Abstract

The self-focusing characteristic of 355 nm, 3.3 ns pulses propagating through phosphate glass samples is found to significantly change during repeated exposure. The results indicate this change is related to the formation of color centers in the material as well as the generation of a transient defect population during exposure to the laser pulses. A model is used to fit the experimental data and obtain an estimated range of values for the modified linear and nonlinear indices of refraction.

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  1. M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron.26(4), 760–769 (1990).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2011

J. H. Campbell, J. S. Hayden, and A. Marker, “High-power solid-state lasers: a laser glass perspective,” Intl. J. Appl. Glass Sci.2, 1–27 (2011).

2007

2004

A. Kameyama, A. Yokotani, and K. Kurosawa, “Second-order optical nonlinearity and change in refractive index in silica glasses by a combination of thermal poling and x-ray irradiation,” J. Appl. Phys.95(8), 4000–4006 (2004).
[CrossRef]

2000

P. R. Ehrmann, J. H. Campbell, T. I. Suratwala, J. S. Hayden, D. Krashkevich, and K. Takeuchi, “Optical loss and Nd3+ nonradiative relaxation by Cu, Fe and several rare earth ion impurities in phosphate laser glasses,” J. Non-Cryst. Solids263–264, 251–262 (2000).
[CrossRef]

Ch. Muhlig, W. Triebel, S. Bark-Zollmann, and D. Grebner, “In situ diagnostics of pulse laser-induced defects in DUV transparent fused silica glasses,” Nucl. Instrum. Meth. B166–167, 698–703 (2000).
[CrossRef]

D. Ehrt, P. Ebeling, and U. Natura, “UV transmission and radiation-induced defects in phosphate and fluoride phosphate glasses,” J. Non-Cryst. Solids240, 263–264 (2000).

M. X. Qiu, R. Vilaseca, C. Cojocaru, J. Martorell, and T. Mizunami, “Second-order nonlinearity generated by doping the surface layer of silica with anions or cations,” J. Appl. Phys.88(8), 4666–4670 (2000).
[CrossRef]

1998

1993

1991

R. A. Betts, T. Tjugiato, Y. L. Xue, and P. L. Chu, “Nonlinear refractive index in Erbium doped optical fiber: theory and experiment,” IEEE J. Quantum Electron.27(4), 908–913 (1991).
[CrossRef]

1990

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

1976

M. D. Feit and D. E. Maiden, “Unstable propagation of a Gaussian laser beam in a plasma waveguide,” Appl. Phys. Lett.28(6), 331–333 (1976).
[CrossRef]

1971

S. N. Vlasov, V. A. Petrishchev, and V. I. Talanov, “Averaged description of wave beams in linear and nonlinear media (the method of moments),” Quantum Electron. Radiophys.14(9), 1062–1070 (1971).
[CrossRef]

1965

V. I. Talanov, “Self-focusing of wave beams in nonlinear media,” Radiophys.9, 138–141 (1965).

P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett.15(26), 1005–1008 (1965).
[CrossRef]

Arkwright, J. W.

Atkins, G. R.

Bark-Zollmann, S.

Ch. Muhlig, W. Triebel, S. Bark-Zollmann, and D. Grebner, “In situ diagnostics of pulse laser-induced defects in DUV transparent fused silica glasses,” Nucl. Instrum. Meth. B166–167, 698–703 (2000).
[CrossRef]

Betts, R. A.

R. A. Betts, T. Tjugiato, Y. L. Xue, and P. L. Chu, “Nonlinear refractive index in Erbium doped optical fiber: theory and experiment,” IEEE J. Quantum Electron.27(4), 908–913 (1991).
[CrossRef]

Campbell, J. H.

J. H. Campbell, J. S. Hayden, and A. Marker, “High-power solid-state lasers: a laser glass perspective,” Intl. J. Appl. Glass Sci.2, 1–27 (2011).

P. R. Ehrmann, J. H. Campbell, T. I. Suratwala, J. S. Hayden, D. Krashkevich, and K. Takeuchi, “Optical loss and Nd3+ nonradiative relaxation by Cu, Fe and several rare earth ion impurities in phosphate laser glasses,” J. Non-Cryst. Solids263–264, 251–262 (2000).
[CrossRef]

Chu, P. L.

R. A. Betts, T. Tjugiato, Y. L. Xue, and P. L. Chu, “Nonlinear refractive index in Erbium doped optical fiber: theory and experiment,” IEEE J. Quantum Electron.27(4), 908–913 (1991).
[CrossRef]

Chung, Y.

