Abstract

Samples in the crystal directions of Z, X(ab) and the non-critical phase matching angle (θ = 90°,φ = 45°) were gained from high-quality ammonium dihydrogen phosphate (NH4H2PO4, ADP) crystals grown in the Z direction and in defined crystallographic direction (θ = 90°, φ = 45°) via the rapid growth method. Z-scan measurements with pico-second pulse laser irradiation at λ = 355nm were implemented to systematically investigate their nonlinear characters, such as the nonlinear absorption coefficient β, nonlinear refractive index n2 and the third order nonlinear susceptibility χ(3). The results displayed the nonlinear absorption and nonlinear refraction, and the ADP crystals exhibit the reverse saturable absorption and self-focusing effect (n2>0). The nonlinear absorption and refraction were anisotropic in the crystal directions of Z, X, and the non-critical phase matching angle (θ = 90°, φ = 45°) sorted as: [110] < X < Z. The remarkable NLA behaviors at 355 nm are identified to the co-existence of 2PA and 3PA, while 2PA is dominant and the occurrence probability of 3PA is rather low. The anisotropy of the NLA of ADP crystals is closely bound up with the damage anisotropy in our experiments.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]

2018 (2)

Y. Lian, M. Xu, L. Zhang, D. Cai, T. Sui, X. Sun, and X. Chai, “the rapid growth of ADP crystal in defined crystallographic direction,” CrystEngComm 20(7), 917–923 (2018).
[Crossref]

T. Sui, Y. Lian, M. Xu, L. Zhang, Y. Li, X. Zhao, and X. Sun, “Stability and electronic structure of hydrogen vacancies in ADP: hybrid DFT with vdW correction,” RSC Advances 8(13), 6931–6939 (2018).
[Crossref]

2017 (3)

H. Gao, B. Teng, Z. Wang, D. Zhong, S. Wang, J. Tang, N. Ullah, and S. Ji, “Room temperature noncritical phase matching fourth harmonic generation properties of ADP, DADP, and DKDP crystals,” Opt. Mater. Express 7(11), 4050–4057 (2017).

X. Chai, Q. Zhu, B. Feng, F. Li, X. Feng, F. Wang, W. Han, and L. Wang, “Nonlinear absorption properties of DKDP crystal at 263nm and 351nm,” Opt. Mater. 64, 262–267 (2017).
[Crossref]

Y. Lian, G. Yu, F. Liu, L. Zhang, M. Xu, H. Zhou, X. Sun, and Q. Gu, “Prismatic morphology of an ADP crystal grown in a defined crystallographic direction,” RSC Advances 7(83), 52962–52969 (2017).
[Crossref]

2016 (4)

F. Zhang, Z. X. Wu, Zh. P. Wang, W. D. Liang, Sh. L. Wang, and X. G. Xu, “Strong optical limiting behavior discovered in black phosphorus,” RSC Advances 6(24), 20027–20033 (2016).
[Crossref]

S. Ji, B. Teng, W. Kong, D. Zhong, X. Sun, and Z. Wang, “The effect of supersaturation levels on the segregation coefficient of deuterium in K(H1−xDx)2PO4 crystals using Raman spectroscopy,” CrystEngComm 18(6), 971–976 (2016).
[Crossref]

Y. Lian, L. Zhu, T. Sui, G. Yu, L. Song, H. Zhou, M. Xu, and X. Sun, “The rapid growth of ADP single crystal,” CrystEngComm 18(39), 7530–7536 (2016).
[Crossref]

Y. B. Zheng, L. Ding, X. D. Zhou, R. S. Ba, J. Yuan, H. L. Xu, J. Na, Y. J. Li, X. Y. Yang, L. Q. Chai, B. Chen, and W. G. Zheng, “Characterization of the influence of polarization orientation on bulk damage in KDP crystal at different wavelengths,” Opt. Mater. 58, 248–252 (2016).
[Crossref]

2015 (1)

H. Zhou, Q. Zhang, B. Wang, X. Xu, Z. Wang, X. Sun, F. Zhang, L.-S. Zhang, B.-A. Liu, and X.-X. Chai, “Raman gains of ADP and KDP crystals,” Chin. Phys. B 24(4), 227–230 (2015).
[Crossref]

2014 (1)

G. Duchateau, M. D. Feit, and S. G. Demos, “Transient material properties during defect-assisted laser breakdown in deuterated potassium dihydrogen phosphate crystals,” J. Appl. Phys. 115(10), 103506 (2014).
[Crossref]

2013 (1)

B. A. Liu, G. H. Hu, Y. A. Zhao, M. X. Xu, S. H. Ji, L. L. Zhu, L. S. Zhang, X. Sun, Z. P. Wang, and X. G. Xu, “Laser induced damage of DKDP crystals with different deuterated degrees,” Opt. Laser Technol. 45, 469–472 (2013).
[Crossref]

2012 (2)

S. Yu, C.-H. Yang, Z. Jiang, S. Hao, and C. Zhu, “Raman spectra analysis for lattice vibration modes in ADP crystals,” Chinese J. Inorgan. Chem.  28(4), 733–738 (2012).

H. Zhang, Stéphane Virally, Qiaoliang Bao, L. K. Ping, Serge Massar, Nicolas Godbout, and Pascal Kockaert, “Z-scan measurement of the nonlinear refractive index of grapheme,” Opt. Lett. 37(11), 1856 (2012).
[Crossref] [PubMed]

2007 (1)

D. S. Correa, L. De Boni, L. Misoguti, I. Cohanoschi, F. E. Hernandez, and C. R. Mendonc, “Z-scan theoretical analysis for three-, four-and five-photon absorption,” Opt. Commun. 277, 440–445 (2007).
[Crossref]

2006 (1)

D. Xu and D. Xue, “Chemical bond analysis of the crystal growth of KDP and ADP,” J. Cryst. Growth 286(1), 108–113 (2006).
[Crossref]

2005 (2)

D. Xu and D. Xue, “Chemical bond and microscopic growth habit of ADP crystals,” Rengong Jingti Xuebao 34, 823–827 (2005).

K. P. Wang, C. S. Fang, J. X. Zhang, C. S. Liu, R. I. Boughton, S. L. Wang, and X. Zhao, “First-principles study of interstitial oxygen in potassium dihydrogen phosphate crystals,” Phys. Rev. B 72, 184105 (2005).

2004 (2)

A. Melninkaitis, M. Šinkevičius, T. Lipinskas, N. Slavinskis, V. Sirutkaitis, H. Bercegol, and L. Lamaignère, “Characterization of the KDP crystals used in large aperture doublers and triplers,” SPIE 5647, 298–305 (2004).

W.-P. Zang, J.-G. Tian, Z.-B. Liu, W.-Y. Zhou, F. Song, and C.-P. Zhang, “Analytic solutions to Z-scan characteristics of thick media with nonlinear refraction and nonlinear absorption,” J. Opt. Soc. Am. B 21(1), 63–66 (2004).
[Crossref]

2003 (3)

C. W. Carr, H. B. Radousky, and S. G. Demos, “Wavelength Dependence of Laser-Induced Damage: Determining the Damage Initiation Mechanisms,” Phys. Rev. Lett. 91(12), 127402 (2003).
[Crossref] [PubMed]

I. A. Kulagin, R. A. Ilya, A. Kulagin, R. A. Ganeev, V. A. Kim, A. I. Ryasnyansky, R. I. Tugushev, T. Usmanov, and A. V. Zinoviev, “Nonlinear refractive indices and third-order susceptibilities of nonlinear-optical crystals,” Proc. SPIE 4972, 182–189 (2003).

C. S. Liu, Q. Zhang, and N. Kioussis, “Electronic structure calculations of intrinsic and extrinsic hydrogen point defects in KH2PO4,” Phys. Rev. B 68(224107), 1–11 (2003).

2002 (2)

C. Görling, U. Leinhos, and K. Mann, “Comparative studies of absorptance behaviour of alkaline-earth fluorides at 193 nm and 157 nm,” Appl. Phys. B 74(3), 259–265 (2002).
[Crossref]

J. J. De Yoreo, A. K. Burnham, and P. K. Whitman, “Developing KH2PO4 and KD2PO4 crystals for the world’s most powerful laser,” Int. Mater. Rev. 47(3), 113–152 (2002).
[Crossref]

2001 (1)

N. Zaitseva and L. Carman, “Rapid growth of KDP-type crystals,” Prog: Cryst. Growth Charact. 43(1), 1–118 (2001).

2000 (1)

H. Yoshida, T. Jitsuno, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, and K. Yoshida, “Investigation of bulk laser damage in KDP crystal as a function of laser irradiation direction, polarization, and wavelength,” Appl. Phys. B 70(2), 195–201 (2000).
[Crossref]

1999 (1)

P. B. Chapple, J. A. Hermann, and R. G. McDuff, “Power saturation effects in thick single-element optical limiters,” Opt. Quantum Electron. 31(5/7), 555–569 (1999).
[Crossref]

1997 (1)

N. P. Zaitseva, J. J. De Yoreo, M. R. Dehaven, R. L. Vital, K. E. Montgomery, M. Richardson, and L. J. Atherton, “Rapid growth of large-scale (40–55 cm) KH2PO4 crystals,” J. Cryst. Growth 180(2), 255–262 (1997).
[Crossref]

1995 (2)

1994 (2)

W. Zang, J. Tian, and G. Zhang, “Theoretical analysis of Z-scan in thick optical nonlinear media,” Wuli Xuebao 3, 476–482 (1994).

