NiNc（NCO）_4化合物单光子诱导激发态双光子吸收特性研究
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摘要
激光与材料相互作用时表现出的非线性光学特性有着重要的应用,因此对材料的非线性光学特性以及光学非线性参数测量的研究受到了人们的广泛关注。NCO自由基是含氮燃料燃烧过程中重要的中间物之一,由于其本身的复杂性,它既存在电子振动相互作用(Renner-Teller效应) ,又存在ν_1′和2ν_2′之间的费米共振,使得该自由基团成为人们研究的热点。
本论文我们应用速率方程理论和Z-扫描方法,研究了四种三能级模型:基态-激发态单光子吸收模型、基态单光子-双光子吸收并存模型、基态双光子吸收诱导激发态单光子吸收模型和单光子吸收诱导激发态双光子吸收模型的光学非线性吸收特性。讨论了NiNc(NCO)_4化合物的光学非线性吸收,主要包括NiNc(NCO)_4化合物的饱和吸收向反饱和吸收的转化和光学非线性吸收参数的测量。
我们对上面述的四种三能级模型进行了稳态分析,研究表明只有单光子诱导激发态双光子吸收模型存在着饱和吸收向反饱和吸收转化的特征。再通过对单光子诱导激发态双光子模型进行动态分析,研究表明该模型还存在反饱和吸收向饱和吸收转化现象。这里我们详述了单光子诱导激发态双光子吸收模型产生饱和吸收和反饱和吸收相互转化的原因和条件。
通过对NiNc(NCO)_4化合物的Z-扫描实验,并利用单光子诱导双光子吸收模型理论进行数据拟合,得到的实验曲线和理论拟合曲线符合的很好,证明了NiNc(NCO)_4化合物中单光子诱导激发态双光子吸收模型的有效性。
Nonlinear optical properties, exhibited by the interaction between laser and materials, have important applications. Thus, the research on the nonlinear optical properties of materials and the measurement of optical nonlinear parameters is attracting wide attention. NCO free radical is one of important intermediates, which is produced from the Nitrogen-containing fuel combustion process. Due to its complexity—existing both veronica interaction (Renner-Teller Effect) and Fermi Resonance betweenν_1′and 2ν_2′, NCO free radical has become a focus for researchers.
This thesis discussed the optical nonlinear absorption of the compound NiNc(NCO)_4, which included optical nonlinear conversion from saturable absorption to reverse saturable absorption and the measurement of optical nonlinearity absorption parameters. We used rate equation theory and the Z-scan method to study the optical nonlinear absorption properties of four kinds of three-level model, including the model of single photon absorption on ground state and excited state, the model of single-photon and two-photon absorption coexistence on ground state, the model of single-photon absorption on excited state induced by two-photon absorption on ground state and the model of two photon absorption on excited state induced by single photon absorption.
The steady-state analysis on the above four models indicated that only the last one, the model of single-photon absorption induced two-photon absorption on excited state, had the conversion phenomena from saturable absorption to reverse saturable absorption. Dynamic analysis was implemented on the model of two-photon absorption on excited state induced by single-photon absorption, from which we found the conversion phenomena from reverse saturable absorption to saturable absorption is also exist. At last, we expanded on the reasons and conditions which resulted in these conversion.
Through Z-scan experiment with NiNc(NCO)_4 compounds, compared with the data fit of the theoretic model of two-photon absorption on excited state induced by single-photon absorption, we found that the experimental curves agree well with the theoretical curves, demonstrating that the model of single-photon absorption induced two-photon excited state exist in NiNc(NCO)_4 compounds was effective.
