光诱导铁电畴反转及准相位匹配光学频率变换
|
摘要
随着激光的出现,人们对于光学的认识发生了重要的变化。当一束激光入射到介质以后,会从介质中出射一束或几束有新频率的光束,人们把这种效应称为非线性效应。光学频率变换是激光及非线性光学领域的一个重要分支,如利用材料的非线性效应可实现二次谐波、三次谐波的产生。频率的转换效率依赖于非线性作用过程中的相位匹配因子。利用材料的双折射性质可以实现非线性作用过程中的相位匹配,然而它受材料的双折射性大小、温度、作用波长及偏振等方面的限制。
1962年,Armstrong[1]等人提出通过周期地改变材料的二阶非线性系数可以增强非线性作用过程中的频率转换效率,即准相位匹配技术的产生,这样的晶体结构称为周期极化结构;1993年,Yamada等人[2]首次报道了利用外加电场极化法在铌酸锂晶体中制成了一维的周期极化结构。近年来,人们发现利用激光辐照的方法可以降低铌酸锂晶体极化反转过程中的外加电场。这一发现不仅使得制备周期极化铌酸锂晶体的难度进一步减小,有利于获得比目前更厚的晶体样品,而且为畴结构的制备提供了一种新的方法。
一维周期极化结构往往会限制非线性作用过程中多个频率的变换。1998年,Berger等人[3]提出了非线性光子晶体的概念,把准相位匹配技术扩展到二维的情况,可以同时实现多个频率的变换。基于二阶非线性系数周期变化的非线性光子晶体是一种极具发展前景的光波长变换材料;而根据二阶非线性系数的变化形式,可以实现准周期甚至无序形式的非线性晶体结构。当激光与这些材料相互作用时,可以同时实现多个非线性相互作用的过程,如宽带的倍频及级联三次谐波的产生。
本论文的内容包括以下几个方面:
第一章对材料的二阶非线性效应及二次谐波、三次谐波的产生过程进行了简单的介绍,概括的介绍了准相位匹配技术的原理、制备方法等,并给出了本论文的工作安排。
第二章研究了可见光聚焦辐照下铌酸锂晶体的光诱导铁电畴反转特性。首先简介了铌酸锂晶体的极化特性,畴反转过程及畴结构的观测方法等。随后,我们在实验和理论上对可见光诱导铌酸锂晶体中畴反转电场降低的机理进行了深入的研究和探讨。我们研究了不同掺杂的铌酸锂晶体在514.5nm可见光聚焦辐照下畴反转电场降低的情况。我们发现,对于不同掺杂的晶体,反转电场降低的最大数值基本相同,并且极化畴总是在晶体的-c面首先成核;不同于一般情况下得到的反转畴结构,用激光诱导方法形成的畴结构十分稳定。通过分析,我们建立了空间电荷场的理论模型,合理的解释了激光诱导铌酸锂晶体畴反转的过程。
第三章在实验及理论上研究了无序铁电畴结构的铌酸锶钡(SBN)晶体中二次谐波及级联三次谐波的产生过程。首先,分析模拟了无序畴结构的倒格矢空间,由于倒格矢量的连续性,使得倍频及和频过程中的相位匹配关系可以同时得到满足,从而在空间域及频域大大增加了谐波的调节范围;随后,我们进行了双光束耦合实验,通过测量和分析二次谐波能量在空间的分布形式等,可以实现短脉冲信号的测量,如脉宽、脉冲序列等;最后,我们首次从实验上发现,在无序畴结构的SBN晶体中同样可以实现级联三次谐波的产生,并对它的产生过程及偏振性质等进行了详细分析,在理论上模拟了谐波的产生过程,表明谐波的能量随着传播距离的增加是一个线性增长的过程。
第四章研究了周期及准周期极化结构中非线性的Cerenkov和Raman-Nath衍射。首先,介绍了二次谐波的Cerenkov及Raman-Nath两种非线性衍射形式,着重分析了Cerenkov衍射环的能量分布及偏振特性;随后,我们通过双光束耦合,首次在实验上观察到了多组二次谐波Cerenkov衍射环,包括虚拟Cerenkov衍射环的产生,对它们的空间能量分布、准相位匹配关系及偏振性质等进行了详细分析;最后,我们实验上首次发现了多个三次谐波衍射环的产生,对它们的产生机理、过程、空间能量分布等进行了深入的研究,发现三次谐波衍射环的产生是基于Cerenkov及Raman-Nath型二次谐波的级联效应。
第五章对本论文的工作进行了总结和展望。
As Laser showed up, people's knowledge towards optics was dramatically changed. Nonlinear optics became one of the interest subjects when laser interacts with some media with one or more new frequency generated, known as frequency conversion processes, such as sum frequency, difference frequency effects. The efficiency of frequency conversion depends on the phase matching conditions, which can usually be fulfilled by the Birefringence method, while the materials dependence, temperature, input wavelength, and polarization limit its further applications.
The concept of Quasi-Phase-Matching (QPM) with periodic modulation of the sign of second-order nonlinear susceptibilityχ(2) was originally suggested by Armstrong and the coworker in 1962. Since then, QPM became an issue of material engineering known as periodically poled crystals, which was successfully fabricated in one-dimensional (1D) lithium niobate crystal by electric poling method by M.Yamada in 1993. While, recent year's studies show that the laser-assisted illumination can decrease the poling electric field of lithium niobate crystal which can make the poling process much easier and also can get much thicker samples, therefore the possibility of light-assisted domain engineering opens up a promising method for domain structuring.
1D periodic structure is limited in simultaneous multi-frequency conversion. The conception of nonlinear photonic crystal was proposed by V.Berger in 1998 by employing a two-dimensional (2D) periodic modulation ofχ(2) in plane, known as 2D QPM, which can simultaneously phase match multi-second-order frequency conversion process. Nonlinear photonic crystal is a promising structure in nonlinear frequency conversion, while based on the modulation style ofχ(2), quasi-periodic and even disordered photonic structures can also be achieved, presenting a broad application, such as broadband second-harmonic and cascaded third harmonic generation.
As my PhD thesis, the following contents are included in this paper: In the first chapter, firstly, the second-order nonlinearity is shortly discussed followed by a section about the second- and third-harmonic generation process. Then, it gives a short introduction to the theory and engineering method of QPM. In the end, the general idea about the research subjects in my PhD thesis is presented.
As the second chapter, the focused-light-induced ferroelectric domain inversion in lithium niobate crystal is deeply investigated. Firstly, the general poling properties and poling process of ferroelectric domains in LN and the corresponding detection method are included. Then, with an emphasis, the origin of light-induced decrease in electric field for domain inversion in LiNbO3 crystals with different dopants are invesigated experiementally and theoritically with focused 514.5nm laser beams. It is found that the light-induced maximum values of electric field for domain reversal are almost the same. Besides, inverted domains always first nucleate on the– c surface and behave very strong stability within the illuminated region. Based on these experimental results and analysis, a qualitative space-electric-filed mode is proposed as a reasonable explanation on the light-induced domain reversal process. In the end, a few methods people using for domain fabrication with the assistance of light-illumination was summarized as a promising way in domain engineering.
In the third chapter, the second-harmonic (SH) and third-harmonic (TH) gene- ration process in strontium barium niobate (SBN) crystal with disordered ferroelectric domains is studied. Firstly, the disordered domain structures can provide a continuous reciprocal space to phase match the harmonic generation process, such as SH and TH, resulting in broadband harmonic generation in space and frequency spectrum. Then, based on the two-coupled-beams experiment, by analyzing the intensity distribution of SH in space, the implementation for characterization of short-pulses is demonstrated, such as enabling the estimation of pulse width, pulse sequence and so on; In the end of this chapter, it is stressed that we demonstrated firstly in the experiment that the disorder allows the realizing of broadband TH generation, followed by the analysis of the quasi-phase-matching conditions and polarization properties. The harmonic generation process is studied numerically showing that the harmonic intensity increases with the propagation distance.
In the fourth chapter, the nonlinear Cerenkov and Raman-Nath diffraction is studied in quasi- and periodic nonlinear photonic structures. Firstly, we introduce the conception of these two kinds of nonlinear diffraction and the corresponding phase-matching condition followed by an emphase on the analysis of intensity distribution and polarization properties of Cerenkov diffraction. Then, based on the two-beams-coupled experiment, multi-Cerenkov second harmonic rings are firstly obtained in experiment including the observation of the virtual one, followed by the analysis of the corresponding nonlinear process and the intensity distribution. Finally, it is worth stressed that it is the first time the multi-TH rings can also be generated in the experiment. Based on the detailed analysis of the corresponding nonlinear processes and intensity distribution in space, we demonstrated that the TH generation is a second-order cascaded process based on the Cerenkov and Raman-nath emission of SH generation.
As the last chapter, we give a summarization of the previous work and the prospect for the further research.
