二阶非线性Maker条纹测试及模拟
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摘要
随着激光的发现及应用,人们越来越关注物质在强光辐照的下所产生光倍频、光参量振荡等非线性现象。这些现象在实际中得到广泛的应用,尤其在光电子器件中的运用使得非线性光学这门学科成为许多学者关注的热点。
本文根据麦克斯韦方程及电磁波在界面上的边界条件,分析入射基频光穿过空气-样品界面、在非线性介质中产生倍频光,以及穿透样品-空气界面后三个步骤,得到经激光与二阶非线性介质作用后,得到倍频光与基频光大小及方向的关系,分析这两束光相位匹配的过程,采用MathCAD软件对波长为1064nm的基频光在二阶非线性介质中的传播进行Maker条纹模拟,得到二阶非线性介质中产生的波长为532nm的倍频光的模拟公式。
采用Maker条纹测试法,利用波长为1064nm的基频光穿过围绕一转轴进行转动的石英晶体样品、电场／温度场极化后的硫系玻璃样品及微晶玻璃样品,根据样品光滑表面与基频光光束之间的夹角的改变,来获得532nm的倍频光的空间周期分布的对称干涉条纹。将所得到的Maker条纹分别与晶体、电场／温度场极化后的硫系玻璃及极性微晶玻璃样品的实际的测量结果相对比,可以得到所模拟的程序与倍频晶体的Maker测量结果相吻合,对于极化后的硫系玻璃及极性微晶玻璃样品,在一定范围内模拟结果与测量结果相一致。本文对所得到的模拟计算方法进行理论分析,可以得到实验过程中偏振光的方向及样品结构的对称性等对其二次谐波的大小及方向的影响。从而对样品制备、Maker条纹测试的实际操作过程及二阶非线性极化机理有一定的指导意义。
With the discovery and application of laser, the optical nonlinear phenomenon which was induced by irradiation of lasers in the materials, such as optical second-harmonic generation, and optical parametric oscillator so on, has been applied widely especially in photonic devices. These developments of applications make the nonlinear optics become the focus of investigation of researchers.
In this paper, we analyzed three steps according to the Maxwell equations and boundary conditions, the transmission of fundamental wave from air to nonlinear medium, the second harmonic generation in the nonlinear medium and the transmission of fundamental and double frequency wave from nonlinear medium to air. According to the analysis of these three steps, the relations of amplitudes and directions between fundamental wave and double frequency wave were obtained to investigate the process of phase matching. The software MathCAD was performed to simulate the process of phase matching to obtain the intensity formula of double frequency wave generated in the nonlinear medium.
When the fundamental wave transmitted the quartz, chalcogenide glasses poled by electrical/thermal fields or crystallized glasses which were rotated on one axe, the angles between the sample surface and fundamental wave would be varied. Due to this variation, the periodical interference fringes were spatially obtained. Comparing with the simulated results of Maker fringes and those three kinds of samples, we analyzed theoretically the simulation method in this paper and the adaptability of this method to different second nonlinear materials. For quartz, the simulated results were suitable to experience results. However, these simulated results were also suitable to those experience results to some extent. In this paper, the influence of polarized direction and samples'symmetry on the intensity and direction of second harmonic generation (SHG) has been obtained. These consequences were directive significance to fabrication of samples, experience of Make fringe measurement and understand of second-order nonlinear mechanism
本文根据麦克斯韦方程及电磁波在界面上的边界条件,分析入射基频光穿过空气-样品界面、在非线性介质中产生倍频光,以及穿透样品-空气界面后三个步骤,得到经激光与二阶非线性介质作用后,得到倍频光与基频光大小及方向的关系,分析这两束光相位匹配的过程,采用MathCAD软件对波长为1064nm的基频光在二阶非线性介质中的传播进行Maker条纹模拟,得到二阶非线性介质中产生的波长为532nm的倍频光的模拟公式。
采用Maker条纹测试法,利用波长为1064nm的基频光穿过围绕一转轴进行转动的石英晶体样品、电场／温度场极化后的硫系玻璃样品及微晶玻璃样品,根据样品光滑表面与基频光光束之间的夹角的改变,来获得532nm的倍频光的空间周期分布的对称干涉条纹。将所得到的Maker条纹分别与晶体、电场／温度场极化后的硫系玻璃及极性微晶玻璃样品的实际的测量结果相对比,可以得到所模拟的程序与倍频晶体的Maker测量结果相吻合,对于极化后的硫系玻璃及极性微晶玻璃样品,在一定范围内模拟结果与测量结果相一致。本文对所得到的模拟计算方法进行理论分析,可以得到实验过程中偏振光的方向及样品结构的对称性等对其二次谐波的大小及方向的影响。从而对样品制备、Maker条纹测试的实际操作过程及二阶非线性极化机理有一定的指导意义。
With the discovery and application of laser, the optical nonlinear phenomenon which was induced by irradiation of lasers in the materials, such as optical second-harmonic generation, and optical parametric oscillator so on, has been applied widely especially in photonic devices. These developments of applications make the nonlinear optics become the focus of investigation of researchers.