Cojocaru, C.

M. X. Qiu, R. Vilaseca, C. Cojocaru, J. Martorell, and T. Mizunami, “Second-order nonlinearity generated by doping the surface layer of silica with anions or cations,” J. Appl. Phys.88(8), 4666–4670 (2000).
[CrossRef]

Digonnet, J. F.

Dubov, M.

Ebeling, P.

D. Ehrt, P. Ebeling, and U. Natura, “UV transmission and radiation-induced defects in phosphate and fluoride phosphate glasses,” J. Non-Cryst. Solids240, 263–264 (2000).

Ehrmann, P. R.

P. R. Ehrmann, J. H. Campbell, T. I. Suratwala, J. S. Hayden, D. Krashkevich, and K. Takeuchi, “Optical loss and Nd3+ nonradiative relaxation by Cu, Fe and several rare earth ion impurities in phosphate laser glasses,” J. Non-Cryst. Solids263–264, 251–262 (2000).
[CrossRef]

Ehrt, D.

D. Ehrt, P. Ebeling, and U. Natura, “UV transmission and radiation-induced defects in phosphate and fluoride phosphate glasses,” J. Non-Cryst. Solids240, 263–264 (2000).

Elango, P.

Fedoruk, M. P.

Feit, M. D.

M. D. Feit and D. E. Maiden, “Unstable propagation of a Gaussian laser beam in a plasma waveguide,” Appl. Phys. Lett.28(6), 331–333 (1976).
[CrossRef]

Grebner, D.

Ch. Muhlig, W. Triebel, S. Bark-Zollmann, and D. Grebner, “In situ diagnostics of pulse laser-induced defects in DUV transparent fused silica glasses,” Nucl. Instrum. Meth. B166–167, 698–703 (2000).
[CrossRef]

Hagan, D. J.

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

Han, W.-T.

Hayden, J. S.

J. H. Campbell, J. S. Hayden, and A. Marker, “High-power solid-state lasers: a laser glass perspective,” Intl. J. Appl. Glass Sci.2, 1–27 (2011).

P. R. Ehrmann, J. H. Campbell, T. I. Suratwala, J. S. Hayden, D. Krashkevich, and K. Takeuchi, “Optical loss and Nd3+ nonradiative relaxation by Cu, Fe and several rare earth ion impurities in phosphate laser glasses,” J. Non-Cryst. Solids263–264, 251–262 (2000).
[CrossRef]

Kamal, A.

Kameyama, A.

A. Kameyama, A. Yokotani, and K. Kurosawa, “Second-order optical nonlinearity and change in refractive index in silica glasses by a combination of thermal poling and x-ray irradiation,” J. Appl. Phys.95(8), 4000–4006 (2004).
[CrossRef]

Kazansky, P. G.

Kelley, P. L.

P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett.15(26), 1005–1008 (1965).
[CrossRef]

Kim, B. H.

Krashkevich, D.

P. R. Ehrmann, J. H. Campbell, T. I. Suratwala, J. S. Hayden, D. Krashkevich, and K. Takeuchi, “Optical loss and Nd3+ nonradiative relaxation by Cu, Fe and several rare earth ion impurities in phosphate laser glasses,” J. Non-Cryst. Solids263–264, 251–262 (2000).
[CrossRef]

Kurosawa, K.

A. Kameyama, A. Yokotani, and K. Kurosawa, “Second-order optical nonlinearity and change in refractive index in silica glasses by a combination of thermal poling and x-ray irradiation,” J. Appl. Phys.95(8), 4000–4006 (2004).
[CrossRef]

Lin, A.

Maiden, D. E.

M. D. Feit and D. E. Maiden, “Unstable propagation of a Gaussian laser beam in a plasma waveguide,” Appl. Phys. Lett.28(6), 331–333 (1976).
[CrossRef]

Marker, A.

J. H. Campbell, J. S. Hayden, and A. Marker, “High-power solid-state lasers: a laser glass perspective,” Intl. J. Appl. Glass Sci.2, 1–27 (2011).

Martorell, J.

M. X. Qiu, R. Vilaseca, C. Cojocaru, J. Martorell, and T. Mizunami, “Second-order nonlinearity generated by doping the surface layer of silica with anions or cations,” J. Appl. Phys.88(8), 4666–4670 (2000).
[CrossRef]

Mezentsev, V. K.

Milam, D.

Mizunami, T.

