[1] [1] Joannopoulos J D, Villeneuve P R, Fan Shanhui. Photonic crystals: putting a new twist on light[J]. Nature, 1997, 386(6621): 143–149.

[2] [2] Benisty H, Weisbuch C, Labilloy D, et al. Optical and con-finement properties of two-dimensional photonic crystals[J]. Journal of Lightwave Technology, 1999, 17(11): 2063–2077.

[3] [3] Srinivasan K, Barclay P E, Painter O, et al. Experimental demonstration of a high quality factor photonic crystal mi-crocavity[J]. Applied Physics Letters, 2003, 83(10): 1915–1917.

[4] [4] Ryu H Y, Kwon S H, Lee Y J, et al. Very-low-threshold photonic band-edge lasers from free-standing triangular photonic crystal slabs[J]. Applied Physics Letters, 2002, 80(19): 3476.

[5] [5] Englund D, Shields B, Rivoire K, et al. Deterministic coupling of a single nitrogen vacancy center to a photonic crystal cavity[J]. Nano Letters, 2010, 10(10): 3922–3926.

[6] [6] McGurn A R. Photonic crystal waveguide weakly interacting with multiple off-channel resonant features formed of Kerr nonlinear dielectric media[J]. Advances in OptoElectronics, 2007, 2007: 92901.

[7] [7] Zayats A V, Smolyaninov I I, Maradudin A A. Nano-optics of surface plasmon polaritons[J]. Physics Reports, 2005, 408(3–4): 131–314.

[8] [8] Pitarke J M, Silkin V M, Chulkov E V, et al. Theory of surface plasmons and surface-plasmon polaritons[J]. Reports on Progress in Physics, 2007, 70: 1–87.

[9] [9] Russell P. Photonic crystal fibers [M]. Beijing: Peking Univer-sity Press, 2013.

[10] [10] Hansen K P. Introduction to nonlinear photonic crystal fi-bers[J]. Journal of Optical and Fiber Communications Reports, 2005, 2(3): 226–254.

[11] [11] Knight J C, Skryabin D V. Nonlinear waveguide optics and photonic crystal fibers[J]. Optics Express, 2007, 15(23): 15365–15376.

[12] [12] Mori D, Baba T. Wideband and low dispersion slow light by chirped photonic crystal coupled waveguide[J]. Optics Ex-press, 2005, 13(23): 9398–9408.

[13] [13] Schulz S A, O'Faolain L, Beggs D M, et al. Dispersion engi-neered slow light in photonic crystals: a comparison[J]. Journal of Optics, 2010, 12(10): 104004.

[14] [14] Shen Hongjun, Tian Huiping, Ji Yuefeng. A novel photonic crystal slab waveguide with dispersionless slow light[J]. Acta Physica Sinica, 2010, 59(4): 2820–2826.

[15] [15] Li Juntao, White T P, O'Faolain L, et al. Systematic design of flat band slow light in photonic crystal waveguides[J]. Optics Express, 2008, 16(9): 6227–6232.

[16] [16] Frandsen L H, Lavrinenko A V, Fage-Pedersen J, et al. Photonic crystal waveguides with semi-slow light and tailored dispersion properties[J]. Optics Express, 2006, 14(20): 9444–9450.

[17] [17] Baba T. Slow light in photonic crystals[J]. Nature Photonics, 2008, 2(8): 465–473.

[18] [18] Pourmand M, Karimkhani A, Moravvej-Farshi M K. Slow light photonic crystal waveguides with large delay-bandwidth product[J]. Optical Engineering, 2016, 55(12): 123108.

[19] [19] Wu Hong, Citrin D S, Jiang Liyong, et al. Polariza-tion-independent slow light in annular photonic crystals[J]. Applied Physics Letters, 2013, 102(14): 141112.

[20] [20] Notomi M, Kuramochi E, Tanabe T. Large-scale arrays of ultrahigh-Q coupled nanocavities[J]. Nature Photonics, 2008, 2(12): 741–747.

[21] [21] Chen Zhigang. Fascinating behavior of optical spatial solitons [J]. Physics, 2001, 30(12): 752–756.

[22] [22] Chen Wei, Mills D L. Gap solitons and the nonlinear optical response of superlattices[J]. Physical Review Letters, 1987, 58(2): 160–163.

[23] [23] Ouzounov D G, Ahmad F R, Müller D, et al. Generation of megawatt optical solitons in hollow-core photonic band-gap fibers[J]. Science, 2003, 301(5640): 1702–1704.

[24] [24] Ouzounov D G, Hensley C J, Gaeta A, et al. Soliton pulse compression in photonic band-gap fibers[J]. Optics Express, 2005, 13(16): 6153–6159.