In this paper, we analyzed three steps according to the Maxwell equations and boundary conditions, the transmission of fundamental wave from air to nonlinear medium, the second harmonic generation in the nonlinear medium and the transmission of fundamental and double frequency wave from nonlinear medium to air. According to the analysis of these three steps, the relations of amplitudes and directions between fundamental wave and double frequency wave were obtained to investigate the process of phase matching. The software MathCAD was performed to simulate the process of phase matching to obtain the intensity formula of double frequency wave generated in the nonlinear medium.
When the fundamental wave transmitted the quartz, chalcogenide glasses poled by electrical/thermal fields or crystallized glasses which were rotated on one axe, the angles between the sample surface and fundamental wave would be varied. Due to this variation, the periodical interference fringes were spatially obtained. Comparing with the simulated results of Maker fringes and those three kinds of samples, we analyzed theoretically the simulation method in this paper and the adaptability of this method to different second nonlinear materials. For quartz, the simulated results were suitable to experience results. However, these simulated results were also suitable to those experience results to some extent. In this paper, the influence of polarized direction and samples'symmetry on the intensity and direction of second harmonic generation (SHG) has been obtained. These consequences were directive significance to fabrication of samples, experience of Make fringe measurement and understand of second-order nonlinear mechanism
引文
[1]. Franken.P.A, Hill.A.E, Peters.C.W, et al., Generation of optical harmonics[J]. Physical Review Letters,1961,7:118-119
[2]. N.Bloembergen著.吴存恺等译.非线性光学[M].北京：科学出版社,1987
[3].黄德群,单振国,干福熹.新型光学材料[M].北京：科学出版社,1991
[4].郝光生,刘颂豪.强光光学浅说[M].北京：科学出版社,1987
[5].顾少轩.GeS2-Ga2S3-CdS体系非线性光学玻璃的制备、结构与性能研究[D].武汉：武汉理工大学,2006
[6].张辉.钾铅硅酸盐玻璃二次谐波发生特性的研究[D].武汉：武汉工业大学,1997
[7].生瑜,章文贡.金属有机非线性光学材料[J].功能材料,1995,26(1)：91-93
[8]. Aitken B, Newhouse M A. Ga-and/or In-containing AsGe sulphide glasses[P]. U.S. Patent, 5,389,584,1995
[9].方敬忠,谢才清,齐亚范.玻璃非线性光学材料及其应用[J].特种玻璃,1991,8：53-59
[10].万群.微晶半导体材料的研究现现状[J].特种玻璃,1991,8：210-214
[11].Nasu H, Kurachi K, Mito A, et al., Second harmonic generation and structure of mixed alkali titanosilicate glass[J]. Journal of Non-Crystalline Solids,1997,217:182-188
[12].杨尊先.若干氧化物玻璃性能与结构研究[D].武汉：武汉理工大学,2001
[13].刘启明.硫系玻璃光学非线性发生特性的研究[D].武汉：武汉工业大学,1999
[14].Kazansky P G, Kamal A. High second-order nonlinearities induced in lead silicate glasses by electro-beam irradation[J], Optics Letters,1993,18(9):1141-1143
[15].J.Jerphagnon, S.K.Kurtz, Maker Fringes:A Detailed Comparison of Theory and Experiment for Isotropic and Uniaxial Crystals[J], Journal of Applied Physics,1970,41:,1667-1681
[16].刘启明,赵修建,干福熹,电子束辐射下Ge-As-S体系玻璃中二阶非线性光学效应[J].光学学报,2001,21(6)：683-585.
