cell imaging through Anderson localizing optical fiber. Adv. Photon., 1, 066001(2019).

[20] I. J. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, Y. Bengio. Generative adversarial nets, 1(2014).

[21] J. Jiang, D. Sell, S. Hoyer, J. Hickey, J. Yang, J. A. Fan. Free-form diffractive metagrating design based on generative adversarial networks. ACS Nano., 13, 8872(2019).

[22] W. Ma, F. Cheng, Y. Xu, Q. Wen, Y. Liu. Probabilistic representation and inverse design of metamaterials based on a deep generative model with semi‐supervised learning strategy. Adv. Mater., 31, 1901111(2019).

[23] Y. Tang, K. Kojima, T. Koike-Akino, Y. Wang, P. Wu, M. TaherSima, D. Jha, K. Parsons, M. Qi. Generative deep learning model for a multi-level nano-optic broadband power splitter, Th1A.1(2020).

[24] H. Zhou, Y. Zhao, G. Xu, X. Wang, Z. Tan, J. Dong, X. Zhang. Chip-scale optical matrix computation for PageRank algorithm. IEEE J. Sel. Top. Quant, 26, 8300910(2020).

[25] H. Zhou, Y. Zhao, X. Wang, D. Gao, J. Dong, X. Zhang. Self-configuring and reconfigurable silicon photonic signal processor. ACS Photon., 7, 792(2020).

[26] H. Zhou, Y. Zhao, Y. Wei, F. Li, J. Dong, X. Zhang. All-in-one silicon photonic polarization processor. Nanophotonics, 8, 2257(2019).

[27] A. M. Hammond, R. M. Camacho. Designing integrated photonic devices using artificial neural networks. Opt. Express, 27, 29620(2019).

[28] P. Baldi, P. Sadowski, D. Whiteson. Searching for exotic particles in high-energy physics with deep learning. Nat. Commun., 5, 4308(2014).

[29] W. J. Brouwer, J. D. Kubicki, J. O. Sofo, C. L. Giles. An investigation of machine learning methods applied to structure prediction in condensed matter(2014).

[30] M. Rupp, A. Tkatchenko, K. Müller, O. A. von Lilienfeld. Fast and accurate modeling of molecular atomization energies with machine learning. Phys. Rev. Lett., 108, 058301(2012).

[31] S. Jiao, Z. Jin, C. Chang, C. Zhou, W. Zou, X. Li. Compression of phase-only holograms with JPEG standard and deep learning. Appl. Sci., 8, 1258(2019).

[32] S. So, J. Mun, J. Rho. Simultaneous inverse design of materials and structures via deep learning: demonstration of dipole resonance engineering using core-shell nanoparticles. ACS Appl. Mater. Inter, 11, 24264(2019).

[33] Y. Chen, J. Zhu, Y. Xie, N. Feng, Q. H. Liu. Smart inverse design of graphene-based photonic metamaterials by an adaptive artificial neural network. Nanoscale, 11, 9749(2019).

[34] T. Zhang, J. Wang, Q. Liu, J. Zhou, J. Dai, X. Han, Y. Zhou, K. Xu. Efficient spectrum prediction and inverse design for plasmonic waveguide systems based on artificial neural networks. Photon. Res., 7, 368(2019).

[35] Z. Liu, D. Zhu, S. P. Rodrigues, K. Lee, W. Cai. Generative model for the inverse design of metasurfaces. Nano Lett., 18, 6570(2018).

[36] J. Peurifoy, Y. Shen, L. Jing, Y. Yang, F. Cano-Renteria, B. G. DeLacy, J. D. Joannopoulos, M. Tegmark, M. Soljacic. Nanophotonic particle simulation and inverse design using artificial neural networks. Sci. Adv., 4, eaar4206(2018).

[37] P. R. Wiecha, O. L. Muskens. Deep learning meets nanophotonics: a generalized accurate predictor for near fields and far fields of arbitrary 3D nanostructures. Nano Lett., 20, 329(2019).

[38] H. Ren, W. Shao, Y. Li, F. Salim, M. Gu. Three-dimensional vectorial holography based on machine learning inverse design. Sci. Adv., 6, eaaz4261(2020).