J.-G. Tian, W.-P. Zang, and G.-Y. Zhang, “Analysis of beam propagation through thick nonlinear media by the variational approach,” Wuli Xuebao 43, 1712–1717 (1994).

1993 (1)

1991 (1)

G. G. Gurzadyan and R. K. Ispiryan, “Two-photon absorption peculiarities of potassium dihydrogen phosphate crystal at 216 nm,” Appl. Phys. Lett. 59(6), 630–631 (1991).
[Crossref]

1990 (2)

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990).
[Crossref]

S. B. Mansoor, A. A. Said, and T. H. Wei, “Senstive measurement of optical nonlinearities using a single beam,” J. Quantum Electron 26(3), 760–769 (1990).

1989 (3)

1977 (1)

John Reintjes and R. C. Eckardt, “Two-photon absorption an ADP and KD*P at 266.1 nm,” IEEE J. Quantum Electron. QE-13(9), 791 (1977).

Atherton, L. J.

N. P. Zaitseva, J. J. De Yoreo, M. R. Dehaven, R. L. Vital, K. E. Montgomery, M. Richardson, and L. J. Atherton, “Rapid growth of large-scale (40–55 cm) KH2PO4 crystals,” J. Cryst. Growth 180(2), 255–262 (1997).
[Crossref]

Ba, R. S.

Y. B. Zheng, L. Ding, X. D. Zhou, R. S. Ba, J. Yuan, H. L. Xu, J. Na, Y. J. Li, X. Y. Yang, L. Q. Chai, B. Chen, and W. G. Zheng, “Characterization of the influence of polarization orientation on bulk damage in KDP crystal at different wavelengths,” Opt. Mater. 58, 248–252 (2016).
[Crossref]

Bao, Qiaoliang

Bercegol, H.

A. Melninkaitis, M. Šinkevičius, T. Lipinskas, N. Slavinskis, V. Sirutkaitis, H. Bercegol, and L. Lamaignère, “Characterization of the KDP crystals used in large aperture doublers and triplers,” SPIE 5647, 298–305 (2004).

Boughton, R. I.

K. P. Wang, C. S. Fang, J. X. Zhang, C. S. Liu, R. I. Boughton, S. L. Wang, and X. Zhao, “First-principles study of interstitial oxygen in potassium dihydrogen phosphate crystals,” Phys. Rev. B 72, 184105 (2005).

Braunlich, Peter

S. C. Jones, Peter Braunlich, R. T Casper, and Xiao-An Shen, “Recent progress on laser-induced modifications and intrinsic bulk damage of wide-gap optical materials,” Opt. Eng. 28(10), 1039–1068 (1989).

Burnham, A. K.

J. J. De Yoreo, A. K. Burnham, and P. K. Whitman, “Developing KH2PO4 and KD2PO4 crystals for the world’s most powerful laser,” Int. Mater. Rev. 47(3), 113–152 (2002).
[Crossref]

Cai, D.

Y. Lian, M. Xu, L. Zhang, D. Cai, T. Sui, X. Sun, and X. Chai, “the rapid growth of ADP crystal in defined crystallographic direction,” CrystEngComm 20(7), 917–923 (2018).
[Crossref]

Carman, L.

N. Zaitseva and L. Carman, “Rapid growth of KDP-type crystals,” Prog: Cryst. Growth Charact. 43(1), 1–118 (2001).

Carr, C. W.

C. W. Carr, H. B. Radousky, and S. G. Demos, “Wavelength Dependence of Laser-Induced Damage: Determining the Damage Initiation Mechanisms,” Phys. Rev. Lett. 91(12), 127402 (2003).
[Crossref] [PubMed]

Casper, R. T

S. C. Jones, Peter Braunlich, R. T Casper, and Xiao-An Shen, “Recent progress on laser-induced modifications and intrinsic bulk damage of wide-gap optical materials,” Opt. Eng. 28(10), 1039–1068 (1989).

Chai, L. Q.

Y. B. Zheng, L. Ding, X. D. Zhou, R. S. Ba, J. Yuan, H. L. Xu, J. Na, Y. J. Li, X. Y. Yang, L. Q. Chai, B. Chen, and W. G. Zheng, “Characterization of the influence of polarization orientation on bulk damage in KDP crystal at different wavelengths,” Opt. Mater. 58, 248–252 (2016).
[Crossref]

Chai, X.

Y. Lian, M. Xu, L. Zhang, D. Cai, T. Sui, X. Sun, and X. Chai, “the rapid growth of ADP crystal in defined crystallographic direction,” CrystEngComm 20(7), 917–923 (2018).
[Crossref]

X. Chai, Q. Zhu, B. Feng, F. Li, X. Feng, F. Wang, W. Han, and L. Wang, “Nonlinear absorption properties of DKDP crystal at 263nm and 351nm,” Opt. Mater. 64, 262–267 (2017).
[Crossref]

Chai, X.-X.

H. Zhou, Q. Zhang, B. Wang, X. Xu, Z. Wang, X. Sun, F. Zhang, L.-S. Zhang, B.-A. Liu, and X.-X. Chai, “Raman gains of ADP and KDP crystals,” Chin. Phys. B 24(4), 227–230 (2015).
[Crossref]

Chapple, P. B.

P. B. Chapple, J. A. Hermann, and R. G. McDuff, “Power saturation effects in thick single-element optical limiters,” Opt. Quantum Electron. 31(5/7), 555–569 (1999).
[Crossref]

Chen, B.

Y. B. Zheng, L. Ding, X. D. Zhou, R. S. Ba, J. Yuan, H. L. Xu, J. Na, Y. J. Li, X. Y. Yang, L. Q. Chai, B. Chen, and W. G. Zheng, “Characterization of the influence of polarization orientation on bulk damage in KDP crystal at different wavelengths,” Opt. Mater. 58, 248–252 (2016).
[Crossref]

Cohanoschi, I.

D. S. Correa, L. De Boni, L. Misoguti, I. Cohanoschi, F. E. Hernandez, and C. R. Mendonc, “Z-scan theoretical analysis for three-, four-and five-photon absorption,” Opt. Commun. 277, 440–445 (2007).
[Crossref]

Correa, D. S.

D. S. Correa, L. De Boni, L. Misoguti, I. Cohanoschi, F. E. Hernandez, and C. R. Mendonc, “Z-scan theoretical analysis for three-, four-and five-photon absorption,” Opt. Commun. 277, 440–445 (2007).
[Crossref]

De Boni, L.

D. S. Correa, L. De Boni, L. Misoguti, I. Cohanoschi, F. E. Hernandez, and C. R. Mendonc, “Z-scan theoretical analysis for three-, four-and five-photon absorption,” Opt. Commun. 277, 440–445 (2007).
[Crossref]

De Yoreo, J. J.

J. J. De Yoreo, A. K. Burnham, and P. K. Whitman, “Developing KH2PO4 and KD2PO4 crystals for the world’s most powerful laser,” Int. Mater. Rev. 47(3), 113–152 (2002).
[Crossref]

N. P. Zaitseva, J. J. De Yoreo, M. R. Dehaven, R. L. Vital, K. E. Montgomery, M. Richardson, and L. J. Atherton, “Rapid growth of large-scale (40–55 cm) KH2PO4 crystals,” J. Cryst. Growth 180(2), 255–262 (1997).
[Crossref]

Dehaven, M. R.

N. P. Zaitseva, J. J. De Yoreo, M. R. Dehaven, R. L. Vital, K. E. Montgomery, M. Richardson, and L. J. Atherton, “Rapid growth of large-scale (40–55 cm) KH2PO4 crystals,” J. Cryst. Growth 180(2), 255–262 (1997).
[Crossref]

Demos, S. G.

G. Duchateau, M. D. Feit, and S. G. Demos, “Transient material properties during defect-assisted laser breakdown in deuterated potassium dihydrogen phosphate crystals,” J. Appl. Phys. 115(10), 103506 (2014).
[Crossref]

C. W. Carr, H. B. Radousky, and S. G. Demos, “Wavelength Dependence of Laser-Induced Damage: Determining the Damage Initiation Mechanisms,” Phys. Rev. Lett. 91(12), 127402 (2003).
[Crossref] [PubMed]

Desalvo, R.

Ding, L.

Y. B. Zheng, L. Ding, X. D. Zhou, R. S. Ba, J. Yuan, H. L. Xu, J. Na, Y. J. Li, X. Y. Yang, L. Q. Chai, B. Chen, and W. G. Zheng, “Characterization of the influence of polarization orientation on bulk damage in KDP crystal at different wavelengths,” Opt. Mater. 58, 248–252 (2016).
[Crossref]

Duchateau, G.

G. Duchateau, M. D. Feit, and S. G. Demos, “Transient material properties during defect-assisted laser breakdown in deuterated potassium dihydrogen phosphate crystals,” J. Appl. Phys. 115(10), 103506 (2014).
[Crossref]

Eckardt, R. C.

John Reintjes and R. C. Eckardt, “Two-photon absorption an ADP and KD*P at 266.1 nm,” IEEE J. Quantum Electron. QE-13(9), 791 (1977).

Fang, C. S.

K. P. Wang, C. S. Fang, J. X. Zhang, C. S. Liu, R. I. Boughton, S. L. Wang, and X. Zhao, “First-principles study of interstitial oxygen in potassium dihydrogen phosphate crystals,” Phys. Rev. B 72, 184105 (2005).

