Abstract

A two-dimensional (2D) numerical model is implemented to describe the movement of ions under thermal poling for the specific case of optical fibers. Three types of cations are considered (representing Na+, Li+ and H3O+) of different mobility values. A cross-sectional map of the carrier concentration is obtained as a function of time. The role of the various cations is investigated. The assumptions of the model are validated by comparing the predictions to experimental data of the time evolution of the nonlinearity induced. A variational analysis of poling parameters including temperature, poling voltage, sign of the bias potential and initial ionic concentrations is performed for a particular fiber geometry. The analysis allows identifying the impact of these parameters on the induced second-order nonlinearity in poled fibers.

© 2014 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  37. A. von Hippel, E. P. Gross, J. G. Jelatis, and M. Geller, “Photocurrent, space-charge buildup and field emission in alkali halide crystals,” Phys. Rev. 91(3), 568–579 (1953).
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2012 (3)

2011 (2)

K. Yadav, C. L. Callender, C. W. Smelser, C. Ledderhof, C. Blanchetiere, S. Jacob, and J. Albert, “Giant enhancement of the second harmonic generation efficiency in poled multilayered silica glass structures,” Opt. Express 19(27), 26975–26983 (2011).
[CrossRef] [PubMed]

A. A. Lipovskii, V. G. Melehin, Y. P. Svirko, and V. V. Zhurikhina, “Bleaching versus poling: Comparison of electric field induced phenomena in glasses and in glass-metal nanocomposites,” J. Appl. Phys. 109(1), 011101 (2011).
[CrossRef]

2009 (2)

2008 (1)

S. Fleming and H. An, “Poled glasses and poled fiber devices,” J. Ceram. Soc. Jpn. 116(1358), 1007–1023 (2008).
[CrossRef]

2007 (2)

A. Michie, I. M. Bassett, J. H. Haywood, and J. Ingram, “Electric field and voltage sensing at 50 Hz using a thermally poled silica optical fiber,” Meas. Sci. Technol. 18(10), 3219–3222 (2007).
[CrossRef]

O. Tarasenko and W. Margulis, “Electro-optical fiber modulation in a Sagnac interferometer,” Opt. Lett. 32(11), 1356–1358 (2007).
[CrossRef] [PubMed]

2005 (3)

2004 (1)

2003 (3)

F. C. Garcia, L. Vogelaar, and R. Kashyap, “Poling of a channel waveguide,” Opt. Express 11(23), 3041–3047 (2003).
[CrossRef] [PubMed]

A. Kudlinski, Y. Quiquempois, M. Lelek, H. Zeghlache, and G. Martinelli, “Complete characterization of the nonlinear spatial distribution induced in poled silica glass with submicron resolution,” Appl. Phys. Lett. 83(17), 3623–3625 (2003).
[CrossRef]

A. L. C. Triques, I. C. S. Carvalho, M. F. Moreira, H. R. Carvalho, R. Fischer, B. Lesche, and W. Margulis, “Time evolution of depletion region in poled silica,” Appl. Phys. Lett. 82(18), 2948–2950 (2003).
[CrossRef]

2001 (2)

D. Faccio, V. Pruneri, and P. G. Kazansky, “Dynamics of the second-order nonlinearity in thermally poled silica glass,” Appl. Phys. Lett. 79(17), 2687–2689 (2001).
[CrossRef]

A. De Francesco and G. E. Town, “Modeling the electrooptic evolution in thermally poled germanosilicate fibers,” IEEE J. Quantum Electron. 37(10), 1312–1320 (2001).
[CrossRef]

2000 (1)

A. C. Liu, M. J. F. Digonnet, G. S. Kino, and E. J. Knystautas, “Improved nonlinear coefficient (0.7 pm/V) in silica thermally poled at high voltage and temperature,” Electron. Lett. 36(6), 555–556 (2000).
[CrossRef]

1999 (2)

T. G. Alley, S. R. J. Brueck, and M. Wiedenbeck, “Secondary ion mass spectrometry study of space-charge formation in thermally poled fused silica,” J. Appl. Phys. 86, 6634–6640 (1999).
[CrossRef]

D. Wong, W. Xu, S. Fleming, M. Janos, and K.-M. Lo, “Frozen-in electrical field in thermally poled fibers,” Opt. Fiber Technol. 5(2), 235–241 (1999).
[CrossRef]

1998 (2)