本论文我们应用速率方程理论和Z-扫描方法,研究了四种三能级模型:基态-激发态单光子吸收模型、基态单光子-双光子吸收并存模型、基态双光子吸收诱导激发态单光子吸收模型和单光子吸收诱导激发态双光子吸收模型的光学非线性吸收特性。讨论了NiNc(NCO)_4化合物的光学非线性吸收,主要包括NiNc(NCO)_4化合物的饱和吸收向反饱和吸收的转化和光学非线性吸收参数的测量。
我们对上面述的四种三能级模型进行了稳态分析,研究表明只有单光子诱导激发态双光子吸收模型存在着饱和吸收向反饱和吸收转化的特征。再通过对单光子诱导激发态双光子模型进行动态分析,研究表明该模型还存在反饱和吸收向饱和吸收转化现象。这里我们详述了单光子诱导激发态双光子吸收模型产生饱和吸收和反饱和吸收相互转化的原因和条件。
通过对NiNc(NCO)_4化合物的Z-扫描实验,并利用单光子诱导双光子吸收模型理论进行数据拟合,得到的实验曲线和理论拟合曲线符合的很好,证明了NiNc(NCO)_4化合物中单光子诱导激发态双光子吸收模型的有效性。
Nonlinear optical properties, exhibited by the interaction between laser and materials, have important applications. Thus, the research on the nonlinear optical properties of materials and the measurement of optical nonlinear parameters is attracting wide attention. NCO free radical is one of important intermediates, which is produced from the Nitrogen-containing fuel combustion process. Due to its complexity—existing both veronica interaction (Renner-Teller Effect) and Fermi Resonance betweenν_1′and 2ν_2′, NCO free radical has become a focus for researchers.
This thesis discussed the optical nonlinear absorption of the compound NiNc(NCO)_4, which included optical nonlinear conversion from saturable absorption to reverse saturable absorption and the measurement of optical nonlinearity absorption parameters. We used rate equation theory and the Z-scan method to study the optical nonlinear absorption properties of four kinds of three-level model, including the model of single photon absorption on ground state and excited state, the model of single-photon and two-photon absorption coexistence on ground state, the model of single-photon absorption on excited state induced by two-photon absorption on ground state and the model of two photon absorption on excited state induced by single photon absorption.
The steady-state analysis on the above four models indicated that only the last one, the model of single-photon absorption induced two-photon absorption on excited state, had the conversion phenomena from saturable absorption to reverse saturable absorption. Dynamic analysis was implemented on the model of two-photon absorption on excited state induced by single-photon absorption, from which we found the conversion phenomena from reverse saturable absorption to saturable absorption is also exist. At last, we expanded on the reasons and conditions which resulted in these conversion.
Through Z-scan experiment with NiNc(NCO)_4 compounds, compared with the data fit of the theoretic model of two-photon absorption on excited state induced by single-photon absorption, we found that the experimental curves agree well with the theoretical curves, demonstrating that the model of single-photon absorption induced two-photon excited state exist in NiNc(NCO)_4 compounds was effective.
引文
1董贤子,陈卫强,赵震声,段宣明.飞秒脉冲激光双光子微纳加工技术及其应用.科学通报. 2008, 53(001): 2-13
2 W. F. Krupke, A. Lasers and C. A. Pleasanton. Ytterbium Solid-State Lasers. The First Decade. IEEE journal of selected topics in quantum electronics. 2000, 6(6): 1287-1296
3 Y. R. Shen. The Principles of Nonlinear Optics. John Wiley&Sons. 1984: 130-141