Feit, M. D.

G. Duchateau, M. D. Feit, and S. G. Demos, “Transient material properties during defect-assisted laser breakdown in deuterated potassium dihydrogen phosphate crystals,” J. Appl. Phys. 115(10), 103506 (2014).
[Crossref]

Feng, B.

X. Chai, Q. Zhu, B. Feng, F. Li, X. Feng, F. Wang, W. Han, and L. Wang, “Nonlinear absorption properties of DKDP crystal at 263nm and 351nm,” Opt. Mater. 64, 262–267 (2017).
[Crossref]

Feng, X.

X. Chai, Q. Zhu, B. Feng, F. Li, X. Feng, F. Wang, W. Han, and L. Wang, “Nonlinear absorption properties of DKDP crystal at 263nm and 351nm,” Opt. Mater. 64, 262–267 (2017).
[Crossref]

Fujita, H.

H. Yoshida, T. Jitsuno, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, and K. Yoshida, “Investigation of bulk laser damage in KDP crystal as a function of laser irradiation direction, polarization, and wavelength,” Appl. Phys. B 70(2), 195–201 (2000).
[Crossref]

Ganeev, R. A.

I. A. Kulagin, R. A. Ilya, A. Kulagin, R. A. Ganeev, V. A. Kim, A. I. Ryasnyansky, R. I. Tugushev, T. Usmanov, and A. V. Zinoviev, “Nonlinear refractive indices and third-order susceptibilities of nonlinear-optical crystals,” Proc. SPIE 4972, 182–189 (2003).

Gao, H.

Godbout, Nicolas

Görling, C.

C. Görling, U. Leinhos, and K. Mann, “Comparative studies of absorptance behaviour of alkaline-earth fluorides at 193 nm and 157 nm,” Appl. Phys. B 74(3), 259–265 (2002).
[Crossref]

Gu, Q.

Y. Lian, G. Yu, F. Liu, L. Zhang, M. Xu, H. Zhou, X. Sun, and Q. Gu, “Prismatic morphology of an ADP crystal grown in a defined crystallographic direction,” RSC Advances 7(83), 52962–52969 (2017).
[Crossref]

Gurzadyan, G. G.

G. G. Gurzadyan and R. K. Ispiryan, “Two-photon absorption peculiarities of potassium dihydrogen phosphate crystal at 216 nm,” Appl. Phys. Lett. 59(6), 630–631 (1991).
[Crossref]

Hagan, D. J.

R. Desalvo, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, “Z-scan measurements of the anisotropy of nonlinear refraction and absorption in crystals,” Opt. Lett. 18(3), 194–196 (1993).
[Crossref] [PubMed]

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990).
[Crossref]

Han, W.

X. Chai, Q. Zhu, B. Feng, F. Li, X. Feng, F. Wang, W. Han, and L. Wang, “Nonlinear absorption properties of DKDP crystal at 263nm and 351nm,” Opt. Mater. 64, 262–267 (2017).
[Crossref]

Hao, S.

S. Yu, C.-H. Yang, Z. Jiang, S. Hao, and C. Zhu, “Raman spectra analysis for lattice vibration modes in ADP crystals,” Chinese J. Inorgan. Chem.  28(4), 733–738 (2012).

Hermann, J. A.

P. B. Chapple, J. A. Hermann, and R. G. McDuff, “Power saturation effects in thick single-element optical limiters,” Opt. Quantum Electron. 31(5/7), 555–569 (1999).
[Crossref]

Hernandez, F. E.

D. S. Correa, L. De Boni, L. Misoguti, I. Cohanoschi, F. E. Hernandez, and C. R. Mendonc, “Z-scan theoretical analysis for three-, four-and five-photon absorption,” Opt. Commun. 277, 440–445 (2007).
[Crossref]

Hu, G. H.

B. A. Liu, G. H. Hu, Y. A. Zhao, M. X. Xu, S. H. Ji, L. L. Zhu, L. S. Zhang, X. Sun, Z. P. Wang, and X. G. Xu, “Laser induced damage of DKDP crystals with different deuterated degrees,” Opt. Laser Technol. 45, 469–472 (2013).
[Crossref]

Ilya, R. A.

I. A. Kulagin, R. A. Ilya, A. Kulagin, R. A. Ganeev, V. A. Kim, A. I. Ryasnyansky, R. I. Tugushev, T. Usmanov, and A. V. Zinoviev, “Nonlinear refractive indices and third-order susceptibilities of nonlinear-optical crystals,” Proc. SPIE 4972, 182–189 (2003).

Ispiryan, R. K.

G. G. Gurzadyan and R. K. Ispiryan, “Two-photon absorption peculiarities of potassium dihydrogen phosphate crystal at 216 nm,” Appl. Phys. Lett. 59(6), 630–631 (1991).
[Crossref]

Ji, S.

H. Gao, B. Teng, Z. Wang, D. Zhong, S. Wang, J. Tang, N. Ullah, and S. Ji, “Room temperature noncritical phase matching fourth harmonic generation properties of ADP, DADP, and DKDP crystals,” Opt. Mater. Express 7(11), 4050–4057 (2017).

S. Ji, B. Teng, W. Kong, D. Zhong, X. Sun, and Z. Wang, “The effect of supersaturation levels on the segregation coefficient of deuterium in K(H1−xDx)2PO4 crystals using Raman spectroscopy,” CrystEngComm 18(6), 971–976 (2016).
[Crossref]

Ji, S. H.

B. A. Liu, G. H. Hu, Y. A. Zhao, M. X. Xu, S. H. Ji, L. L. Zhu, L. S. Zhang, X. Sun, Z. P. Wang, and X. G. Xu, “Laser induced damage of DKDP crystals with different deuterated degrees,” Opt. Laser Technol. 45, 469–472 (2013).
[Crossref]

Jiang, Z.

S. Yu, C.-H. Yang, Z. Jiang, S. Hao, and C. Zhu, “Raman spectra analysis for lattice vibration modes in ADP crystals,” Chinese J. Inorgan. Chem.  28(4), 733–738 (2012).

Jitsuno, T.

H. Yoshida, T. Jitsuno, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, and K. Yoshida, “Investigation of bulk laser damage in KDP crystal as a function of laser irradiation direction, polarization, and wavelength,” Appl. Phys. B 70(2), 195–201 (2000).
[Crossref]

Jones, S. C.

S. C. Jones, Peter Braunlich, R. T Casper, and Xiao-An Shen, “Recent progress on laser-induced modifications and intrinsic bulk damage of wide-gap optical materials,” Opt. Eng. 28(10), 1039–1068 (1989).

Kim, V. A.

I. A. Kulagin, R. A. Ilya, A. Kulagin, R. A. Ganeev, V. A. Kim, A. I. Ryasnyansky, R. I. Tugushev, T. Usmanov, and A. V. Zinoviev, “Nonlinear refractive indices and third-order susceptibilities of nonlinear-optical crystals,” Proc. SPIE 4972, 182–189 (2003).

Kioussis, N.

C. S. Liu, Q. Zhang, and N. Kioussis, “Electronic structure calculations of intrinsic and extrinsic hydrogen point defects in KH2PO4,” Phys. Rev. B 68(224107), 1–11 (2003).

Kockaert, Pascal

Kong, W.

S. Ji, B. Teng, W. Kong, D. Zhong, X. Sun, and Z. Wang, “The effect of supersaturation levels on the segregation coefficient of deuterium in K(H1−xDx)2PO4 crystals using Raman spectroscopy,” CrystEngComm 18(6), 971–976 (2016).
[Crossref]

Kulagin, A.

I. A. Kulagin, R. A. Ilya, A. Kulagin, R. A. Ganeev, V. A. Kim, A. I. Ryasnyansky, R. I. Tugushev, T. Usmanov, and A. V. Zinoviev, “Nonlinear refractive indices and third-order susceptibilities of nonlinear-optical crystals,” Proc. SPIE 4972, 182–189 (2003).

Kulagin, I. A.

I. A. Kulagin, R. A. Ilya, A. Kulagin, R. A. Ganeev, V. A. Kim, A. I. Ryasnyansky, R. I. Tugushev, T. Usmanov, and A. V. Zinoviev, “Nonlinear refractive indices and third-order susceptibilities of nonlinear-optical crystals,” Proc. SPIE 4972, 182–189 (2003).

Lamaignère, L.

A. Melninkaitis, M. Šinkevičius, T. Lipinskas, N. Slavinskis, V. Sirutkaitis, H. Bercegol, and L. Lamaignère, “Characterization of the KDP crystals used in large aperture doublers and triplers,” SPIE 5647, 298–305 (2004).

Leinhos, U.

C. Görling, U. Leinhos, and K. Mann, “Comparative studies of absorptance behaviour of alkaline-earth fluorides at 193 nm and 157 nm,” Appl. Phys. B 74(3), 259–265 (2002).
[Crossref]

Li, F.

X. Chai, Q. Zhu, B. Feng, F. Li, X. Feng, F. Wang, W. Han, and L. Wang, “Nonlinear absorption properties of DKDP crystal at 263nm and 351nm,” Opt. Mater. 64, 262–267 (2017).
[Crossref]

Li, Y.

T. Sui, Y. Lian, M. Xu, L. Zhang, Y. Li, X. Zhao, and X. Sun, “Stability and electronic structure of hydrogen vacancies in ADP: hybrid DFT with vdW correction,” RSC Advances 8(13), 6931–6939 (2018).
[Crossref]

Li, Y. J.