F. C. Garcia, I. C. S. Carvalho, E. Hering, W. Margulis, and B. Lesche, “Inducing a large second order optical nonlinearity in soft glasses by poling,” Appl. Phys. Lett. 72(25), 3252–3254 (1998).
[CrossRef]

T. G. Alley, S. R. J. Brueck, and R. A. Myers, “Space-charge dynamics in thermally poled fused silica,” J. Non-Cryst. Solids 242(2–3), 165–176 (1998).
[CrossRef]

1996 (1)

1994 (3)

P. G. Kazansky, L. Dong, and P. S. Russell, “High second-order nonlinearities in poled silicate fibers,” Opt. Lett. 19(10), 701–703 (1994).
[CrossRef] [PubMed]

X. C. Long, R. A. Myers, and S. R. J. Brueck, “Measurement of linear electro-optic effect in temperature/electric-field poled optical fibres,” Electron. Lett. 30(25), 2162–2163 (1994).
[CrossRef]

P. G. Kazansky and P. St. J. Russel, “Thermally poled glass: Frozen-in electric field or oriented dipoles?” Opt. Commun. 110(5–6), 611–614 (1994).
[CrossRef]

1993 (2)

R. A. Myers, N. Mukherjee, and S. R. J. Brueck, “Temporal and spectral studies of large χ(2) in fused silica,” Proc. SPIE 2044, 2–10 (1993).
[CrossRef]

D. W. Shin and M. Tomozawa, “Electrical resistivity of silica glasses,” J. Non-Cryst. Solids 163(2), 203–210 (1993).
[CrossRef]

1991 (1)

1974 (1)

D. E. Carlson, K. W. Hang, and G. F. Stockdale, “Ion depletion of glass at a blocking anode: II, properties of ion-depleted glasses,” J. Am. Ceram. Soc. 57(7), 295–300 (1974).
[CrossRef]

1969 (1)

R. H. Doremus, “Electrolysis of alkali ions in silica glass,” Phys. Chem. Glasses 10, 28 (1969).

1968 (1)

G. Frischat, “Sodium diffusion in SiO2 glass,” J. Am. Ceram. Soc. 51(9), 528–530 (1968).
[CrossRef]

1963 (1)

T. Drury and J. P. Roberts, “Diffusion in silica glass following reaction with tritiated water vapor,” Phys. Chem. Glasses 4, 79–90 (1963).

1953 (1)

A. von Hippel, E. P. Gross, J. G. Jelatis, and M. Geller, “Photocurrent, space-charge buildup and field emission in alkali halide crystals,” Phys. Rev. 91(3), 568–579 (1953).
[CrossRef]

Albert, J.

Alley, T. G.

T. G. Alley, S. R. J. Brueck, and M. Wiedenbeck, “Secondary ion mass spectrometry study of space-charge formation in thermally poled fused silica,” J. Appl. Phys. 86, 6634–6640 (1999).
[CrossRef]

T. G. Alley, S. R. J. Brueck, and R. A. Myers, “Space-charge dynamics in thermally poled fused silica,” J. Non-Cryst. Solids 242(2–3), 165–176 (1998).
[CrossRef]

An, H.

Bassett, I. M.

A. Michie, I. M. Bassett, J. H. Haywood, and J. Ingram, “Electric field and voltage sensing at 50 Hz using a thermally poled silica optical fiber,” Meas. Sci. Technol. 18(10), 3219–3222 (2007).
[CrossRef]

Blanchetiere, C.

Brueck, S. R. J.

T. G. Alley, S. R. J. Brueck, and M. Wiedenbeck, “Secondary ion mass spectrometry study of space-charge formation in thermally poled fused silica,” J. Appl. Phys. 86, 6634–6640 (1999).
[CrossRef]

T. G. Alley, S. R. J. Brueck, and R. A. Myers, “Space-charge dynamics in thermally poled fused silica,” J. Non-Cryst. Solids 242(2–3), 165–176 (1998).
[CrossRef]

X. C. Long, R. A. Myers, and S. R. J. Brueck, “Measurement of linear electro-optic effect in temperature/electric-field poled optical fibres,” Electron. Lett. 30(25), 2162–2163 (1994).
[CrossRef]

R. A. Myers, N. Mukherjee, and S. R. J. Brueck, “Temporal and spectral studies of large χ(2) in fused silica,” Proc. SPIE 2044, 2–10 (1993).
[CrossRef]

R. A. Myers, N. Mukherjee, and S. R. J. Brueck, “Large second-order nonlinearity in poled fused silica,” Opt. Lett. 16(22), 1732–1734 (1991).
[CrossRef] [PubMed]

Callender, C. L.