[17].刘启明,赵修建,干福熹Ge-As-S体系玻璃中光学二次谐波发生及其极化机理分析[J].物理学报,2000,49(5)：1726-1729
[18].费浩生编,非线性光学[M].北京：高等教育出版社,1990
[19].王奎雄编,非线性光学[M].北京：国防工业出版社,1988
[20].刘颂豪,郝光生编,强光光学及其应用[M].广州：广东科技出版社,1995
[21].Yamashita M, Yamanaka H. Formation and ionic conductivity of Li2S-GeS2-Ga2S3 glasses and thin films[J]. Solid State Ionics,2003,158(1-2):151-156
[22].Elliott SR, Chalcogenide glasses, Materials Science and Technology[M], ed. by Cahn RW, 1991
[23].Govindarajan S K. Synthesis and characterization of chalcogenide glasses for fiber optic light sources in the 2 to 1Oμm region:[PHD paper].
[24].Usuki T, Araki F, Uemura O, et al., Structure changes during amorphization of Ge-Se alloys by mechanical milling[J]. Materials Transactions,2003,44(3):344-350
[25].过已吉主编,非线性光学[M],西北电讯工程学院出版社,1986
[26].U. Osterberg, W. Margulis. Dye laser pumped by Nd:YAG laser pulses frequency doubled in a glass optical fiber[J]. Optics Letters,1986,11:516-518
[27].R.A. Myers, N. Mukherjee, S.R.J. Brueck. Large second-order nonlinearity in poled fused silica[J]. Optics Letters,1991,16:1732-1734
[28].H.Nasu,.Kuraehi, K.Kamiya, A.Mito. Second-and third-order optical non-linearity of homogenous glasses[J]. Journal of Non-crystalline Solids,1994,178:23-40
[29].H.Nasu, K.Kuraehi, H,Okamoto, J.Matsuoka, K.Kamiya, A.Mito. Second Harmonic generation from an eleetrieally polarized TiO2-containing silicate glass[J]. Journal of Non-crystalline Solids,1993,32:83-86
[30].K.Tanaka, K.Kamiya, K.Hirao, N.Soga, A.Mito, H.Nasu. Second harmonic generation in the electrically poled Li2O-Nb2O5-TeO2glasses[J]. Journal of Non-crystalline Solids,1995,185:123-126
[31].K.Tanaka,Y.Yamamoto,H.Nasu,T.Hashimoto,K.Kamiya. Optical second harmonic generation in poled MgO-ZnO-TeO2 and BeO3-TeO2 glasses[J]. Journal of Non-crystalline Solids,1996, 203,:49-54
[32].H.Nasu et al.,第十七届国际玻璃大会论文集(第三卷)[C].1995,75
[33].R.A.Myers et al., Stable second-order nonlinearity in SiO2-based waveguides on Si using temperature/electric-field poling[J]. SPIE,1994,2289:158-166
[34].P.G Kazansky et al., High second-order nonlinearities induced in lead silicate glass by electron-beam irradiation[J]. Optics Letters,1993,18(9):693-695
[35].P.G Kazansky et al., Erasure of thermally poled second-order nonlinearity in fused silica by electron implantation[J]. Optics Letters,1993,18(14):1141-1143
[36].P.S.J. Rusell et al., Electron implantation:a new technique for creation and modification of second-order susceptibility in glasses[J].SPIE,1993,2044:192-201
[37].Q. Liu, F. Gan, X. Zhao, et al, Second harmonic generation in Ge20As25S55glass irradiated by an electron beam[J]. Optics Letters,2001,26:1347-1349
[38].A. Podlipensky, J. Lange, G Seifert, H. Graener, and I. Cravetchi. Second-harmonic generation from ellipsoidal silver nanoparticles embedded in silica glass[J]. Optics Letters, 2003,28(9):716-718
[39].Kurtz S.K, Perry T.T. A Powder Technique for the Evaluation of Nonlinear Optical Materials[J]. Journal of Applied Physics,1968,54:3798-3813
[40].Bosshard C, Knopfle.E, Pretre P, et al. Second-order polarizabilities of nitropyridine derivatives determined with electric-field-induced second harmonic generation and a solvatochromic method:a comparative study[J]. Journal of Applied Physics,1992,71(4): 1594-1605