[39] W. Ma, Y. Liu. A data-efficient self-supervised deep learning model for design and characterization of nanophotonic structures. Sci. China Phys. Mech. Astron., 63, 284212(2020).

[40] Z. Liu, D. Zhu, K. Lee, A. S. Kim, L. Raju, W. Cai. Compounding meta-atoms into meta-molecules with hybrid artificial intelligence techniques. Adv. Mater., 32, 1904790(2019).

[41] O. Hemmatyar, S. Abdollahramezani, Y. Kiarashinejad, M. Zandehshahvar, A. Adibi. Full color generation with Fano-type resonant HfO2 nanopillars designed by a deep-learning approach. Nanoscale, 11, 21266(2019).

[42] S. So, T. Badloe, J. Noh, J. Bravo-Abad, J. Rho. Deep learning with coherent nanophotonic circuits. Nanophotonics, 9, 1041(2020).

[43] Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, M. Soljačić. Deep learning enabled inverse design in nanophotonics. Nat. Photon., 11, 441(2017).

[44] J. Feldmann, N. Youngblood, C. D. Wright, H. Bhaskaran, W. H. P. Pernice. All-optical spiking neurosynaptic networks with self-learning capabilities. Nature, 569, 208(2019).

[45] M. Veli, Y. Luo, A. Ozcan, M. Jarrahi, Y. Rivenson, N. T. Yardimei, X. Lin. All-optical machine learning using diffractive deep neural networks. Science, 361, 1004(2018).

[46] S. Jiao, J. Feng, Y. Gao, T. Lei, Z. Xie, X. Yuan. Optical machine learning with incoherent light and a single-pixel detector. Opt. Lett., 44, 5186(2019).

[47] E. Khoram, A. Chen, D. Liu, L. Ying, Q. Wang, M. Yuan, Z. Yu. Nanophotonic media for artificial neural inference. Opt. Lett., 7, 823(2019).

[48] J. Chang, V. Sitzmann, X. Dun, W. Heidrich, G. Wetzstein. Hybrid optical-electronic convolutional neural networks with optimized diffractive optics for image classification. Sci. Rep., 8, 12324(2018).

[49] J. Jiang, J. A. Fan. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Lett., 19, 5366(2019).

[50] I. Sajedian, J. Kim, J. Rho. Finding the optical properties of plasmonic structures by image processing using a combination of convolutional neural networks and recurrent neural networks. Microsyst. Nanoeng., 5, 27(2019).

[51] Y. Qu, L. Jing, Y. Shen, M. Qiu, M. Soljačić. Basic instincts. ACS Photon., 6, 1168(2019).

[52] M. Hutson. Migrating knowledge between physical scenarios based on artificial neural networks. Science., 360, 845(2018).

[53] S. Jiao, Y. Gao, J. Feng, T. Lei, X. Yuan. Does deep learning always outperform simple linear regression in optical imaging?. Opt. Express, 28, 3717(2020).

[54] E. Goi, Q. Zhang, X. Chen, H. Luan, M. Gu. Perspective on photonic memristive neuromorphic computing. PhotoniX, 1, 3(2020).

[55] T. Chen, J. van Gelder, B. van de Ven, S. V. Amitonov, B. de Wilde, H. Ruiz Euler, H. Broersma, P. A. Bobbert, F. A. Zwanenburg, W. G. van der Wiel. Classification with a disordered dopant-atom network in silicon. Nature, 577, 341(2020).

[56] Y. Kiarashinejad, S. Abdollahramezani, A. Adibi. Deep learning approach based on dimensionality reduction for designing electromagnetic nanostructures. NPJ Comput. Mater., 6, 12(2020).

[57] T. Han, C. Liu, W. Yang, D. Jiang. Deep transfer network with joint distribution adaptation: a new intelligent fault diagnosis framework for industry application. ISA Trans., 97, 269(2020).

[58] M. Wang, W. Deng. Deep visual domain adaptation: a survey. Neurocomputing, 312, 135(2018).