1962年,Armstrong[1]等人提出通过周期地改变材料的二阶非线性系数可以增强非线性作用过程中的频率转换效率,即准相位匹配技术的产生,这样的晶体结构称为周期极化结构;1993年,Yamada等人[2]首次报道了利用外加电场极化法在铌酸锂晶体中制成了一维的周期极化结构。近年来,人们发现利用激光辐照的方法可以降低铌酸锂晶体极化反转过程中的外加电场。这一发现不仅使得制备周期极化铌酸锂晶体的难度进一步减小,有利于获得比目前更厚的晶体样品,而且为畴结构的制备提供了一种新的方法。
一维周期极化结构往往会限制非线性作用过程中多个频率的变换。1998年,Berger等人[3]提出了非线性光子晶体的概念,把准相位匹配技术扩展到二维的情况,可以同时实现多个频率的变换。基于二阶非线性系数周期变化的非线性光子晶体是一种极具发展前景的光波长变换材料;而根据二阶非线性系数的变化形式,可以实现准周期甚至无序形式的非线性晶体结构。当激光与这些材料相互作用时,可以同时实现多个非线性相互作用的过程,如宽带的倍频及级联三次谐波的产生。
本论文的内容包括以下几个方面:
第一章对材料的二阶非线性效应及二次谐波、三次谐波的产生过程进行了简单的介绍,概括的介绍了准相位匹配技术的原理、制备方法等,并给出了本论文的工作安排。
第二章研究了可见光聚焦辐照下铌酸锂晶体的光诱导铁电畴反转特性。首先简介了铌酸锂晶体的极化特性,畴反转过程及畴结构的观测方法等。随后,我们在实验和理论上对可见光诱导铌酸锂晶体中畴反转电场降低的机理进行了深入的研究和探讨。我们研究了不同掺杂的铌酸锂晶体在514.5nm可见光聚焦辐照下畴反转电场降低的情况。我们发现,对于不同掺杂的晶体,反转电场降低的最大数值基本相同,并且极化畴总是在晶体的-c面首先成核;不同于一般情况下得到的反转畴结构,用激光诱导方法形成的畴结构十分稳定。通过分析,我们建立了空间电荷场的理论模型,合理的解释了激光诱导铌酸锂晶体畴反转的过程。
第三章在实验及理论上研究了无序铁电畴结构的铌酸锶钡(SBN)晶体中二次谐波及级联三次谐波的产生过程。首先,分析模拟了无序畴结构的倒格矢空间,由于倒格矢量的连续性,使得倍频及和频过程中的相位匹配关系可以同时得到满足,从而在空间域及频域大大增加了谐波的调节范围;随后,我们进行了双光束耦合实验,通过测量和分析二次谐波能量在空间的分布形式等,可以实现短脉冲信号的测量,如脉宽、脉冲序列等;最后,我们首次从实验上发现,在无序畴结构的SBN晶体中同样可以实现级联三次谐波的产生,并对它的产生过程及偏振性质等进行了详细分析,在理论上模拟了谐波的产生过程,表明谐波的能量随着传播距离的增加是一个线性增长的过程。
第四章研究了周期及准周期极化结构中非线性的Cerenkov和Raman-Nath衍射。首先,介绍了二次谐波的Cerenkov及Raman-Nath两种非线性衍射形式,着重分析了Cerenkov衍射环的能量分布及偏振特性;随后,我们通过双光束耦合,首次在实验上观察到了多组二次谐波Cerenkov衍射环,包括虚拟Cerenkov衍射环的产生,对它们的空间能量分布、准相位匹配关系及偏振性质等进行了详细分析;最后,我们实验上首次发现了多个三次谐波衍射环的产生,对它们的产生机理、过程、空间能量分布等进行了深入的研究,发现三次谐波衍射环的产生是基于Cerenkov及Raman-Nath型二次谐波的级联效应。
第五章对本论文的工作进行了总结和展望。
As Laser showed up, people's knowledge towards optics was dramatically changed. Nonlinear optics became one of the interest subjects when laser interacts with some media with one or more new frequency generated, known as frequency conversion processes, such as sum frequency, difference frequency effects. The efficiency of frequency conversion depends on the phase matching conditions, which can usually be fulfilled by the Birefringence method, while the materials dependence, temperature, input wavelength, and polarization limit its further applications.
The concept of Quasi-Phase-Matching (QPM) with periodic modulation of the sign of second-order nonlinear susceptibilityχ(2) was originally suggested by Armstrong and the coworker in 1962. Since then, QPM became an issue of material engineering known as periodically poled crystals, which was successfully fabricated in one-dimensional (1D) lithium niobate crystal by electric poling method by M.Yamada in 1993. While, recent year's studies show that the laser-assisted illumination can decrease the poling electric field of lithium niobate crystal which can make the poling process much easier and also can get much thicker samples, therefore the possibility of light-assisted domain engineering opens up a promising method for domain structuring.
1D periodic structure is limited in simultaneous multi-frequency conversion. The conception of nonlinear photonic crystal was proposed by V.Berger in 1998 by employing a two-dimensional (2D) periodic modulation ofχ(2) in plane, known as 2D QPM, which can simultaneously phase match multi-second-order frequency conversion process. Nonlinear photonic crystal is a promising structure in nonlinear frequency conversion, while based on the modulation style ofχ(2), quasi-periodic and even disordered photonic structures can also be achieved, presenting a broad application, such as broadband second-harmonic and cascaded third harmonic generation.
As my PhD thesis, the following contents are included in this paper: In the first chapter, firstly, the second-order nonlinearity is shortly discussed followed by a section about the second- and third-harmonic generation process. Then, it gives a short introduction to the theory and engineering method of QPM. In the end, the general idea about the research subjects in my PhD thesis is presented.
As the second chapter, the focused-light-induced ferroelectric domain inversion in lithium niobate crystal is deeply investigated. Firstly, the general poling properties and poling process of ferroelectric domains in LN and the corresponding detection method are included. Then, with an emphasis, the origin of light-induced decrease in electric field for domain inversion in LiNbO3 crystals with different dopants are invesigated experiementally and theoritically with focused 514.5nm laser beams. It is found that the light-induced maximum values of electric field for domain reversal are almost the same. Besides, inverted domains always first nucleate on the– c surface and behave very strong stability within the illuminated region. Based on these experimental results and analysis, a qualitative space-electric-filed mode is proposed as a reasonable explanation on the light-induced domain reversal process. In the end, a few methods people using for domain fabrication with the assistance of light-illumination was summarized as a promising way in domain engineering.
In the third chapter, the second-harmonic (SH) and third-harmonic (TH) gene- ration process in strontium barium niobate (SBN) crystal with disordered ferroelectric domains is studied. Firstly, the disordered domain structures can provide a continuous reciprocal space to phase match the harmonic generation process, such as SH and TH, resulting in broadband harmonic generation in space and frequency spectrum. Then, based on the two-coupled-beams experiment, by analyzing the intensity distribution of SH in space, the implementation for characterization of short-pulses is demonstrated, such as enabling the estimation of pulse width, pulse sequence and so on; In the end of this chapter, it is stressed that we demonstrated firstly in the experiment that the disorder allows the realizing of broadband TH generation, followed by the analysis of the quasi-phase-matching conditions and polarization properties. The harmonic generation process is studied numerically showing that the harmonic intensity increases with the propagation distance.
In the fourth chapter, the nonlinear Cerenkov and Raman-Nath diffraction is studied in quasi- and periodic nonlinear photonic structures. Firstly, we introduce the conception of these two kinds of nonlinear diffraction and the corresponding phase-matching condition followed by an emphase on the analysis of intensity distribution and polarization properties of Cerenkov diffraction. Then, based on the two-beams-coupled experiment, multi-Cerenkov second harmonic rings are firstly obtained in experiment including the observation of the virtual one, followed by the analysis of the corresponding nonlinear process and the intensity distribution. Finally, it is worth stressed that it is the first time the multi-TH rings can also be generated in the experiment. Based on the detailed analysis of the corresponding nonlinear processes and intensity distribution in space, we demonstrated that the TH generation is a second-order cascaded process based on the Cerenkov and Raman-nath emission of SH generation.
As the last chapter, we give a summarization of the previous work and the prospect for the further research.
引文
1 Armstrong.J.A, Bloembergen.N, Ducuing J, et al. Interaction between light waves in a nonlinear dielectric. Physical Review B, 1962, 127: 1918～1939.
2 Yamada.M, Nada.N, Saitoh.M, et al. First-order quasi-phase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second-harmonic generation. Applied Physics Letters, 1993, 62: 435～436.
3 V.Berger. Nonlinear photonic crystals. Physics Review Letters, 1998, 81: 4136～4139.
4 A.Chowdhury, S.Hagness, C.Susan, et al. Simultaneous optcial wavelength interchange with a two-dimensional second-order nonlinear photonic crystal. Optics Letters, 2000, 25: 832～834.
5 N.G.R.Broderick, G.W.Ross, H.L.Offerhaus, et al. Hexagonally Poled Lithium Niobate: A Two-Dimensional Nonlinear Photonic Crystal. Physical Review Letters, 2000, 84: 4345～4348.
6 S.Saltiel, Y.Kivshar. Phase matching in nonlinearχ(2) photonic crystals. Optics Letters. 2000, 25: 1204～1206.
7 L.H.Peng, C.C.Hsu, Jimmy.Ng, et al. Wavelength tunability of second-harmonic generation from two-dimensionalχ(2) nonlinear photonic crystals with a tetragonal lattice structure. Applied Physics Letters, 2004, 84: 3250～3252.
8 L.H.Peng, C.C.Hsu, Y.C.Shih. Second-harmonic green generation from two- dimmensionalχ(2) nonlinear photonic crystal with orthorhombic lattice structrue, Applied Physics Letters, 2003, 83: 3447～3449.
9 Shi-ning Zhu, Yong-yuan Zhu, Nai-ben Ming. Quasi-Phase-Matched Third-Harmonic Generation in a Quasi-Periodic Optical Superlattice. Science, 1997, 278: 843～846.
10 K.Fradkin-Kashi, A.Arie, P.Urenski, et al. Multiple Nonlinear Optical Interactions with Arbitrary Wave Vector Differences. Physcis Review Letters, 2002, 88: 023903.
11 R.Lifshitz, A.Arie, A.Bahabad. Photonic Quasicrystals for Nonlinear Optical Frequency Conversion. Physics Review Letters, 2005, 95: 133901.