[41].P.D. Maker, R.W. Terhune, C.M. Savage. Effects of dispersion and focusing on theproduction of optical harmonics[J]. Physical Review Letters,1962,8(1):21-22
[42].J.A.Amstrong, N.Bloembergen, J.Ducuing, P.S.Pershan, Interactions between light waves in a nonlinear dielectric[J]. Physical Review,1962,127:1918-1939
[43].Ulrich Muller, Inorganic Structural Chemistry[M], John Wiley & Sons A Textbook Series
[44].Minoshima K, Taiji M, Kobayashi T, Femtosecond time-resolved interferometry for the determination of complex nonlinear susceptibility[J]. Optics Letters,1991,16:1683-1685
[45]. Wang X, Gu S, Yu J, Zhao X, Tao H, Formation and properties of chalcogenide glasses in the GeS2-Ga2S3-CdS system[J], Materials Chemistry and Physics,2004,83:284-288
[46].Maker P D, Terhune R W, Nisenoff M, et al. Effects of dispersion and focusing on the production of optical harmonics[J]. Physical Review Letters,1962,8 (1):21-22
[47].Gu S, Hu H, Guo H, Tao H, Second-Harmonic generation in transparent surface crystallized GeS2-Ga2S3-CdS chalcogenide glasses[J], Optics Communication,2008,281:2651-2655
[48].Yoshihiro Takahashi, Yasuhiko Benino, Takumi Fujiwara, Takayuki Komatsu. Large second-order optical nonlinearities of fresnoite-type crystals in transparent surface-crystallized glasses[J], Journal of Applied Physics,2004; 95:3503-3508
[2]. N.Bloembergen著.吴存恺等译.非线性光学[M].北京：科学出版社,1987
[3].黄德群,单振国,干福熹.新型光学材料[M].北京：科学出版社,1991
[4].郝光生,刘颂豪.强光光学浅说[M].北京：科学出版社,1987
[5].顾少轩.GeS2-Ga2S3-CdS体系非线性光学玻璃的制备、结构与性能研究[D].武汉：武汉理工大学,2006
[6].张辉.钾铅硅酸盐玻璃二次谐波发生特性的研究[D].武汉：武汉工业大学,1997
[7].生瑜,章文贡.金属有机非线性光学材料[J].功能材料,1995,26(1)：91-93
[8]. Aitken B, Newhouse M A. Ga-and/or In-containing AsGe sulphide glasses[P]. U.S. Patent, 5,389,584,1995
[9].方敬忠,谢才清,齐亚范.玻璃非线性光学材料及其应用[J].特种玻璃,1991,8：53-59
[10].万群.微晶半导体材料的研究现现状[J].特种玻璃,1991,8：210-214
[11].Nasu H, Kurachi K, Mito A, et al., Second harmonic generation and structure of mixed alkali titanosilicate glass[J]. Journal of Non-Crystalline Solids,1997,217:182-188
[12].杨尊先.若干氧化物玻璃性能与结构研究[D].武汉：武汉理工大学,2001
[13].刘启明.硫系玻璃光学非线性发生特性的研究[D].武汉：武汉工业大学,1999
[14].Kazansky P G, Kamal A. High second-order nonlinearities induced in lead silicate glasses by electro-beam irradation[J], Optics Letters,1993,18(9):1141-1143
[15].J.Jerphagnon, S.K.Kurtz, Maker Fringes:A Detailed Comparison of Theory and Experiment for Isotropic and Uniaxial Crystals[J], Journal of Applied Physics,1970,41:,1667-1681
[16].刘启明,赵修建,干福熹,电子束辐射下Ge-As-S体系玻璃中二阶非线性光学效应[J].光学学报,2001,21(6)：683-585.
[17].刘启明,赵修建,干福熹Ge-As-S体系玻璃中光学二次谐波发生及其极化机理分析[J].物理学报,2000,49(5)：1726-1729
[18].费浩生编,非线性光学[M].北京：高等教育出版社,1990
[19].王奎雄编,非线性光学[M].北京：国防工业出版社,1988
[20].刘颂豪,郝光生编,强光光学及其应用[M].广州：广东科技出版社,1995
[21].Yamashita M, Yamanaka H. Formation and ionic conductivity of Li2S-GeS2-Ga2S3 glasses and thin films[J]. Solid State Ionics,2003,158(1-2):151-156
[22].Elliott SR, Chalcogenide glasses, Materials Science and Technology[M], ed. by Cahn RW, 1991
[23].Govindarajan S K. Synthesis and characterization of chalcogenide glasses for fiber optic light sources in the 2 to 1Oμm region:[PHD paper].