M. X. Qiu, R. Vilaseca, C. Cojocaru, J. Martorell, and T. Mizunami, “Second-order nonlinearity generated by doping the surface layer of silica with anions or cations,” J. Appl. Phys.88(8), 4666–4670 (2000).
[CrossRef]

Moon, D. S.

Muhlig, Ch.

Ch. Muhlig, W. Triebel, S. Bark-Zollmann, and D. Grebner, “In situ diagnostics of pulse laser-induced defects in DUV transparent fused silica glasses,” Nucl. Instrum. Meth. B166–167, 698–703 (2000).
[CrossRef]

Natura, U.

D. Ehrt, P. Ebeling, and U. Natura, “UV transmission and radiation-induced defects in phosphate and fluoride phosphate glasses,” J. Non-Cryst. Solids240, 263–264 (2000).

Petrishchev, V. A.

S. N. Vlasov, V. A. Petrishchev, and V. I. Talanov, “Averaged description of wave beams in linear and nonlinear media (the method of moments),” Quantum Electron. Radiophys.14(9), 1062–1070 (1971).
[CrossRef]

Podivilov, E. V.

Qiu, M. X.

M. X. Qiu, R. Vilaseca, C. Cojocaru, J. Martorell, and T. Mizunami, “Second-order nonlinearity generated by doping the surface layer of silica with anions or cations,” J. Appl. Phys.88(8), 4666–4670 (2000).
[CrossRef]

Rubenchik, A. M.

Russell, P. S. J.

Said, A. A.

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

Sheik-Bahae, M.

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

Suratwala, T. I.

P. R. Ehrmann, J. H. Campbell, T. I. Suratwala, J. S. Hayden, D. Krashkevich, and K. Takeuchi, “Optical loss and Nd3+ nonradiative relaxation by Cu, Fe and several rare earth ion impurities in phosphate laser glasses,” J. Non-Cryst. Solids263–264, 251–262 (2000).
[CrossRef]

Takeuchi, K.

P. R. Ehrmann, J. H. Campbell, T. I. Suratwala, J. S. Hayden, D. Krashkevich, and K. Takeuchi, “Optical loss and Nd3+ nonradiative relaxation by Cu, Fe and several rare earth ion impurities in phosphate laser glasses,” J. Non-Cryst. Solids263–264, 251–262 (2000).
[CrossRef]

Talanov, V. I.

S. N. Vlasov, V. A. Petrishchev, and V. I. Talanov, “Averaged description of wave beams in linear and nonlinear media (the method of moments),” Quantum Electron. Radiophys.14(9), 1062–1070 (1971).
[CrossRef]

V. I. Talanov, “Self-focusing of wave beams in nonlinear media,” Radiophys.9, 138–141 (1965).

Tjugiato, T.

R. A. Betts, T. Tjugiato, Y. L. Xue, and P. L. Chu, “Nonlinear refractive index in Erbium doped optical fiber: theory and experiment,” IEEE J. Quantum Electron.27(4), 908–913 (1991).
[CrossRef]

Triebel, W.

Ch. Muhlig, W. Triebel, S. Bark-Zollmann, and D. Grebner, “In situ diagnostics of pulse laser-induced defects in DUV transparent fused silica glasses,” Nucl. Instrum. Meth. B166–167, 698–703 (2000).
[CrossRef]

Turitsyn, S. K.

Van Stryland, E. W.

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

Vilaseca, R.

M. X. Qiu, R. Vilaseca, C. Cojocaru, J. Martorell, and T. Mizunami, “Second-order nonlinearity generated by doping the surface layer of silica with anions or cations,” J. Appl. Phys.88(8), 4666–4670 (2000).
[CrossRef]

Vlasov, S. N.

S. N. Vlasov, V. A. Petrishchev, and V. I. Talanov, “Averaged description of wave beams in linear and nonlinear media (the method of moments),” Quantum Electron. Radiophys.14(9), 1062–1070 (1971).
[CrossRef]

Wei, T.-H.

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

Whitbread, T.

Xue, Y. L.

R. A. Betts, T. Tjugiato, Y. L. Xue, and P. L. Chu, “Nonlinear refractive index in Erbium doped optical fiber: theory and experiment,” IEEE J. Quantum Electron.27(4), 908–913 (1991).
[CrossRef]

Yokotani, A.