12 Y. Sheng, J. Dou, B. Cheng, et al. Effective generation of red-green-blue laser in a two-dimensional decagonal photonic superlattice. Applied Physics B: Lasers and Optics, 2007, 87: 603～606.
13 Yan Sheng, Junhong Dou, Boqin Ma, et al. Broadband efficient second harmonic generation in media with a short-range order. Applied Physics Letters, 2007, 91: 011101～011103.
14 Yan Sheng, Kaloian Koynov, Daozhong Zhang. Colinear second harmonic generation of 20 wavelengths in a single two-dimensional decagonal nonlinear photonic quasi-crystal. Optics Communiations, 2009, 282: 3602～3606.
15 J.S.Shirk, A.Rosenberg. Photonic Crystals: Intensity-dependent transmission protects sensors.Laser Focus World, 2000, 36: 121～122.
16 B. G. Levi. Nobel Prize Honors Kohn and Pople for Methods of Quantum Chemistry. Phys.Today, 1999, 52: 20～22.
17 F.Charra, F.Kajzar, J.M.Nunzi, et al. Light-induced second-harmonic generation in azo-dye polymers. Optics Letters, 1993, 18: 941～943.
18 Bin Xu, Nai-Ben Ming. Experimental observations of bistability and instability in a two-dimensional nonlinear optical superlattice. Physics Review Letters, 1993, 71: 3959～3963.
19 Bin Xu, Nai-Ben Ming. Optical bistability in a two-dimensional nonlinear superlattice. Physcis Review Letters, 1993, 71: 1003～1006.
20 Yun-Lin Chen, Jing-Jun Xu, Xiao-Jun Chen, et al. Domain reversion process in near-stoichiometric LiNbO3 Crystals. Optics Communiations, 2001, 188: 359～364.
21 L. E. Myers, R. C. Eckardt, M. M. Fejer, et al. Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3. Journal of the Optical Society of America B, 1995, 12: 2102～2116.
22 Svhur V Y, Batchko R G,Rumyantsev E L, et al. Domain engineering: periodic domain patterning in lithium niobate. Proc 11th ISAF, Piscataway, NJ: IEEE, 1999, 399～406.
23 Yamada M and Saitoh M. Fabrication of a periodically poled laminar domain structure with a pitch of a few micrometers by applying an external electric field. Journal of Applied Physics, 1998, 84: 2199～2206.
24 L.Arizmendi. Photonic applications of lithium niobate crystals. Physica Status Solidi (a), 2004, 201: 253～283.
25 R.Batchko, V.Shur, M.Fejer, et al. Backswitch poling in lithium niobate for high-fidelity domain patterning and efficient blue light generation. Applied Physics Letters, 1999, 75: 1673～1675.
26 C. E. Valdivia, C. L. Sones, S. Mailis, et al. Ultrashort-Pulse Optically-Assisted Domain Engineering in Lithium Niobate. Ferroelectrics, 2006, 340: 75～82.
27 Ballman A A. Growth of Piezoelectric and Ferroelectric Materials by the CzochraIski Technique. Journal of American Ceramic Society, 1965, 48:112～113.
28 Lerner P,Legras C and Dumas J P.Stoechiométrie des monocristaux de métaniobate de lithium.Journal of Crystal Growth, 1968, 3-4: 231～235.
29 Wong K K. Properties of Lithium Niobate. London:INSPEC. The Institute of Electrical Engineers, 2002.
30 HouéM, Townsend P D. An introduction to methods of periodic poling for second-harmonic generation. Journal of Physics D: Applied Physics, 1995, 28: 1747～1763.
31 Abernethy J A, Gawith C B E, Eason R W, et al. Demonstration and optical characteristics of electro-optic Bragg modulators in periodically poled lithium niobate in the near-infrared. Applied Physics Letters, 2002, 81: 2514～2516.
32 Coppola G, Ferraro P, Iodice M, et al. Visualization of optical deflection and switchingoperations by a domain engineered-based LiNbO3 electro-optic device. Optics Express, 2003, 11: 1212～1222.
33 Broderick N G R, Ross G W, Offerhaus H L, et al. Hexagonally Poled Lithium Niobate: A Two-Dimensional Nonlinear Photonic Crystal. Physics Review Letters, 2000, 81: 4345～4348.
34 Nassau K, Levinstein H J, Loiacono G M. The Domain Structure and Etching of Ferroelectric Lithium Niobate. Applied Physics Letters, 1965, 6: 228～229.
35 Li M, Wang J, Zhuang L, et al. Fabrication of circular optical structures with a 20 nm minimum feature size using nanoimprint lithography, Applied Physics Letters, 2000, 76: 673～675.
36 Rothschild M, Bloomstein T M, Fedynyshyn T H, et al. Recent Trends in Optical Lithography. Lincoln Laboratory Journal, 2003, 14: 221～236.
37 Sones C L. Domain Engineering Techniques and Devices in Lithium Niobate: [dissertation].Southampton: University of Southampton, 2003.
38 Agronin A, Rosenwaks Y, Rosenman G. Ferroelectric domain reversal in LiNbO3 crystals using high-voltage atomic force microscopy. Applied Physics Letters, 2004, 85: 452～454.
39 Rosenwaks Y, Dahan D, M Molotskii, et al. Ferroelectric domain engineering using atomic force microscopy tip arrays in the domain breakdown regime. Applied Physics Letters, 2005, 86: 012909～012911.
40 Nassau K, Levinstein H J. Ferroelectric Behavior of Lithium Niobate. Applied Physics Letters, 1965, 7: 69～70.
41 Gopalan V, Cupta M C. Origin and Characteristics of Internal Fields in LiNbO3 Crystals. Ferroelectrics, 1997, 198: 49～59.
42 Gopalan V, Mictchell T E, Sickafus K E. Switching kinetics of 180°domains in congruent LiNbO3 and LiTaO3 crystals. Solid State Communications, 1999, 109: 111～117.
43 Gopalan V, Gupta M C. Origin of internal field and visualization of 180°domains in congruent LiTaO3 crystals. Journal of Applied Physics, 1996, 80: 6099～6106.
44 Kim S, Gopalan V, Kitamura K, et al. Domain reversal and nonstoichiometry in lithium tantalite. Journal of Applied Physics, 2001, 90: 2949～2963.
45 Shur V Y. Kinetics of ferroelectric domains: Application of general approach to LiNbO3 and LiTaO3. Journal of Materials Science. 2006, 41: 199~210.
46 Ueda T, Takai Y, Shimizu R, et al. Cross-Sectional Transmission Electron Microscopic Observation of Etch Hillocks and Etch Pits in LiTaO3 Single Crystal. Japanese Journal of Applied Physics Part I, 2000, 39: 1200~1202.
47 Ohnishi N, Lizuka T. Etching study of microdomains in LiNbO3 single crystals. Journal of Applied Physics, 1974, 46: 1063~1067.
48 Shur V Y, Nikolaeva E V, Shishkin E I, et al. Polarization reversal in congruent and stoichiometric lithium tantalite. Applied Physics Letters, 2001, 79 : 3146~3148.
49 Gopalan V, Jia Q X, Mitchell T E. In situ video observation of 180°domain kinetics incongruent LiNbO3 crystals. Applied Physics Letters, 1999, 75: 2482~2484.
50 Kim S, Gopalan V, Gruverman A. Coercive fields in ferroelectrics: A case study in lithium niobate and lithium tantalite. Applied Physics Letters, 2002, 80: 2740~2742.
51 Wengler M C, Müller M, Soergel E, et al. Poling dynamics of lithium niobate crystals. Appl Phys B, 2003, 76:393～396.
52 Zheng Y,Shi E,Wang S,et al. Domain structures and etching morphologies of lithium niobate crystals with different Li contents grown by TSSG and double crucible Czochralski method. Crystla Research and Crystal Technology, 2004, 39: 387～395.
53 Webjorn J. Structural influence of proton exchange on domain-inverted lithium niobate revealed by means of selective etching. Journal of Lightwave Technology, 1993, 11: 589～594.
54 Nassau K, Levinstein H J, Loiacono G M. Ferroelectric lithium niobate. 1. Growth, domain structure, dislocations and etching. Journal of Physics and Chemistry of Solids, 1966, 27: 983～988.
55 Sones C L, Mailis S, Brocklesby W S, et al. Differential etch rates in z-cut LiNbO3 for variable HF/HNO3 concentrations. Journal of Material Chemistry, 2002, 12: 295～298.
56 H.D.Liu, Y.F.Kong, Q.Hu, et al. Light-Induced Domian Inversion in Mg-doped near Stoichiometric Lithium Niobate Crystals. Chinese Physics Letters, 2007, 24: 1720～1723.
57 M.C.Wengler, M.Muller, E.Soergel, et al. Poling dynamics of lithium niobate crystals. Applied Physics B: Laser and Optics, 2003, 76: 393～396.
58 Missey M, Russell S, Dominic V, et al. Real-time visualization of domain formation in periodically poled lithium niobate. Optics Express, 2000, 6: 186～195.
59 Grilli S, P Ferraro, M Paturzo, et al. In-situ visualization, monitoring and analysis of electric field domain reversal process in ferroelectric crystals by digital holography. Optics Express, 2004, 12: 1832～1842.
60 Grilli S, Ferraro P, Nicola S De, et al. Investigation on reversed domain structures in lithium niobate crystals patterned by interference lithography. Optics Express, 2003, 11: 392～405.
61 Bermúdez V, Huang L, Hui D, et al. Role of stoichiometric point defect in electric-field- poling lithium niobate. Applied Physics A, 2000, 70: 591～594.