Y. B. Zheng, L. Ding, X. D. Zhou, R. S. Ba, J. Yuan, H. L. Xu, J. Na, Y. J. Li, X. Y. Yang, L. Q. Chai, B. Chen, and W. G. Zheng, “Characterization of the influence of polarization orientation on bulk damage in KDP crystal at different wavelengths,” Opt. Mater. 58, 248–252 (2016).
[Crossref]

Lian, Y.

T. Sui, Y. Lian, M. Xu, L. Zhang, Y. Li, X. Zhao, and X. Sun, “Stability and electronic structure of hydrogen vacancies in ADP: hybrid DFT with vdW correction,” RSC Advances 8(13), 6931–6939 (2018).
[Crossref]

Y. Lian, M. Xu, L. Zhang, D. Cai, T. Sui, X. Sun, and X. Chai, “the rapid growth of ADP crystal in defined crystallographic direction,” CrystEngComm 20(7), 917–923 (2018).
[Crossref]

Y. Lian, G. Yu, F. Liu, L. Zhang, M. Xu, H. Zhou, X. Sun, and Q. Gu, “Prismatic morphology of an ADP crystal grown in a defined crystallographic direction,” RSC Advances 7(83), 52962–52969 (2017).
[Crossref]

Y. Lian, L. Zhu, T. Sui, G. Yu, L. Song, H. Zhou, M. Xu, and X. Sun, “The rapid growth of ADP single crystal,” CrystEngComm 18(39), 7530–7536 (2016).
[Crossref]

Liang, W. D.

F. Zhang, Z. X. Wu, Zh. P. Wang, W. D. Liang, Sh. L. Wang, and X. G. Xu, “Strong optical limiting behavior discovered in black phosphorus,” RSC Advances 6(24), 20027–20033 (2016).
[Crossref]

Lipinskas, T.

A. Melninkaitis, M. Šinkevičius, T. Lipinskas, N. Slavinskis, V. Sirutkaitis, H. Bercegol, and L. Lamaignère, “Characterization of the KDP crystals used in large aperture doublers and triplers,” SPIE 5647, 298–305 (2004).

Liu, B. A.

B. A. Liu, G. H. Hu, Y. A. Zhao, M. X. Xu, S. H. Ji, L. L. Zhu, L. S. Zhang, X. Sun, Z. P. Wang, and X. G. Xu, “Laser induced damage of DKDP crystals with different deuterated degrees,” Opt. Laser Technol. 45, 469–472 (2013).
[Crossref]

Liu, B.-A.

H. Zhou, Q. Zhang, B. Wang, X. Xu, Z. Wang, X. Sun, F. Zhang, L.-S. Zhang, B.-A. Liu, and X.-X. Chai, “Raman gains of ADP and KDP crystals,” Chin. Phys. B 24(4), 227–230 (2015).
[Crossref]

Liu, C. S.

K. P. Wang, C. S. Fang, J. X. Zhang, C. S. Liu, R. I. Boughton, S. L. Wang, and X. Zhao, “First-principles study of interstitial oxygen in potassium dihydrogen phosphate crystals,” Phys. Rev. B 72, 184105 (2005).

C. S. Liu, Q. Zhang, and N. Kioussis, “Electronic structure calculations of intrinsic and extrinsic hydrogen point defects in KH2PO4,” Phys. Rev. B 68(224107), 1–11 (2003).

Liu, F.

Y. Lian, G. Yu, F. Liu, L. Zhang, M. Xu, H. Zhou, X. Sun, and Q. Gu, “Prismatic morphology of an ADP crystal grown in a defined crystallographic direction,” RSC Advances 7(83), 52962–52969 (2017).
[Crossref]

Liu, Z.-B.

Mann, K.

C. Görling, U. Leinhos, and K. Mann, “Comparative studies of absorptance behaviour of alkaline-earth fluorides at 193 nm and 157 nm,” Appl. Phys. B 74(3), 259–265 (2002).
[Crossref]

Mansoor, S. B.

S. B. Mansoor, A. A. Said, and T. H. Wei, “Senstive measurement of optical nonlinearities using a single beam,” J. Quantum Electron 26(3), 760–769 (1990).

Massar, Serge

McDuff, R. G.

P. B. Chapple, J. A. Hermann, and R. G. McDuff, “Power saturation effects in thick single-element optical limiters,” Opt. Quantum Electron. 31(5/7), 555–569 (1999).
[Crossref]

Melninkaitis, A.

A. Melninkaitis, M. Šinkevičius, T. Lipinskas, N. Slavinskis, V. Sirutkaitis, H. Bercegol, and L. Lamaignère, “Characterization of the KDP crystals used in large aperture doublers and triplers,” SPIE 5647, 298–305 (2004).

Mendonc, C. R.

D. S. Correa, L. De Boni, L. Misoguti, I. Cohanoschi, F. E. Hernandez, and C. R. Mendonc, “Z-scan theoretical analysis for three-, four-and five-photon absorption,” Opt. Commun. 277, 440–445 (2007).
[Crossref]

Misoguti, L.

D. S. Correa, L. De Boni, L. Misoguti, I. Cohanoschi, F. E. Hernandez, and C. R. Mendonc, “Z-scan theoretical analysis for three-, four-and five-photon absorption,” Opt. Commun. 277, 440–445 (2007).
[Crossref]

Montgomery, K. E.

N. P. Zaitseva, J. J. De Yoreo, M. R. Dehaven, R. L. Vital, K. E. Montgomery, M. Richardson, and L. J. Atherton, “Rapid growth of large-scale (40–55 cm) KH2PO4 crystals,” J. Cryst. Growth 180(2), 255–262 (1997).
[Crossref]

Na, J.

Y. B. Zheng, L. Ding, X. D. Zhou, R. S. Ba, J. Yuan, H. L. Xu, J. Na, Y. J. Li, X. Y. Yang, L. Q. Chai, B. Chen, and W. G. Zheng, “Characterization of the influence of polarization orientation on bulk damage in KDP crystal at different wavelengths,” Opt. Mater. 58, 248–252 (2016).
[Crossref]

Nakatsuka, M.

H. Yoshida, T. Jitsuno, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, and K. Yoshida, “Investigation of bulk laser damage in KDP crystal as a function of laser irradiation direction, polarization, and wavelength,” Appl. Phys. B 70(2), 195–201 (2000).
[Crossref]

Ping, L. K.

Radousky, H. B.

C. W. Carr, H. B. Radousky, and S. G. Demos, “Wavelength Dependence of Laser-Induced Damage: Determining the Damage Initiation Mechanisms,” Phys. Rev. Lett. 91(12), 127402 (2003).
[Crossref] [PubMed]

Reintjes, John

John Reintjes and R. C. Eckardt, “Two-photon absorption an ADP and KD*P at 266.1 nm,” IEEE J. Quantum Electron. QE-13(9), 791 (1977).

Richardson, M.

N. P. Zaitseva, J. J. De Yoreo, M. R. Dehaven, R. L. Vital, K. E. Montgomery, M. Richardson, and L. J. Atherton, “Rapid growth of large-scale (40–55 cm) KH2PO4 crystals,” J. Cryst. Growth 180(2), 255–262 (1997).
[Crossref]

Ryasnyansky, A. I.

I. A. Kulagin, R. A. Ilya, A. Kulagin, R. A. Ganeev, V. A. Kim, A. I. Ryasnyansky, R. I. Tugushev, T. Usmanov, and A. V. Zinoviev, “Nonlinear refractive indices and third-order susceptibilities of nonlinear-optical crystals,” Proc. SPIE 4972, 182–189 (2003).

Said, A. A.

Sasaki, T.

H. Yoshida, T. Jitsuno, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, and K. Yoshida, “Investigation of bulk laser damage in KDP crystal as a function of laser irradiation direction, polarization, and wavelength,” Appl. Phys. B 70(2), 195–201 (2000).
[Crossref]

Sheik-Bahae, M.

Shen, Xiao-An

S. C. Jones, Peter Braunlich, R. T Casper, and Xiao-An Shen, “Recent progress on laser-induced modifications and intrinsic bulk damage of wide-gap optical materials,” Opt. Eng. 28(10), 1039–1068 (1989).

Šinkevicius, M.

A. Melninkaitis, M. Šinkevičius, T. Lipinskas, N. Slavinskis, V. Sirutkaitis, H. Bercegol, and L. Lamaignère, “Characterization of the KDP crystals used in large aperture doublers and triplers,” SPIE 5647, 298–305 (2004).

Sirutkaitis, V.

A. Melninkaitis, M. Šinkevičius, T. Lipinskas, N. Slavinskis, V. Sirutkaitis, H. Bercegol, and L. Lamaignère, “Characterization of the KDP crystals used in large aperture doublers and triplers,” SPIE 5647, 298–305 (2004).

Slavinskis, N.

A. Melninkaitis, M. Šinkevičius, T. Lipinskas, N. Slavinskis, V. Sirutkaitis, H. Bercegol, and L. Lamaignère, “Characterization of the KDP crystals used in large aperture doublers and triplers,” SPIE 5647, 298–305 (2004).

Song, F.

Song, L.

Y. Lian, L. Zhu, T. Sui, G. Yu, L. Song, H. Zhou, M. Xu, and X. Sun, “The rapid growth of ADP single crystal,” CrystEngComm 18(39), 7530–7536 (2016).
[Crossref]

Sui, T.

