[1] Shen Y R. The Principles of Nonlinear Optics[M]. New Yk: Wiley, 1984.

[2] Boyd R W. Nonlinear Optics[M]. New Yk: Academic, 2008.

[3] Armstrong J A, Bloembergen N, Ducuing J. Interactions between light waves in a nonlinear dielectric[J]. Physical Review, 1962, 127(6): 1918-1939.

[4] Fejer M M, Magel G A, Jundt D H. Quasi-phase-matched 2nd harmonic-generation-tuning and tolerances[J]. IEEE Journal of Quantum Electronics, 1992, 28(11): 2631-2654.

[5] Yamada M, Nada N, Saitoh M. First‐order quasi‐phase matched linbo₃ waveguide periodically poled by applying an external field for efficient blue second‐harmonic generation[J]. Applied Physics Letters, 1993, 62(5): 435-436.

[6] Myers L E, Eckardt R C, Fejer M M. Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO₃[J]. Journal of the Optical Society of America B-Optical Physics, 1995, 12(11): 2102-2116.

[7] Kildishev A V, Boltasseva A, Shalaev V M. Planar photonics with metasurfaces[J]. Science, 2013, 339(6125): 1232009.

[8] Meinzer N, Barnes W L, Hooper I R. Plasmonic meta-atoms and metasurfaces[J]. Nature Photonics, 2014, 8(12): 889-898.

[9] Yu N F, Capasso F. Flat optics with designer metasurfaces[J]. Nature Materials, 2014, 13(2): 139-150.

[10] Klein M W, Enkrich C, Wegener M. Second-harmonic generation from magnetic metamaterials[J]. Science, 2006, 313(5786): 502-504.

[11] Valev V K, Smisdom N, Silhanek A V. Plasmonic ratchet wheels: Switching circular dichroism by arranging chiral nanostructures[J]. Nano Letters, 2009, 9(11): 3945-3948.

[12] Husu H, Siikanen R, Makitalo J. Metamaterials with tailored nonlinear optical response[J]. Nano Letters, 2012, 12(2): 673-677.

[13] Celebrano M, Wu X, Baselli M. Mode matching in multiresonant plasmonic nanoantennas for enhanced second harmonic generation[J]. Nature Nanotechnology, 2015, 10(5): 412-417.

[14] Gui L, Bagheri S, Strohfeldt N. Nonlinear refractory plasmonics with titanium nitride nanoantennas[J]. Nano Letters, 2016, 16(9): 5708-5713.

[15] Liu S, Sinclair M B, Saravi S. Resonantly enhanced second-harmonic generation using iii-v semiconductor all-dielectric metasurfaces[J]. Nano Letters, 2016, 16(9): 5426-5432.

[16] Vabishchevich P P, Liu S, Sinclair M B. Enhanced second-harmonic generation using broken symmetry iii–v semiconductor fano metasurfaces[J]. ACS Photonics, 2018, 5(5): 1685-1690.

[17] Koshelev K, Kruk S, Melik-Gaykazyan E. Subwavelength dielectric resonators for nonlinear nanophotonics[J]. Science, 2020, 367(6475): 288-292.

[18] Lee J, Tymchenko M, Argyropoulos C. Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions[J]. Nature, 2014, 511(7507): 65-69.

[19] Lee J, Nookala N, Gomez‐Diaz J S. Ultrathin second‐harmonic metasurfaces with record-high nonlinear optical response[J]. Advanced Optical Materials, 2016, 4(5): 664-670.

[20] Kang L, Cui Y H, Lan S F. Electrifying photonic metamaterials for tunable nonlinear optics[J]. Nature Communications, 2014, 5(1): 4680.

[21] Lee K-T, Taghinejad M, Yan J. Electrically biased silicon metasurfaces with magnetic mie sesonance for tunable harmonic generation of light[J]. ACS Photonics, 2019, 6(11): 2663-2670.

[22] Klein M W, Wegener M, Feth N. Experiments on second- and third-harmonic generation from magnetic metamaterials[J]. Opt Express, 2007, 15(8): 5238-5247.

[23] Hentschel M, Utikal T, Giessen H. Quantitative modeling of the third harmonic emission spectrum of plasmonic nanoantennas[J]. Nano Letters, 2012, 12(7): 3778-3782.

[24] Metzger B, Schumacher T, Hentschel M. Third harmonic mechanism in complex plasmonic fano structures[J]. ACS Photonics, 2014, 1(6): 471-476.

[25] Shcherbakov M R, Neshev D N, Hopkins B. Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response[J]. Nano Letters, 2014, 14(11): 6488-6492.

[26] Yang Y, Wang W, Boulesbaa A. Nonlinear fano-resonant dielectric metasurfaces[J]. Nano Lett, 2015, 15(11): 7388-7393.

[27] Shibanuma T, Grinblat G, Albella P. Efficient third harmonic generation from metal-dielectric hybrid nanoantennas[J]. Nano Lett, 2017, 17(4): 2647-2651.