62 Chen Y, Yan W, Guo J, et al. Effect of Mg concentration on the domain reversal of Mg-doped LiNbO3. Applied Physics Letters, 2005, 87: 212904.
63 Kumaragurubaran S, Takekawa S, Nakamura M, et al. Polarization Switching and Defect Structure in Pure and MgO Doped Near-Stoichiometric LiNbO3 Crystals. Ferroelectrics, 2005, 326: 113～116.
64 Ishizuki H, Shoji I, Taira T. Periodical poling characteristics of congruent MgO:LiNbO3 crystals at elevated temperature. Applied Physics Letters, 2003, 82: 4062～4064.
65 Eggert H A, Hecking B, Buse K. Electrical fixing in near-stoichiometric lithium niobate crystals. Optics Letters, 2004, 29: 2476～2478.
66 Eggert H A, Kalkum F, Hecking B, et al. Optimization of electrical fixing in near-stoichiometric iron-doped lithium niobate crystals. Journal of the Optical Society of America B, 2005, 22: 2553～2559.
67 Fujimura M, Sohmura T, Suhara T. Fabrication of domain-inverted gratings in MgO:LiNbO3 by applying voltage under ultraviolet irradiation through photomask at room temperature. Electronics Letters, 2003, 39: 719～721.
68 M.Müller, E.Soerger, K.Buse. Influence of ultraviolet illumination on the poling characteristics of lithium niobate crystals. Applied Physics Letters, 2003, 83: 1824～1826.
69 Wengler M C, Fassbender B, Soergel E, et al. Impact of ultraviolet light on coercive field, poling dynamics and poling quality of various lithium niobate crystals from different sources. Journal of Applied Physics, 2004, 96: 2816～2820.
70 Wengler M C, Heinemeyer U, Soergel E, et al. Ultraviolet light-assisted domain inversion in magnesium-doped lithium niobate crystals. Journal of Applied Physics, 2005, 98: 064104.
71 Sones C L, Wengler M C, Valdivia C E, et al. Light-induced order-of-magnitude decrease in the electric field for domain nucleation in MgO-doped lithium niobate crystals. Applied Physics Letters, 2005, 86: 212901.
72 LI Da-Shan, LIU De-An, ZHI Ya-Nan, et al. Red Laser-Induced Domain Inversion in MgO-Doped Lithium Niobate Crystals. Chiness Physics Letters, 2007, 24: 971～974.
73 Zhi Y, Liu D, Qu W, et al. Wavelength dependence of light-induced domain nucleation in MgO-doped congruent LiNbO3 crystal. Applied Physics Letters, 2007, 90: 042904.
74 Zhi.Y, Liu.D, Yan.A, et al. Primary and secondary threshold intensities of ultraviolet-laser-induced domain nucleation in nearly stoichiometric LiTaO3. Applied Physics Letters, 2008, 92: 082904.
75 V.Dierolf, C.Sandmann. Direct-write method for domain inversion patterns in LiNbO3. Applied Physics Letters, 2004, 84: 3987～3989.
76 M.Müller, E.Soergel, K.Buse. Influence of ultraviolet illumination on the poling characteristics of lithium niobate crystals. Applied Physics Letters, 2003, 83: 1824～1826.
77 W.Wang, Y.Kong, H.Liu, et al. Light-induced domain reveral in doped lithium niobate crystals. Journal of Applied Physics, 2009, 105: 043105.
78 Y.Kong, S.Liu, Y.Zhao, et al. Highly optical damage resistant crystal: Zirconium–oxide -doped lithium niobate. Applied Physcis Letters, 2007, 91: 081908.
79 F.Liu, Y.Kong, W.Li, et al. High resistance against ultraviolet photorefraction in zirconium-doped lithium niobate crystals. Optics Letters, 2010, 35: 10～12.
80 W.Yan, L.Shi, H.Chen, et al. Investigations on the UV photorefractivity of LiNbO3:Hf. Optics Letters, 2010, 35: 601～603.
81 X.Li, Y.Kong, H.Liu, et al. Origin of the generally defined absorption edge of non-stoichiometric lithium niobate crystals, Solid State Communications. 2007, 141: 113～116.
82 H.Zeng, Y.Kong, T.Tian, et al. Transcription of domain patterns in near-stoichiometric magnesium-doped lithium niobate. Applied Physics Letters, 2010, 97: 201901.
83 H.Zeng, Y.Kong, H.Liu, et al. Light-induced superlow electric field for domian reversal in near-stoichiometric magnesium-doped lithium niobate. Journal of Applied Physics, 2010, 107: 063514.
84 Baudrier-Raybaut, M.Ha?dar, R..Kupecek, et al. Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials. Nature , 2004, 432: 374～376.
85 Sergey E. Skipetrov. Disorder is the new order. Nature (London), 2004, 432: 285～286.
86 Pablo.Molina, Maria.de, Luisa.E.Bausa. Strontium Barium Niobate as a Multifunctional Two-Dimensional Nonliear "photonic Glass". Advanced Functional Materials, 2008, 18: 709～715.
87 T.Granzow, T.Woike, M.Wohlecke, M.Imlau, W.Kleemann. Polarization-Based Adjustable Memory Behavior in Relaxor Ferroelectrics. Physical Review Letters, 2002, 89: 127601-4～127601-4.
88 Granzow T, Woike T, W?hlecke.M, et al. Polarization-Based Adjustable Memory Behavior in Relaxor Ferroelectrics. Physical Review Letters, 2002, 89: 127601.
89 Tian L, Scrymgeour D A, Sharan Alok, et al. Anomalous electro-optic effect in Sr0.6Ba0.4Nb2O6 single crystals and its application in two-dimensional laser scanning. Applied Physics Letters, 2003, 83: 4375～4377.
90 A.A.Ballman, H.Brown. The growth and properties of stronitium barium metaniobate Sr1-xBaxNb2O6 a tungsten bronze ferroelectric. Journal of Crystal Growth, 1967, 1:311～314.
91 J.C.Brice, O.F.Hill, P.A.C.Whiffin, et al. The Czochralski growth of barium stronitium niobate crystals. Journal of Crystal Growth, 1971, 10: 133～138.
92 J.J.Romero, D.Jaque, J.Garcia.Sole, et al. Diffuse multiself-frequency conversion processes in the blue and green by quasicylindirical ferroelectric domians in Nd3+:Sr0.6Ba0.4(NbO3)2 laser crystal. Applied Physics Letters, 2001, 78:1961～1963.
93 P.B.Jameson, S.C.Abrahams, J.L.Bernshtein. Ferroelectric Tungsten Bronze– Type Crystal Structures. I. Barium Strontium Niobate Ba0.27Sr0.75Nb2O5.78. Journal of Chemistry Physics, 1968, 42: 5048～5057.
94 R.Fischer, S.M.Saltiel, D.N.Neshev, et al. Broadband femtosecond frequency doubling in random media. Applied Physics Letters, 2006, 89: 191105.
95 V.Roppo, W.Wang, K.Krolikowski, et al. The role of ferroelectric domain structure in second harmonic generation in random quadratic media. Optics Express, 2010, 18: 4012～4022.
96 G.Dolino. Effects of Domian Shapes on Second-Harmonic Scattering in Triglycine Sulfate. Physical Review B, 1972, 6: 4025～4035.
97 Y.Le.Grand, D.Rouede, C.Odin, et al. Second-harmonic scattering by domains in RbH2PO4. Ferroelectrics. 2001, 200: 249～260.
98 Jose Trull, Crina Cojocaru, Robert Fischer, et al. Second-harmonic parametric scatteriing in ferroelectric crystals with disordered nonlinear domain structure. Optics Express, 2007, 15:15868～15877.
99 M.Horowitz, A.Bekker, B.Fisher. Broadband second-harmonic generation in SrxBa1-xNb2O6 by spread spectrum phase matching with controllable domain gratings. Applied Physics Letters, 1993, 62: 2619～2622.
100 S.Kawai, T.Ogawa, H.S.Lee, et al. Second-harmonic generation from needlike ferroelectric domians in Sr0.6Ba0.4Nd2O6 single crystal. Applied Physics Letter, 1998, 73: 768～770.
101 K.A.Kuznetsov, G.Kh.Kitaeva, A.V.Shevlyuga, et al. Second Harmonic Generation in a Strontium Barium Niobate Crystal with a Random Domain Structure. JETP Letters (Letters to Journal of Experimental and Theoretical Physics), 2008, 87: 98～102.
102 Arthur R. Tunyagi, Michael Ulex, Klaus Betzler. Noncollinear Optical Frequency Doubling in Strontium Barium Niobate. Physical Review Letters, 2003, 90: 243901.
103 Authur R.Tunyagi. Non-Colinear Second Harmonic Generation in Strontium Barium Niobate. PhD thesis, Fachbereich Physik, Universitat Osnabruck, Germany, 2004.
104 D.J.Kane, R.Trebino. Single-shot measurement of the intensity and phase of an arbitrary ultrashort pulse by using frequency-resolved optical grating. Optics Letters, 1993, 18: 823～825.
105 C.Iaconis, I.A.Walmsley. Spectral phase interferometry for direct electric-filed reconstruction of ultrashort optical pulses. Optics Letters, 1998, 23:792～793.
106 P.O'Shea, M.Kimmel, X.Gu, et al. Highly simplified device for ultrashourt-pulse measurement, Optics Letters, 2001, 26: 932～934.
107 Vito Roppo, David Dumay, Jose Trull, et al. Planar second-harmonic generation with noncolinear pumps in disordered media. Optcis Express, 2008, 16: 14192～14199.
