Abstract

We have built a setup with high temporal resolution to measure the very fast photoelastic lensing effect, which is on the scale of microseconds in a Ti:sapphire crystal pumped by very strong laser pulses (up to 5J/cm2). The experimental results measured by this method and the real multimode beam profile taken by a CCD camera are applied to a three-dimensional crystal model to calculate one of the photoelastic constants of Ti:sapphire crystal, which is found to be p31=0.03±0.01. This value is helpful to evaluate the photoelastic lensing effect in Ti:sapphire crystal for a laser beam polarized along the c axis, commonly used for laser amplification.

© 2012 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2008

2006

V. Ramanathan, J. Lee, S. Xu, X. Wang, and D. H. Reitze, “Analysis of thermal aberrations in a high average power single-stage Ti:sapphire regenerative chirped pulse amplifier: simulation and experiment,” Rev. Sci. Instrum. 77, 103103 (2006).
[CrossRef]

2005

2002

S. Ito, H. Nagaoka, T. Miura, K. Kobayashi, A. Endo, and K. Torizuka, “Measurement of thermal lensing in a power amplifier of a terawatt Ti:sapphire laser,” Appl. Phys. B 74, 343–347 (2002).
[CrossRef]

2000

M. Zavelani-Rossi, F. Lindner, C. Le Blanc, G. Chériaux, and J. P. Chambaret, “Control of thermal effects for high-intensity Ti:sapphire laser chains,” Appl. Phys. B 70, S193–S196 (2000).
[CrossRef]

1998

R. Weber, B. Neuenschwander, M. Mac Donald, M. B. Roos, and Heinz P. Weber, “Cooling schemes for longitudinally diode laser-pumped Nd:YAG rods,” IEEE J. Quantum Electron. 34, 1046–1053 (1998).
[CrossRef]

1992

H. Eilers, E. Strauss, and W. M. Yen, “Photoelastic effect in Ti3+-doped sapphire,” Phys. Rev. B 45, 9604–9610 (1992).
[CrossRef]

1989

Aggarwal, R. L.

Amir, W.

Chambaret, J. P.

M. Zavelani-Rossi, F. Lindner, C. Le Blanc, G. Chériaux, and J. P. Chambaret, “Control of thermal effects for high-intensity Ti:sapphire laser chains,” Appl. Phys. B 70, S193–S196 (2000).
[CrossRef]

Chériaux, G.

M. Zavelani-Rossi, F. Lindner, C. Le Blanc, G. Chériaux, and J. P. Chambaret, “Control of thermal effects for high-intensity Ti:sapphire laser chains,” Appl. Phys. B 70, S193–S196 (2000).
[CrossRef]

Childress, C.

Durfee, C. G.

Eilers, H.

H. Eilers, E. Strauss, and W. M. Yen, “Photoelastic effect in Ti3+-doped sapphire,” Phys. Rev. B 45, 9604–9610 (1992).
[CrossRef]

Endo, A.

S. Ito, H. Nagaoka, T. Miura, K. Kobayashi, A. Endo, and K. Torizuka, “Measurement of thermal lensing in a power amplifier of a terawatt Ti:sapphire laser,” Appl. Phys. B 74, 343–347 (2002).
[CrossRef]

Fahey, R. E.

Gottlieb, M.

M. Gottlieb, CRC Handbook of Laser Sciences and Technology, M. J. Weber, ed. (CRC Press, 1986), Vol. IV, p. 319.

Ito, S.

S. Ito, H. Nagaoka, T. Miura, K. Kobayashi, A. Endo, and K. Torizuka, “Measurement of thermal lensing in a power amplifier of a terawatt Ti:sapphire laser,” Appl. Phys. B 74, 343–347 (2002).
[CrossRef]

Kobayashi, K.

S. Ito, H. Nagaoka, T. Miura, K. Kobayashi, A. Endo, and K. Torizuka, “Measurement of thermal lensing in a power amplifier of a terawatt Ti:sapphire laser,” Appl. Phys. B 74, 343–347 (2002).
[CrossRef]

Koechner, W.

W. Koechner, Solid-State Laser Engineering (Springer, 1999), p. 440.

Le Blanc, C.

M. Zavelani-Rossi, F. Lindner, C. Le Blanc, G. Chériaux, and J. P. Chambaret, “Control of thermal effects for high-intensity Ti:sapphire laser chains,” Appl. Phys. B 70, S193–S196 (2000).
[CrossRef]

Lee, J.