[59] K. Chadan, P. C. Sabatier, R. G. Newton. Inverse Problems in Quantum Scattering Theory(1988).

[60] A. Y. Piggott, J. Petykiewicz, L. Su, J. Vučković. Fabrication-constrained nanophotonic inverse design. Sci. Rep., 7, 1786(2017).

[61] C. Dory, D. Vercruysse, K. Y. Yang, N. V. Sapra, A. E. Rugar, S. Sun, D. M. Lukin, A. Y. Piggott, J. L. Zhang, M. Radulaski, K. G. Lagoudakis, L. Su, J. Vučković. Inverse-designed diamond photonics. Nat. Commun., 10, 3309(2019).

[62] J. Lu, J. Vučković. Nanophotonic computational design. Opt. Express, 21, 13351(2013).

[63] N. V. Sapra, D. Vercruysse, L. Su, K. Y. Yang, J. Skarda, A. Y. Piggott, J. Vuckovic. Inverse design and demonstration of broadband grating couplers. IEEE J. Sel. Top. Quantum., 25, 6100207(2019).

[64] A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, J. Vučković. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nat. Photon., 9, 374(2015).

[65] L. Su, A. Y. Piggott, N. V. Sapra, J. Petykiewicz, J. Vučković. Inverse design and demonstration of a compact on-chip narrowband three-channel wavelength demultiplexer. ACS Photon., 5, 301(2017).

[66] N. V. Sapra, K. Y. Yang, D. Vercruysse, K. J. Leedle, D. S. Black, R. J. England, L. Su, R. Trivedi, Y. Miao, O. Solgaard, R. L. Byer, J. Vučković. On-chip integrated laser-driven particle accelerator. Science, 367, 79(2020).

[67] K. Y. Yang, J. Skarda, M. Cotrufo, A. Dutt, G. H. Ahn, M. Sawaby, D. Vercruysse, A. Arbabian, S. Fan, A. Alù, J. Vučković. Inverse-designed non-reciprocal pulse router for chip-based LiDAR. Nat. Photon., 14, 369(2020).

[68] P. Camayd-Muñoz, G. Roberts, C. Ballew, M. Debbas, A. Faraon. Inverse designed shape-reconfigurable multifunctional photonics, FW3B.2(2020).

[69] J.-K. Byun, J.-H. Ko, H.-B. Lee, J.-S. Park, H.-S. Kim. Application of the sensitivity analysis to the optimal design of the microstrip low-pass filter with defected ground structure. IEEE Trans. Mag., 45, 1462(2009).

[70] J. Lehtinen. A framework for precomputed and captured light transport. ACM Trans. Graphics, 26, 13(2007).

[71] J. C. Finlay, T. H. Foster. Recovery of hemoglobin oxygen saturation and intrinsic fluorescence with a forward-adjoint model. Appl. Opt., 44, 1917(2005).

[72] S. Forest. Genetic algorithms-principles of natural-selection applied to computation. Science, 261, 872(1993).

[73] G. Pu, L. Yi, L. Zhang, W. Hu. Intelligent programmable mode-locked fiber laser with a human-like algorithm. Optica, 6, 362(2019).

[74] Z. Yu, H. Cui, X. Sun. Genetic-algorithm-optimized wideband on-chip polarization rotator with an ultrasmall footprint. Opt. Lett., 42, 3093(2017).

[75] A. C. S. Chan, A. K. S. Lau, K. K. Y. Wong, E. Y. Lam, K. K. Tsia. Arbitrary two-dimensional spectrally encoded pattern generation—a new strategy for high-speed patterned illumination imaging. Optica, 2, 1037(2015).

[76] D. J. Poxson, M. F. Schubert, F. W. Mont, E. F. Schubert, J. K. Kim. Broadband omnidirectional antireflection coatings optimized by genetic algorithm. Opt. Lett., 34, 728(2009).

[77] Z. Yu, H. Ccui, X. Sun. Optimal design of integrally gated CNT field-emission devices using a genetic algorithm. Photon. Res., 5, B15(2017).