[28] Xu L, Rahmani M, Zangeneh Kamali K. Boosting third-harmonic generation by a mirror-enhanced anapole resonator[J]. Light Sci Appl, 2018, 7: 44.

[29] Koshelev K, Tang Y, Li K. Nonlinear metasurfaces governed by bound states in the continuum[J]. ACS Photonics, 2019, 6(7): 1639-1644.

[30] Liu Z, Xu Y, Lin Y. High-Q quasibound states in the continuum for nonlinear metasurfaces[J]. Physical Review Letters, 2019, 123(25): 253901.

[31] Krausz F, Ivanov M. Attosecond physics[J]. Reviews of Modern Physics, 2009, 81(1): 163-234.

[32] Corkum P B, Krausz F. Attosecond science[J]. Nature Physics, 2007, 3(6): 381-387.

[33] Stolow A, Bragg A E, Neumark D M. Femtosecond time-resolved photoelectron spectroscopy[J]. Chemical Reviews, 2004, 104(4): 1719-1757.

[34] Cavalieri A L, Mueller N, Uphues T. Attosecond spectroscopy in condensed matter[J]. Nature, 2007, 449(7165): 1029-1032.

[35] He R, Lin Z S, Zheng T. Energy band gap engineering in borate ultraviolet nonlinear optical crystals: Ab initio studies[J]. Journal of Physics-Condensed Matter, 2012, 24(14): 145503.

[36] Wu M, Ghimire S, Reis D A. High-harmonic generation from bloch electrons in solids[J]. Physical Review A, 2015, 91(4): 043839.

[37] Ghimire S, Reis D A. High-harmonic generation from solids[J]. Nature Physics, 2019, 15(1): 10-16.

[38] Kim S, Jin J, Kim Y-J. High-harmonic generation by resonant plasmon field enhancement[J]. Nature, 2008, 453(7196): 757-760.

[39] Sivis M, Duwe M, Abel B. Extreme-ultraviolet light generation in plasmonic nanostructures[J]. Nature Physics, 2013, 9(5): 304-309.

[40] Han S, Kim H, Kim Y W. High-harmonic generation by field enhanced femtosecond pulses in metal-sapphire nanostructure[J]. Nature Communications, 2016, 7(1): 13105.

[41] Vampa G, Ghamsari B G, Siadat Mousavi S. Plasmon-enhanced high-harmonic generation from silicon[J]. Nature Physics, 2017, 13(7): 659-662.

[42] Liu H, Guo C, Vampa G. Enhanced high-harmonic generation from an all-dielectric metasurface[J]. Nature Physics, 2018, 14(10): 1006-1010.

[43] Liu S, Vabishchevich P P, Vaskin A. An all-dielectric metasurface as a broadband optical frequency mixer[J]. Nature Communications, 2018, 9(1): 2507.

[44] Zhang X C, Xu J. Introduction to THz Wave Photonics[M]. New Yk: Springer, 2010.

[45] Nahata A, Weling A S, Heinz T F. A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling[J]. Applied Physics Letters, 1996, 69(16): 2321-2323.

[46] Wu Q, Litz M, Zhang X C. Broadband detection capability of znte electro-optic field detectors[J]. Applied Physics Letters, 1996, 68(21): 2924-2926.

[47] Yeh K L, Hoffmann M C, Hebling J. Generation of 10 μJ ultrashort terahertz pulses by optical rectification[J]. Applied Physics Letters, 2007, 90(17): 171121.

[48] Blanchard F, Sharma G, Razzari L. Generation of intense terahertz radiation via optical methods[J]. IEEE Journal of Selected Topics in Quantum Electronics, 2011, 17(1): 5-16.

[49] Tani M, Fukasawa R, Abe H. Terahertz radiation from coherent phonons excited in semiconductors[J]. Journal of Applied Physics, 1998, 83(5): 2473-2477.

[50] Luo L, Chatzakis I, Wang J. Broadband terahertz generation from metamaterials[J]. Nature Communications, 2014, 5(1): 3055.

[51] Fang M, Niu K, Huang Z. Investigation of broadband terahertz generation from metasurface[J]. Opt Express, 2018, 26(11): 14241-14250.

[52] Berry M V. Quantal phase-factors accompanying adiabatic changes[J]. Proceedings of the Royal Society of London Series a-Mathematical and Physical Sciences, 1984, 392(1802): 45-57.

[53] Pancharatnam S. Generalized theory of interference and its applications. I. Coherent pensils[J]. Proceedings of the Indian Academy of Sciences, Section A, 1956, 44(5): 247-262.

[54] Li G X, Chen S M, Pholchai N. Continuous control of the nonlinearity phase for harmonic generations[J]. Nature Materials, 2015, 14(6): 607-612.

[55] Wang L, Kruk S, Koshelev K. Nonlinear wavefront control with all-dielectric metasurfaces[J]. Nano Lett, 2018, 18(6): 3978-3984.

[56] Ye W M, Zeuner F, Li X. Spin and wavelength multiplexed nonlinear metasurface holography[J]. Nature Communications, 2016, 7(1): 11930.