108 Robert Fischer, Dragomir N.Neshev, Solomom M.Saltiel, et al. Monitoring ultrashort pulses by transverse frequency doubling of counterpropagating pulses in random media. Applied Physics Letters, 2007, 91:031104.
109 J.Trull, S.Saltiel, V.Roppo, C.Cojocaru, et al. Characterization of femtosecond pulses via transverse second-harmonic generation in random nonlinear media. Applied Physcis B: Laser and Optics, 2009, 95: 609～615.
110 J.Janszky, G.Corradi, R.N.Gyuzalian. On a possibility of analysing the temporal charateristics of short pulses. Optics Communications. 1977, 23: 293～298.
111 S.M.Saltiel, S.D.Savov, I.V.Tomov, et al. Subnanosecond pulse duration measurements by noncolinear second harmonic generation. Optics Communiations, 1981, 38: 443～447.
112 D.J.Kane, R.Trebino. Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating. IEEE Journal of Quantum Electronics, 1993, 29:571.
113 C.Iaconis, I.A.Walmsley. Self-referencing spectral intererometry for measuring ultrashourt optical pulses. IEEE Journal of Quantum Electrionics, 1999, 35: 501～509.
114 J.Hebling. Derivation of the pulse front tilt caused by angular disperson. Optical and Quantum Electrionics, 1996, 28: 1759～1763.
115 Zs.Bor, B.Racz. Group velocity dispersion in prisms and its application to pulse compressionand travelling-wave excitation. Optcis Communications, 1985, 54: 165～170.
116 W.Wang, V.Roppo, K.Kalinowski, et al. Third-harmonic generation via broadband cascading in disordered quadratic nonlinear media. Optics Express, 2009, 17: 20117～20123.
117 W.Wang, K.Kalinowski, V.Roppo, et al. Second- and third-harmonic parametric scattering in disordered quadratic media. Journal of Physics B: Atomic, Molecular and Optical Physics, 2010, 43: 215404.
118 B.F.Johnston, P.Dekker, M.J.Withford, et al. Simultaneous phase matching and internal interference of two second-order nonlinear parametric process. Optics Express, 2006, 14:11756～11765.
119 Th.Woike, T.Granzow, U.Dorfler, et al. Refractive Indices of Congruently Melting Sr0.61Ba0.39Nb2O6. Physica Status Solidi(a), 2001, 186: R13～R15.
120 P.A.Cerenkov. Visible Radiation Produced by Electrons Moving in a Medium with Velocities Exceeding that of Light. Physical Review. 1937, 52: 378～379.
121 D.H.Auston. Subpicosecond electro-optic shock waves. Applied Physics Letters, 1983, 43: 713～715.
122 M.Bass, P.A.Franken, J.F.Ward, et al. Optical Rectification. Physical Review Letters, 1962, 9: 446～448.
123 K.H.Yang, P.L.Richards, Y.R.Shen. Generation of Far-Infrared Radiation by Picosecond Light Pulses in LiNbO3. Applied Physics Letters, 1971, 19: 320～324.
124 D.H.Auston, K.P.Cheung, J.A.Valdmanis, et al. Cherenkov Radiation from Femtosecond Optical Pulses in Electro-Optic Media. Physical Review Letters, 1984, 53: 1555～1559.
125 M.G.Moharam, L.Young. Criterion for Bragg and Raman-Nath diffraction regimes. Applied Optics, 1978, 17: 1757～1759.
126 M.G.Moharam, T.K.Gaylord, R.Magnusson. Criteria for Raman-Nath regime diffraction by phse gratings. Optics Communications, 1980, 32: 19～23.
127 S.Saltiel, D.Neshev, W.Krolikowski, et al. Generation of Second-Harmonic Conical Waves Via Nonlinear Bragg Diffraction. Physical Review Letters. 2008, 100: 103902.
128 Solomon M.Saltiel, Dragomir N.Neshev, Wieslaw Krolikowski, et al. Multiorder nonlinear diffraction in frequency doubling processes. Optics Letters, 2009, 34: 848:850.
129 Cerenkov.Pavel.A. Visible emission of clean liquids by action ofγradiation. Doklady Akademii Nauk SSSR, 1934, 2: 451.
130 J.V.Jelley. Cerenkov radiation and its applications. Journal of Applied Physics. 1955, 6: 227～233.
131 K.F.Casey, C.Yeh, Z.A.Kaprielian. Cerenkov Radiation in Inhomogeneous Periodic Media. Physical Review, 1965, 140: B768～B775.
132 S.J.Smith, E.M.Purcell. Visible Light from Localized Surface Charges Moving across a Grating. Physical Review, 1953, 92: 1069～1069.
133 Chiyan Luo, Mihai Ibanescu, Steven G. Johnson, et al. Cerenkov Radiation in Photonic Crystals. Science, 2003, 299: 368～371.
134 Ernst.Mathieu. Conditions for Quasi Cerenkov Radiation Generated by Optcial Second Harmonic Polarisation in a Nonlinear Cristal. Zeitschrift Für Angewand Te Mathematik Und Physik (ZAMP), 1969, 20: 433～439.
135 A.Zembrod, H.Puell, J.Giordmaine. Surface radiation from nonlinear optical polarization. Opto-electronics, 1969, 1: 64～64.
136 S.M.Saltiel, Y.Sheng, N.Bloch, et al. Cerenkov-type Second-harmonic generation in two-dimensional nonlinear photonic structures. IEEE Journal of Quantum Electronics, 2009, 45: 1465～1472.
137 Y.Sheng, S.M.Saltiel, W.Krolikowski, et al. Cerenko-type second-harmonic generation with fundamental beams of different polarizations. Optics Letters, 2010, 35: 1317～1319.
138 Y.Zhang, F.Wang, K.Geren, et al. Second-harmonic imaging from a modulated domain structures. Optics Letters, 2010, 35: 178～180.
139 Solomon M.Saltiel, Dragomir N.Neshev. Wieslaw Krolikowski, et al. Nonlinear Diffraction from a Virtual Beam. Physical Review Letters, 2010, 140: 083902.
140 P.Molina, M.O.Ramirez, B.J.Garcia, et al. Directional dependance of the second harmonic response in two-dimensional nonlinear photonic crystals. Applied Physics Letters, 2010, 96: 261111.
141 Solomon M.Saltiel, Dragomir N.Neshev, Wieslaw Krolikowski, et al. Multi-conical second harmonic waves via nonliear diffractions in circularly poled nonlinear media. SPIE, Burgas, 2008.
142 A. Ganany, A. Arie, S. M. Saltiel. Quasi-phase matching in LiNbO3 using nonlinear coefficients in the XY plane. Applied Physics B: Lasers and Optics, 2006, 85: 97～100.
143 D.N.Nikogosyan. Nonlinear Opctical Crystals: A complete Survey (Springer Science + Business Media, Inc), 2005.
144 F.Charra, G.G.Gurzadyan. Nonlinear Dieeletric Susceptibilities, edited by D.F.Nelson Springer, Berlin, 2000.
145 Y.Sheng, J.Dou, J.Li, et al. Temperature and anlge tuning of second harmonic generation in media with a short-range order. Applied Physics Letters, 2007, 91: 101109.
146 Y.Sheng, T.Wang, B.Ma, et al. Anisotropy of domain broadening in periodically poled lithium niobate crystals. Applied Physics Letters, 2006, 88: 041121.
147 G.Rosenman, Kh.Garb, A.Skliar. Domain broadening in quasi-phase-matched nonlinear optical devices. Applied Physics Letters, 1998, 73: 865～867.
148 A.Arie, N.Habshoosh, A.Bahabad. Quasi phase matching in two-dimensional nonlinear photonic crystals. Optical and Quantum Electronics, 2007, 39: 361～375.
149 A.Aire, A.Bahabad, N.Habshoosh. Nonlinear interactions in periodic and quasi-periodic nonlinear photonic crystals, Chapter 10, 259～284 in "Ferroelectric crystals for Photonic Applications". P.Ferraro, S.Grilli and P.DeNatale. Springer Verlag Berlin Heidelberg, 2009.
150 Wenjie Wang, Yan Sheng, Yongfa Kong, et al. Multiple Cerenkov second-harmonic waves in a two-dimensional nonlinear photonic strucures. Optics Letters, 2010, 35: 3790～3792.
151 Yan Sheng, Junhong Dou, Boqin Ma, et al. Broadband efficient second harmonic generation in media with a short-range order. Applied Physics letters, 2007, 91: 011101.
152 D. Kasimov, A. Arie, E. Winebrand, et al. Annular symmety nonlinear frequency converters. Optics Express, 2006, 14: 9371～9376.
2 Yamada.M, Nada.N, Saitoh.M, et al. First-order quasi-phase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second-harmonic generation. Applied Physics Letters, 1993, 62: 435～436.
3 V.Berger. Nonlinear photonic crystals. Physics Review Letters, 1998, 81: 4136～4139.
4 A.Chowdhury, S.Hagness, C.Susan, et al. Simultaneous optcial wavelength interchange with a two-dimensional second-order nonlinear photonic crystal. Optics Letters, 2000, 25: 832～834.
5 N.G.R.Broderick, G.W.Ross, H.L.Offerhaus, et al. Hexagonally Poled Lithium Niobate: A Two-Dimensional Nonlinear Photonic Crystal. Physical Review Letters, 2000, 84: 4345～4348.
6 S.Saltiel, Y.Kivshar. Phase matching in nonlinearχ(2) photonic crystals. Optics Letters. 2000, 25: 1204～1206.
7 L.H.Peng, C.C.Hsu, Jimmy.Ng, et al. Wavelength tunability of second-harmonic generation from two-dimensionalχ(2) nonlinear photonic crystals with a tetragonal lattice structure. Applied Physics Letters, 2004, 84: 3250～3252.