Y. Lian, M. Xu, L. Zhang, D. Cai, T. Sui, X. Sun, and X. Chai, “the rapid growth of ADP crystal in defined crystallographic direction,” CrystEngComm 20(7), 917–923 (2018).
[Crossref]

T. Sui, Y. Lian, M. Xu, L. Zhang, Y. Li, X. Zhao, and X. Sun, “Stability and electronic structure of hydrogen vacancies in ADP: hybrid DFT with vdW correction,” RSC Advances 8(13), 6931–6939 (2018).
[Crossref]

Y. Lian, L. Zhu, T. Sui, G. Yu, L. Song, H. Zhou, M. Xu, and X. Sun, “The rapid growth of ADP single crystal,” CrystEngComm 18(39), 7530–7536 (2016).
[Crossref]

Sun, X.

Y. Lian, M. Xu, L. Zhang, D. Cai, T. Sui, X. Sun, and X. Chai, “the rapid growth of ADP crystal in defined crystallographic direction,” CrystEngComm 20(7), 917–923 (2018).
[Crossref]

T. Sui, Y. Lian, M. Xu, L. Zhang, Y. Li, X. Zhao, and X. Sun, “Stability and electronic structure of hydrogen vacancies in ADP: hybrid DFT with vdW correction,” RSC Advances 8(13), 6931–6939 (2018).
[Crossref]

Y. Lian, G. Yu, F. Liu, L. Zhang, M. Xu, H. Zhou, X. Sun, and Q. Gu, “Prismatic morphology of an ADP crystal grown in a defined crystallographic direction,” RSC Advances 7(83), 52962–52969 (2017).
[Crossref]

Y. Lian, L. Zhu, T. Sui, G. Yu, L. Song, H. Zhou, M. Xu, and X. Sun, “The rapid growth of ADP single crystal,” CrystEngComm 18(39), 7530–7536 (2016).
[Crossref]

S. Ji, B. Teng, W. Kong, D. Zhong, X. Sun, and Z. Wang, “The effect of supersaturation levels on the segregation coefficient of deuterium in K(H1−xDx)2PO4 crystals using Raman spectroscopy,” CrystEngComm 18(6), 971–976 (2016).
[Crossref]

H. Zhou, Q. Zhang, B. Wang, X. Xu, Z. Wang, X. Sun, F. Zhang, L.-S. Zhang, B.-A. Liu, and X.-X. Chai, “Raman gains of ADP and KDP crystals,” Chin. Phys. B 24(4), 227–230 (2015).
[Crossref]

B. A. Liu, G. H. Hu, Y. A. Zhao, M. X. Xu, S. H. Ji, L. L. Zhu, L. S. Zhang, X. Sun, Z. P. Wang, and X. G. Xu, “Laser induced damage of DKDP crystals with different deuterated degrees,” Opt. Laser Technol. 45, 469–472 (2013).
[Crossref]

Tang, J.

Teng, B.

H. Gao, B. Teng, Z. Wang, D. Zhong, S. Wang, J. Tang, N. Ullah, and S. Ji, “Room temperature noncritical phase matching fourth harmonic generation properties of ADP, DADP, and DKDP crystals,” Opt. Mater. Express 7(11), 4050–4057 (2017).

S. Ji, B. Teng, W. Kong, D. Zhong, X. Sun, and Z. Wang, “The effect of supersaturation levels on the segregation coefficient of deuterium in K(H1−xDx)2PO4 crystals using Raman spectroscopy,” CrystEngComm 18(6), 971–976 (2016).
[Crossref]

Tian, J.

W. Zang, J. Tian, and G. Zhang, “Theoretical analysis of Z-scan in thick optical nonlinear media,” Wuli Xuebao 3, 476–482 (1994).

Tian, J.-G.

Tugushev, R. I.

I. A. Kulagin, R. A. Ilya, A. Kulagin, R. A. Ganeev, V. A. Kim, A. I. Ryasnyansky, R. I. Tugushev, T. Usmanov, and A. V. Zinoviev, “Nonlinear refractive indices and third-order susceptibilities of nonlinear-optical crystals,” Proc. SPIE 4972, 182–189 (2003).

Ullah, N.

Usmanov, T.

I. A. Kulagin, R. A. Ilya, A. Kulagin, R. A. Ganeev, V. A. Kim, A. I. Ryasnyansky, R. I. Tugushev, T. Usmanov, and A. V. Zinoviev, “Nonlinear refractive indices and third-order susceptibilities of nonlinear-optical crystals,” Proc. SPIE 4972, 182–189 (2003).

Van Stryland, E. W.

Virally, Stéphane

Vital, R. L.

N. P. Zaitseva, J. J. De Yoreo, M. R. Dehaven, R. L. Vital, K. E. Montgomery, M. Richardson, and L. J. Atherton, “Rapid growth of large-scale (40–55 cm) KH2PO4 crystals,” J. Cryst. Growth 180(2), 255–262 (1997).
[Crossref]

Wang, B.

H. Zhou, Q. Zhang, B. Wang, X. Xu, Z. Wang, X. Sun, F. Zhang, L.-S. Zhang, B.-A. Liu, and X.-X. Chai, “Raman gains of ADP and KDP crystals,” Chin. Phys. B 24(4), 227–230 (2015).
[Crossref]

Wang, F.

X. Chai, Q. Zhu, B. Feng, F. Li, X. Feng, F. Wang, W. Han, and L. Wang, “Nonlinear absorption properties of DKDP crystal at 263nm and 351nm,” Opt. Mater. 64, 262–267 (2017).
[Crossref]

Wang, K. P.

K. P. Wang, C. S. Fang, J. X. Zhang, C. S. Liu, R. I. Boughton, S. L. Wang, and X. Zhao, “First-principles study of interstitial oxygen in potassium dihydrogen phosphate crystals,” Phys. Rev. B 72, 184105 (2005).

Wang, L.

X. Chai, Q. Zhu, B. Feng, F. Li, X. Feng, F. Wang, W. Han, and L. Wang, “Nonlinear absorption properties of DKDP crystal at 263nm and 351nm,” Opt. Mater. 64, 262–267 (2017).
[Crossref]

Wang, S.

Wang, S. L.

K. P. Wang, C. S. Fang, J. X. Zhang, C. S. Liu, R. I. Boughton, S. L. Wang, and X. Zhao, “First-principles study of interstitial oxygen in potassium dihydrogen phosphate crystals,” Phys. Rev. B 72, 184105 (2005).

Wang, Sh. L.

F. Zhang, Z. X. Wu, Zh. P. Wang, W. D. Liang, Sh. L. Wang, and X. G. Xu, “Strong optical limiting behavior discovered in black phosphorus,” RSC Advances 6(24), 20027–20033 (2016).
[Crossref]

Wang, Z.

H. Gao, B. Teng, Z. Wang, D. Zhong, S. Wang, J. Tang, N. Ullah, and S. Ji, “Room temperature noncritical phase matching fourth harmonic generation properties of ADP, DADP, and DKDP crystals,” Opt. Mater. Express 7(11), 4050–4057 (2017).

S. Ji, B. Teng, W. Kong, D. Zhong, X. Sun, and Z. Wang, “The effect of supersaturation levels on the segregation coefficient of deuterium in K(H1−xDx)2PO4 crystals using Raman spectroscopy,” CrystEngComm 18(6), 971–976 (2016).
[Crossref]

H. Zhou, Q. Zhang, B. Wang, X. Xu, Z. Wang, X. Sun, F. Zhang, L.-S. Zhang, B.-A. Liu, and X.-X. Chai, “Raman gains of ADP and KDP crystals,” Chin. Phys. B 24(4), 227–230 (2015).
[Crossref]

Wang, Z. P.

B. A. Liu, G. H. Hu, Y. A. Zhao, M. X. Xu, S. H. Ji, L. L. Zhu, L. S. Zhang, X. Sun, Z. P. Wang, and X. G. Xu, “Laser induced damage of DKDP crystals with different deuterated degrees,” Opt. Laser Technol. 45, 469–472 (2013).
[Crossref]

Wang, Zh. P.

F. Zhang, Z. X. Wu, Zh. P. Wang, W. D. Liang, Sh. L. Wang, and X. G. Xu, “Strong optical limiting behavior discovered in black phosphorus,” RSC Advances 6(24), 20027–20033 (2016).
[Crossref]

Wei, T.

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990).
[Crossref]

Wei, T. H.

S. B. Mansoor, A. A. Said, and T. H. Wei, “Senstive measurement of optical nonlinearities using a single beam,” J. Quantum Electron 26(3), 760–769 (1990).

Whitman, P. K.

J. J. De Yoreo, A. K. Burnham, and P. K. Whitman, “Developing KH2PO4 and KD2PO4 crystals for the world’s most powerful laser,” Int. Mater. Rev. 47(3), 113–152 (2002).
[Crossref]

Wu, Z. X.

F. Zhang, Z. X. Wu, Zh. P. Wang, W. D. Liang, Sh. L. Wang, and X. G. Xu, “Strong optical limiting behavior discovered in black phosphorus,” RSC Advances 6(24), 20027–20033 (2016).
[Crossref]

Xie, S. W.

Xu, D.

D. Xu and D. Xue, “Chemical bond analysis of the crystal growth of KDP and ADP,” J. Cryst. Growth 286(1), 108–113 (2006).
[Crossref]

D. Xu and D. Xue, “Chemical bond and microscopic growth habit of ADP crystals,” Rengong Jingti Xuebao 34, 823–827 (2005).