[25] [25] Chiao R Y. Introduction to spatial solitons[M]. Trillo S, Torru-ellas W. Spatial Solitons. Berlin Heidelberg: Springer, 2001: 1–18.

[26] [26] Duree Jr G, Shultz J L, Salamo G J, et al. Observation of self-trapping of an optical beam due to the photorefractive effect[J]. Physical Review Letters, 1993, 71(4): 533–536.

[27] [27] Chen Zhigang, Segev M, Christodoulides D N. Optical spatial solitons: historical overview and recent advances[J]. Reports on Progress in Physics Physical Society, 2012, 75(8): 086401.

[28] [28] Sukhorukov A A, Kivshar Y S. Spatial optical solitons in non-linear photonic crystals[J]. Physical Review E, 2002, 65(3): 036609.

[29] [29] Gorza S P, Taillaert D, Baets R, et al. Experimental charac-terization of optical-gap solitons in a one-dimensional pho-tonic crystal made of a corrugated semiconductor planar waveguide[J]. Physical Review B, 2006, 74(23): 235327.

[30] [30] Xie Ping, Zhang Zhaoqing, Zhang Xiangdong. Gap solitons and soliton trains in finite-sized two-dimensional periodic and quasiperiodic photonic crystals[J]. Physical Review E, 2003, 67(2): 026607.

[31] [31] Tian Huiping, Yang Daquan, Liu Lingyu, et al. Broadband and low-power bright soliton propagation in line-defect photonic crystal waveguide[J]. Optical Engineering, 2013, 52(5): 055006.

[32] [32] Zeng Jianhua, Malomed B A. Two-dimensional intraband solitons in lattice potentials with local defects and self-focusing nonlinearity[J]. Journal of the Optical Society of America B, 2013, 30(7): 1786–1793.

[33] [33] Inoue K, Oda H, Ikeda N, et al. Enhanced third-order non-linear effects in slow-light photonic-crystal slab waveguides of line-defect.[J]. Optics Express, 2009, 17(9):7206-16.

[34] [34] Monat C, Corcoran B, Ebnali-Heidari M, et al. Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides[J]. Optics Express, 2009, 17(4): 2944– 2953.

[35] [35] Peccianti M, Ferrera M, Razzari L, et al. Subpicosecond optical pulse compression via an integrated nonlinear chirp-er[J]. Optics Express, 2010, 18(8): 7625–7633.

[36] [36] Liao Meisong, Chaudhari C, Qin Guanshi, et al. Tellurite microstructure fibers with small hexagonal core for supercon-tinuum generation[J]. Optics Express, 2009, 17(14): 12174–12182.

[37] [37] Colman P, Husko C, Combrié S, et al. Temporal solitons and pulse compression in photonic crystal waveguides[J]. Nature Photonics, 2010, 4(12): 862–868.

[38] [38] Blanco-Redondo A, Husko C, Eades D, et al. Observation of soliton compression in silicon photonic crystals[J]. Nature Communications, 2014, 5: 3160.

[39] [39] Eisaman M D, André A, Massou F, et al. Electromagnetically induced transparency with tunable single-photon pulses[J]. Nature, 2005, 438(7069): 837–841.

[40] [40] Fleischhauer M, Imamoglu A, Marangos J P. Electromag-netically induced transparency: Optics in coherent media[J]. Reviews of Modern Physics, 2005, 77(2): 633–673.

[41] [41] Boller K J, Imamolu A, Harris S E. Observation of electro-magnetically induced transparency[J]. Physical Review Let-ters, 1991, 66(20): 2593–2596.

[42] [42] Yanik M F, Suh W, Wang Zheng, et al. Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency[J]. Physical Review Letters, 2005, 93(23): 233903.

[43] [43] Xu Qianfan, Sandhu S, Povinelli M L, et al. Experimental realization of an on-chip all-optical analogue to electromag-netically induced transparency[J]. Physical Review Letters, 2006, 96(12): 123901.

[44] [44] Xiao Y F, Gao J, Zou X B, et al. Coupled quantum electro-dynamics in photonic crystal cavities towards controlled phase gate operations[J]. New Journal of Physics, 2008, 10(12): 123013.

[45] [45] Yang Xiaodong, Yu Mingbin, Kwong D L, et al. All-optical analog to electromagnetically induced transparency in multi-ple coupled photonic crystal cavities[J]. Physical Review Letters, 2009, 102(17): 173902.

[46] [46] Kocaman S, Yang X, McMillan J F, et al. Observations of temporal group delays in slow-light multiple coupled photonic crystal cavities[J]. Applied Physics Letters, 2010, 96(22): 221111.

[47] [47] Wang Dan, Wu Jinze, Zhang Junxiang. Optical control of light propagation in photonic crystal based on electromagnetically induced transparency[J]. Chinese Physics B, 2016, 25(6): 064202.