A. Kameyama, A. Yokotani, and K. Kurosawa, “Second-order optical nonlinearity and change in refractive index in silica glasses by a combination of thermal poling and x-ray irradiation,” J. Appl. Phys.95(8), 4000–4006 (2004).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

M. D. Feit and D. E. Maiden, “Unstable propagation of a Gaussian laser beam in a plasma waveguide,” Appl. Phys. Lett.28(6), 331–333 (1976).
[CrossRef]

IEEE J. Quantum Electron.

R. A. Betts, T. Tjugiato, Y. L. Xue, and P. L. Chu, “Nonlinear refractive index in Erbium doped optical fiber: theory and experiment,” IEEE J. Quantum Electron.27(4), 908–913 (1991).
[CrossRef]

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

Intl. J. Appl. Glass Sci.

J. H. Campbell, J. S. Hayden, and A. Marker, “High-power solid-state lasers: a laser glass perspective,” Intl. J. Appl. Glass Sci.2, 1–27 (2011).

J. Appl. Phys.

M. X. Qiu, R. Vilaseca, C. Cojocaru, J. Martorell, and T. Mizunami, “Second-order nonlinearity generated by doping the surface layer of silica with anions or cations,” J. Appl. Phys.88(8), 4666–4670 (2000).
[CrossRef]

A. Kameyama, A. Yokotani, and K. Kurosawa, “Second-order optical nonlinearity and change in refractive index in silica glasses by a combination of thermal poling and x-ray irradiation,” J. Appl. Phys.95(8), 4000–4006 (2004).
[CrossRef]

J. Lightwave Technol.

J. Non-Cryst. Solids

P. R. Ehrmann, J. H. Campbell, T. I. Suratwala, J. S. Hayden, D. Krashkevich, and K. Takeuchi, “Optical loss and Nd3+ nonradiative relaxation by Cu, Fe and several rare earth ion impurities in phosphate laser glasses,” J. Non-Cryst. Solids263–264, 251–262 (2000).
[CrossRef]

D. Ehrt, P. Ebeling, and U. Natura, “UV transmission and radiation-induced defects in phosphate and fluoride phosphate glasses,” J. Non-Cryst. Solids240, 263–264 (2000).

Nucl. Instrum. Meth. B

Ch. Muhlig, W. Triebel, S. Bark-Zollmann, and D. Grebner, “In situ diagnostics of pulse laser-induced defects in DUV transparent fused silica glasses,” Nucl. Instrum. Meth. B166–167, 698–703 (2000).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett.15(26), 1005–1008 (1965).
[CrossRef]

Quantum Electron. Radiophys.

S. N. Vlasov, V. A. Petrishchev, and V. I. Talanov, “Averaged description of wave beams in linear and nonlinear media (the method of moments),” Quantum Electron. Radiophys.14(9), 1062–1070 (1971).
[CrossRef]

Radiophys.

V. I. Talanov, “Self-focusing of wave beams in nonlinear media,” Radiophys.9, 138–141 (1965).

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Figures (5)

Fig. 1
Fig. 1

Schematic depiction of the experimental system. Images show in gray scale the entrance and exit beam images at equi-distant planes from the lens corresponding to the exit plane of the sample in the presence of self-focusing.

Fig. 2
Fig. 2

The fluence profiles of the transmitted pulses through sample LG-770 averaged along a 2 µm section that transverses the central region of the digitized image of the beam for a pristine and a pre-irradiated site under similar excitation conditions.

Fig. 3
Fig. 3

Intensification (ratio of the measured peak fluence over the reference peak fluence) as a function of the output energy and reference peak fluence (open circles) obtained from a pre-irradiated site (open circles) and corresponding measured transmission (solid circles) in sample LG-770. Solid line represents the fit to the data using the self-focusing model below.

Fig. 4
Fig. 4

Intensification (open circles) and the corresponding measured transmission (solid circles) as a function the number of exposure pulses in sample LHG-8.

Fig. 5
Fig. 5

Calculated induced transient linear or nonlinear refractive indices as a function of peak input laser fluence obtained from fit to the experimental data shown in Fig. 3.

Equations (3)

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

i E z = 2 E 2k kΔn 2 n 0 ( r a ) 2 E k n 2 n 0 | E | 2 E
Intensification= 1 1+ ( z z R ) 2 n 2 I 2 n 0 ( z a ) 2 = 1 1+ ( z z R ) 2 n 2 ϕ 2 n 0 τ ( z a ) 2
Intensification= 1 1+( ( a z R ) 2 n 0 Δn 1 ) sin 2 ( Δn n 0 z a )

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