[24].Usuki T, Araki F, Uemura O, et al., Structure changes during amorphization of Ge-Se alloys by mechanical milling[J]. Materials Transactions,2003,44(3):344-350
[25].过已吉主编,非线性光学[M],西北电讯工程学院出版社,1986
[26].U. Osterberg, W. Margulis. Dye laser pumped by Nd:YAG laser pulses frequency doubled in a glass optical fiber[J]. Optics Letters,1986,11:516-518
[27].R.A. Myers, N. Mukherjee, S.R.J. Brueck. Large second-order nonlinearity in poled fused silica[J]. Optics Letters,1991,16:1732-1734
[28].H.Nasu,.Kuraehi, K.Kamiya, A.Mito. Second-and third-order optical non-linearity of homogenous glasses[J]. Journal of Non-crystalline Solids,1994,178:23-40
[29].H.Nasu, K.Kuraehi, H,Okamoto, J.Matsuoka, K.Kamiya, A.Mito. Second Harmonic generation from an eleetrieally polarized TiO2-containing silicate glass[J]. Journal of Non-crystalline Solids,1993,32:83-86
[30].K.Tanaka, K.Kamiya, K.Hirao, N.Soga, A.Mito, H.Nasu. Second harmonic generation in the electrically poled Li2O-Nb2O5-TeO2glasses[J]. Journal of Non-crystalline Solids,1995,185:123-126
[31].K.Tanaka,Y.Yamamoto,H.Nasu,T.Hashimoto,K.Kamiya. Optical second harmonic generation in poled MgO-ZnO-TeO2 and BeO3-TeO2 glasses[J]. Journal of Non-crystalline Solids,1996, 203,:49-54
[32].H.Nasu et al.,第十七届国际玻璃大会论文集(第三卷)[C].1995,75
[33].R.A.Myers et al., Stable second-order nonlinearity in SiO2-based waveguides on Si using temperature/electric-field poling[J]. SPIE,1994,2289:158-166
[34].P.G Kazansky et al., High second-order nonlinearities induced in lead silicate glass by electron-beam irradiation[J]. Optics Letters,1993,18(9):693-695
[35].P.G Kazansky et al., Erasure of thermally poled second-order nonlinearity in fused silica by electron implantation[J]. Optics Letters,1993,18(14):1141-1143
[36].P.S.J. Rusell et al., Electron implantation:a new technique for creation and modification of second-order susceptibility in glasses[J].SPIE,1993,2044:192-201
[37].Q. Liu, F. Gan, X. Zhao, et al, Second harmonic generation in Ge20As25S55glass irradiated by an electron beam[J]. Optics Letters,2001,26:1347-1349
[38].A. Podlipensky, J. Lange, G Seifert, H. Graener, and I. Cravetchi. Second-harmonic generation from ellipsoidal silver nanoparticles embedded in silica glass[J]. Optics Letters, 2003,28(9):716-718
[39].Kurtz S.K, Perry T.T. A Powder Technique for the Evaluation of Nonlinear Optical Materials[J]. Journal of Applied Physics,1968,54:3798-3813
[40].Bosshard C, Knopfle.E, Pretre P, et al. Second-order polarizabilities of nitropyridine derivatives determined with electric-field-induced second harmonic generation and a solvatochromic method:a comparative study[J]. Journal of Applied Physics,1992,71(4): 1594-1605
[41].P.D. Maker, R.W. Terhune, C.M. Savage. Effects of dispersion and focusing on theproduction of optical harmonics[J]. Physical Review Letters,1962,8(1):21-22
[42].J.A.Amstrong, N.Bloembergen, J.Ducuing, P.S.Pershan, Interactions between light waves in a nonlinear dielectric[J]. Physical Review,1962,127:1918-1939
[43].Ulrich Muller, Inorganic Structural Chemistry[M], John Wiley & Sons A Textbook Series
[44].Minoshima K, Taiji M, Kobayashi T, Femtosecond time-resolved interferometry for the determination of complex nonlinear susceptibility[J]. Optics Letters,1991,16:1683-1685
[45]. Wang X, Gu S, Yu J, Zhao X, Tao H, Formation and properties of chalcogenide glasses in the GeS2-Ga2S3-CdS system[J], Materials Chemistry and Physics,2004,83:284-288
[46].Maker P D, Terhune R W, Nisenoff M, et al. Effects of dispersion and focusing on the production of optical harmonics[J]. Physical Review Letters,1962,8 (1):21-22
[47].Gu S, Hu H, Guo H, Tao H, Second-Harmonic generation in transparent surface crystallized GeS2-Ga2S3-CdS chalcogenide glasses[J], Optics Communication,2008,281:2651-2655
[48].Yoshihiro Takahashi, Yasuhiko Benino, Takumi Fujiwara, Takayuki Komatsu. Large second-order optical nonlinearities of fresnoite-type crystals in transparent surface-crystallized glasses[J], Journal of Applied Physics,2004; 95:3503-3508