[48] [48] Wang Dawei, Zhou Haitao, Guo Miaojun, et al. Optical diode made from a moving photonic crystal[J]. Physical Review Letters, 2013, 110(9): 093901.

[49] [49] Ooi C H R, Kam C H. Controlling quantum resonances in photonic crystals and thin films with electromagnetically in-duced transparency[J]. Physical Review B, 2010, 81(19): 195119.

[50] [50] Li Yongyao, Malomed B A, Feng Mingneng, et al. Arrayed and checkerboard optical waveguides controlled by the electro-magnetically induced transparency[J]. Physical Review A, 2010, 82(6): 063813.

[51] [51] Yu N E, Ro J H, Cha M, et al. Broadband qua-si-phase-matched second-harmonic generation in MgO-doped periodically poled LiNbO3 at the communications band[J]. Optics Letters, 2002, 27(12): 1046–1048.

[52] [52] Ashihara S, Shimura T, Kuroda K. Group-velocity matched second-harmonic generation in tilted quasi-phase-matched gratings[J]. Journal of the Optical Society of America B, 2003, 20(5): 853–856.

[53] [53] Arie A, Habshoosh N, Bahabad A. Quasi phase matching in two-dimensional quadratic nonlinear photonic crystals[M]. Sibilia C, Benson T M, Marciniak M, et al. Photonic Crystals: Physics and Technology. Milan: Springer, 2008: 45–60.

[54] [54] Ren Mingliang, Ma Dongli, Li Zhiyuan. Experimental demon-stration of super quasi-phase matching in nonlinear photonic crystal[J]. Optics Letters, 2011, 36(18): 3696–3698.

[55] [55] Eshniezov B E, Eshchanov B K, Yusupov D B, et al. On the theory of second-harmonic generation in 2D nonlinear pho-tonic crystals with arbitrary domain structures[J]. Physics of Wave Phenomena, 2016, 24(4): 268–271.

[56] [56] Mattiucci N, Bloemer M J, D'Aguanno G. Phase-matched second harmonic generation at the Dirac point of a 2-D photonic crystal[J]. Optics Express, 2014, 22(6): 6381–6390.

[57] [57] Kopylov D A, Svyakhovskiy S E, Dergacheva L V, et al. Observation of optical second-harmonic generation in po-rous-silicon-based photonic crystals in the Laue diffraction scheme[J]. Physical Review A, 2016, 93(5): 053840.

[58] [58] Genereux F, Leonard S W, van Driel H M, et al. Large bire-fringence in two-dimensional silicon photonic crystals[J]. Physical Review B, 2001, 63(16): 161101.

[59] [59] Mandatori A, Sibilia C, Centini M, et al. Birefringence in one-dimensional finite photonic band gap structure[J]. Journal of the Optical Society of America B, 2003, 20(3): 504–513.

[60] [60] Rivoire K, Lin Ziliang, Hatami F, et al. Second harmonic generation in gallium phosphide photonic crystal nanocavities with ultralow continuous wave pump power[J]. Optics Express, 2009, 17(25): 22609–22615.

[61] [61] Yamada S, Song B S, Jeon S, et al. Second-harmonic gen-eration in a silicon-carbide-based photonic crystal nanocavi-ty[J]. Optics Letters, 2014, 39(7): 1768–1771.

[62] [62] Zeng Y, Roland I, Checoury X, et al. Resonant second harmonic generation in a gallium nitride two-dimensional photonic crystal on silicon[J]. Applied Physics Letters, 2015, 106(8): 081105.

[63] [63] Kleinman D A. Nonlinear dielectric polarization in optical media[J]. Physical Review, 1962, 126(6): 1977–1979.

[64] [64] Pershan P S. Nonlinear optical properties of solids: energy considerations[J]. Physical Review, 1963, 130(3): 919–929.

[65] [65] D'Aguanno G, Centini M, Scalora M, et al. Photonic band edge effects in finite structures and applications to χ2 inter-actions[J]. Physical Review E, 2001, 64(1): 016609.

[66] [66] Shi Jianping, Luo Xiangang, Chen Xunan, et al. Analysis of optical SHG in photonic crystal consisting of centro-symmetric dielectric[J]. Optics Express, 2004, 12(22): 5307–5313.

[67] [67] Luo Xiangang, Ishihara T. Engineered second harmonic generation in photonic-crystal slabs consisting of centro-symmetric materials[J]. Advanced Functional Materials, 2004, 14(9): 905–912.

[68] [68] Galli M, Gerace D, Welna K, et al. Low-power continu-ous-wave generation of visible harmonics in silicon photonic crystal nanocavities[J]. Optics Express, 2010, 18(25): 26613–26624.