[78] L. Sanchis, A. Håkansson, D. López-Zanón, J. Bravo-Abad, J. Sánchez-Dehesa. Genetically optimized on-chip wideband ultracompact reflectors and Fabry–Perot cavities. Appl. Phys. Lett., 84, 4460(2004).

[79] P. Y. Chen, C. H. Chen, J. S. Wu, H. C. Wen, W. P. Wang. Integrated optical devices design by genetic algorithm. Nanotechnology, 18, 395203(2007).

[80] M. Liu, Y. Xie, T. Feng, Y. Xu. Resonant broadband unidirectional light scattering based on genetic algorithm. Opt. Lett., 45, 968(2020).

[81] K. Liao, T. Gan, X. Hu, Q. Gong. AI-assisted on-chip nanophotonic convolver based on silicon metasurface. Nanophotonics, 9, 3315(2020).

[82] Z. Lin, X. Li, R. Zhao, X. Song, Y. Wang, L. Huang. High-efficiency Bessel beam array generation by Huygens metasurfaces. Nanophotonics, 8, 1079(2019).

[83] Y. Khorrami, D. Fathi, R. C. Rumpf. Fast optimal design of optical components using the cultural algorithm. Opt. Express, 28, 15954(2020).

[84] N. Padhye. Topology optimization of compliant mechanism using multi-objective particle swarm optimization, 1831(2008).

[85] J. F. Schutte, J. A. Reinbolt, B. J. Fregly, R. T. Haftka, A. D. George. Parallel global optimization with the particle swarm algorithm. Int. J. Numer. Meth. Eng., 61, 2296(2004).

[86] M. Djavid, S. A. Mirtaheri, M. S. Abrishamian. Photonic crystal notch-filter design using particle swarm optimization theory and finite-difference time-domain analysis. J. Opt. Soc. Am. B, 26, 849(2009).

[87] C. Forestiere, M. Donelli, G. F. Walsh, E. Zeni, G. Miano, L. Dal Negro. Particle-swarm optimization of broadband nanoplasmonic arrays. Opt. Lett., 35, 133(2010).

[88] E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, N. I. Zheludev. A super-oscillatory lens optical microscope for subwavelength imaging. Nat. Mater., 11, 432(2012).

[89] M. Passoni, D. Gerace, L. Carroll, L. C. Andreani. Grating couplers in silicon-on-insulator: the role of photonic guided resonances on lineshape and bandwidth. Appl. Phys. Lett., 110, 41107(2017).

[90] J. C. C. Mak, C. Sideris, J. Jeong, A. Hajimiri, J. K. S. Poon. Binary particle swarm optimized 2 × 2 power splitters in a standard foundry silicon photonic platform. Opt. Lett., 41, 3868(2016).

[91] Y. Ha, Y. Guo, M. Pu, F. Zhang, X. Li, X. Ma, M. Xu, X. Luo. Minimized two- and four-step varifocal lens based on silicon photonic integrated nanoapertures. Opt. Express, 28, 7943(2020).

[92] B. Wohlfeil, L. Zimmermann, K. Petermann. Optimization of fiber grating couplers on SOI using advanced search algorithms. Opt. Lett., 39, 3201(2014).

[93] N. Zhu, H. J. Sun, N. F. Zhou. Ant colony optimization for dynamic RWA in WDM networks with partial wavelength conversion. Photon. Network Commun., 11, 229(2006).

[94] I. Saouane, A. Chaker, B. Zaidi, C. Shekhar. Optimal angle of polycrystalline silicon solar panels placed in a building using the ant colony optimization algorithm. Eur. Phys. J. Plus., 132, 106(2017).

[95] X. Guo, H. Y. Zhou, S. Guo, X. X. Luan, W. K. Cui, Y. F. Ma, L. Shi. Design of broadband omnidirectional antireflection coatings using ant colony algorithm. Opt. Express, 22, A1137(2014).

[96] M. Lundy. Convergence of an annealing algorithm. Math. Programm., 34, 111(1986).

[97] M. Čepin. Assessment of Power System Reliability(2011).

[98] A. Basu, L. N. Fraze. Rapid determination of the critical temperature in simulated annealing inversion. Science, 249, 1409(1990).