[57] Almeida E, Bitton O, Prior Y. Nonlinear metamaterials for holography[J]. Nature Communications, 2016, 7(1): 12533.

[58] Gao Y, Fan Y, Wang Y. Nonlinear holographic all-dielectric metasurfaces[J]. Nano Letters, 2018, 18(12): 8054-8061.

[59] Reineke B, Sain B, Zhao R. Silicon metasurfaces for third harmonic geometric phase manipulation and multiplexed holography[J]. Nano Letters, 2019, 19(9): 6585-6591.

[60] Li Z, Liu W, Li Z. Tripling the capacity of optical vortices by nonlinear metasurface[J]. Laser & Photonics Reviews, 2018, 12(11): 1800164.

[61] Zang W, Qin Z, Yang X. Polarization generation and manipulation based on nonlinear plasmonic metasurfaces[J]. Advanced Optical Materials, 2019, 7(10).

[62] Almeida V R, Barrios C A, Panepucci R R. All-optical control of light on a silicon chip[J]. Nature, 2004, 431(7012): 1081-1084.

[63] Pelc J S, Rivoire K, Vo S. Picosecond all-optical switching in hydrogenated amorphous silicon microring resonators[J]. Opt Express, 2014, 22(4): 3797-3810.

[64] Shcherbakov M R, Vabishchevich P P, Shorokhov A S. Ultrafast all-optical switching with magnetic resonances in nonlinear dielectric nanostructures[J]. Nano Lett, 2015, 15(10): 6985-6990.

[65] Del Fatti N, Bouffanais R, Vallee F. Nonequilibrium electron interactions in metal films[J]. Physical Review Letters, 1998, 81(4): 922-925.

[66] Sun C K, Vallee F, Acioli L. Femtosecond investigation of electron thermalization in gold[J]. Physical Review B, 1993, 48(16): 12365-12368.

[67] Baida H, Mongin D, Christofilos D. Ultrafast nonlinear optical response of a single gold nanorod near its surface plasmon resonance[J]. Physical Review Letters, 2011, 107(5): 057402.

[68] Wurtz G A, Pollard R, Hendren W. Designed ultrafast optical nonlinearity in a plasmonic nanorod metamaterial enhanced by nonlocality[J]. Nature Nanotechnology, 2011, 6(2): 106-110.

[69] Ren M X, Jia B H, Ou J Y. Nanostructured plasmonic medium for terahertz bandwidth all-optical switching[J]. Adv Mater, 2011, 23(46): 5540-5544.

[70] Taghinejad M, Taghinejad H, Xu Z. Hot-electron-assisted femtosecond all-optical modulation in plasmonics[J]. Adv Mater, 2018, 30(9): 1704915.

[71] Caspani L, Kaipurath R P, Clerici M. Enhanced nonlinear refractive index in epsilon-near-zero materials[J]. Phys Rev Lett, 2016, 116(23): 233901.

[72] Alam M Z, De Leon I, Boyd R W. Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region[J]. Science, 2016, 352(6287): 795-797.

[73] Kinsey N, DeVault C, Kim J. Epsilon-near-zero al-doped zno for ultrafast switching at telecom wavelengths[J]. Optica, 2015, 2(7): 616-622.

[74] Clerici M, Kinsey N, DeVault C. Controlling hybrid nonlinearities in transparent conducting oxides via two-colour excitation[J]. Nature Communications, 2017, 8(1): 15829.

[75] Yang Y M, Kelley K, Sachet E. Femtosecond optical polarization switching using a cadmium oxide-based perfect absorber[J]. Nature Photonics, 2017, 11(6): 390-395.

[76] Alam M Z, Schulz S A, Upham J. Large optical nonlinearity of nanoantennas coupled to an epsilon-near-zero material[J]. Nature Photonics, 2018, 12(2): 79-83.

[77] Wang J, Coillet A, Demichel O. Saturable plasmonic metasurfaces for laser mode locking[J]. Light Sci Appl, 2020, 9: 50.

[78] Hughes T W, Minkov M, Williamson I A D. Adjoint method and inverse design for nonlinear nanophotonic devices[J]. ACS Photonics, 2018, 5(12): 4781-4787.

[79] Lin Z, Liang X, Loncar M. Cavity-enhanced second-harmonic generation via nonlinear-overlap optimization[J]. Optica, 2016, 3(3): 233-238.

[80] Lei X, Rahmani M, Yixuan M. Enhanced light-matter interactions in dielectric nanostructures via machine-learning approach[J]. Advanced Photonics, 2020, 2(2): 026003.

[81] Marino G, Solntsev A S, Xu L. Spontaneous photon-pair generation from a dielectric nanoantenna[J]. Optica, 2019, 6(11): 1416.

[82] Keren-Zur S, Tal M, Fleischer S. Generation of spatiotemporally tailored terahertz wavepackets by nonlinear metasurfaces[J]. Nature Communications, 2019, 10(1): 1778.

[83] Sivis M, Taucer M, Vampa G. Tailored semiconductors for high-harmonic optoelectronics[J]. Science, 2017, 357(6348): 303-306.