8 L.H.Peng, C.C.Hsu, Y.C.Shih. Second-harmonic green generation from two- dimmensionalχ(2) nonlinear photonic crystal with orthorhombic lattice structrue, Applied Physics Letters, 2003, 83: 3447～3449.
9 Shi-ning Zhu, Yong-yuan Zhu, Nai-ben Ming. Quasi-Phase-Matched Third-Harmonic Generation in a Quasi-Periodic Optical Superlattice. Science, 1997, 278: 843～846.
10 K.Fradkin-Kashi, A.Arie, P.Urenski, et al. Multiple Nonlinear Optical Interactions with Arbitrary Wave Vector Differences. Physcis Review Letters, 2002, 88: 023903.
11 R.Lifshitz, A.Arie, A.Bahabad. Photonic Quasicrystals for Nonlinear Optical Frequency Conversion. Physics Review Letters, 2005, 95: 133901.
12 Y. Sheng, J. Dou, B. Cheng, et al. Effective generation of red-green-blue laser in a two-dimensional decagonal photonic superlattice. Applied Physics B: Lasers and Optics, 2007, 87: 603～606.
13 Yan Sheng, Junhong Dou, Boqin Ma, et al. Broadband efficient second harmonic generation in media with a short-range order. Applied Physics Letters, 2007, 91: 011101～011103.
14 Yan Sheng, Kaloian Koynov, Daozhong Zhang. Colinear second harmonic generation of 20 wavelengths in a single two-dimensional decagonal nonlinear photonic quasi-crystal. Optics Communiations, 2009, 282: 3602～3606.
15 J.S.Shirk, A.Rosenberg. Photonic Crystals: Intensity-dependent transmission protects sensors.Laser Focus World, 2000, 36: 121～122.
16 B. G. Levi. Nobel Prize Honors Kohn and Pople for Methods of Quantum Chemistry. Phys.Today, 1999, 52: 20～22.
17 F.Charra, F.Kajzar, J.M.Nunzi, et al. Light-induced second-harmonic generation in azo-dye polymers. Optics Letters, 1993, 18: 941～943.
18 Bin Xu, Nai-Ben Ming. Experimental observations of bistability and instability in a two-dimensional nonlinear optical superlattice. Physics Review Letters, 1993, 71: 3959～3963.
19 Bin Xu, Nai-Ben Ming. Optical bistability in a two-dimensional nonlinear superlattice. Physcis Review Letters, 1993, 71: 1003～1006.
20 Yun-Lin Chen, Jing-Jun Xu, Xiao-Jun Chen, et al. Domain reversion process in near-stoichiometric LiNbO3 Crystals. Optics Communiations, 2001, 188: 359～364.
21 L. E. Myers, R. C. Eckardt, M. M. Fejer, et al. Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3. Journal of the Optical Society of America B, 1995, 12: 2102～2116.
22 Svhur V Y, Batchko R G,Rumyantsev E L, et al. Domain engineering: periodic domain patterning in lithium niobate. Proc 11th ISAF, Piscataway, NJ: IEEE, 1999, 399～406.
23 Yamada M and Saitoh M. Fabrication of a periodically poled laminar domain structure with a pitch of a few micrometers by applying an external electric field. Journal of Applied Physics, 1998, 84: 2199～2206.
24 L.Arizmendi. Photonic applications of lithium niobate crystals. Physica Status Solidi (a), 2004, 201: 253～283.
25 R.Batchko, V.Shur, M.Fejer, et al. Backswitch poling in lithium niobate for high-fidelity domain patterning and efficient blue light generation. Applied Physics Letters, 1999, 75: 1673～1675.
26 C. E. Valdivia, C. L. Sones, S. Mailis, et al. Ultrashort-Pulse Optically-Assisted Domain Engineering in Lithium Niobate. Ferroelectrics, 2006, 340: 75～82.
27 Ballman A A. Growth of Piezoelectric and Ferroelectric Materials by the CzochraIski Technique. Journal of American Ceramic Society, 1965, 48:112～113.
28 Lerner P,Legras C and Dumas J P.Stoechiométrie des monocristaux de métaniobate de lithium.Journal of Crystal Growth, 1968, 3-4: 231～235.
29 Wong K K. Properties of Lithium Niobate. London:INSPEC. The Institute of Electrical Engineers, 2002.
30 HouéM, Townsend P D. An introduction to methods of periodic poling for second-harmonic generation. Journal of Physics D: Applied Physics, 1995, 28: 1747～1763.
31 Abernethy J A, Gawith C B E, Eason R W, et al. Demonstration and optical characteristics of electro-optic Bragg modulators in periodically poled lithium niobate in the near-infrared. Applied Physics Letters, 2002, 81: 2514～2516.
32 Coppola G, Ferraro P, Iodice M, et al. Visualization of optical deflection and switchingoperations by a domain engineered-based LiNbO3 electro-optic device. Optics Express, 2003, 11: 1212～1222.
33 Broderick N G R, Ross G W, Offerhaus H L, et al. Hexagonally Poled Lithium Niobate: A Two-Dimensional Nonlinear Photonic Crystal. Physics Review Letters, 2000, 81: 4345～4348.
34 Nassau K, Levinstein H J, Loiacono G M. The Domain Structure and Etching of Ferroelectric Lithium Niobate. Applied Physics Letters, 1965, 6: 228～229.
35 Li M, Wang J, Zhuang L, et al. Fabrication of circular optical structures with a 20 nm minimum feature size using nanoimprint lithography, Applied Physics Letters, 2000, 76: 673～675.
36 Rothschild M, Bloomstein T M, Fedynyshyn T H, et al. Recent Trends in Optical Lithography. Lincoln Laboratory Journal, 2003, 14: 221～236.
37 Sones C L. Domain Engineering Techniques and Devices in Lithium Niobate: [dissertation].Southampton: University of Southampton, 2003.
38 Agronin A, Rosenwaks Y, Rosenman G. Ferroelectric domain reversal in LiNbO3 crystals using high-voltage atomic force microscopy. Applied Physics Letters, 2004, 85: 452～454.
39 Rosenwaks Y, Dahan D, M Molotskii, et al. Ferroelectric domain engineering using atomic force microscopy tip arrays in the domain breakdown regime. Applied Physics Letters, 2005, 86: 012909～012911.
40 Nassau K, Levinstein H J. Ferroelectric Behavior of Lithium Niobate. Applied Physics Letters, 1965, 7: 69～70.
41 Gopalan V, Cupta M C. Origin and Characteristics of Internal Fields in LiNbO3 Crystals. Ferroelectrics, 1997, 198: 49～59.
42 Gopalan V, Mictchell T E, Sickafus K E. Switching kinetics of 180°domains in congruent LiNbO3 and LiTaO3 crystals. Solid State Communications, 1999, 109: 111～117.
43 Gopalan V, Gupta M C. Origin of internal field and visualization of 180°domains in congruent LiTaO3 crystals. Journal of Applied Physics, 1996, 80: 6099～6106.
44 Kim S, Gopalan V, Kitamura K, et al. Domain reversal and nonstoichiometry in lithium tantalite. Journal of Applied Physics, 2001, 90: 2949～2963.
45 Shur V Y. Kinetics of ferroelectric domains: Application of general approach to LiNbO3 and LiTaO3. Journal of Materials Science. 2006, 41: 199~210.
46 Ueda T, Takai Y, Shimizu R, et al. Cross-Sectional Transmission Electron Microscopic Observation of Etch Hillocks and Etch Pits in LiTaO3 Single Crystal. Japanese Journal of Applied Physics Part I, 2000, 39: 1200~1202.
47 Ohnishi N, Lizuka T. Etching study of microdomains in LiNbO3 single crystals. Journal of Applied Physics, 1974, 46: 1063~1067.
48 Shur V Y, Nikolaeva E V, Shishkin E I, et al. Polarization reversal in congruent and stoichiometric lithium tantalite. Applied Physics Letters, 2001, 79 : 3146~3148.
49 Gopalan V, Jia Q X, Mitchell T E. In situ video observation of 180°domain kinetics incongruent LiNbO3 crystals. Applied Physics Letters, 1999, 75: 2482~2484.
50 Kim S, Gopalan V, Gruverman A. Coercive fields in ferroelectrics: A case study in lithium niobate and lithium tantalite. Applied Physics Letters, 2002, 80: 2740~2742.
51 Wengler M C, Müller M, Soergel E, et al. Poling dynamics of lithium niobate crystals. Appl Phys B, 2003, 76:393～396.
52 Zheng Y,Shi E,Wang S,et al. Domain structures and etching morphologies of lithium niobate crystals with different Li contents grown by TSSG and double crucible Czochralski method. Crystla Research and Crystal Technology, 2004, 39: 387～395.
53 Webjorn J. Structural influence of proton exchange on domain-inverted lithium niobate revealed by means of selective etching. Journal of Lightwave Technology, 1993, 11: 589～594.
54 Nassau K, Levinstein H J, Loiacono G M. Ferroelectric lithium niobate. 1. Growth, domain structure, dislocations and etching. Journal of Physics and Chemistry of Solids, 1966, 27: 983～988.
55 Sones C L, Mailis S, Brocklesby W S, et al. Differential etch rates in z-cut LiNbO3 for variable HF/HNO3 concentrations. Journal of Material Chemistry, 2002, 12: 295～298.
56 H.D.Liu, Y.F.Kong, Q.Hu, et al. Light-Induced Domian Inversion in Mg-doped near Stoichiometric Lithium Niobate Crystals. Chinese Physics Letters, 2007, 24: 1720～1723.