[99] K. Hara, T. Iwamoto, K. Kyuma. Optimum design technique for optoelectronic devices using simulated annealing. Electron. Commun. Japan, 79, 22(1996).

[100] L. D. Khalaf, A. F. Peterson. Performance of the simulated annealing and genetic algorithms for the design of periodic devices. Int. J. Microwave Millimeter-Wave Comput. Aided Eng., 7, 108(1997).

[101] Y. T. Lu, Y. Q. Zhou. Design of multilayer microwave absorbers using hybrid binary lightning search algorithm and simulated annealing. Photon. Network Commun., 78, 75(2017).

[102] Z. Xie, T. Lei, F. Li, H. Qiu, Z. Zhang, H. Wang, C. Min, L. Du, Z. Li, X. Yuan. Ultra-broadband on-chip twisted light emitter for optical communications. Light: Sci. Appl., 7, 18001(2018).

[103] Z. Xie, T. Lei, H. Qiu, Z. Zhang, H. Wang, X. Yuan. Broadband on-chip photonic spin Hall element via inverse design. Photon. Res., 8, 121(2020).

[104] S. J. Russell, P. Norvig. Artificial Intelligence: A Modern Approach(2003).

[105] T. Lin, F. Tian, P. Shi, F. S. Chau, G. Zhou, X. Tang, J. Deng. Design of mechanically-tunable photonic crystal split-beam nanocavity. Opt. Lett., 40, 3504(2015).

[106] Q. Quan, P. B. Deotare, M. Loncar. Photonic crystal nanobeam cavity strongly coupled to the feeding waveguide. Appl. Phys. Lett., 96, 203102(2010).

[107] E. Tabli. Metaheuristics: From Design to Implementation(2009).

[108] H. Youssef, S. M. Sait, H. Adiche. Evolutionary algorithms, simulated annealing and tabu search: a comparative study. Eng. Appl. Artif. Intel., 14, 167(2001).

[109] D. Gagnon, J. Dumont, L. J. Dubé. Multiobjective optimization in integrated photonics design. Opt. Lett., 38, 2181(2013).

[110] D. Gagnon, J. Dumont, J. Déziel, L. J. Dubé. Optimization of integrated polarization filters. Opt. Lett., 39, 5768(2014).

[111] M. A. Seldowitz, J. P. Allebach, D. W. Sweeney. Synthesis of digital holograms by direct binary search. Appl. Opt., 26, 2788(1987).

[112] B. B. Chhetri, S. Yang, T. Shimomura. Stochastic approach in the efficient design of the direct-binary-search algorithm for hologram synthesis. Appl. Opt., 39, 5956(2000).

[113] B. Shen, P. Wang, R. Polson, R. Menon. An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4 µm2 footprint. Nat. Photon., 9, 378(2015).

[114] B. Shen, P. Wang, R. Menon. Optimization and analysis of 3D nanostructures for power-density enhancement in ultra-thin photovoltaics under oblique illumination. Opt. Express, 22, A311(2014).

[115] B. Shen, P. Wang, R. Polson, R. Menon. Ultra-high-efficiency metamaterial polarizer. Optica, 1, 356(2014).

[116] P. Wang, R. Menon. Optimization of periodic nanostructures for enhanced light-trapping in ultra-thin photovoltaics. Opt. Express, 21, 6274(2013).

[117] G. Kim, J. A. Dominguez-Caballero, R. Menon. Design and analysis of multi-wavelength diffractive optics. Opt. Express, 20, 2814(2012).

[118] G. Kim, J. A. Dominguez-Caballero, H. Lee, D. J. Friedman, R. Menon. Increased photovoltaic power output via diffractive spectrum separation. Phys. Rev. Lett., 110, 123901(2013).

[119] T. R. Sales, D. H. Raguin. Multiwavelength operation with thin diffractive elements. Appl. Opt., 38, 3012(1999).

[120] B. Shen, P. Wang, R. Polson, R. Menon. Integrated metamaterials for efficient and compact free-space-to-waveguide coupling. Opt. Express, 22, 27175(2014).