V. Ramanathan, J. Lee, S. Xu, X. Wang, and D. H. Reitze, “Analysis of thermal aberrations in a high average power single-stage Ti:sapphire regenerative chirped pulse amplifier: simulation and experiment,” Rev. Sci. Instrum. 77, 103103 (2006).
[CrossRef]

Lindner, F.

M. Zavelani-Rossi, F. Lindner, C. Le Blanc, G. Chériaux, and J. P. Chambaret, “Control of thermal effects for high-intensity Ti:sapphire laser chains,” Appl. Phys. B 70, S193–S196 (2000).
[CrossRef]

Mac Donald, M.

R. Weber, B. Neuenschwander, M. Mac Donald, M. B. Roos, and Heinz P. Weber, “Cooling schemes for longitudinally diode laser-pumped Nd:YAG rods,” IEEE J. Quantum Electron. 34, 1046–1053 (1998).
[CrossRef]

Miura, T.

S. Ito, H. Nagaoka, T. Miura, K. Kobayashi, A. Endo, and K. Torizuka, “Measurement of thermal lensing in a power amplifier of a terawatt Ti:sapphire laser,” Appl. Phys. B 74, 343–347 (2002).
[CrossRef]

Nagaoka, H.

S. Ito, H. Nagaoka, T. Miura, K. Kobayashi, A. Endo, and K. Torizuka, “Measurement of thermal lensing in a power amplifier of a terawatt Ti:sapphire laser,” Appl. Phys. B 74, 343–347 (2002).
[CrossRef]

Neuenschwander, B.

R. Weber, B. Neuenschwander, M. Mac Donald, M. B. Roos, and Heinz P. Weber, “Cooling schemes for longitudinally diode laser-pumped Nd:YAG rods,” IEEE J. Quantum Electron. 34, 1046–1053 (1998).
[CrossRef]

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Clarendon, 1957), pp. 82–92.

Planchon, T. A.

Ramanathan, V.

V. Ramanathan, J. Lee, S. Xu, X. Wang, and D. H. Reitze, “Analysis of thermal aberrations in a high average power single-stage Ti:sapphire regenerative chirped pulse amplifier: simulation and experiment,” Rev. Sci. Instrum. 77, 103103 (2006).
[CrossRef]

Reitze, D. H.

V. Ramanathan, J. Lee, S. Xu, X. Wang, and D. H. Reitze, “Analysis of thermal aberrations in a high average power single-stage Ti:sapphire regenerative chirped pulse amplifier: simulation and experiment,” Rev. Sci. Instrum. 77, 103103 (2006).
[CrossRef]

Roos, M. B.

R. Weber, B. Neuenschwander, M. Mac Donald, M. B. Roos, and Heinz P. Weber, “Cooling schemes for longitudinally diode laser-pumped Nd:YAG rods,” IEEE J. Quantum Electron. 34, 1046–1053 (1998).
[CrossRef]

Sciacca, M. D.

Shiler, M.

Siegman, A. E.

A. E. Siegman, “Ray optics and ray matrices,” in Lasers, A. Kelly, ed. (University Science, 1986).

Squier, J. A.

Strauss, A. J.

Strauss, E.

H. Eilers, E. Strauss, and W. M. Yen, “Photoelastic effect in Ti3+-doped sapphire,” Phys. Rev. B 45, 9604–9610 (1992).
[CrossRef]

Torizuka, K.

S. Ito, H. Nagaoka, T. Miura, K. Kobayashi, A. Endo, and K. Torizuka, “Measurement of thermal lensing in a power amplifier of a terawatt Ti:sapphire laser,” Appl. Phys. B 74, 343–347 (2002).
[CrossRef]

Wagner, G.

Wall, K. F.

Wang, X.

V. Ramanathan, J. Lee, S. Xu, X. Wang, and D. H. Reitze, “Analysis of thermal aberrations in a high average power single-stage Ti:sapphire regenerative chirped pulse amplifier: simulation and experiment,” Rev. Sci. Instrum. 77, 103103 (2006).
[CrossRef]

Weber, Heinz P.

R. Weber, B. Neuenschwander, M. Mac Donald, M. B. Roos, and Heinz P. Weber, “Cooling schemes for longitudinally diode laser-pumped Nd:YAG rods,” IEEE J. Quantum Electron. 34, 1046–1053 (1998).
[CrossRef]

Weber, R.

R. Weber, B. Neuenschwander, M. Mac Donald, M. B. Roos, and Heinz P. Weber, “Cooling schemes for longitudinally diode laser-pumped Nd:YAG rods,” IEEE J. Quantum Electron. 34, 1046–1053 (1998).
[CrossRef]

Wulfmeyer, V.

Xu, S.