Canagasabey, A.

Carlson, D. E.

D. E. Carlson, K. W. Hang, and G. F. Stockdale, “Ion depletion of glass at a blocking anode: II, properties of ion-depleted glasses,” J. Am. Ceram. Soc. 57(7), 295–300 (1974).
[CrossRef]

Carvalho, H. R.

A. L. C. Triques, I. C. S. Carvalho, M. F. Moreira, H. R. Carvalho, R. Fischer, B. Lesche, and W. Margulis, “Time evolution of depletion region in poled silica,” Appl. Phys. Lett. 82(18), 2948–2950 (2003).
[CrossRef]

Carvalho, I. C. S.

Y. Quiquempois, A. Kudlinski, G. Martinelli, W. Margulis, and I. C. S. Carvalho, “Near-surface modification of the third-order nonlinear susceptibility in thermally poled Infrasil glasses,” Appl. Phys. Lett. 86(18), 181106 (2005).
[CrossRef]

A. L. C. Triques, I. C. S. Carvalho, M. F. Moreira, H. R. Carvalho, R. Fischer, B. Lesche, and W. Margulis, “Time evolution of depletion region in poled silica,” Appl. Phys. Lett. 82(18), 2948–2950 (2003).
[CrossRef]

F. C. Garcia, I. C. S. Carvalho, E. Hering, W. Margulis, and B. Lesche, “Inducing a large second order optical nonlinearity in soft glasses by poling,” Appl. Phys. Lett. 72(25), 3252–3254 (1998).
[CrossRef]

F. Mezzapesa, I. C. S. Carvalho, C. Corbari, P. G. Kazansky, J. S. Wilkinson, and G. Chen, “Voltage assisted cooling: a new route to enhance χ(2) during poling,” in Conference on Lasers and Electro-Otics, CLEO 2005, Baltimore, USA (2005), 408–410.
[CrossRef]

Chen, G.

F. Mezzapesa, I. C. S. Carvalho, C. Corbari, P. G. Kazansky, J. S. Wilkinson, and G. Chen, “Voltage assisted cooling: a new route to enhance χ(2) during poling,” in Conference on Lasers and Electro-Otics, CLEO 2005, Baltimore, USA (2005), 408–410.
[CrossRef]

Corbari, C.

A. Canagasabey, C. Corbari, A. V. Gladyshev, F. Liegeois, S. Guillemet, Y. Hernandez, M. V. Yashkov, A. Kosolapov, E. M. Dianov, M. Ibsen, and P. G. Kazansky, “High-average-power second-harmonic generation from periodically poled silica fibers,” Opt. Lett. 34(16), 2483–2485 (2009).
[CrossRef] [PubMed]

F. Mezzapesa, I. C. S. Carvalho, C. Corbari, P. G. Kazansky, J. S. Wilkinson, and G. Chen, “Voltage assisted cooling: a new route to enhance χ(2) during poling,” in Conference on Lasers and Electro-Otics, CLEO 2005, Baltimore, USA (2005), 408–410.
[CrossRef]

De Francesco, A.

A. De Francesco and G. E. Town, “Modeling the electrooptic evolution in thermally poled germanosilicate fibers,” IEEE J. Quantum Electron. 37(10), 1312–1320 (2001).
[CrossRef]

Dianov, E. M.

Digonnet, M. J. F.

A. C. Liu, M. J. F. Digonnet, G. S. Kino, and E. J. Knystautas, “Improved nonlinear coefficient (0.7 pm/V) in silica thermally poled at high voltage and temperature,” Electron. Lett. 36(6), 555–556 (2000).
[CrossRef]

Dong, L.

Doremus, R. H.

R. H. Doremus, “Electrolysis of alkali ions in silica glass,” Phys. Chem. Glasses 10, 28 (1969).

Drury, T.

T. Drury and J. P. Roberts, “Diffusion in silica glass following reaction with tritiated water vapor,” Phys. Chem. Glasses 4, 79–90 (1963).

Faccio, D.

D. Faccio, V. Pruneri, and P. G. Kazansky, “Dynamics of the second-order nonlinearity in thermally poled silica glass,” Appl. Phys. Lett. 79(17), 2687–2689 (2001).
[CrossRef]

Fischer, R.