57 M.C.Wengler, M.Muller, E.Soergel, et al. Poling dynamics of lithium niobate crystals. Applied Physics B: Laser and Optics, 2003, 76: 393～396.
58 Missey M, Russell S, Dominic V, et al. Real-time visualization of domain formation in periodically poled lithium niobate. Optics Express, 2000, 6: 186～195.
59 Grilli S, P Ferraro, M Paturzo, et al. In-situ visualization, monitoring and analysis of electric field domain reversal process in ferroelectric crystals by digital holography. Optics Express, 2004, 12: 1832～1842.
60 Grilli S, Ferraro P, Nicola S De, et al. Investigation on reversed domain structures in lithium niobate crystals patterned by interference lithography. Optics Express, 2003, 11: 392～405.
61 Bermúdez V, Huang L, Hui D, et al. Role of stoichiometric point defect in electric-field- poling lithium niobate. Applied Physics A, 2000, 70: 591～594.
62 Chen Y, Yan W, Guo J, et al. Effect of Mg concentration on the domain reversal of Mg-doped LiNbO3. Applied Physics Letters, 2005, 87: 212904.
63 Kumaragurubaran S, Takekawa S, Nakamura M, et al. Polarization Switching and Defect Structure in Pure and MgO Doped Near-Stoichiometric LiNbO3 Crystals. Ferroelectrics, 2005, 326: 113～116.
64 Ishizuki H, Shoji I, Taira T. Periodical poling characteristics of congruent MgO:LiNbO3 crystals at elevated temperature. Applied Physics Letters, 2003, 82: 4062～4064.
65 Eggert H A, Hecking B, Buse K. Electrical fixing in near-stoichiometric lithium niobate crystals. Optics Letters, 2004, 29: 2476～2478.
66 Eggert H A, Kalkum F, Hecking B, et al. Optimization of electrical fixing in near-stoichiometric iron-doped lithium niobate crystals. Journal of the Optical Society of America B, 2005, 22: 2553～2559.
67 Fujimura M, Sohmura T, Suhara T. Fabrication of domain-inverted gratings in MgO:LiNbO3 by applying voltage under ultraviolet irradiation through photomask at room temperature. Electronics Letters, 2003, 39: 719～721.
68 M.Müller, E.Soerger, K.Buse. Influence of ultraviolet illumination on the poling characteristics of lithium niobate crystals. Applied Physics Letters, 2003, 83: 1824～1826.
69 Wengler M C, Fassbender B, Soergel E, et al. Impact of ultraviolet light on coercive field, poling dynamics and poling quality of various lithium niobate crystals from different sources. Journal of Applied Physics, 2004, 96: 2816～2820.
70 Wengler M C, Heinemeyer U, Soergel E, et al. Ultraviolet light-assisted domain inversion in magnesium-doped lithium niobate crystals. Journal of Applied Physics, 2005, 98: 064104.
71 Sones C L, Wengler M C, Valdivia C E, et al. Light-induced order-of-magnitude decrease in the electric field for domain nucleation in MgO-doped lithium niobate crystals. Applied Physics Letters, 2005, 86: 212901.
72 LI Da-Shan, LIU De-An, ZHI Ya-Nan, et al. Red Laser-Induced Domain Inversion in MgO-Doped Lithium Niobate Crystals. Chiness Physics Letters, 2007, 24: 971～974.
73 Zhi Y, Liu D, Qu W, et al. Wavelength dependence of light-induced domain nucleation in MgO-doped congruent LiNbO3 crystal. Applied Physics Letters, 2007, 90: 042904.
74 Zhi.Y, Liu.D, Yan.A, et al. Primary and secondary threshold intensities of ultraviolet-laser-induced domain nucleation in nearly stoichiometric LiTaO3. Applied Physics Letters, 2008, 92: 082904.
75 V.Dierolf, C.Sandmann. Direct-write method for domain inversion patterns in LiNbO3. Applied Physics Letters, 2004, 84: 3987～3989.
76 M.Müller, E.Soergel, K.Buse. Influence of ultraviolet illumination on the poling characteristics of lithium niobate crystals. Applied Physics Letters, 2003, 83: 1824～1826.
77 W.Wang, Y.Kong, H.Liu, et al. Light-induced domain reveral in doped lithium niobate crystals. Journal of Applied Physics, 2009, 105: 043105.
78 Y.Kong, S.Liu, Y.Zhao, et al. Highly optical damage resistant crystal: Zirconium–oxide -doped lithium niobate. Applied Physcis Letters, 2007, 91: 081908.
79 F.Liu, Y.Kong, W.Li, et al. High resistance against ultraviolet photorefraction in zirconium-doped lithium niobate crystals. Optics Letters, 2010, 35: 10～12.
80 W.Yan, L.Shi, H.Chen, et al. Investigations on the UV photorefractivity of LiNbO3:Hf. Optics Letters, 2010, 35: 601～603.
81 X.Li, Y.Kong, H.Liu, et al. Origin of the generally defined absorption edge of non-stoichiometric lithium niobate crystals, Solid State Communications. 2007, 141: 113～116.
82 H.Zeng, Y.Kong, T.Tian, et al. Transcription of domain patterns in near-stoichiometric magnesium-doped lithium niobate. Applied Physics Letters, 2010, 97: 201901.
83 H.Zeng, Y.Kong, H.Liu, et al. Light-induced superlow electric field for domian reversal in near-stoichiometric magnesium-doped lithium niobate. Journal of Applied Physics, 2010, 107: 063514.
84 Baudrier-Raybaut, M.Ha?dar, R..Kupecek, et al. Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials. Nature , 2004, 432: 374～376.
85 Sergey E. Skipetrov. Disorder is the new order. Nature (London), 2004, 432: 285～286.
86 Pablo.Molina, Maria.de, Luisa.E.Bausa. Strontium Barium Niobate as a Multifunctional Two-Dimensional Nonliear "photonic Glass". Advanced Functional Materials, 2008, 18: 709～715.
87 T.Granzow, T.Woike, M.Wohlecke, M.Imlau, W.Kleemann. Polarization-Based Adjustable Memory Behavior in Relaxor Ferroelectrics. Physical Review Letters, 2002, 89: 127601-4～127601-4.
88 Granzow T, Woike T, W?hlecke.M, et al. Polarization-Based Adjustable Memory Behavior in Relaxor Ferroelectrics. Physical Review Letters, 2002, 89: 127601.
89 Tian L, Scrymgeour D A, Sharan Alok, et al. Anomalous electro-optic effect in Sr0.6Ba0.4Nb2O6 single crystals and its application in two-dimensional laser scanning. Applied Physics Letters, 2003, 83: 4375～4377.
90 A.A.Ballman, H.Brown. The growth and properties of stronitium barium metaniobate Sr1-xBaxNb2O6 a tungsten bronze ferroelectric. Journal of Crystal Growth, 1967, 1:311～314.
91 J.C.Brice, O.F.Hill, P.A.C.Whiffin, et al. The Czochralski growth of barium stronitium niobate crystals. Journal of Crystal Growth, 1971, 10: 133～138.
92 J.J.Romero, D.Jaque, J.Garcia.Sole, et al. Diffuse multiself-frequency conversion processes in the blue and green by quasicylindirical ferroelectric domians in Nd3+:Sr0.6Ba0.4(NbO3)2 laser crystal. Applied Physics Letters, 2001, 78:1961～1963.
93 P.B.Jameson, S.C.Abrahams, J.L.Bernshtein. Ferroelectric Tungsten Bronze– Type Crystal Structures. I. Barium Strontium Niobate Ba0.27Sr0.75Nb2O5.78. Journal of Chemistry Physics, 1968, 42: 5048～5057.
94 R.Fischer, S.M.Saltiel, D.N.Neshev, et al. Broadband femtosecond frequency doubling in random media. Applied Physics Letters, 2006, 89: 191105.
95 V.Roppo, W.Wang, K.Krolikowski, et al. The role of ferroelectric domain structure in second harmonic generation in random quadratic media. Optics Express, 2010, 18: 4012～4022.
96 G.Dolino. Effects of Domian Shapes on Second-Harmonic Scattering in Triglycine Sulfate. Physical Review B, 1972, 6: 4025～4035.
97 Y.Le.Grand, D.Rouede, C.Odin, et al. Second-harmonic scattering by domains in RbH2PO4. Ferroelectrics. 2001, 200: 249～260.
98 Jose Trull, Crina Cojocaru, Robert Fischer, et al. Second-harmonic parametric scatteriing in ferroelectric crystals with disordered nonlinear domain structure. Optics Express, 2007, 15:15868～15877.
99 M.Horowitz, A.Bekker, B.Fisher. Broadband second-harmonic generation in SrxBa1-xNb2O6 by spread spectrum phase matching with controllable domain gratings. Applied Physics Letters, 1993, 62: 2619～2622.
100 S.Kawai, T.Ogawa, H.S.Lee, et al. Second-harmonic generation from needlike ferroelectric domians in Sr0.6Ba0.4Nd2O6 single crystal. Applied Physics Letter, 1998, 73: 768～770.
101 K.A.Kuznetsov, G.Kh.Kitaeva, A.V.Shevlyuga, et al. Second Harmonic Generation in a Strontium Barium Niobate Crystal with a Random Domain Structure. JETP Letters (Letters to Journal of Experimental and Theoretical Physics), 2008, 87: 98～102.
102 Arthur R. Tunyagi, Michael Ulex, Klaus Betzler. Noncollinear Optical Frequency Doubling in Strontium Barium Niobate. Physical Review Letters, 2003, 90: 243901.