4 Y. Chen, L. Gao, M. Feng, L. Gu, N. He, J. Wang, Y. Araki, W. Blau and O. Ito. Photophysical and Optical Limiting Properties of Axially Modified Phthalocyanines. Mini-Reviews in Organic Chemistry. 2009, 6(1): 55-65
5 M. G?ppert-Mayer. ber Elementarakte Mit Zwei Quantensprüngen. Annalen der Physik. 1931, 401: 273-294
6 F. Terenziani, C. Katan, E. Badaeva, S. Tretiak and M. Blanchard-Desce. Enhanced Two-Photon Absorption of Organic Chromophores: Theoretical and Experimental Assessments. Advanced Materials. 2008, 20(24): 4641-4678
7 M. Buist and B. Squier. Real Time Two-Photon Absorption Microscopy Using Multi Point Excitation. Journal of microscopy. 2008, 192(2): 217-226
8 H. Fang, Q. Chen, J. Yang, H. Xia, Y. Ma, H. Wang and H. Sun. Two-Photon Excited Highly Polarized and Directional Upconversion Emission from Slab Organic Crystals. Optics Letters. 2010, 35(3): 441-443
9 F. Ahmad, Y. Tseng, M. Kats and F. Rana. Energy Limits Imposed by Two-Photon Absorption for Pulse Amplification in High-Power Semiconductor Optical Amplifiers. Optics Letters. 2008, 33(10): 1041-1043
10 R. Steiner, M. Kessler, O. Fugger, F. Dolp and D. Russ. Two-Photon Excited Fluorescence of the Lens for the Diagnosis of Presbyopia. Optics and Spectroscopy. 2009, 107(3): 469-473
11 L. Canioni, M. Bellec, A. Royon, B. Bousquet and T. Cardinal. Three-Dimensional Optical Data Storage Using Third-Harmonic Generation in Silver Zinc Phosphate Glass. Optics Letters. 2008, 33(4): 360-362
12 E. Walker and P. Rentzepis. Two-Photon Technology: A New Dimension.Nature Photonics. 2008, 2(7): 406-408
13 S. Hughes, G. Spruce, B. S. Wherrett, K. R. Welford and A. D. Lloyd. The Saturation Limit to Picosecond, Induced Absorption in Dyes. Optics Communications. 1993, 100(1-4): 113-117
14 J. Si, M. Yang, Y. Wang, L. Zhang, C. Li, D. Wang, S. Dong and W. Sun. Nonlinear Excited State Absorption in Cadmium Texaphyrin Solution. Applied Physics Letters. 1994, 64: 3083-3085
15杨淼,王玉晓.一种新型激发态非线性光吸收的研究.中国激光. 1996, 23(009): 824-826
16邓晓旭,张学如,王玉晓,宋瑛林,刘树田,李淳飞.有机分子系统中反饱和吸收向饱和吸收转化的条件.光学学报. 2000, 20(003): 330-334
17 D. Dini, S. Vagin, M. Hanack, V. Amendola and M. Meneghetti. Nonlinear Optical Effects Related to Saturable and Reverse Saturable Absorption by Subphthalocyanines at 532nm. Chemical Communications. 2005, (30): 3796-3798
18 H. I. Elim, J. Yang, J. Y. Lee, J. Mi and W. Ji. Observation of Saturable and Reverse-Saturable Absorption at Longitudinal Surface Plasmon Resonance in Gold Nanorods. Applied Physics Letters. 2006, 88: 083107
19 U. Gurudas, E. Brooks, D. M. Bubb, S. Heiroth, T. Lippert and A. Wokaun. Saturable and Reverse Saturable Absorption in Silver Nanodots at 532nm Using Picosecond Laser Pulses. Journal of Applied Physics. 2008, 104(7): 073107
20 G. Sreekumar, P. G. Frobel, C. I. Muneera, K. Sathiyamoorthy, C. Vijayan and C. Mukherjee. Saturable and Reverse Saturable Absorption and Nonlinear Refraction in Nanoclustered Amido Black Dye–Polymer Films under Low Power Continuous Wave He–Ne Laser Light Excitation. Journal of Optics A: Pure and Applied Optics. 2009, 11: 125204
21 T. Y. Popova, A. K. Popov, S. G. Rautian and R. I. Sokolovskii. Nonlinear Interference Processes in Emission, Absorption and Generation Spectra. Zh. Eksp. Teor. Fiz. 1969, 57: 850-863