A. L. C. Triques, I. C. S. Carvalho, M. F. Moreira, H. R. Carvalho, R. Fischer, B. Lesche, and W. Margulis, “Time evolution of depletion region in poled silica,” Appl. Phys. Lett. 82(18), 2948–2950 (2003).
[CrossRef]

Fleming, S.

H. An and S. Fleming, “Investigating the effectiveness of thermally poling optical fibers with various internal electrode configurations,” Opt. Express 20(7), 7436–7444 (2012).
[CrossRef] [PubMed]

S. Fleming and H. An, “Poled glasses and poled fiber devices,” J. Ceram. Soc. Jpn. 116(1358), 1007–1023 (2008).
[CrossRef]

D. Wong, W. Xu, S. Fleming, M. Janos, and K.-M. Lo, “Frozen-in electrical field in thermally poled fibers,” Opt. Fiber Technol. 5(2), 235–241 (1999).
[CrossRef]

Fokine, M.

M. Fokine, L. Kjellberg, P. Helander, N. Myren, L. Norin, H. Olsson, N. Sjodin, and W. Margulis, “A fibre-based kerr switch and modulator,” in 30th European Conference on Optical Communications ECOC 2004, Stockholm, Sweden (2004), Vol. 1, pp. 43–44.

Frischat, G.

G. Frischat, “Sodium diffusion in SiO2 glass,” J. Am. Ceram. Soc. 51(9), 528–530 (1968).
[CrossRef]

Garcia, F. C.

F. C. Garcia, L. Vogelaar, and R. Kashyap, “Poling of a channel waveguide,” Opt. Express 11(23), 3041–3047 (2003).
[CrossRef] [PubMed]

F. C. Garcia, I. C. S. Carvalho, E. Hering, W. Margulis, and B. Lesche, “Inducing a large second order optical nonlinearity in soft glasses by poling,” Appl. Phys. Lett. 72(25), 3252–3254 (1998).
[CrossRef]

Geller, M.

A. von Hippel, E. P. Gross, J. G. Jelatis, and M. Geller, “Photocurrent, space-charge buildup and field emission in alkali halide crystals,” Phys. Rev. 91(3), 568–579 (1953).
[CrossRef]

Gladyshev, A. V.

Gross, E. P.

A. von Hippel, E. P. Gross, J. G. Jelatis, and M. Geller, “Photocurrent, space-charge buildup and field emission in alkali halide crystals,” Phys. Rev. 91(3), 568–579 (1953).
[CrossRef]

Guillemet, S.

Hang, K. W.

D. E. Carlson, K. W. Hang, and G. F. Stockdale, “Ion depletion of glass at a blocking anode: II, properties of ion-depleted glasses,” J. Am. Ceram. Soc. 57(7), 295–300 (1974).
[CrossRef]

Haywood, J. H.

A. Michie, I. M. Bassett, J. H. Haywood, and J. Ingram, “Electric field and voltage sensing at 50 Hz using a thermally poled silica optical fiber,” Meas. Sci. Technol. 18(10), 3219–3222 (2007).
[CrossRef]

Helander, P.

N. Myrén, H. Olsson, L. Norin, N. Sjödin, P. Helander, J. Svennebrink, and W. Margulis, “Wide wedge-shaped depletion region in thermally poled fiber with alloy electrodes,” Opt. Express 12(25), 6093–6099 (2004).
[CrossRef] [PubMed]

M. Fokine, L. Kjellberg, P. Helander, N. Myren, L. Norin, H. Olsson, N. Sjodin, and W. Margulis, “A fibre-based kerr switch and modulator,” in 30th European Conference on Optical Communications ECOC 2004, Stockholm, Sweden (2004), Vol. 1, pp. 43–44.

Hering, E.

F. C. Garcia, I. C. S. Carvalho, E. Hering, W. Margulis, and B. Lesche, “Inducing a large second order optical nonlinearity in soft glasses by poling,” Appl. Phys. Lett. 72(25), 3252–3254 (1998).
[CrossRef]

Hernandez, Y.

Ibsen, M.

Ingram, J.

A. Michie, I. M. Bassett, J. H. Haywood, and J. Ingram, “Electric field and voltage sensing at 50 Hz using a thermally poled silica optical fiber,” Meas. Sci. Technol. 18(10), 3219–3222 (2007).
[CrossRef]

Jacob, S.

Janos, M.

D. Wong, W. Xu, S. Fleming, M. Janos, and K.-M. Lo, “Frozen-in electrical field in thermally poled fibers,” Opt. Fiber Technol. 5(2), 235–241 (1999).
[CrossRef]

Jelatis, J. G.

