[1] ARMSTRONG J A, BLOEMBERGEN N, DUCUING J, et al. Interaction between light waves in a nonlinear dielectric［J］. Physical Review, 1962, 127(6): 1918-1939.

[2] ZHU Shi-ning, ZHU Yong-yuan, QIN Yi-qiang, et al. Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3［J］. Physics Review Letters, 1997, 78(14): 2752-2755.

[3] ZHU Yong-yuan, QIN Yi-qiang, ZHANG Chao, et al. Nolinear optical characterization of the generalized Fibonacci optical superlattices and their ‘isotopes’［J］. Journal of Physics, 2000, 12(50): 10639-10645.

[4] LIFSHITA R, ARIE A, BAHABAD A. Photonic quasi crystals for nonlinear optical frequency conversion［J］. Physics Review Letters, 2005, 95(13): 133901.

[5] CHEN Xian-feng, WU Fei, ZENG Xian-long, et al. Multiple quasi-phase-matching in a nonperiodic domain-inverted optical superlattice［J］. Physics Review A, 2004, 69(1): 013818.

[6] ARBORE M A, MARCO O, FEJER M M. Pulse compression during second-harmonic generation in aperiodic quasi-phase-matching gratings［J］. Optics Letters, 1997, 22(12): 865-867.

[7] LEE Y W, FAN F C, HUANG Y C, et al. Nonlinear multiwavelength conversion based on an aperiodic optical superlattice in lithium niogate［J］. Optics Letters, 2002, 27(24): 2191-2193.

[8] GU Xi, CHEN Xian-feng, CHEN Yu-ping, et al. Narrowband multiple wavelengths filter in aperiodic optical superlattice［J］. Optics Communications, 2004, 237(1): 53-58.

[9] CHEN Li-jun, CHEN Xian-feng, CHEN Yu-ping, et al. Multiple quasi-phase-matching in two-dimentional domain-inverted aperiodic optical superlattice［J］. Physics Letters A, 2006, 349(6): 484-487.

[10] VIDAL X, MARTORED J. Generation of light in media with a random distribution of nonlinear domains［J］. Physics Review Letters, 2006, 97(1): 013902.

[11] FISCHER R, SALTIEL S M, NESSHEV D N, et al. Broadband femtosecond frequency doubling in random media［J］. Applied Physics Letters, 2006, 89(19): 191105.

[12] ZHAO Li-ming, YUE Gue-kuan, ZHOU Yun-song, et al. Effect of pump depletion on second harmonic generation in multiple quasi-phase-matching gratings［J］. Optics Express, 2013, 21(15): 17592-17601.

[13] ZHAO Li-ming, YUE Gue-kuan, ZHOU Yun-song, et al. Effect of the pump depletion itself on the quasi-phase-matching for second-harmonic generation［J］. Europhysics Letters, 2012, 99(3): 34002.

[14] ZHAO Li-ming, YUE Gue-kuan, ZHOU Yun-song, et al. Effect of the pump depletion on the quasi-phase-matching for χ2 nonlinearities［J］. Optics Communication, 2015, 347: 92-97.

[15] RUSTAGI K C, MEHENDALE, MEENAKSHI S. Optical frequency conversion in quasi-phase-matched stacks of nonlinear crystals［J］. IEEE Journal of Quantum Electronics, 1982, 18(6)： 1029-1041.

[16] ZHAO Li-ming, GU Ben-yuan, YANG Guo-zhen, et al. Optimal design of aperiodic optical superlattices for achieving parametric amplification of second harmonic generation with consideration of te depletion of pumping light power［J］. Journal of Nonlinear Optical Physics&Materials, 2005, 14(1): 115-131.

[17] SAPAEV U K. Optimum formation of the response of aperiodic nonlinear crystals in the process of second harmonic generation［J］. Optics and Spectroscopy, 2007, 102(6): 939-943.

[18] BAO Gang, DOBSON D C. Second harmonic generation in nonlinear optical films［J］. Journal of Mathematics Physics, 1994, 35(4): 1622-1633.

[19] XIA Jin-an. Enhancement of second harmonic generation in one-dimensional nonlinear photonic-crystal microcavities［J］.Optics Express, 2009, 17(22): 20069-20077.

[20] REN Ming-liang, LI Zhi-yuan. Exact iterative solution of second harmonic generation in quasi-phase-matched structures［J］. Optics Express, 2010, 18(7): 7288-7299.

[21] BUFFA R, CAVALIERI S. Optimal control of type I second-harmonic generation with ultrashort laser pulses［J］. Journal of the Optical Society of America B, 2000, 17(11): 1901-1905.

[22] SAPAEV U K, ASSANTO G. Femtosecond pulse synthesis by efficient second-harmonic generationin engineered quasi phase matching gratings［J］. Optics Express, 2007, 15(12): 7448-7457.

[23] AVRIEL M. Programming: analysis and methods［M］. Englewoos cliffs, NJ: Prentice-Hall, 1976.

[24] DMITRIEV V G, GURAZDYAN G G, NIKOGOSYAN D N. Handbook of nonlinear optical crystals［M］. Berlin: Spring, 1997.

[25] ZHAO Li-ming, YUE Gue-kuan, ZHOU Yun-song, et al. A promising nonlinear conjugate-gradient method proposed to design nonlinear domains with a disordered distribution［J］. Modern Physics Letters B, 2015, 29(19): 1550030.