[69] [69] Soljai M, Ibanescu M, Johnson S G, et al. Optimal bistable switching in nonlinear photonic crystals[J]. Physical Review E, 2002, 66(5): 055601.

[70] [70] Notomi M, Shinya A, Mitsugi S, et al. Optical bistable switching action of Si high-Q photonic-crystal nanocavities[J]. Optics Express, 2005, 13(7): 2678–2687.

[71] [71] Almeida V R, Lipson M. Optical bistability on a silicon chip[J]. Optics Letters, 2004, 29(20): 2387–2389.

[72] [72] Yang Xiaodong, Husko C, Wong C W, et al. Observation of femtojoule optical bistability involving Fano resonances in high- Q/Vm, silicon photonic crystal nanocavities[J]. Applied Physics Letters, 2007, 91(5): 051113.

[73] [73] Zhang Yong, Li Danping, Zeng Cheng, et al. Ultralow power nonlinear response in an Si photonic crystal nanocavity[J]. IEEE Photonics Journal, 2013, 5(4): 6601409.

[74] [74] Zhang Yong, Li Danping, Zeng Cheng, et al. Low power and large modulation depth optical bistability in an Si photonic crystal L3 cavity[J]. IEEE Photonics Technology Letters, 2014, 26(23): 2399–2402.

[75] [75] Nozaki K, Tanabe T, Shinya A, et al. Sub-femtojoule all-optical switching using a photonic-crystal nanocavity[J]. Nature Photonics, 2010, 4(7): 477–483.

[76] [76] Morita K, Takahashi T, Kanbara T, et al. Large optical Kerr signal of GaAs/AlAs multilayer cavity with InAs quantum dots embedded in strain-relaxed barriers[J]. Physica E: Low-dimensional Systems and Nanostructures, 2010, 42(10): 2505–2508.

[77] [77] Lyubchanskii I L, Dadoenkova N N, Zabolotin A E, et al. Optical bistability in one-dimensional magnetic photonic crystal with two defect layers[J]. Journal of Applied Physics, 2008, 103(7): 07B321.

[78] [78] Hu Xiaoyong, Jiang Ping, Ding Chengyuan, et al. Picosecond and low-power all-optical switching based on an organic photonic-bandgap microcavity[J]. Nature Photonics, 2008, 2(3): 185–189.

[79] [79] Sodagar M, Miri M, Eftekhar A A, et al. Optical bistability in a one-dimensional photonic crystal resonator using a re-verse-biased pn-junction[J]. Optics Express, 2015, 23(3): 2676–2685.

[80] [80] Aas S, Müstecaplolu E. Optical bistability in one-dimensional doped photonic crystals with spontaneously generated coherence[J]. Physical Review A, 2013, 88(5): 053846.

[81] [81] Asadpour S H, Solookinejad G, Panahi M, et al. Managing optical bistability and multistability by embedding quantum dot nanostructures in a photonic crystal[J]. The European Physical Journal Plus, 2016, 131(11): 406.

[82] [82] Moslemi F, Jamshidi-Ghaleh K. Electrically tunable optical bistability based on one-dimensional photonic crystals with nonlinear nanocomposite materials[J]. Journal of Applied Physics, 2016, 119(9): 093101.

[84] [84] Gong Qihuang. Progress of ultrafast low-power photonic crystal all-optical switching[J]. China Basic Science, 2009, 11(1): 13–15.

[85] [85] Nozaki K, Lacraz A, Shinya A, et al. All-optical switching for 10-Gb/s packet data by using an ultralow-power optical bi-stability of photonic-crystal nanocavities[J]. Optics Express, 2015, 23(23): 30379–30392.

[86] [86] Dolev I, Arie A. Three wave mixing of airy beams in a quadratic nonlinear photonic crystals[J]. Applied Physics Letters, 2010, 97(17): 171102.

[87] [87] Kanakis P, Kamalakis T, Sphicopoulos T. Designing photonic crystal waveguides for broadband four-wave mixing applica-tions[J]. Optics Letters, 2015, 40(6): 1041–1044.

[88] [88] Cerjan A, Raman A, Fan Shanhui. Exceptional contours and band structure design in parity-time symmetric photonic crystals[J]. Physical Review Letters, 2016, 116(20): 203902.

[89] [89] Mock A. Parity-time-symmetry breaking in two-dimensional photonic crystals: square lattice[J]. Physical Review A, 2016, 93(6): 063812.

[90] [90] Young A B, Thijssen A C T, Beggs D M, et al. Polarization engineering in photonic crystal waveguides for spin-photon entanglers[J]. Physical Review Letters, 2015, 115(15): 153901.

[91] [91] Matsuda N, Takesue H. Generation and manipulation of entangled photons on silicon chips[J]. Nanophotonics, 2016, 5(3): 440–455.