[1] [1] Armstrong J A, Bloembergen N, Ducuing J, et al.. Interactions between light waves in a nonlinear dielectric[J]. Physical Review, 1962, 127(6): 1918-1939.

[2] [2] Mandelbrot B. Fractals: Form, Chance and Dimension[M]. San Francisco: WH Freeman, 1977.

[5] [5] Sheng Yan, Roppo Vito, Ren Mingliang, et al.. Multi-directional C erenkov second harmonic generation in two-dimensional nonlinear photonic crystal[J]. Optics Express, 2012, 20(4): 3948-3953.

[6] [6] Zhao Xiaohui, Zheng Yuanlin, Ren Huaijin, et al.. Cherenkov second-harmonic Talbot effect in one-dimension nonlinear photonic crystal [J]. Optics Letters, 2014, 39(20): 5885-5887.

[7] [7] Ayoub Mousa, Roedig Philip, Imbrock Jorg, et al.. Cascaded C erenkov third-harmonic generation in random quadratic media[J]. Applied Physics Letters, 2011, 99(24): 241109.

[8] [8] Ren Huaijin, Deng Xuewei, Zheng Yuanlin, et al.. Nonlinear Cherenkov radiation in an anomalous dispersive medium[J]. Physical Review Letters, 2012, 108(22): 223901.

[9] [9] Saltiel Solomon Mois, Sheng Yan, Voloch-Bloch Noa, et al.. C erenkov - type second-harmonic generation in two-dimensional nonlinear photonic structures[J]. IEEE Journal of Quantum Electronics, 2009, 45(11): 1465-1472.

[10] [10] Zhang Y, Gao Z D, Qi Z, et al.. Nonlinear C erenkov radiation in nonlinear photonic crystal waveguides[J]. Physical Review Letters, 2008, 100(16): 163904.

[11] [11] Edwards G J, Lawrence M. A temperature-dependent dispersion equation for congruently grown lithium niobate[J]. Optical and Quantum Electronics, 1984, 16(4): 373-375.

[12] [12] P Ferraro, S Grilli, P De Natale. Ferroelectric Crystals for Photonic Applications[M]. Berlin Heidelberg: Springer Verlag, 2009: 259-284.

[13] [13] Sheng Yan, Wang Wenjie, Shiloh Roy, et al.. C erenkov third-harmonic generation in c(2) nonlinear photonic crystal[J]. Applied Physics Letters, 2011, 98(24): 241114.