Xu, H. L.

Y. B. Zheng, L. Ding, X. D. Zhou, R. S. Ba, J. Yuan, H. L. Xu, J. Na, Y. J. Li, X. Y. Yang, L. Q. Chai, B. Chen, and W. G. Zheng, “Characterization of the influence of polarization orientation on bulk damage in KDP crystal at different wavelengths,” Opt. Mater. 58, 248–252 (2016).
[Crossref]

Xu, M.

T. Sui, Y. Lian, M. Xu, L. Zhang, Y. Li, X. Zhao, and X. Sun, “Stability and electronic structure of hydrogen vacancies in ADP: hybrid DFT with vdW correction,” RSC Advances 8(13), 6931–6939 (2018).
[Crossref]

Y. Lian, M. Xu, L. Zhang, D. Cai, T. Sui, X. Sun, and X. Chai, “the rapid growth of ADP crystal in defined crystallographic direction,” CrystEngComm 20(7), 917–923 (2018).
[Crossref]

Y. Lian, G. Yu, F. Liu, L. Zhang, M. Xu, H. Zhou, X. Sun, and Q. Gu, “Prismatic morphology of an ADP crystal grown in a defined crystallographic direction,” RSC Advances 7(83), 52962–52969 (2017).
[Crossref]

Y. Lian, L. Zhu, T. Sui, G. Yu, L. Song, H. Zhou, M. Xu, and X. Sun, “The rapid growth of ADP single crystal,” CrystEngComm 18(39), 7530–7536 (2016).
[Crossref]

Xu, M. X.

B. A. Liu, G. H. Hu, Y. A. Zhao, M. X. Xu, S. H. Ji, L. L. Zhu, L. S. Zhang, X. Sun, Z. P. Wang, and X. G. Xu, “Laser induced damage of DKDP crystals with different deuterated degrees,” Opt. Laser Technol. 45, 469–472 (2013).
[Crossref]

Xu, X.

H. Zhou, Q. Zhang, B. Wang, X. Xu, Z. Wang, X. Sun, F. Zhang, L.-S. Zhang, B.-A. Liu, and X.-X. Chai, “Raman gains of ADP and KDP crystals,” Chin. Phys. B 24(4), 227–230 (2015).
[Crossref]

Xu, X. G.

F. Zhang, Z. X. Wu, Zh. P. Wang, W. D. Liang, Sh. L. Wang, and X. G. Xu, “Strong optical limiting behavior discovered in black phosphorus,” RSC Advances 6(24), 20027–20033 (2016).
[Crossref]

B. A. Liu, G. H. Hu, Y. A. Zhao, M. X. Xu, S. H. Ji, L. L. Zhu, L. S. Zhang, X. Sun, Z. P. Wang, and X. G. Xu, “Laser induced damage of DKDP crystals with different deuterated degrees,” Opt. Laser Technol. 45, 469–472 (2013).
[Crossref]

Xue, D.

D. Xu and D. Xue, “Chemical bond analysis of the crystal growth of KDP and ADP,” J. Cryst. Growth 286(1), 108–113 (2006).
[Crossref]

D. Xu and D. Xue, “Chemical bond and microscopic growth habit of ADP crystals,” Rengong Jingti Xuebao 34, 823–827 (2005).

Yang, C.-H.

S. Yu, C.-H. Yang, Z. Jiang, S. Hao, and C. Zhu, “Raman spectra analysis for lattice vibration modes in ADP crystals,” Chinese J. Inorgan. Chem.  28(4), 733–738 (2012).

Yang, X. L.

Yang, X. Y.

Y. B. Zheng, L. Ding, X. D. Zhou, R. S. Ba, J. Yuan, H. L. Xu, J. Na, Y. J. Li, X. Y. Yang, L. Q. Chai, B. Chen, and W. G. Zheng, “Characterization of the influence of polarization orientation on bulk damage in KDP crystal at different wavelengths,” Opt. Mater. 58, 248–252 (2016).
[Crossref]

Yoshida, H.

H. Yoshida, T. Jitsuno, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, and K. Yoshida, “Investigation of bulk laser damage in KDP crystal as a function of laser irradiation direction, polarization, and wavelength,” Appl. Phys. B 70(2), 195–201 (2000).
[Crossref]

Yoshida, K.

H. Yoshida, T. Jitsuno, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, and K. Yoshida, “Investigation of bulk laser damage in KDP crystal as a function of laser irradiation direction, polarization, and wavelength,” Appl. Phys. B 70(2), 195–201 (2000).
[Crossref]

Yoshimura, M.

H. Yoshida, T. Jitsuno, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, and K. Yoshida, “Investigation of bulk laser damage in KDP crystal as a function of laser irradiation direction, polarization, and wavelength,” Appl. Phys. B 70(2), 195–201 (2000).
[Crossref]

Yu, G.

Y. Lian, G. Yu, F. Liu, L. Zhang, M. Xu, H. Zhou, X. Sun, and Q. Gu, “Prismatic morphology of an ADP crystal grown in a defined crystallographic direction,” RSC Advances 7(83), 52962–52969 (2017).
[Crossref]

Y. Lian, L. Zhu, T. Sui, G. Yu, L. Song, H. Zhou, M. Xu, and X. Sun, “The rapid growth of ADP single crystal,” CrystEngComm 18(39), 7530–7536 (2016).
[Crossref]

Yu, S.

S. Yu, C.-H. Yang, Z. Jiang, S. Hao, and C. Zhu, “Raman spectra analysis for lattice vibration modes in ADP crystals,” Chinese J. Inorgan. Chem.  28(4), 733–738 (2012).

Yuan, J.

Y. B. Zheng, L. Ding, X. D. Zhou, R. S. Ba, J. Yuan, H. L. Xu, J. Na, Y. J. Li, X. Y. Yang, L. Q. Chai, B. Chen, and W. G. Zheng, “Characterization of the influence of polarization orientation on bulk damage in KDP crystal at different wavelengths,” Opt. Mater. 58, 248–252 (2016).
[Crossref]

Zaitseva, N.

N. Zaitseva and L. Carman, “Rapid growth of KDP-type crystals,” Prog: Cryst. Growth Charact. 43(1), 1–118 (2001).

Zaitseva, N. P.

N. P. Zaitseva, J. J. De Yoreo, M. R. Dehaven, R. L. Vital, K. E. Montgomery, M. Richardson, and L. J. Atherton, “Rapid growth of large-scale (40–55 cm) KH2PO4 crystals,” J. Cryst. Growth 180(2), 255–262 (1997).
[Crossref]

Zang, W.

W. Zang, J. Tian, and G. Zhang, “Theoretical analysis of Z-scan in thick optical nonlinear media,” Wuli Xuebao 3, 476–482 (1994).

Zang, W.-P.

Zhang, C.-P.

Zhang, C.-Z.

Zhang, F.

F. Zhang, Z. X. Wu, Zh. P. Wang, W. D. Liang, Sh. L. Wang, and X. G. Xu, “Strong optical limiting behavior discovered in black phosphorus,” RSC Advances 6(24), 20027–20033 (2016).
[Crossref]

H. Zhou, Q. Zhang, B. Wang, X. Xu, Z. Wang, X. Sun, F. Zhang, L.-S. Zhang, B.-A. Liu, and X.-X. Chai, “Raman gains of ADP and KDP crystals,” Chin. Phys. B 24(4), 227–230 (2015).
[Crossref]

Zhang, G.

J.-G. Tian, W.-P. Zang, C.-Z. Zhang, and G. Zhang, “Analysis of beam propagation in thick nonlinear media,” Appl. Opt. 34(21), 4331–4336 (1995).
[Crossref] [PubMed]

W. Zang, J. Tian, and G. Zhang, “Theoretical analysis of Z-scan in thick optical nonlinear media,” Wuli Xuebao 3, 476–482 (1994).

Zhang, G.-Y.

J.-G. Tian, W.-P. Zang, and G.-Y. Zhang, “Analysis of beam propagation through thick nonlinear media by the variational approach,” Wuli Xuebao 43, 1712–1717 (1994).

Zhang, H.

Zhang, J. X.

K. P. Wang, C. S. Fang, J. X. Zhang, C. S. Liu, R. I. Boughton, S. L. Wang, and X. Zhao, “First-principles study of interstitial oxygen in potassium dihydrogen phosphate crystals,” Phys. Rev. B 72, 184105 (2005).

Zhang, L.

T. Sui, Y. Lian, M. Xu, L. Zhang, Y. Li, X. Zhao, and X. Sun, “Stability and electronic structure of hydrogen vacancies in ADP: hybrid DFT with vdW correction,” RSC Advances 8(13), 6931–6939 (2018).
[Crossref]

Y. Lian, M. Xu, L. Zhang, D. Cai, T. Sui, X. Sun, and X. Chai, “the rapid growth of ADP crystal in defined crystallographic direction,” CrystEngComm 20(7), 917–923 (2018).
[Crossref]

Y. Lian, G. Yu, F. Liu, L. Zhang, M. Xu, H. Zhou, X. Sun, and Q. Gu, “Prismatic morphology of an ADP crystal grown in a defined crystallographic direction,” RSC Advances 7(83), 52962–52969 (2017).
[Crossref]

Zhang, L. S.

B. A. Liu, G. H. Hu, Y. A. Zhao, M. X. Xu, S. H. Ji, L. L. Zhu, L. S. Zhang, X. Sun, Z. P. Wang, and X. G. Xu, “Laser induced damage of DKDP crystals with different deuterated degrees,” Opt. Laser Technol. 45, 469–472 (2013).
[Crossref]

Zhang, L.-S.

H. Zhou, Q. Zhang, B. Wang, X. Xu, Z. Wang, X. Sun, F. Zhang, L.-S. Zhang, B.-A. Liu, and X.-X. Chai, “Raman gains of ADP and KDP crystals,” Chin. Phys. B 24(4), 227–230 (2015).
[Crossref]

Zhang, Q.

H. Zhou, Q. Zhang, B. Wang, X. Xu, Z. Wang, X. Sun, F. Zhang, L.-S. Zhang, B.-A. Liu, and X.-X. Chai, “Raman gains of ADP and KDP crystals,” Chin. Phys. B 24(4), 227–230 (2015).
[Crossref]

C. S. Liu, Q. Zhang, and N. Kioussis, “Electronic structure calculations of intrinsic and extrinsic hydrogen point defects in KH2PO4,” Phys. Rev. B 68(224107), 1–11 (2003).

Zhao, X.

T. Sui, Y. Lian, M. Xu, L. Zhang, Y. Li, X. Zhao, and X. Sun, “Stability and electronic structure of hydrogen vacancies in ADP: hybrid DFT with vdW correction,” RSC Advances 8(13), 6931–6939 (2018).
[Crossref]

K. P. Wang, C. S. Fang, J. X. Zhang, C. S. Liu, R. I. Boughton, S. L. Wang, and X. Zhao, “First-principles study of interstitial oxygen in potassium dihydrogen phosphate crystals,” Phys. Rev. B 72, 184105 (2005).

Zhao, Y. A.

B. A. Liu, G. H. Hu, Y. A. Zhao, M. X. Xu, S. H. Ji, L. L. Zhu, L. S. Zhang, X. Sun, Z. P. Wang, and X. G. Xu, “Laser induced damage of DKDP crystals with different deuterated degrees,” Opt. Laser Technol. 45, 469–472 (2013).
[Crossref]

Zheng, W. G.

Y. B. Zheng, L. Ding, X. D. Zhou, R. S. Ba, J. Yuan, H. L. Xu, J. Na, Y. J. Li, X. Y. Yang, L. Q. Chai, B. Chen, and W. G. Zheng, “Characterization of the influence of polarization orientation on bulk damage in KDP crystal at different wavelengths,” Opt. Mater. 58, 248–252 (2016).
[Crossref]

Zheng, Y. B.

Y. B. Zheng, L. Ding, X. D. Zhou, R. S. Ba, J. Yuan, H. L. Xu, J. Na, Y. J. Li, X. Y. Yang, L. Q. Chai, B. Chen, and W. G. Zheng, “Characterization of the influence of polarization orientation on bulk damage in KDP crystal at different wavelengths,” Opt. Mater. 58, 248–252 (2016).
[Crossref]

Zhong, D.

H. Gao, B. Teng, Z. Wang, D. Zhong, S. Wang, J. Tang, N. Ullah, and S. Ji, “Room temperature noncritical phase matching fourth harmonic generation properties of ADP, DADP, and DKDP crystals,” Opt. Mater. Express 7(11), 4050–4057 (2017).

S. Ji, B. Teng, W. Kong, D. Zhong, X. Sun, and Z. Wang, “The effect of supersaturation levels on the segregation coefficient of deuterium in K(H1−xDx)2PO4 crystals using Raman spectroscopy,” CrystEngComm 18(6), 971–976 (2016).
[Crossref]

Zhou, H.

Y. Lian, G. Yu, F. Liu, L. Zhang, M. Xu, H. Zhou, X. Sun, and Q. Gu, “Prismatic morphology of an ADP crystal grown in a defined crystallographic direction,” RSC Advances 7(83), 52962–52969 (2017).
[Crossref]

Y. Lian, L. Zhu, T. Sui, G. Yu, L. Song, H. Zhou, M. Xu, and X. Sun, “The rapid growth of ADP single crystal,” CrystEngComm 18(39), 7530–7536 (2016).
[Crossref]

H. Zhou, Q. Zhang, B. Wang, X. Xu, Z. Wang, X. Sun, F. Zhang, L.-S. Zhang, B.-A. Liu, and X.-X. Chai, “Raman gains of ADP and KDP crystals,” Chin. Phys. B 24(4), 227–230 (2015).
[Crossref]

Zhou, W.-Y.

Zhou, X. D.

Y. B. Zheng, L. Ding, X. D. Zhou, R. S. Ba, J. Yuan, H. L. Xu, J. Na, Y. J. Li, X. Y. Yang, L. Q. Chai, B. Chen, and W. G. Zheng, “Characterization of the influence of polarization orientation on bulk damage in KDP crystal at different wavelengths,” Opt. Mater. 58, 248–252 (2016).
[Crossref]

Zhu, C.

S. Yu, C.-H. Yang, Z. Jiang, S. Hao, and C. Zhu, “Raman spectra analysis for lattice vibration modes in ADP crystals,” Chinese J. Inorgan. Chem.  28(4), 733–738 (2012).

Zhu, L.

Y. Lian, L. Zhu, T. Sui, G. Yu, L. Song, H. Zhou, M. Xu, and X. Sun, “The rapid growth of ADP single crystal,” CrystEngComm 18(39), 7530–7536 (2016).
[Crossref]

Zhu, L. L.

B. A. Liu, G. H. Hu, Y. A. Zhao, M. X. Xu, S. H. Ji, L. L. Zhu, L. S. Zhang, X. Sun, Z. P. Wang, and X. G. Xu, “Laser induced damage of DKDP crystals with different deuterated degrees,” Opt. Laser Technol. 45, 469–472 (2013).
[Crossref]

Zhu, Q.

X. Chai, Q. Zhu, B. Feng, F. Li, X. Feng, F. Wang, W. Han, and L. Wang, “Nonlinear absorption properties of DKDP crystal at 263nm and 351nm,” Opt. Mater. 64, 262–267 (2017).
[Crossref]

Zinoviev, A. V.

I. A. Kulagin, R. A. Ilya, A. Kulagin, R. A. Ganeev, V. A. Kim, A. I. Ryasnyansky, R. I. Tugushev, T. Usmanov, and A. V. Zinoviev, “Nonlinear refractive indices and third-order susceptibilities of nonlinear-optical crystals,” Proc. SPIE 4972, 182–189 (2003).

Appl. Opt. (2)

Appl. Phys. B (2)

C. Görling, U. Leinhos, and K. Mann, “Comparative studies of absorptance behaviour of alkaline-earth fluorides at 193 nm and 157 nm,” Appl. Phys. B 74(3), 259–265 (2002).
[Crossref]

H. Yoshida, T. Jitsuno, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, and K. Yoshida, “Investigation of bulk laser damage in KDP crystal as a function of laser irradiation direction, polarization, and wavelength,” Appl. Phys. B 70(2), 195–201 (2000).
[Crossref]

Appl. Phys. Lett. (1)

G. G. Gurzadyan and R. K. Ispiryan, “Two-photon absorption peculiarities of potassium dihydrogen phosphate crystal at 216 nm,” Appl. Phys. Lett. 59(6), 630–631 (1991).
[Crossref]

Chin. Phys. B (1)

H. Zhou, Q. Zhang, B. Wang, X. Xu, Z. Wang, X. Sun, F. Zhang, L.-S. Zhang, B.-A. Liu, and X.-X. Chai, “Raman gains of ADP and KDP crystals,” Chin. Phys. B 24(4), 227–230 (2015).
[Crossref]

Chinese J. Inorgan. Chem (1)

S. Yu, C.-H. Yang, Z. Jiang, S. Hao, and C. Zhu, “Raman spectra analysis for lattice vibration modes in ADP crystals,” Chinese J. Inorgan. Chem.  28(4), 733–738 (2012).

CrystEngComm (3)

Y. Lian, L. Zhu, T. Sui, G. Yu, L. Song, H. Zhou, M. Xu, and X. Sun, “The rapid growth of ADP single crystal,” CrystEngComm 18(39), 7530–7536 (2016).
[Crossref]

S. Ji, B. Teng, W. Kong, D. Zhong, X. Sun, and Z. Wang, “The effect of supersaturation levels on the segregation coefficient of deuterium in K(H1−xDx)2PO4 crystals using Raman spectroscopy,” CrystEngComm 18(6), 971–976 (2016).
[Crossref]

Y. Lian, M. Xu, L. Zhang, D. Cai, T. Sui, X. Sun, and X. Chai, “the rapid growth of ADP crystal in defined crystallographic direction,” CrystEngComm 20(7), 917–923 (2018).
[Crossref]

IEEE J. Quantum Electron. (2)

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990).
[Crossref]

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Int. Mater. Rev. (1)

J. J. De Yoreo, A. K. Burnham, and P. K. Whitman, “Developing KH2PO4 and KD2PO4 crystals for the world’s most powerful laser,” Int. Mater. Rev. 47(3), 113–152 (2002).
[Crossref]

J. Appl. Phys. (1)

G. Duchateau, M. D. Feit, and S. G. Demos, “Transient material properties during defect-assisted laser breakdown in deuterated potassium dihydrogen phosphate crystals,” J. Appl. Phys. 115(10), 103506 (2014).
[Crossref]

J. Cryst. Growth (2)

D. Xu and D. Xue, “Chemical bond analysis of the crystal growth of KDP and ADP,” J. Cryst. Growth 286(1), 108–113 (2006).
[Crossref]

N. P. Zaitseva, J. J. De Yoreo, M. R. Dehaven, R. L. Vital, K. E. Montgomery, M. Richardson, and L. J. Atherton, “Rapid growth of large-scale (40–55 cm) KH2PO4 crystals,” J. Cryst. Growth 180(2), 255–262 (1997).
[Crossref]

J. Opt. Soc. Am. B (1)

J. Quantum Electron (1)

S. B. Mansoor, A. A. Said, and T. H. Wei, “Senstive measurement of optical nonlinearities using a single beam,” J. Quantum Electron 26(3), 760–769 (1990).