V. Ramanathan, J. Lee, S. Xu, X. Wang, and D. H. Reitze, “Analysis of thermal aberrations in a high average power single-stage Ti:sapphire regenerative chirped pulse amplifier: simulation and experiment,” Rev. Sci. Instrum. 77, 103103 (2006).
[CrossRef]

Yen, W. M.

H. Eilers, E. Strauss, and W. M. Yen, “Photoelastic effect in Ti3+-doped sapphire,” Phys. Rev. B 45, 9604–9610 (1992).
[CrossRef]

Zavelani-Rossi, M.

M. Zavelani-Rossi, F. Lindner, C. Le Blanc, G. Chériaux, and J. P. Chambaret, “Control of thermal effects for high-intensity Ti:sapphire laser chains,” Appl. Phys. B 70, S193–S196 (2000).
[CrossRef]

Zeiger, H. J.

Appl. Phys. B

M. Zavelani-Rossi, F. Lindner, C. Le Blanc, G. Chériaux, and J. P. Chambaret, “Control of thermal effects for high-intensity Ti:sapphire laser chains,” Appl. Phys. B 70, S193–S196 (2000).
[CrossRef]

S. Ito, H. Nagaoka, T. Miura, K. Kobayashi, A. Endo, and K. Torizuka, “Measurement of thermal lensing in a power amplifier of a terawatt Ti:sapphire laser,” Appl. Phys. B 74, 343–347 (2002).
[CrossRef]

IEEE J. Quantum Electron.

R. Weber, B. Neuenschwander, M. Mac Donald, M. B. Roos, and Heinz P. Weber, “Cooling schemes for longitudinally diode laser-pumped Nd:YAG rods,” IEEE J. Quantum Electron. 34, 1046–1053 (1998).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

H. Eilers, E. Strauss, and W. M. Yen, “Photoelastic effect in Ti3+-doped sapphire,” Phys. Rev. B 45, 9604–9610 (1992).
[CrossRef]

Rev. Sci. Instrum.

V. Ramanathan, J. Lee, S. Xu, X. Wang, and D. H. Reitze, “Analysis of thermal aberrations in a high average power single-stage Ti:sapphire regenerative chirped pulse amplifier: simulation and experiment,” Rev. Sci. Instrum. 77, 103103 (2006).
[CrossRef]

Other

A. E. Siegman, “Ray optics and ray matrices,” in Lasers, A. Kelly, ed. (University Science, 1986).

W. Koechner, Solid-State Laser Engineering (Springer, 1999), p. 440.

M. Gottlieb, CRC Handbook of Laser Sciences and Technology, M. J. Weber, ed. (CRC Press, 1986), Vol. IV, p. 319.

J. F. Nye, Physical Properties of Crystals (Clarendon, 1957), pp. 82–92.

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Figures (9)

Fig. 1.
Fig. 1.

Schematic of the experimental setup to measure the fast nonthermal lensing effect.

Fig. 2.
Fig. 2.

Comparison between geometrical optics approximation (diamond) and Gaussian beam propagation (circle) calculations.

Fig. 3.
Fig. 3.

Time-dependent measurement of the lensing effect (pump energy is 500 mJ, test beam is p polarized): (a) original data and the fitted curve, (b) calculated focal length based on the fitted curve.

Fig. 4.
Fig. 4.

Comparison between the focal length of the crystal measured by oscilloscope and measured directly using an iris and a power meter.

Fig. 5.
Fig. 5.

Photodiode signal when the pump energy is 700 mJ and the test beam is p polarized (the smooth line is the expected relaxation curve if not saturated).

Fig. 6.
Fig. 6.

Photodiode signal when the pump energy is 500 mJ and the test beam is s polarized.

Fig. 7.
Fig. 7.

Pump beam profile taken by a CCD camera (QuantaRay PRO-290).

Fig. 8.
Fig. 8.

Population density in the sagittal plane of the crystal when pump energy is 500 mJ.

Fig. 9.
Fig. 9.

Radius-dependent OPD in sagittal plane and quadratic fit.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

P(r)=P[1exp(2r2w2)],
w={2r2ln[1P(r)P]}1/2.
wl=wfLf,
fc=wcdwcwl,
M=[cos(l2dn/n0)(2dnn0)1sin(l2dn/n0)2dnn0sin(l2dn/n0)cos(l2dn/n0)].
M=M1MiMm=M1[cos(dl2dnx,y,i/n0)(2dnx,y,in0)1sin(dl2dnx,y,i/n0)2dnx,y,in0sin(dl2dnx,y,i/n0)cos(dl2dnx,y,i/n0)]Mm,
OPD(r)=OPD0r22f.

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