[121] G. Kim, R. Menon. An ultra-small three dimensional computational microscope. Appl. Phys. Lett., 105, 061114(2014).

[122] Y. Liu, S. Wang, Y. Wang, W. Liu. Subwavelength polarization splitter–rotator with ultra-compact footprint. Opt. Lett., 44, 4495(2019).

[123] A. Majumder, B. Shen, R. Polson, T. Andrew, R. Menon. An ultra-compact nanophotonic optical modulator using multi-state topological optimization(2017).

[124] B. Shen, R. Polson, R. Menon. Increasing the density of passive photonic-integrated circuits via nanophotonic cloaking. Nat. Commun., 7, 13126(2016).

[125] H. Xie, Y. Liu, S. Wang, Y. Wang, Y. Yao, Q. Song, J. Du, Z. He, K. Xu. Highly compact and efficient four-mode multiplexer based on pixelated waveguides. IEEE Photon. Tech. Lett., 32, 166(2020).

[126] Y. Liu, K. Xu, S. Wang, W. Shen, H. Xie, Y. Wang, S. Xiao, Y. Yao, J. Du, Z. He, Q. Song. Arbitrarily routed mode-division multiplexed photonic circuits for dense integration. Nat. Commun., 10, 3263(2019).

[127] Y. Liu, W. Sun, H. Xie, N. Zhang, K. Xu, Y. Yao, S. Xiao, Q. Song. Very sharp adiabatic bends based on an inverse design. Opt. Lett., 43, 2482(2018).

[128] H. Xie, Y. Liu, Y. Wang, Y. Wang, Y. Yao, Q. Song, J. Du, Z. He, K. Xu. An ultra-compact 3-dB power splitter for three modes based on pixelated meta-structure. IEEE Photon. Tech. Lett., 32, 341(2020).

[129] H. Ma, J. Huang, K. Zhang, J. Yang. Arbitrary-direction, multichannel and ultra-compact power splitters by inverse design method. Opt. Commun., 462, 125329(2020).

[130] Y. Deng, Z. Liu, C. Song, P. Hao, Y. Wu, Y. Liu, J. G. Korvink. Topology optimization of metal nanostructures for localized surface plasmon resonances. Struct. Multidiscip. Optim., 53, 967(2016).

[131] J. Huang, J. Yang, D. Chen, W. Bai, J. Han, Z. Zhang, J. Zhang, X. He, Y. Han, L. Liang. Implementation of on-chip multi-channel focusing wavelength demultiplexer with regularized digital metamaterials. Nanophotonics, 9, 159(2020).

[132] Y. Chen, Y. Hu, J. Zhao, Y. Deng, Z. Wang, X. Cheng, D. Lei, Y. Deng, H. Duan. Topology optimization‐based inverse design of plasmonic nanodimer with maximum near‐field enhancement. Adv. Funct. Mater., 30, 2000642(2020).

[133] C. Y. Kao, S. Osher, E. Yablonovitch. Maximizing band gaps in two-dimensional photonic crystals by using level set methods. Appl. Phys. B, 81, 235(2005).

[134] S. Osher, J. A. Sethian. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys., 79, 12(1988).

[135] F. Stanley, J. Osher. Level set methods for optimization problems involving geometry and constraints. J. Comput. Phys., 171, 1(2001).

[136] A. K. S. Heinrich, H. Niederreiter. Monte Carlo and Quasi-Monte Carlo Methods(2006).

[137] K. Binder. Applications of the Monte Carlo method in Statistical Physics(1987).

[138] R. Y. Rubinstein, D. P. Kroese. Simulation and the Monte Carlo Method(2008).

[139] Y. Zhao, X. Cao, J. Gao, Y. Sun, H. Yang, X. Liu, Y. Zhou, T. Han, W. Chen. Broadband diffusion metasurface based on a single anisotropic element and optimized by the Simulated Annealing algorithm. Sci. Rep., 6, 23896(2016).

[140] L. Baranyai. Laser induced diffuse reflectance imaging – Monte Carlo simulation of backscattering measured on the surface. MethodsX, 7, 100958(2020).