A. von Hippel, E. P. Gross, J. G. Jelatis, and M. Geller, “Photocurrent, space-charge buildup and field emission in alkali halide crystals,” Phys. Rev. 91(3), 568–579 (1953).
[CrossRef]

Kashyap, R.

Kazansky, P. G.

A. Canagasabey, C. Corbari, A. V. Gladyshev, F. Liegeois, S. Guillemet, Y. Hernandez, M. V. Yashkov, A. Kosolapov, E. M. Dianov, M. Ibsen, and P. G. Kazansky, “High-average-power second-harmonic generation from periodically poled silica fibers,” Opt. Lett. 34(16), 2483–2485 (2009).
[CrossRef] [PubMed]

D. Faccio, V. Pruneri, and P. G. Kazansky, “Dynamics of the second-order nonlinearity in thermally poled silica glass,” Appl. Phys. Lett. 79(17), 2687–2689 (2001).
[CrossRef]

H. Takebe, P. G. Kazansky, P. St. J. Russell, and K. Morinaga, “Effect of poling conditions on second-harmonic generation in fused silica,” Opt. Lett. 21(7), 468–470 (1996).
[CrossRef] [PubMed]

P. G. Kazansky and P. St. J. Russel, “Thermally poled glass: Frozen-in electric field or oriented dipoles?” Opt. Commun. 110(5–6), 611–614 (1994).
[CrossRef]

P. G. Kazansky, L. Dong, and P. S. Russell, “High second-order nonlinearities in poled silicate fibers,” Opt. Lett. 19(10), 701–703 (1994).
[CrossRef] [PubMed]

F. Mezzapesa, I. C. S. Carvalho, C. Corbari, P. G. Kazansky, J. S. Wilkinson, and G. Chen, “Voltage assisted cooling: a new route to enhance χ(2) during poling,” in Conference on Lasers and Electro-Otics, CLEO 2005, Baltimore, USA (2005), 408–410.
[CrossRef]

Kino, G. S.

A. C. Liu, M. J. F. Digonnet, G. S. Kino, and E. J. Knystautas, “Improved nonlinear coefficient (0.7 pm/V) in silica thermally poled at high voltage and temperature,” Electron. Lett. 36(6), 555–556 (2000).
[CrossRef]

Kjellberg, L.

M. Fokine, L. Kjellberg, P. Helander, N. Myren, L. Norin, H. Olsson, N. Sjodin, and W. Margulis, “A fibre-based kerr switch and modulator,” in 30th European Conference on Optical Communications ECOC 2004, Stockholm, Sweden (2004), Vol. 1, pp. 43–44.

Knystautas, E. J.

A. C. Liu, M. J. F. Digonnet, G. S. Kino, and E. J. Knystautas, “Improved nonlinear coefficient (0.7 pm/V) in silica thermally poled at high voltage and temperature,” Electron. Lett. 36(6), 555–556 (2000).
[CrossRef]

Kosolapov, A.

Kudlinsk, A.

A. Kudlinsk, Y. Quiquempois, and G. Martinelli, “Why the thermal poling could be innefficient in fibres,” in 30th European Conference on Optical Communications, Stockholm, Sweden (2004), Vol. 2, pp. 236–237.

Kudlinski, A.

Y. Quiquempois, A. Kudlinski, G. Martinelli, W. Margulis, and I. C. S. Carvalho, “Near-surface modification of the third-order nonlinear susceptibility in thermally poled Infrasil glasses,” Appl. Phys. Lett. 86(18), 181106 (2005).
[CrossRef]

A. Kudlinski, Y. Quiquempois, and G. Martinelli, “Modeling of the χ(2) susceptibility time-evolution in thermally poled fused silica,” Opt. Express 13(20), 8015–8024 (2005).
[CrossRef] [PubMed]

Y. Quiquempois, A. Kudlinski, and G. Martinelli, “Zero-potential condition in thermally poled silica samples: evidence of a negative electric field outside the depletion layer,” J. Opt. Soc. Am. B 22(3), 598–604 (2005).
[CrossRef]

A. Kudlinski, Y. Quiquempois, M. Lelek, H. Zeghlache, and G. Martinelli, “Complete characterization of the nonlinear spatial distribution induced in poled silica glass with submicron resolution,” Appl. Phys. Lett. 83(17), 3623–3625 (2003).
[CrossRef]

Ledderhof, C.

Lelek, M.

A. Kudlinski, Y. Quiquempois, M. Lelek, H. