Abstract

Noncritical phase matching (NCPM) fourth-harmonic-generation (FHG) experiments were conducted on different deuterium content DKDP crystals by adjusting crystal temperature to generate 266 nm deep UV laser. Specially, near room temperature NCPM is realized in extremely high deuterium content DKDP crystal at 38.6 °C, which is the lowest temperature to the best of our knowledge. NCPM temperature of DKDP crystals in 60-100% deuterium content range and 1050-1070 nm wavelength range are determined by a linear relationship according to the experimental and calculated results. Angular tuning properties are independent with deuterium content in medium and higher deuterium content DKDP crystals. All of these results will provide good references for future FHG applications of 1 μm laser with DKDP crystals.

© 2015 Optical Society of America

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    [Crossref]
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    [Crossref]
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    [Crossref]

2015 (2)

F. Wang, F. Q. Li, X. X. Chai, L. Q. Wang, W. Han, H. T. Jia, L. D. Zhou, B. Feng, and Y. Xiang, “Efficient fourth harmonic generation of Nd: glass lasers in ADP and DKDP crystals,” Proc. SPIE 9255, 92551R (2015).

L. S. Zhang, M. X. Xu, B. A. Liu, L. L. Zhu, B. Wang, H. L. Zhou, F. F. Liu, and X. Sun, “New annealing method to improve KD2PO4 crystal quality: learning from high temperature phase transition,” CrystEngComm 17(25), 4705–4711 (2015).
[Crossref]

2013 (3)

L. L. Zhu, X. Zhang, M. X. Xu, B. A. Liu, S. H. Ji, L. S. Zhang, H. L. Zhou, F. F. Liu, Z. P. Wang, and X. Sun, “Refractive indices in the whole transmission range of partially deuterated KDP crystals,” AIP Adv. 3(11), 112114 (2013).
[Crossref]

S. Ji, F. Wang, M. Xu, L. Zhu, X. Xu, Z. Wang, and X. Sun, “Room temperature, high-efficiency, noncritical phase-matching fourth harmonic generation in partially deuterated ADP crystal,” Opt. Lett. 38(10), 1679–1681 (2013).
[Crossref] [PubMed]

S. Ji, F. Wang, L. Zhu, X. Xu, Z. Wang, and X. Sun, “Non-critical phase-matching fourth harmonic generation of a 1053-nm laser in an ADP crystal,” Sci. Rep. 3, 1605 (2013).
[Crossref] [PubMed]

2012 (1)

2011 (1)

2009 (1)

A. Dyan, G. Duchateau, S. Eslava, J. L. Stehle, D. Damiani, and H. Piombini, “Transmission measurements in rapid growth KDP and DKDP crystals,” J. Mod. Opt. 56(1), 27–31 (2009).
[Crossref]

2002 (1)

G. Kruglik, N. Kondratyuk, and A. Shagov, “Efficient fourth harmonic generation of Nd:YAG laser in DKDP crystals,” Proc. SPIE 4751, 137–144 (2002).
[Crossref]

1997 (1)

L. N. Rashkovich and N. V. Kronsky, “Influence of Fe3+ and Al3+ ions on the kinetics of steps on the {100} faces of KDP,” J. Cryst. Growth 182(3-4), 434–441 (1997).
[Crossref]

1992 (4)

1991 (1)

1990 (1)

T. Ukachi, R. J. Lane, W. R. Babenberg, and C. L. Tang, “Measurements of noncritically phase-matched second-harmonic generation in a LiB3O5 crystal,” Appl. Phys. Lett. 57(10), 980–982 (1990).
[Crossref]

1989 (1)

W. P. Risk, R. N. Payne, W. Lenth, C. Harder, and H. Meier, “Noncritically phase-matched frequency doubling using 994 nm dye and diode laser radiation in KTiOPO4,” Appl. Phys. Lett. 55(12), 1179–1181 (1989).
[Crossref]

1987 (2)

K. W. Kirby and L. G. DeShazer, “Refractive indices of 14 nonlinear crystals isomorphic to KH2PO4,” J. Opt. Soc. Am. B 4(7), 1072–1078 (1987).
[Crossref]

D. Eimerl, L. Davis, S. Velsko, E. K. Graham, and A. Zalkin, “Optical, mechanical, and thermal properties of barium borate,” J. Appl. Phys. 62(5), 1968–1983 (1987).
[Crossref]

1985 (2)

P. E. Perkins and T. S. Fahlen, “Half watt average power at 25 kHz from fourth harmonic of Nd:YAG,” IEEE J. Quantum Electron. 21(10), 1636–1638 (1985).
[Crossref]

E. Diéguez, A. Cintas, P. Hernández, and J. M. Cabrera, “Ultraviolet absorption and growth bands in KDP,” J. Cryst. Growth 73(1), 193–195 (1985).
[Crossref]

1982 (3)

K. Kato, “High-efficiency high-power parametric oscillation in KNbO3,” IEEE J. Quantum Electron. 18(4), 451–452 (1982).
[Crossref]

N. P. Barnes, D. J. Gettemy, and R. S. Adhav, “Variation of the refractive index with temperature and the tuning rate for KDP isomorphs,” J. Opt. Soc. Am. 72(7), 895–898 (1982).
[Crossref]

G. C. Ghosh and G. C. Bhar, “Temperature dispersion in ADP, KDP, and KD*P for nonlinear devices,” IEEE J. Quantum Electron. 18(2), 143–145 (1982).
[Crossref]

1979 (1)

M. D. Jones and G. A. Massey, “Milliwatt-level 213 nm source based on a repetitively Q-switched, cw-pumped Nd:YAG laser,” IEEE J. Quantum Electron. 15(4), 204–206 (1979).
[Crossref]

1978 (1)

G. A. Massey, M. D. Jones, and J. C. Johnson, “Generation of pulse bursts at 21 2.8 nm by intracavity modulation of an Nd:YAG laser,” IEEE J. Quantum Electron. 14(7), 527–532 (1978).
[Crossref]

1977 (2)

V. I. Bredikhin, V. N. Genkin, S. P. Kuznetsov, and M. A. Novikov, “90° phase matching in KD2xH2(1-x)PO4 crystals upon doubling of the second harmonic of a Nd: laser,” Sov. Tech. Phys. Lett. 3, 165–166 (1977).

J. Reintjes and R. C. Eckardt, “Efficient harmonic generation from 532 to 266 nm in ADP and KDP,” Appl. Phys. Lett. 30(2), 91–93 (1977).
[Crossref]

1976 (1)

Y. S. Liu, W. B. Jones, and J. P. Chernoch, “High-efficiency high-power coherent UV generation at 266 nm in 90° phase-matched deuterated KDP,” Appl. Phys. Lett. 29(1), 32–34 (1976).
[Crossref]

1974 (1)

G. M. Loiacono, J. F. Balascio, and W. Osborne, “Effect of deuteration on the ferroelectric transition temperature and the distribution coefficient of deuterium in K(H1-xDx)2PO4,” Appl. Phys. Lett. 24(10), 455–456 (1974).
[Crossref]

1973 (2)

K. Kato, “Efficient second harmonic generation in CDA,” Opt. Commun. 9(3), 249–251 (1973).
[Crossref]

R. S. Adhav and R. W. Wallace, “Second harmonic generation in 90° phase-matched KDP isomorphs,” IEEE J. Quantum Electron. 9(8), 855–856 (1973).
[Crossref]

1968 (1)

H. Fay, W. J. Alford, and H. M. Dess, “Dependence of second-harmonic phase-matching temperature in LiNbO3 crystals on melt composition,” Appl. Phys. Lett. 12(3), 89–92 (1968).
[Crossref]

1966 (2)

1942 (1)

W. Bantle, “The specific heat of seignette-electric substances, dielectric measurements on KD2PO4 crystals,” Helv. Phys. Acta. 15, 373–404 (1942).

Adhav, R. S.

N. P. Barnes, D. J. Gettemy, and R. S. Adhav, “Variation of the refractive index with temperature and the tuning rate for KDP isomorphs,” J. Opt. Soc. Am. 72(7), 895–898 (1982).
[Crossref]

R. S. Adhav and R. W. Wallace, “Second harmonic generation in 90° phase-matched KDP isomorphs,” IEEE J. Quantum Electron. 9(8), 855–856 (1973).
[Crossref]

Alford, W. J.

H. Fay, W. J. Alford, and H. M. Dess, “Dependence of second-harmonic phase-matching temperature in LiNbO3 crystals on melt composition,” Appl. Phys. Lett. 12(3), 89–92 (1968).
[Crossref]

Babenberg, W. R.

T. Ukachi, R. J. Lane, W. R. Babenberg, and C. L. Tang, “Measurements of noncritically phase-matched second-harmonic generation in a LiB3O5 crystal,” Appl. Phys. Lett. 57(10), 980–982 (1990).
[Crossref]

Balascio, J. F.

G. M. Loiacono, J. F. Balascio, and W. Osborne, “Effect of deuteration on the ferroelectric transition temperature and the distribution coefficient of deuterium in K(H1-xDx)2PO4,” Appl. Phys. Lett. 24(10), 455–456 (1974).
[Crossref]

Bantle, W.

W. Bantle, “The specific heat of seignette-electric substances, dielectric measurements on KD2PO4 crystals,” Helv. Phys. Acta. 15, 373–404 (1942).

Barnes, N. P.

Bhar, G. C.

G. C. Ghosh and G. C. Bhar, “Temperature dispersion in ADP, KDP, and KD*P for nonlinear devices,” IEEE J. Quantum Electron. 18(2), 143–145 (1982).
[Crossref]

Bielecki, J. P.

Bordui, P. F.

Bosenberg, W. R.

Bredikhin, V. I.

V. I. Bredikhin, V. N. Genkin, S. P. Kuznetsov, and M. A. Novikov, “90° phase matching in KD2xH2(1-x)PO4 crystals upon doubling of the second harmonic of a Nd: laser,” Sov. Tech. Phys. Lett. 3, 165–166 (1977).

Byer, R. L.

Cabrera, J. M.

E. Diéguez, A. Cintas, P. Hernández, and J. M. Cabrera, “Ultraviolet absorption and growth bands in KDP,” J. Cryst. Growth 73(1), 193–195 (1985).
[Crossref]

Chai, X. X.

F. Wang, F. Q. Li, X. X. Chai, L. Q. Wang, W. Han, H. T. Jia, L. D. Zhou, B. Feng, and Y. Xiang, “Efficient fourth harmonic generation of Nd: glass lasers in ADP and DKDP crystals,” Proc. SPIE 9255, 92551R (2015).

Chernoch, J. P.

Y. S. Liu, W. B. Jones, and J. P. Chernoch, “High-efficiency high-power coherent UV generation at 266 nm in 90° phase-matched deuterated KDP,” Appl. Phys. Lett. 29(1), 32–34 (1976).
[Crossref]

Cintas, A.

E. Diéguez, A. Cintas, P. Hernández, and J. M. Cabrera, “Ultraviolet absorption and growth bands in KDP,” J. Cryst. Growth 73(1), 193–195 (1985).
[Crossref]

Damiani, D.

A. Dyan, G. Duchateau, S. Eslava, J. L. Stehle, D. Damiani, and H. Piombini, “Transmission measurements in rapid growth KDP and DKDP crystals,” J. Mod. Opt. 56(1), 27–31 (2009).
[Crossref]

Davis, L.

D. Eimerl, L. Davis, S. Velsko, E. K. Graham, and A. Zalkin, “Optical, mechanical, and thermal properties of barium borate,” J. Appl. Phys. 62(5), 1968–1983 (1987).
[Crossref]

DeShazer, L. G.

Dess, H. M.

H. Fay, W. J. Alford, and H. M. Dess, “Dependence of second-harmonic phase-matching temperature in LiNbO3 crystals on melt composition,” Appl. Phys. Lett. 12(3), 89–92 (1968).
[Crossref]

Diéguez, E.

E. Diéguez, A. Cintas, P. Hernández, and J. M. Cabrera, “Ultraviolet absorption and growth bands in KDP,” J. Cryst. Growth 73(1), 193–195 (1985).
[Crossref]

Duchateau, G.

A. Dyan, G. Duchateau, S. Eslava, J. L. Stehle, D. Damiani, and H. Piombini, “Transmission measurements in rapid growth KDP and DKDP crystals,” J. Mod. Opt. 56(1), 27–31 (2009).
[Crossref]

Dyan, A.

A. Dyan, G. Duchateau, S. Eslava, J. L. Stehle, D. Damiani, and H. Piombini, “Transmission measurements in rapid growth KDP and DKDP crystals,” J. Mod. Opt. 56(1), 27–31 (2009).
[Crossref]

Eckardt, R. C.

J. Reintjes and R. C. Eckardt, “Efficient harmonic generation from 532 to 266 nm in ADP and KDP,” Appl. Phys. Lett. 30(2), 91–93 (1977).
[Crossref]

Eimerl, D.

M. S. Webb, D. Eimerl, and S. P. Velsko, “Wavelength insensitive phase-matched second-harmonic generation in partially deuterated KDP,” J. Opt. Soc. Am. B 9(7), 1118–1127 (1992).
[Crossref]

D. Eimerl, L. Davis, S. Velsko, E. K. Graham, and A. Zalkin, “Optical, mechanical, and thermal properties of barium borate,” J. Appl. Phys. 62(5), 1968–1983 (1987).
[Crossref]

Ellgehausen, D.

Eslava, S.

A. Dyan, G. Duchateau, S. Eslava, J. L. Stehle, D. Damiani, and H. Piombini, “Transmission measurements in rapid growth KDP and DKDP crystals,” J. Mod. Opt. 56(1), 27–31 (2009).
[Crossref]

Fahlen, T. S.

P. E. Perkins and T. S. Fahlen, “Half watt average power at 25 kHz from fourth harmonic of Nd:YAG,” IEEE J. Quantum Electron. 21(10), 1636–1638 (1985).
[Crossref]

Fay, H.

H. Fay, W. J. Alford, and H. M. Dess, “Dependence of second-harmonic phase-matching temperature in LiNbO3 crystals on melt composition,” Appl. Phys. Lett. 12(3), 89–92 (1968).
[Crossref]

Fejer, M. M.

Feng, B.

F. Wang, F. Q. Li, X. X. Chai, L. Q. Wang, W. Han, H. T. Jia, L. D. Zhou, B. Feng, and Y. Xiang, “Efficient fourth harmonic generation of Nd: glass lasers in ADP and DKDP crystals,” Proc. SPIE 9255, 92551R (2015).

Genkin, V. N.

V. I. Bredikhin, V. N. Genkin, S. P. Kuznetsov, and M. A. Novikov, “90° phase matching in KD2xH2(1-x)PO4 crystals upon doubling of the second harmonic of a Nd: laser,” Sov. Tech. Phys. Lett. 3, 165–166 (1977).

Gettemy, D. J.

Ghosh, G. C.

G. C. Ghosh and G. C. Bhar, “Temperature dispersion in ADP, KDP, and KD*P for nonlinear devices,” IEEE J. Quantum Electron. 18(2), 143–145 (1982).
[Crossref]

Graham, E. K.

D. Eimerl, L. Davis, S. Velsko, E. K. Graham, and A. Zalkin, “Optical, mechanical, and thermal properties of barium borate,” J. Appl. Phys. 62(5), 1968–1983 (1987).
[Crossref]

Han, W.

F. Wang, F. Q. Li, X. X. Chai, L. Q. Wang, W. Han, H. T. Jia, L. D. Zhou, B. Feng, and Y. Xiang, “Efficient fourth harmonic generation of Nd: glass lasers in ADP and DKDP crystals,” Proc. SPIE 9255, 92551R (2015).

Harder, C.

W. P. Risk, R. N. Payne, W. Lenth, C. Harder, and H. Meier, “Noncritically phase-matched frequency doubling using 994 nm dye and diode laser radiation in KTiOPO4,” Appl. Phys. Lett. 55(12), 1179–1181 (1989).
[Crossref]

Henesian, M. A.

Hernández, P.

E. Diéguez, A. Cintas, P. Hernández, and J. M. Cabrera, “Ultraviolet absorption and growth bands in KDP,” J. Cryst. Growth 73(1), 193–195 (1985).
[Crossref]

Ji, S.

S. Ji, F. Wang, L. Zhu, X. Xu, Z. Wang, and X. Sun, “Non-critical phase-matching fourth harmonic generation of a 1053-nm laser in an ADP crystal,” Sci. Rep. 3, 1605 (2013).
[Crossref] [PubMed]

S. Ji, F. Wang, M. Xu, L. Zhu, X. Xu, Z. Wang, and X. Sun, “Room temperature, high-efficiency, noncritical phase-matching fourth harmonic generation in partially deuterated ADP crystal,” Opt. Lett. 38(10), 1679–1681 (2013).
[Crossref] [PubMed]

Ji, S. H.

L. L. Zhu, X. Zhang, M. X. Xu, B. A. Liu, S. H. Ji, L. S. Zhang, H. L. Zhou, F. F. Liu, Z. P. Wang, and X. Sun, “Refractive indices in the whole transmission range of partially deuterated KDP crystals,” AIP Adv. 3(11), 112114 (2013).
[Crossref]

S. H. Ji, S. J. Zhang, M. X. Xu, B. A. Liu, L. L. Zhu, L. S. Zhang, X. G. Xu, Z. P. Wang, and X. Sun, “Non-critical phase-matching conditions for fourth harmonic generation of DKDP crystal,” Opt. Mater. Express 2(6), 735–739 (2012).
[Crossref]

Jia, H. T.

F. Wang, F. Q. Li, X. X. Chai, L. Q. Wang, W. Han, H. T. Jia, L. D. Zhou, B. Feng, and Y. Xiang, “Efficient fourth harmonic generation of Nd: glass lasers in ADP and DKDP crystals,” Proc. SPIE 9255, 92551R (2015).

Johnson, J. C.

G. A. Massey, M. D. Jones, and J. C. Johnson, “Generation of pulse bursts at 21 2.8 nm by intracavity modulation of an Nd:YAG laser,” IEEE J. Quantum Electron. 14(7), 527–532 (1978).
[Crossref]

Jones, M. D.

M. D. Jones and G. A. Massey, “Milliwatt-level 213 nm source based on a repetitively Q-switched, cw-pumped Nd:YAG laser,” IEEE J. Quantum Electron. 15(4), 204–206 (1979).
[Crossref]

G. A. Massey, M. D. Jones, and J. C. Johnson, “Generation of pulse bursts at 21 2.8 nm by intracavity modulation of an Nd:YAG laser,” IEEE J. Quantum Electron. 14(7), 527–532 (1978).
[Crossref]

Jones, W. B.

Y. S. Liu, W. B. Jones, and J. P. Chernoch, “High-efficiency high-power coherent UV generation at 266 nm in 90° phase-matched deuterated KDP,” Appl. Phys. Lett. 29(1), 32–34 (1976).
[Crossref]

Jundt, D. H.

Kato, K.

K. Kato, “High-efficiency high-power parametric oscillation in KNbO3,” IEEE J. Quantum Electron. 18(4), 451–452 (1982).
[Crossref]

K. Kato, “Efficient second harmonic generation in CDA,” Opt. Commun. 9(3), 249–251 (1973).
[Crossref]

Kimble, H. J.

Kirby, K. W.

Kondratyuk, N.

G. Kruglik, N. Kondratyuk, and A. Shagov, “Efficient fourth harmonic generation of Nd:YAG laser in DKDP crystals,” Proc. SPIE 4751, 137–144 (2002).
[Crossref]

Kortz, P.

Kronsky, N. V.

L. N. Rashkovich and N. V. Kronsky, “Influence of Fe3+ and Al3+ ions on the kinetics of steps on the {100} faces of KDP,” J. Cryst. Growth 182(3-4), 434–441 (1997).
[Crossref]

Kruglik, G.

G. Kruglik, N. Kondratyuk, and A. Shagov, “Efficient fourth harmonic generation of Nd:YAG laser in DKDP crystals,” Proc. SPIE 4751, 137–144 (2002).
[Crossref]

Kuznetsov, S. P.

V. I. Bredikhin, V. N. Genkin, S. P. Kuznetsov, and M. A. Novikov, “90° phase matching in KD2xH2(1-x)PO4 crystals upon doubling of the second harmonic of a Nd: laser,” Sov. Tech. Phys. Lett. 3, 165–166 (1977).

Lane, R. J.

T. Ukachi, R. J. Lane, W. R. Bosenberg, and C. L. Tang, “Phase-matched second-harmonic generation and growth of a LiB3O5 crystal,” J. Opt. Soc. Am. B 9(7), 1128–1133 (1992).
[Crossref]

T. Ukachi, R. J. Lane, W. R. Babenberg, and C. L. Tang, “Measurements of noncritically phase-matched second-harmonic generation in a LiB3O5 crystal,” Appl. Phys. Lett. 57(10), 980–982 (1990).
[Crossref]

Lenth, W.

W. P. Risk, R. N. Payne, W. Lenth, C. Harder, and H. Meier, “Noncritically phase-matched frequency doubling using 994 nm dye and diode laser radiation in KTiOPO4,” Appl. Phys. Lett. 55(12), 1179–1181 (1989).
[Crossref]

Li, F. Q.

F. Wang, F. Q. Li, X. X. Chai, L. Q. Wang, W. Han, H. T. Jia, L. D. Zhou, B. Feng, and Y. Xiang, “Efficient fourth harmonic generation of Nd: glass lasers in ADP and DKDP crystals,” Proc. SPIE 9255, 92551R (2015).

Liu, B. A.

L. S. Zhang, M. X. Xu, B. A. Liu, L. L. Zhu, B. Wang, H. L. Zhou, F. F. Liu, and X. Sun, “New annealing method to improve KD2PO4 crystal quality: learning from high temperature phase transition,” CrystEngComm 17(25), 4705–4711 (2015).
[Crossref]

L. L. Zhu, X. Zhang, M. X. Xu, B. A. Liu, S. H. Ji, L. S. Zhang, H. L. Zhou, F. F. Liu, Z. P. Wang, and X. Sun, “Refractive indices in the whole transmission range of partially deuterated KDP crystals,” AIP Adv. 3(11), 112114 (2013).
[Crossref]

S. H. Ji, S. J. Zhang, M. X. Xu, B. A. Liu, L. L. Zhu, L. S. Zhang, X. G. Xu, Z. P. Wang, and X. Sun, “Non-critical phase-matching conditions for fourth harmonic generation of DKDP crystal,” Opt. Mater. Express 2(6), 735–739 (2012).
[Crossref]

Liu, F. F.

L. S. Zhang, M. X. Xu, B. A. Liu, L. L. Zhu, B. Wang, H. L. Zhou, F. F. Liu, and X. Sun, “New annealing method to improve KD2PO4 crystal quality: learning from high temperature phase transition,” CrystEngComm 17(25), 4705–4711 (2015).
[Crossref]

L. L. Zhu, X. Zhang, M. X. Xu, B. A. Liu, S. H. Ji, L. S. Zhang, H. L. Zhou, F. F. Liu, Z. P. Wang, and X. Sun, “Refractive indices in the whole transmission range of partially deuterated KDP crystals,” AIP Adv. 3(11), 112114 (2013).
[Crossref]

Liu, Y. S.

Y. S. Liu, W. B. Jones, and J. P. Chernoch, “High-efficiency high-power coherent UV generation at 266 nm in 90° phase-matched deuterated KDP,” Appl. Phys. Lett. 29(1), 32–34 (1976).
[Crossref]

Loiacono, G. M.

G. M. Loiacono, J. F. Balascio, and W. Osborne, “Effect of deuteration on the ferroelectric transition temperature and the distribution coefficient of deuterium in K(H1-xDx)2PO4,” Appl. Phys. Lett. 24(10), 455–456 (1974).
[Crossref]

Luthi, R. L.

Massey, G. A.

M. D. Jones and G. A. Massey, “Milliwatt-level 213 nm source based on a repetitively Q-switched, cw-pumped Nd:YAG laser,” IEEE J. Quantum Electron. 15(4), 204–206 (1979).
[Crossref]

G. A. Massey, M. D. Jones, and J. C. Johnson, “Generation of pulse bursts at 21 2.8 nm by intracavity modulation of an Nd:YAG laser,” IEEE J. Quantum Electron. 14(7), 527–532 (1978).
[Crossref]

Meier, H.

W. P. Risk, R. N. Payne, W. Lenth, C. Harder, and H. Meier, “Noncritically phase-matched frequency doubling using 994 nm dye and diode laser radiation in KTiOPO4,” Appl. Phys. Lett. 55(12), 1179–1181 (1989).
[Crossref]

Midwinter, J.

F. Zernike and J. Midwinter, Applied Nonlinear Optics (Wiley, 1973).

Mizell, G.

Norwood, R. G.

Novikov, M. A.

V. I. Bredikhin, V. N. Genkin, S. P. Kuznetsov, and M. A. Novikov, “90° phase matching in KD2xH2(1-x)PO4 crystals upon doubling of the second harmonic of a Nd: laser,” Sov. Tech. Phys. Lett. 3, 165–166 (1977).

Ogawa, T.

Osborne, W.

G. M. Loiacono, J. F. Balascio, and W. Osborne, “Effect of deuteration on the ferroelectric transition temperature and the distribution coefficient of deuterium in K(H1-xDx)2PO4,” Appl. Phys. Lett. 24(10), 455–456 (1974).
[Crossref]

Ou, Z. Y.

Payne, R. N.

W. P. Risk, R. N. Payne, W. Lenth, C. Harder, and H. Meier, “Noncritically phase-matched frequency doubling using 994 nm dye and diode laser radiation in KTiOPO4,” Appl. Phys. Lett. 55(12), 1179–1181 (1989).
[Crossref]

Pereira, S. F.

Perkins, P. E.

P. E. Perkins and T. S. Fahlen, “Half watt average power at 25 kHz from fourth harmonic of Nd:YAG,” IEEE J. Quantum Electron. 21(10), 1636–1638 (1985).
[Crossref]

Phillips, R. A.

Piombini, H.

A. Dyan, G. Duchateau, S. Eslava, J. L. Stehle, D. Damiani, and H. Piombini, “Transmission measurements in rapid growth KDP and DKDP crystals,” J. Mod. Opt. 56(1), 27–31 (2009).
[Crossref]

Polzik, E. S.

Rashkovich, L. N.

L. N. Rashkovich and N. V. Kronsky, “Influence of Fe3+ and Al3+ ions on the kinetics of steps on the {100} faces of KDP,” J. Cryst. Growth 182(3-4), 434–441 (1997).
[Crossref]

Reintjes, J.

J. Reintjes and R. C. Eckardt, “Efficient harmonic generation from 532 to 266 nm in ADP and KDP,” Appl. Phys. Lett. 30(2), 91–93 (1977).
[Crossref]

Risk, W. P.

W. P. Risk, R. N. Payne, W. Lenth, C. Harder, and H. Meier, “Noncritically phase-matched frequency doubling using 994 nm dye and diode laser radiation in KTiOPO4,” Appl. Phys. Lett. 55(12), 1179–1181 (1989).
[Crossref]

Rytz, D.

Seelert, W.

Shagov, A.

G. Kruglik, N. Kondratyuk, and A. Shagov, “Efficient fourth harmonic generation of Nd:YAG laser in DKDP crystals,” Proc. SPIE 4751, 137–144 (2002).
[Crossref]

Stehle, J. L.

A. Dyan, G. Duchateau, S. Eslava, J. L. Stehle, D. Damiani, and H. Piombini, “Transmission measurements in rapid growth KDP and DKDP crystals,” J. Mod. Opt. 56(1), 27–31 (2009).
[Crossref]

Sun, X.

L. S. Zhang, M. X. Xu, B. A. Liu, L. L. Zhu, B. Wang, H. L. Zhou, F. F. Liu, and X. Sun, “New annealing method to improve KD2PO4 crystal quality: learning from high temperature phase transition,” CrystEngComm 17(25), 4705–4711 (2015).
[Crossref]

L. L. Zhu, X. Zhang, M. X. Xu, B. A. Liu, S. H. Ji, L. S. Zhang, H. L. Zhou, F. F. Liu, Z. P. Wang, and X. Sun, “Refractive indices in the whole transmission range of partially deuterated KDP crystals,” AIP Adv. 3(11), 112114 (2013).
[Crossref]

S. Ji, F. Wang, L. Zhu, X. Xu, Z. Wang, and X. Sun, “Non-critical phase-matching fourth harmonic generation of a 1053-nm laser in an ADP crystal,” Sci. Rep. 3, 1605 (2013).
[Crossref] [PubMed]

S. Ji, F. Wang, M. Xu, L. Zhu, X. Xu, Z. Wang, and X. Sun, “Room temperature, high-efficiency, noncritical phase-matching fourth harmonic generation in partially deuterated ADP crystal,” Opt. Lett. 38(10), 1679–1681 (2013).
[Crossref] [PubMed]

S. H. Ji, S. J. Zhang, M. X. Xu, B. A. Liu, L. L. Zhu, L. S. Zhang, X. G. Xu, Z. P. Wang, and X. Sun, “Non-critical phase-matching conditions for fourth harmonic generation of DKDP crystal,” Opt. Mater. Express 2(6), 735–739 (2012).
[Crossref]

Tang, C. L.

T. Ukachi, R. J. Lane, W. R. Bosenberg, and C. L. Tang, “Phase-matched second-harmonic generation and growth of a LiB3O5 crystal,” J. Opt. Soc. Am. B 9(7), 1128–1133 (1992).
[Crossref]

T. Ukachi, R. J. Lane, W. R. Babenberg, and C. L. Tang, “Measurements of noncritically phase-matched second-harmonic generation in a LiB3O5 crystal,” Appl. Phys. Lett. 57(10), 980–982 (1990).
[Crossref]

Ukachi, T.

T. Ukachi, R. J. Lane, W. R. Bosenberg, and C. L. Tang, “Phase-matched second-harmonic generation and growth of a LiB3O5 crystal,” J. Opt. Soc. Am. B 9(7), 1128–1133 (1992).
[Crossref]

T. Ukachi, R. J. Lane, W. R. Babenberg, and C. L. Tang, “Measurements of noncritically phase-matched second-harmonic generation in a LiB3O5 crystal,” Appl. Phys. Lett. 57(10), 980–982 (1990).
[Crossref]

Velsko, S.

D. Eimerl, L. Davis, S. Velsko, E. K. Graham, and A. Zalkin, “Optical, mechanical, and thermal properties of barium borate,” J. Appl. Phys. 62(5), 1968–1983 (1987).
[Crossref]

Velsko, S. P.

Vickers, J. L.

Wallace, R. W.

R. S. Adhav and R. W. Wallace, “Second harmonic generation in 90° phase-matched KDP isomorphs,” IEEE J. Quantum Electron. 9(8), 855–856 (1973).
[Crossref]

Wang, B.

L. S. Zhang, M. X. Xu, B. A. Liu, L. L. Zhu, B. Wang, H. L. Zhou, F. F. Liu, and X. Sun, “New annealing method to improve KD2PO4 crystal quality: learning from high temperature phase transition,” CrystEngComm 17(25), 4705–4711 (2015).
[Crossref]

Wang, F.

F. Wang, F. Q. Li, X. X. Chai, L. Q. Wang, W. Han, H. T. Jia, L. D. Zhou, B. Feng, and Y. Xiang, “Efficient fourth harmonic generation of Nd: glass lasers in ADP and DKDP crystals,” Proc. SPIE 9255, 92551R (2015).

S. Ji, F. Wang, L. Zhu, X. Xu, Z. Wang, and X. Sun, “Non-critical phase-matching fourth harmonic generation of a 1053-nm laser in an ADP crystal,” Sci. Rep. 3, 1605 (2013).
[Crossref] [PubMed]

S. Ji, F. Wang, M. Xu, L. Zhu, X. Xu, Z. Wang, and X. Sun, “Room temperature, high-efficiency, noncritical phase-matching fourth harmonic generation in partially deuterated ADP crystal,” Opt. Lett. 38(10), 1679–1681 (2013).
[Crossref] [PubMed]

Wang, L. Q.

F. Wang, F. Q. Li, X. X. Chai, L. Q. Wang, W. Han, H. T. Jia, L. D. Zhou, B. Feng, and Y. Xiang, “Efficient fourth harmonic generation of Nd: glass lasers in ADP and DKDP crystals,” Proc. SPIE 9255, 92551R (2015).

Wang, Z.

S. Ji, F. Wang, L. Zhu, X. Xu, Z. Wang, and X. Sun, “Non-critical phase-matching fourth harmonic generation of a 1053-nm laser in an ADP crystal,” Sci. Rep. 3, 1605 (2013).
[Crossref] [PubMed]

S. Ji, F. Wang, M. Xu, L. Zhu, X. Xu, Z. Wang, and X. Sun, “Room temperature, high-efficiency, noncritical phase-matching fourth harmonic generation in partially deuterated ADP crystal,” Opt. Lett. 38(10), 1679–1681 (2013).
[Crossref] [PubMed]

Wang, Z. P.

L. L. Zhu, X. Zhang, M. X. Xu, B. A. Liu, S. H. Ji, L. S. Zhang, H. L. Zhou, F. F. Liu, Z. P. Wang, and X. Sun, “Refractive indices in the whole transmission range of partially deuterated KDP crystals,” AIP Adv. 3(11), 112114 (2013).
[Crossref]

S. H. Ji, S. J. Zhang, M. X. Xu, B. A. Liu, L. L. Zhu, L. S. Zhang, X. G. Xu, Z. P. Wang, and X. Sun, “Non-critical phase-matching conditions for fourth harmonic generation of DKDP crystal,” Opt. Mater. Express 2(6), 735–739 (2012).
[Crossref]

Webb, M. S.

Wegner, P. J.

Weiland, T. L.

Xiang, Y.

F. Wang, F. Q. Li, X. X. Chai, L. Q. Wang, W. Han, H. T. Jia, L. D. Zhou, B. Feng, and Y. Xiang, “Efficient fourth harmonic generation of Nd: glass lasers in ADP and DKDP crystals,” Proc. SPIE 9255, 92551R (2015).

Xu, M.

Xu, M. X.

L. S. Zhang, M. X. Xu, B. A. Liu, L. L. Zhu, B. Wang, H. L. Zhou, F. F. Liu, and X. Sun, “New annealing method to improve KD2PO4 crystal quality: learning from high temperature phase transition,” CrystEngComm 17(25), 4705–4711 (2015).
[Crossref]

L. L. Zhu, X. Zhang, M. X. Xu, B. A. Liu, S. H. Ji, L. S. Zhang, H. L. Zhou, F. F. Liu, Z. P. Wang, and X. Sun, “Refractive indices in the whole transmission range of partially deuterated KDP crystals,” AIP Adv. 3(11), 112114 (2013).
[Crossref]

S. H. Ji, S. J. Zhang, M. X. Xu, B. A. Liu, L. L. Zhu, L. S. Zhang, X. G. Xu, Z. P. Wang, and X. Sun, “Non-critical phase-matching conditions for fourth harmonic generation of DKDP crystal,” Opt. Mater. Express 2(6), 735–739 (2012).
[Crossref]

Xu, X.

S. Ji, F. Wang, L. Zhu, X. Xu, Z. Wang, and X. Sun, “Non-critical phase-matching fourth harmonic generation of a 1053-nm laser in an ADP crystal,” Sci. Rep. 3, 1605 (2013).
[Crossref] [PubMed]

S. Ji, F. Wang, M. Xu, L. Zhu, X. Xu, Z. Wang, and X. Sun, “Room temperature, high-efficiency, noncritical phase-matching fourth harmonic generation in partially deuterated ADP crystal,” Opt. Lett. 38(10), 1679–1681 (2013).
[Crossref] [PubMed]

Xu, X. G.

Yamazaki, M.

Yang, S. T.

Zalkin, A.

D. Eimerl, L. Davis, S. Velsko, E. K. Graham, and A. Zalkin, “Optical, mechanical, and thermal properties of barium borate,” J. Appl. Phys. 62(5), 1968–1983 (1987).
[Crossref]

Zernike, F.

F. Zernike and J. Midwinter, Applied Nonlinear Optics (Wiley, 1973).

Zhang, L. S.

L. S. Zhang, M. X. Xu, B. A. Liu, L. L. Zhu, B. Wang, H. L. Zhou, F. F. Liu, and X. Sun, “New annealing method to improve KD2PO4 crystal quality: learning from high temperature phase transition,” CrystEngComm 17(25), 4705–4711 (2015).
[Crossref]

L. L. Zhu, X. Zhang, M. X. Xu, B. A. Liu, S. H. Ji, L. S. Zhang, H. L. Zhou, F. F. Liu, Z. P. Wang, and X. Sun, “Refractive indices in the whole transmission range of partially deuterated KDP crystals,” AIP Adv. 3(11), 112114 (2013).
[Crossref]

S. H. Ji, S. J. Zhang, M. X. Xu, B. A. Liu, L. L. Zhu, L. S. Zhang, X. G. Xu, Z. P. Wang, and X. Sun, “Non-critical phase-matching conditions for fourth harmonic generation of DKDP crystal,” Opt. Mater. Express 2(6), 735–739 (2012).
[Crossref]

Zhang, S. J.

Zhang, X.

L. L. Zhu, X. Zhang, M. X. Xu, B. A. Liu, S. H. Ji, L. S. Zhang, H. L. Zhou, F. F. Liu, Z. P. Wang, and X. Sun, “Refractive indices in the whole transmission range of partially deuterated KDP crystals,” AIP Adv. 3(11), 112114 (2013).
[Crossref]

Zhou, H. L.

L. S. Zhang, M. X. Xu, B. A. Liu, L. L. Zhu, B. Wang, H. L. Zhou, F. F. Liu, and X. Sun, “New annealing method to improve KD2PO4 crystal quality: learning from high temperature phase transition,” CrystEngComm 17(25), 4705–4711 (2015).
[Crossref]

L. L. Zhu, X. Zhang, M. X. Xu, B. A. Liu, S. H. Ji, L. S. Zhang, H. L. Zhou, F. F. Liu, Z. P. Wang, and X. Sun, “Refractive indices in the whole transmission range of partially deuterated KDP crystals,” AIP Adv. 3(11), 112114 (2013).
[Crossref]

Zhou, L. D.

F. Wang, F. Q. Li, X. X. Chai, L. Q. Wang, W. Han, H. T. Jia, L. D. Zhou, B. Feng, and Y. Xiang, “Efficient fourth harmonic generation of Nd: glass lasers in ADP and DKDP crystals,” Proc. SPIE 9255, 92551R (2015).

Zhu, L.

S. Ji, F. Wang, L. Zhu, X. Xu, Z. Wang, and X. Sun, “Non-critical phase-matching fourth harmonic generation of a 1053-nm laser in an ADP crystal,” Sci. Rep. 3, 1605 (2013).
[Crossref] [PubMed]

S. Ji, F. Wang, M. Xu, L. Zhu, X. Xu, Z. Wang, and X. Sun, “Room temperature, high-efficiency, noncritical phase-matching fourth harmonic generation in partially deuterated ADP crystal,” Opt. Lett. 38(10), 1679–1681 (2013).
[Crossref] [PubMed]

Zhu, L. L.

L. S. Zhang, M. X. Xu, B. A. Liu, L. L. Zhu, B. Wang, H. L. Zhou, F. F. Liu, and X. Sun, “New annealing method to improve KD2PO4 crystal quality: learning from high temperature phase transition,” CrystEngComm 17(25), 4705–4711 (2015).
[Crossref]

L. L. Zhu, X. Zhang, M. X. Xu, B. A. Liu, S. H. Ji, L. S. Zhang, H. L. Zhou, F. F. Liu, Z. P. Wang, and X. Sun, “Refractive indices in the whole transmission range of partially deuterated KDP crystals,” AIP Adv. 3(11), 112114 (2013).
[Crossref]

S. H. Ji, S. J. Zhang, M. X. Xu, B. A. Liu, L. L. Zhu, L. S. Zhang, X. G. Xu, Z. P. Wang, and X. Sun, “Non-critical phase-matching conditions for fourth harmonic generation of DKDP crystal,” Opt. Mater. Express 2(6), 735–739 (2012).
[Crossref]

Zysset, B.

AIP Adv. (1)

L. L. Zhu, X. Zhang, M. X. Xu, B. A. Liu, S. H. Ji, L. S. Zhang, H. L. Zhou, F. F. Liu, Z. P. Wang, and X. Sun, “Refractive indices in the whole transmission range of partially deuterated KDP crystals,” AIP Adv. 3(11), 112114 (2013).
[Crossref]

Appl. Phys. Lett. (6)

G. M. Loiacono, J. F. Balascio, and W. Osborne, “Effect of deuteration on the ferroelectric transition temperature and the distribution coefficient of deuterium in K(H1-xDx)2PO4,” Appl. Phys. Lett. 24(10), 455–456 (1974).
[Crossref]

J. Reintjes and R. C. Eckardt, “Efficient harmonic generation from 532 to 266 nm in ADP and KDP,” Appl. Phys. Lett. 30(2), 91–93 (1977).
[Crossref]

T. Ukachi, R. J. Lane, W. R. Babenberg, and C. L. Tang, “Measurements of noncritically phase-matched second-harmonic generation in a LiB3O5 crystal,” Appl. Phys. Lett. 57(10), 980–982 (1990).
[Crossref]

W. P. Risk, R. N. Payne, W. Lenth, C. Harder, and H. Meier, “Noncritically phase-matched frequency doubling using 994 nm dye and diode laser radiation in KTiOPO4,” Appl. Phys. Lett. 55(12), 1179–1181 (1989).
[Crossref]

H. Fay, W. J. Alford, and H. M. Dess, “Dependence of second-harmonic phase-matching temperature in LiNbO3 crystals on melt composition,” Appl. Phys. Lett. 12(3), 89–92 (1968).
[Crossref]

Y. S. Liu, W. B. Jones, and J. P. Chernoch, “High-efficiency high-power coherent UV generation at 266 nm in 90° phase-matched deuterated KDP,” Appl. Phys. Lett. 29(1), 32–34 (1976).
[Crossref]

CrystEngComm (1)

L. S. Zhang, M. X. Xu, B. A. Liu, L. L. Zhu, B. Wang, H. L. Zhou, F. F. Liu, and X. Sun, “New annealing method to improve KD2PO4 crystal quality: learning from high temperature phase transition,” CrystEngComm 17(25), 4705–4711 (2015).
[Crossref]

Helv. Phys. Acta. (1)

W. Bantle, “The specific heat of seignette-electric substances, dielectric measurements on KD2PO4 crystals,” Helv. Phys. Acta. 15, 373–404 (1942).

IEEE J. Quantum Electron. (6)

R. S. Adhav and R. W. Wallace, “Second harmonic generation in 90° phase-matched KDP isomorphs,” IEEE J. Quantum Electron. 9(8), 855–856 (1973).
[Crossref]

G. A. Massey, M. D. Jones, and J. C. Johnson, “Generation of pulse bursts at 21 2.8 nm by intracavity modulation of an Nd:YAG laser,” IEEE J. Quantum Electron. 14(7), 527–532 (1978).
[Crossref]

M. D. Jones and G. A. Massey, “Milliwatt-level 213 nm source based on a repetitively Q-switched, cw-pumped Nd:YAG laser,” IEEE J. Quantum Electron. 15(4), 204–206 (1979).
[Crossref]

P. E. Perkins and T. S. Fahlen, “Half watt average power at 25 kHz from fourth harmonic of Nd:YAG,” IEEE J. Quantum Electron. 21(10), 1636–1638 (1985).
[Crossref]

K. Kato, “High-efficiency high-power parametric oscillation in KNbO3,” IEEE J. Quantum Electron. 18(4), 451–452 (1982).
[Crossref]

G. C. Ghosh and G. C. Bhar, “Temperature dispersion in ADP, KDP, and KD*P for nonlinear devices,” IEEE J. Quantum Electron. 18(2), 143–145 (1982).
[Crossref]

J. Appl. Phys. (1)

D. Eimerl, L. Davis, S. Velsko, E. K. Graham, and A. Zalkin, “Optical, mechanical, and thermal properties of barium borate,” J. Appl. Phys. 62(5), 1968–1983 (1987).
[Crossref]

J. Cryst. Growth (2)

E. Diéguez, A. Cintas, P. Hernández, and J. M. Cabrera, “Ultraviolet absorption and growth bands in KDP,” J. Cryst. Growth 73(1), 193–195 (1985).
[Crossref]

L. N. Rashkovich and N. V. Kronsky, “Influence of Fe3+ and Al3+ ions on the kinetics of steps on the {100} faces of KDP,” J. Cryst. Growth 182(3-4), 434–441 (1997).
[Crossref]

J. Mod. Opt. (1)

A. Dyan, G. Duchateau, S. Eslava, J. L. Stehle, D. Damiani, and H. Piombini, “Transmission measurements in rapid growth KDP and DKDP crystals,” J. Mod. Opt. 56(1), 27–31 (2009).
[Crossref]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. B (3)

Opt. Commun. (1)

K. Kato, “Efficient second harmonic generation in CDA,” Opt. Commun. 9(3), 249–251 (1973).
[Crossref]

Opt. Lett. (5)

Opt. Mater. Express (1)

Proc. SPIE (2)

G. Kruglik, N. Kondratyuk, and A. Shagov, “Efficient fourth harmonic generation of Nd:YAG laser in DKDP crystals,” Proc. SPIE 4751, 137–144 (2002).
[Crossref]

F. Wang, F. Q. Li, X. X. Chai, L. Q. Wang, W. Han, H. T. Jia, L. D. Zhou, B. Feng, and Y. Xiang, “Efficient fourth harmonic generation of Nd: glass lasers in ADP and DKDP crystals,” Proc. SPIE 9255, 92551R (2015).

Sci. Rep. (1)

S. Ji, F. Wang, L. Zhu, X. Xu, Z. Wang, and X. Sun, “Non-critical phase-matching fourth harmonic generation of a 1053-nm laser in an ADP crystal,” Sci. Rep. 3, 1605 (2013).
[Crossref] [PubMed]

Sov. Tech. Phys. Lett. (1)

V. I. Bredikhin, V. N. Genkin, S. P. Kuznetsov, and M. A. Novikov, “90° phase matching in KD2xH2(1-x)PO4 crystals upon doubling of the second harmonic of a Nd: laser,” Sov. Tech. Phys. Lett. 3, 165–166 (1977).

Other (2)

F. Zernike and J. Midwinter, Applied Nonlinear Optics (Wiley, 1973).

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, third revised edition (Springer, 1999).

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Figures (8)

Fig. 1
Fig. 1 Temperature tuning curves of different deuterium content DKDP crystals. The black dots are experimental data and the solid red lines are fitted by sin2x/x2.
Fig. 2
Fig. 2 Deuterium content dependent TNCPM. The black dots are fitting data from temperature tuning curves, and the solid red lines are linear fit of the black dots.
Fig. 3
Fig. 3 Deuterium content tuning curve at 40°C. The black dots are experimental data and the solid red lines are fitted by sin2x/x2.
Fig. 4
Fig. 4 Calculated diagram of NCPM temperature in the 60-100% deuterium content range and 1050-1070 nm wavelength range.
Fig. 5
Fig. 5 Angle tuning curves of a 99% deuterium content DKDP crystal under different temperature. The color dots are experimental data.
Fig. 6
Fig. 6 Relationship of Tpm and Δθ in different deuterium content DKDP crystals. The black dots are experimental data and the solid red lines are fitted by a quadratic equation.
Fig. 7
Fig. 7 Angle tuning curve of different deuterium content DKDP crystals. The black dots are experimental data and the solid color lines are fitted by sin2x/x2.
Fig. 8
Fig. 8 Transimittance of different deuterium content DKDP crystals in 200-300 nm range.

Tables (4)

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Table 1 FWHM of the temperature tuning curve and βT for different deuterium content DKDP crystals.

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Table 2 A comparison between our calculation and the previously reported experimental results.

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Table 3 Comparison of indirectly calculated β θ ' and directly calculated β θ ' .

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Table 4 Transimittance at 266 nm and FHG conversion efficiency of different deuterated DKDP crystals.

Equations (18)

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I F H G sin 2 ( 1 / 2 Δ k L ) ( 1 / 2 Δ k L ) 2
Δ k = 4 π λ 1 [ n o ( λ 1 , T , X D ) n e ( λ 2 , T , X D ) ]
Δ k ( k X D ) λ , T ( X D X D 0 ) + ( k T ) λ , X D ( T T 0 ) + ( k λ ) T , X D ( λ λ 0 ) β X D ( X D X D 0 ) + β T ( T T 0 ) + β λ ( λ λ 0 )
β X D = 4 π λ 1 ( n o 1 X D n e 2 X D )
β T = 4 π λ 1 ( n o 1 T n e 2 T )
β λ = 4 π λ 1 ( n o 1 λ 1 2 n e 2 λ )
β T δ T + β X D δ X D = 0
β X D = β T ( d T d X D )
β λ = β T ( d T d λ )
β X D = 5.566 Δ X D L
β λ = 5.566 Δ λ L
β T = 5.566 Δ T L
Δ k = ( Δ k ( Δ θ ) ) δ ( Δ θ ) + 1 2 ( 2 Δ k ( Δ θ ) 2 ) δ ( Δ θ ) 2 + = β θ δ ( Δ θ ) + 1 2 β θ ' δ ( Δ θ ) 2 +
β T δ T + β θ δ Δ θ = 0
β θ = β T ( d T d ( Δ θ ) )
β θ ' = ( β θ ( Δ θ ) ) = ( β T ( Δ θ ) ) ( T ( Δ θ ) ) β T ( 2 T ( Δ θ ) 2 ) = β T ( 2 T ( Δ θ ) 2 )
Δ θ 22.26 β θ ' L
T p m = A ( Δ θ ) 2 + B ( Δ θ ) + C

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