22 S. Hirose and K. Yoneda. Development of Optical Six-Axial Force Sensor and Its Signalcalibration Considering Nonlinear Interference. IEEE International Conference on Robotics and Automation. 1990: 46-53
23 S. Calle, J. P. Remenieras, O. Bou Matar and F. Patat. Presence of Nonlinear Interference Effects as a Source of Low Frequency Excitation Force inVibro-Acoustography. Ultrasonics. 2002, 40(1-8): 873-878
24 A. K. Popov, S. A. Myslivets and T. F. George. Nonlinear Interference Effects and All-Optical Switching in Optically Dense Inhomogeneously Broadened Media. Physical Review A. 2005, 71(4): 43811
25 A. Yariv and D. M. Pepper. Amplified Reflection, Phase Conjugation, and Oscillation in Degenerate Four-Wave Mixing. Optics Letters. 1977, 1(1): 16-18
26 R. L. Abrams and R. C. Lind. Degenerate Four-Wave Mixing in Absorbing Media. Optics letters. 1978, 2(4): 94-96
27 R. K. Jain and R. C. Lind. Degenerate Four-Wave Mixing in Semiconductor Doped Glasses. LASER. 1982, 1: 647-653
28 V. L. Vinetski, N. V. Kukhtarev, S. G. Odulov and M. S. Soskin. Dynamic Self-Diffraction of Coherent Light Beams. Physics-Uspekhi. 1979, 22(9): 742-756
29 R. Danielius, P. Di Trapani, A. P. Dubietis, D. Podenas and G. P. Banfi. Self-Diffraction through Cascaded Second-Order Frequency-Mixing Effects in F8-Barium Borate. Optics Letters. 1993: 574-576
30 A. Owyoung. Ellipse Rotation Studies in Laser Host Materials. IEEE Journal of Quantum Electronics. 1973, 9(11): 1064-1069
31 G. E. Trahey, P. D. Freiburger, L. F. Nock and D. C. Sullivan. In Vivo Measurements of Ultrasonic Beam Distortion in the Breast. Ultrasonic imaging. 1991, 13(1): 71-90
32 H. L. Liu, N. McDannold and K. Hynynen. Focal Beam Distortion and Treatment Planning in Abdominal Focused Ultrasound Surgery. Medical physics. 2005, 32: 1270-1280
33 W. T. Pollard, S. Y. Lee and R. A. Mathies. Wave Packet Theory of Dynamic Absorption Spectra in Femtosecond Pump–Probe Experiments. The Journal of Chemical Physics. 1990, 92: 4012-4029
34 S. Woutersen, U. Emmerichs and H. J. Bakker. Femtosecond Mid-Ir Pump-Probe Spectroscopy of Liquid Water: Evidence for a Two-Component Structure. Science. 1997, 278(5338): 658-660
35 M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan and E. W. Van Stryland. Sensitive Measurement of Optical Nonlinearities Using a Single Beam. IEEE Journal of Quantum Electronics. 1990, 26(4): 760-769
36 M. Sheik-Bahae, A. A. Said and E. W. Van Stryland. High-Sensitivity,Single-Beam n2 Measurements. Optics letters. 1989, 14(17): 955-957
37 P. B. Chapple, J. Staromlynska, J. A. Hermann, T. J. McKay and R. G. McDuff. Single-Beam Z-Scan:. Measurement Techniques and Analysis. Journal of Nonlinear Optical Physics and Materials. 1997, 6: 251-293
38 W. Zhao and P. Palffy-Muhoray. Z-Scan Technique Using Top-Hat Beams. Applied Physics Letters. 1993, 63: 1613-1615
39 D. V. Petrov, A. S. L. Gomes and C. B. de Araújo. Reflection Z-Scan Technique for Measurements of Optical Properties of Surfaces. Applied Physics Letters. 1994, 65: 1067-1069
40 S. V. Kershaw. Analysis of the Ez-Scan Measurement Technique. Journal of Modern Optics. 1995, 42(7): 1361-1366
41 J. Wang, M. Sheik-Bahae, A. A. Said, D. J. Hagan and E. W. Van Stryland. Time-Resolved Z-Scan Measurements of Optical Nonlinearities. Journal of the Optical Society of America B. 1994, 11(6): 1009-1017
42 S. M. Mian, B. Taheri and J. P. Wicksted. Effects of Beam Ellipticity on Z-Scan Measurements. Journal of the Optical Society of America B. 1996, 13(5): 856-863
43 M. Sheik-Bahae, J. Wang, R. DeSalvo, D. J. Hagan and E. W. V. Stryland. Measurement of Nondegenerate Nonlinearities Using a Two-Color Z-Scan. Optics letters. 1992, 17(4): 258-260
44 J. Castillo and V. P. Kozich. Thermal Lensing Resulting from One-and Two-Photon Absorption Studied with a Two-Color Time-Resolved Z-Scan. Optics Letters. 1994, 19: 171–173
45 L. Yang, R. Dorsinville, Q. Z. Wang, P. X. Ye, R. R. Alfano, R. Zamboni and C. Taliani. Excited-State Nonlinearity in Polythiophene Thin Films Investigated by the Z-Scan Technique. Optics letters. 1992, 17(5): 323-325
46 Y. Liu, W. Zang, Z. Liu, S. Qi and J. Tian. Study on Z-Scan Characteristics of Multilayer Nonlinear Media Using Coordinate Transformation Method. Optik-International Journal for Light and Electron Optics. 2010: 1-4
47 J. G. Tian, W. P. Zang and G. Y. Zhang. Analysis of Beam Propagation through Thick Nonlinear Media by Variational Approach. CHINESE PHYSICAL SOCIETY. 1994, 43: 1712-1717
48 B. Yao, L. Ren and X. Hou. Z-Scan Theory Based on a Diffraction Model. Journal of the Optical Society of America B. 2003, 20(6): 1290-1294
49 M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau and E. W. Van Stryland. Nonlinear Refraction and Optical Limiting in Thick Media. Opt. Eng. 1991, 30(8): 1228-1235
50 J. A. Hermann. Nonlinear Optical Absorption in Thick Media. Journal of the Optical Society of America B. 1997, 14(4): 814-823
51 B. Gu, W. Ji, P. S. Patil, S. M. Dharmaprakash and H. T. Wang. Two-Photon-Induced Excited-State Absorption: Theory and Experiment. Applied Physics Letters. 2008, 92(9): 091118
2 W. F. Krupke, A. Lasers and C. A. Pleasanton. Ytterbium Solid-State Lasers. The First Decade. IEEE journal of selected topics in quantum electronics. 2000, 6(6): 1287-1296
3 Y. R. Shen. The Principles of Nonlinear Optics. John Wiley&Sons. 1984: 130-141
4 Y. Chen, L. Gao, M. Feng, L. Gu, N. He, J. Wang, Y. Araki, W. Blau and O. Ito. Photophysical and Optical Limiting Properties of Axially Modified Phthalocyanines. Mini-Reviews in Organic Chemistry. 2009, 6(1): 55-65
5 M. G?ppert-Mayer. ber Elementarakte Mit Zwei Quantensprüngen. Annalen der Physik. 1931, 401: 273-294
6 F. Terenziani, C. Katan, E. Badaeva, S. Tretiak and M. Blanchard-Desce. Enhanced Two-Photon Absorption of Organic Chromophores: Theoretical and Experimental Assessments. Advanced Materials. 2008, 20(24): 4641-4678
7 M. Buist and B. Squier. Real Time Two-Photon Absorption Microscopy Using Multi Point Excitation. Journal of microscopy. 2008, 192(2): 217-226
8 H. Fang, Q. Chen, J. Yang, H. Xia, Y. Ma, H. Wang and H. Sun. Two-Photon Excited Highly Polarized and Directional Upconversion Emission from Slab Organic Crystals. Optics Letters. 2010, 35(3): 441-443
9 F. Ahmad, Y. Tseng, M. Kats and F. Rana. Energy Limits Imposed by Two-Photon Absorption for Pulse Amplification in High-Power Semiconductor Optical Amplifiers. Optics Letters. 2008, 33(10): 1041-1043
10 R. Steiner, M. Kessler, O. Fugger, F. Dolp and D. Russ. Two-Photon Excited Fluorescence of the Lens for the Diagnosis of Presbyopia. Optics and Spectroscopy. 2009, 107(3): 469-473
11 L. Canioni, M. Bellec, A. Royon, B. Bousquet and T. Cardinal. Three-Dimensional Optical Data Storage Using Third-Harmonic Generation in Silver Zinc Phosphate Glass. Optics Letters. 2008, 33(4): 360-362
12 E. Walker and P. Rentzepis. Two-Photon Technology: A New Dimension.Nature Photonics. 2008, 2(7): 406-408
13 S. Hughes, G. Spruce, B. S. Wherrett, K. R. Welford and A. D. Lloyd. The Saturation Limit to Picosecond, Induced Absorption in Dyes. Optics Communications. 1993, 100(1-4): 113-117
14 J. Si, M. Yang, Y. Wang, L. Zhang, C. Li, D. Wang, S. Dong and W. Sun. Nonlinear Excited State Absorption in Cadmium Texaphyrin Solution. Applied Physics Letters. 1994, 64: 3083-3085
15杨淼,王玉晓.一种新型激发态非线性光吸收的研究.中国激光. 1996, 23(009): 824-826
16邓晓旭,张学如,王玉晓,宋瑛林,刘树田,李淳飞.有机分子系统中反饱和吸收向饱和吸收转化的条件.光学学报. 2000, 20(003): 330-334
17 D. Dini, S. Vagin, M. Hanack, V. Amendola and M. Meneghetti. Nonlinear Optical Effects Related to Saturable and Reverse Saturable Absorption by Subphthalocyanines at 532nm. Chemical Communications. 2005, (30): 3796-3798
18 H. I. Elim, J. Yang, J. Y. Lee, J. Mi and W. Ji. Observation of Saturable and Reverse-Saturable Absorption at Longitudinal Surface Plasmon Resonance in Gold Nanorods. Applied Physics Letters. 2006, 88: 083107
19 U. Gurudas, E. Brooks, D. M. Bubb, S. Heiroth, T. Lippert and A. Wokaun. Saturable and Reverse Saturable Absorption in Silver Nanodots at 532nm Using Picosecond Laser Pulses. Journal of Applied Physics. 2008, 104(7): 073107
20 G. Sreekumar, P. G. Frobel, C. I. Muneera, K. Sathiyamoorthy, C. Vijayan and C. Mukherjee. Saturable and Reverse Saturable Absorption and Nonlinear Refraction in Nanoclustered Amido Black Dye–Polymer Films under Low Power Continuous Wave He–Ne Laser Light Excitation. Journal of Optics A: Pure and Applied Optics. 2009, 11: 125204
21 T. Y. Popova, A. K. Popov, S. G. Rautian and R. I. Sokolovskii. Nonlinear Interference Processes in Emission, Absorption and Generation Spectra. Zh. Eksp. Teor. Fiz. 1969, 57: 850-863
22 S. Hirose and K. Yoneda. Development of Optical Six-Axial Force Sensor and Its Signalcalibration Considering Nonlinear Interference. IEEE International Conference on Robotics and Automation. 1990: 46-53
23 S. Calle, J. P. Remenieras, O. Bou Matar and F. Patat. Presence of Nonlinear Interference Effects as a Source of Low Frequency Excitation Force inVibro-Acoustography. Ultrasonics. 2002, 40(1-8): 873-878
24 A. K. Popov, S. A. Myslivets and T. F. George. Nonlinear Interference Effects and All-Optical Switching in Optically Dense Inhomogeneously Broadened Media. Physical Review A. 2005, 71(4): 43811
25 A. Yariv and D. M. Pepper. Amplified Reflection, Phase Conjugation, and Oscillation in Degenerate Four-Wave Mixing. Optics Letters. 1977, 1(1): 16-18
26 R. L. Abrams and R. C. Lind. Degenerate Four-Wave Mixing in Absorbing Media. Optics letters. 1978, 2(4): 94-96
27 R. K. Jain and R. C. Lind. Degenerate Four-Wave Mixing in Semiconductor Doped Glasses. LASER. 1982, 1: 647-653