103 Authur R.Tunyagi. Non-Colinear Second Harmonic Generation in Strontium Barium Niobate. PhD thesis, Fachbereich Physik, Universitat Osnabruck, Germany, 2004.
104 D.J.Kane, R.Trebino. Single-shot measurement of the intensity and phase of an arbitrary ultrashort pulse by using frequency-resolved optical grating. Optics Letters, 1993, 18: 823～825.
105 C.Iaconis, I.A.Walmsley. Spectral phase interferometry for direct electric-filed reconstruction of ultrashort optical pulses. Optics Letters, 1998, 23:792～793.
106 P.O'Shea, M.Kimmel, X.Gu, et al. Highly simplified device for ultrashourt-pulse measurement, Optics Letters, 2001, 26: 932～934.
107 Vito Roppo, David Dumay, Jose Trull, et al. Planar second-harmonic generation with noncolinear pumps in disordered media. Optcis Express, 2008, 16: 14192～14199.
108 Robert Fischer, Dragomir N.Neshev, Solomom M.Saltiel, et al. Monitoring ultrashort pulses by transverse frequency doubling of counterpropagating pulses in random media. Applied Physics Letters, 2007, 91:031104.
109 J.Trull, S.Saltiel, V.Roppo, C.Cojocaru, et al. Characterization of femtosecond pulses via transverse second-harmonic generation in random nonlinear media. Applied Physcis B: Laser and Optics, 2009, 95: 609～615.
110 J.Janszky, G.Corradi, R.N.Gyuzalian. On a possibility of analysing the temporal charateristics of short pulses. Optics Communications. 1977, 23: 293～298.
111 S.M.Saltiel, S.D.Savov, I.V.Tomov, et al. Subnanosecond pulse duration measurements by noncolinear second harmonic generation. Optics Communiations, 1981, 38: 443～447.
112 D.J.Kane, R.Trebino. Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating. IEEE Journal of Quantum Electronics, 1993, 29:571.
113 C.Iaconis, I.A.Walmsley. Self-referencing spectral intererometry for measuring ultrashourt optical pulses. IEEE Journal of Quantum Electrionics, 1999, 35: 501～509.
114 J.Hebling. Derivation of the pulse front tilt caused by angular disperson. Optical and Quantum Electrionics, 1996, 28: 1759～1763.
115 Zs.Bor, B.Racz. Group velocity dispersion in prisms and its application to pulse compressionand travelling-wave excitation. Optcis Communications, 1985, 54: 165～170.
116 W.Wang, V.Roppo, K.Kalinowski, et al. Third-harmonic generation via broadband cascading in disordered quadratic nonlinear media. Optics Express, 2009, 17: 20117～20123.
117 W.Wang, K.Kalinowski, V.Roppo, et al. Second- and third-harmonic parametric scattering in disordered quadratic media. Journal of Physics B: Atomic, Molecular and Optical Physics, 2010, 43: 215404.
118 B.F.Johnston, P.Dekker, M.J.Withford, et al. Simultaneous phase matching and internal interference of two second-order nonlinear parametric process. Optics Express, 2006, 14:11756～11765.
119 Th.Woike, T.Granzow, U.Dorfler, et al. Refractive Indices of Congruently Melting Sr0.61Ba0.39Nb2O6. Physica Status Solidi(a), 2001, 186: R13～R15.
120 P.A.Cerenkov. Visible Radiation Produced by Electrons Moving in a Medium with Velocities Exceeding that of Light. Physical Review. 1937, 52: 378～379.
121 D.H.Auston. Subpicosecond electro-optic shock waves. Applied Physics Letters, 1983, 43: 713～715.
122 M.Bass, P.A.Franken, J.F.Ward, et al. Optical Rectification. Physical Review Letters, 1962, 9: 446～448.
123 K.H.Yang, P.L.Richards, Y.R.Shen. Generation of Far-Infrared Radiation by Picosecond Light Pulses in LiNbO3. Applied Physics Letters, 1971, 19: 320～324.
124 D.H.Auston, K.P.Cheung, J.A.Valdmanis, et al. Cherenkov Radiation from Femtosecond Optical Pulses in Electro-Optic Media. Physical Review Letters, 1984, 53: 1555～1559.
125 M.G.Moharam, L.Young. Criterion for Bragg and Raman-Nath diffraction regimes. Applied Optics, 1978, 17: 1757～1759.
126 M.G.Moharam, T.K.Gaylord, R.Magnusson. Criteria for Raman-Nath regime diffraction by phse gratings. Optics Communications, 1980, 32: 19～23.
127 S.Saltiel, D.Neshev, W.Krolikowski, et al. Generation of Second-Harmonic Conical Waves Via Nonlinear Bragg Diffraction. Physical Review Letters. 2008, 100: 103902.
128 Solomon M.Saltiel, Dragomir N.Neshev, Wieslaw Krolikowski, et al. Multiorder nonlinear diffraction in frequency doubling processes. Optics Letters, 2009, 34: 848:850.
129 Cerenkov.Pavel.A. Visible emission of clean liquids by action ofγradiation. Doklady Akademii Nauk SSSR, 1934, 2: 451.
130 J.V.Jelley. Cerenkov radiation and its applications. Journal of Applied Physics. 1955, 6: 227～233.
131 K.F.Casey, C.Yeh, Z.A.Kaprielian. Cerenkov Radiation in Inhomogeneous Periodic Media. Physical Review, 1965, 140: B768～B775.
132 S.J.Smith, E.M.Purcell. Visible Light from Localized Surface Charges Moving across a Grating. Physical Review, 1953, 92: 1069～1069.
133 Chiyan Luo, Mihai Ibanescu, Steven G. Johnson, et al. Cerenkov Radiation in Photonic Crystals. Science, 2003, 299: 368～371.
134 Ernst.Mathieu. Conditions for Quasi Cerenkov Radiation Generated by Optcial Second Harmonic Polarisation in a Nonlinear Cristal. Zeitschrift Für Angewand Te Mathematik Und Physik (ZAMP), 1969, 20: 433～439.
135 A.Zembrod, H.Puell, J.Giordmaine. Surface radiation from nonlinear optical polarization. Opto-electronics, 1969, 1: 64～64.
136 S.M.Saltiel, Y.Sheng, N.Bloch, et al. Cerenkov-type Second-harmonic generation in two-dimensional nonlinear photonic structures. IEEE Journal of Quantum Electronics, 2009, 45: 1465～1472.
137 Y.Sheng, S.M.Saltiel, W.Krolikowski, et al. Cerenko-type second-harmonic generation with fundamental beams of different polarizations. Optics Letters, 2010, 35: 1317～1319.
138 Y.Zhang, F.Wang, K.Geren, et al. Second-harmonic imaging from a modulated domain structures. Optics Letters, 2010, 35: 178～180.
139 Solomon M.Saltiel, Dragomir N.Neshev. Wieslaw Krolikowski, et al. Nonlinear Diffraction from a Virtual Beam. Physical Review Letters, 2010, 140: 083902.
140 P.Molina, M.O.Ramirez, B.J.Garcia, et al. Directional dependance of the second harmonic response in two-dimensional nonlinear photonic crystals. Applied Physics Letters, 2010, 96: 261111.
141 Solomon M.Saltiel, Dragomir N.Neshev, Wieslaw Krolikowski, et al. Multi-conical second harmonic waves via nonliear diffractions in circularly poled nonlinear media. SPIE, Burgas, 2008.
142 A. Ganany, A. Arie, S. M. Saltiel. Quasi-phase matching in LiNbO3 using nonlinear coefficients in the XY plane. Applied Physics B: Lasers and Optics, 2006, 85: 97～100.
143 D.N.Nikogosyan. Nonlinear Opctical Crystals: A complete Survey (Springer Science + Business Media, Inc), 2005.
144 F.Charra, G.G.Gurzadyan. Nonlinear Dieeletric Susceptibilities, edited by D.F.Nelson Springer, Berlin, 2000.
145 Y.Sheng, J.Dou, J.Li, et al. Temperature and anlge tuning of second harmonic generation in media with a short-range order. Applied Physics Letters, 2007, 91: 101109.
146 Y.Sheng, T.Wang, B.Ma, et al. Anisotropy of domain broadening in periodically poled lithium niobate crystals. Applied Physics Letters, 2006, 88: 041121.
147 G.Rosenman, Kh.Garb, A.Skliar. Domain broadening in quasi-phase-matched nonlinear optical devices. Applied Physics Letters, 1998, 73: 865～867.
148 A.Arie, N.Habshoosh, A.Bahabad. Quasi phase matching in two-dimensional nonlinear photonic crystals. Optical and Quantum Electronics, 2007, 39: 361～375.
149 A.Aire, A.Bahabad, N.Habshoosh. Nonlinear interactions in periodic and quasi-periodic nonlinear photonic crystals, Chapter 10, 259～284 in "Ferroelectric crystals for Photonic Applications". P.Ferraro, S.Grilli and P.DeNatale. Springer Verlag Berlin Heidelberg, 2009.
150 Wenjie Wang, Yan Sheng, Yongfa Kong, et al. Multiple Cerenkov second-harmonic waves in a two-dimensional nonlinear photonic strucures. Optics Letters, 2010, 35: 3790～3792.
151 Yan Sheng, Junhong Dou, Boqin Ma, et al. Broadband efficient second harmonic generation in media with a short-range order. Applied Physics letters, 2007, 91: 011101.
152 D. Kasimov, A. Arie, E. Winebrand, et al. Annular symmety nonlinear frequency converters. Optics Express, 2006, 14: 9371～9376.