Opt. Commun. (1)

D. S. Correa, L. De Boni, L. Misoguti, I. Cohanoschi, F. E. Hernandez, and C. R. Mendonc, “Z-scan theoretical analysis for three-, four-and five-photon absorption,” Opt. Commun. 277, 440–445 (2007).
[Crossref]

Opt. Eng. (1)

S. C. Jones, Peter Braunlich, R. T Casper, and Xiao-An Shen, “Recent progress on laser-induced modifications and intrinsic bulk damage of wide-gap optical materials,” Opt. Eng. 28(10), 1039–1068 (1989).

Opt. Laser Technol. (1)

B. A. Liu, G. H. Hu, Y. A. Zhao, M. X. Xu, S. H. Ji, L. L. Zhu, L. S. Zhang, X. Sun, Z. P. Wang, and X. G. Xu, “Laser induced damage of DKDP crystals with different deuterated degrees,” Opt. Laser Technol. 45, 469–472 (2013).
[Crossref]

Opt. Lett. (4)

Opt. Mater. (2)

X. Chai, Q. Zhu, B. Feng, F. Li, X. Feng, F. Wang, W. Han, and L. Wang, “Nonlinear absorption properties of DKDP crystal at 263nm and 351nm,” Opt. Mater. 64, 262–267 (2017).
[Crossref]

Y. B. Zheng, L. Ding, X. D. Zhou, R. S. Ba, J. Yuan, H. L. Xu, J. Na, Y. J. Li, X. Y. Yang, L. Q. Chai, B. Chen, and W. G. Zheng, “Characterization of the influence of polarization orientation on bulk damage in KDP crystal at different wavelengths,” Opt. Mater. 58, 248–252 (2016).
[Crossref]

Opt. Mater. Express (1)

Opt. Quantum Electron. (1)

P. B. Chapple, J. A. Hermann, and R. G. McDuff, “Power saturation effects in thick single-element optical limiters,” Opt. Quantum Electron. 31(5/7), 555–569 (1999).
[Crossref]

Phys. Rev. B (2)

C. S. Liu, Q. Zhang, and N. Kioussis, “Electronic structure calculations of intrinsic and extrinsic hydrogen point defects in KH2PO4,” Phys. Rev. B 68(224107), 1–11 (2003).

K. P. Wang, C. S. Fang, J. X. Zhang, C. S. Liu, R. I. Boughton, S. L. Wang, and X. Zhao, “First-principles study of interstitial oxygen in potassium dihydrogen phosphate crystals,” Phys. Rev. B 72, 184105 (2005).

Phys. Rev. Lett. (1)

C. W. Carr, H. B. Radousky, and S. G. Demos, “Wavelength Dependence of Laser-Induced Damage: Determining the Damage Initiation Mechanisms,” Phys. Rev. Lett. 91(12), 127402 (2003).
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Proc. SPIE (1)

I. A. Kulagin, R. A. Ilya, A. Kulagin, R. A. Ganeev, V. A. Kim, A. I. Ryasnyansky, R. I. Tugushev, T. Usmanov, and A. V. Zinoviev, “Nonlinear refractive indices and third-order susceptibilities of nonlinear-optical crystals,” Proc. SPIE 4972, 182–189 (2003).

Prog: Cryst. Growth Charact. (1)

N. Zaitseva and L. Carman, “Rapid growth of KDP-type crystals,” Prog: Cryst. Growth Charact. 43(1), 1–118 (2001).

Rengong Jingti Xuebao (1)

D. Xu and D. Xue, “Chemical bond and microscopic growth habit of ADP crystals,” Rengong Jingti Xuebao 34, 823–827 (2005).

RSC Advances (3)

Y. Lian, G. Yu, F. Liu, L. Zhang, M. Xu, H. Zhou, X. Sun, and Q. Gu, “Prismatic morphology of an ADP crystal grown in a defined crystallographic direction,” RSC Advances 7(83), 52962–52969 (2017).
[Crossref]

F. Zhang, Z. X. Wu, Zh. P. Wang, W. D. Liang, Sh. L. Wang, and X. G. Xu, “Strong optical limiting behavior discovered in black phosphorus,” RSC Advances 6(24), 20027–20033 (2016).
[Crossref]

T. Sui, Y. Lian, M. Xu, L. Zhang, Y. Li, X. Zhao, and X. Sun, “Stability and electronic structure of hydrogen vacancies in ADP: hybrid DFT with vdW correction,” RSC Advances 8(13), 6931–6939 (2018).
[Crossref]

SPIE (1)

A. Melninkaitis, M. Šinkevičius, T. Lipinskas, N. Slavinskis, V. Sirutkaitis, H. Bercegol, and L. Lamaignère, “Characterization of the KDP crystals used in large aperture doublers and triplers,” SPIE 5647, 298–305 (2004).

Wuli Xuebao (2)

W. Zang, J. Tian, and G. Zhang, “Theoretical analysis of Z-scan in thick optical nonlinear media,” Wuli Xuebao 3, 476–482 (1994).

J.-G. Tian, W.-P. Zang, and G.-Y. Zhang, “Analysis of beam propagation through thick nonlinear media by the variational approach,” Wuli Xuebao 43, 1712–1717 (1994).

Other (2)

L. N. Rashkovich, KDP-Family Single Crystal (IOP Publishing Ltd, 1991).

D. N. Nikogosyan, Nonlinear Optical Crystals: A Complete Survey (Springer, 2001.

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Figures (5)

Fig. 1
Fig. 1 Schematic of samples cut along the direction of (a) Z (sample Z-Z and D-Z), a (sample Z-X and D-X, and (b) (θ = 90°, φ = 45°) (sample Z-[110] and D-[110]).
Fig. 2
Fig. 2 Schematic diagram of experimental set-up for Z-scan measurements.
Fig. 3
Fig. 3 Transmittance spectra of the ADP samples.
Fig. 4
Fig. 4 Open-aperture Z-scan measurements results of ADP samples at 355nm. (a) and (b) illustrate the NLA of samples grown in Z direction and in defined direction, respectively.
Fig. 5
Fig. 5 Closed-aperture Z-scan measurements results of ADP samples at 355nm. (a)-(e) illustrate the nonlinear refraction of the samples Z-Z, Z-X, Z-[110], D-Z, D-X and D-[110].

Tables (2)

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Table 1 The detailed parameters and computed results of the nonlinear absorption and nonlinear refraction.

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Table 2 the LDTs of ADP crystals grown in Z direction and grown in defined direction via 1-on-1 method (J/cm2) [13].

Equations (15)

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α(I)=α+βI+γ I 2 +
T=1+ 4Δ φ 0 (t)x ( x 2 +1)( x 2 +9) +O[Δ φ 0 (t) 2 ]
T= i=1 n [1+ 4Δ φ 0i x i ( x i 2 +1)( x i 2 +9) ] exp[ i=1 n 4Δ φ 0i x i ( x i 2 +1)( x i 2 +9) ]
T= { [ (x+l) 2 +1]×( x 2 +9) [ (x+l) 2 +9]×( x 2 +1) } Δ φ R (t)/4
C φ (t)Δ φ R (t)+tanh(l/3 )× [Δ φ R (t)] 2 /4 + [Δ φ R (t)] 3 / 16
T= { [ (x+l) 2 +1]×( x 2 +9) [ (x+l) 2 +9]×( x 2 +1) } C φ (t)/4
T= 1 q 0 (x,t) ln[1+ q 0 (x,t)]
T= i=1 n { 1 q 0i ( x i ,t) ln[1+ q 0i ( x i ,t)] } 1 1 2 i=1 n q 0i (x,t) + [ 1 2 i=1 n q 0i (x,t) ] 2 +O{ [ 1 2 i=1 n q 0i (x,t) ] 3 }
T'= 1 1+ 1 2 i=1 n q 0i (x',t) = 1 1+ 1 2 x x+l' q 0 (x',t)dx' = 1 1+ 1 2 Q R (t)[ tan 1 (x+l) tan 1 (x)]
C q (t) Q R (t)×( 1+tanh(l/2 )×{ 3Δ φ R (t)/ 10 + [Δ φ R (t)] 2 /8 } )
T'= 1 1+ 1 2 C q (t)[ tan 1 (x+l) tan 1 (x)]
χ (3) = χ R (3) +i χ I (3)
χ R (3) (esu)=c n 0 2 n 2 /120 π 2 ( m 2 /W)
χ I (3) (esu)= c 2 n 0 2 β/240 π 2 ω(m/W)
χ k (3) = 1 4 [3( χ xxxx + χ xxyy )+( χ xxxx χ xxyy )cos4φ] cos 4 θ+ 3 2 χ yyzz sin 2 2θ+ χ zzzz sin 4 θ