28 V. L. Vinetski, N. V. Kukhtarev, S. G. Odulov and M. S. Soskin. Dynamic Self-Diffraction of Coherent Light Beams. Physics-Uspekhi. 1979, 22(9): 742-756
29 R. Danielius, P. Di Trapani, A. P. Dubietis, D. Podenas and G. P. Banfi. Self-Diffraction through Cascaded Second-Order Frequency-Mixing Effects in F8-Barium Borate. Optics Letters. 1993: 574-576
30 A. Owyoung. Ellipse Rotation Studies in Laser Host Materials. IEEE Journal of Quantum Electronics. 1973, 9(11): 1064-1069
31 G. E. Trahey, P. D. Freiburger, L. F. Nock and D. C. Sullivan. In Vivo Measurements of Ultrasonic Beam Distortion in the Breast. Ultrasonic imaging. 1991, 13(1): 71-90
32 H. L. Liu, N. McDannold and K. Hynynen. Focal Beam Distortion and Treatment Planning in Abdominal Focused Ultrasound Surgery. Medical physics. 2005, 32: 1270-1280
33 W. T. Pollard, S. Y. Lee and R. A. Mathies. Wave Packet Theory of Dynamic Absorption Spectra in Femtosecond Pump–Probe Experiments. The Journal of Chemical Physics. 1990, 92: 4012-4029
34 S. Woutersen, U. Emmerichs and H. J. Bakker. Femtosecond Mid-Ir Pump-Probe Spectroscopy of Liquid Water: Evidence for a Two-Component Structure. Science. 1997, 278(5338): 658-660
35 M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan and E. W. Van Stryland. Sensitive Measurement of Optical Nonlinearities Using a Single Beam. IEEE Journal of Quantum Electronics. 1990, 26(4): 760-769
36 M. Sheik-Bahae, A. A. Said and E. W. Van Stryland. High-Sensitivity,Single-Beam n2 Measurements. Optics letters. 1989, 14(17): 955-957
37 P. B. Chapple, J. Staromlynska, J. A. Hermann, T. J. McKay and R. G. McDuff. Single-Beam Z-Scan:. Measurement Techniques and Analysis. Journal of Nonlinear Optical Physics and Materials. 1997, 6: 251-293
38 W. Zhao and P. Palffy-Muhoray. Z-Scan Technique Using Top-Hat Beams. Applied Physics Letters. 1993, 63: 1613-1615
39 D. V. Petrov, A. S. L. Gomes and C. B. de Araújo. Reflection Z-Scan Technique for Measurements of Optical Properties of Surfaces. Applied Physics Letters. 1994, 65: 1067-1069
40 S. V. Kershaw. Analysis of the Ez-Scan Measurement Technique. Journal of Modern Optics. 1995, 42(7): 1361-1366
41 J. Wang, M. Sheik-Bahae, A. A. Said, D. J. Hagan and E. W. Van Stryland. Time-Resolved Z-Scan Measurements of Optical Nonlinearities. Journal of the Optical Society of America B. 1994, 11(6): 1009-1017
42 S. M. Mian, B. Taheri and J. P. Wicksted. Effects of Beam Ellipticity on Z-Scan Measurements. Journal of the Optical Society of America B. 1996, 13(5): 856-863
43 M. Sheik-Bahae, J. Wang, R. DeSalvo, D. J. Hagan and E. W. V. Stryland. Measurement of Nondegenerate Nonlinearities Using a Two-Color Z-Scan. Optics letters. 1992, 17(4): 258-260
44 J. Castillo and V. P. Kozich. Thermal Lensing Resulting from One-and Two-Photon Absorption Studied with a Two-Color Time-Resolved Z-Scan. Optics Letters. 1994, 19: 171–173
45 L. Yang, R. Dorsinville, Q. Z. Wang, P. X. Ye, R. R. Alfano, R. Zamboni and C. Taliani. Excited-State Nonlinearity in Polythiophene Thin Films Investigated by the Z-Scan Technique. Optics letters. 1992, 17(5): 323-325
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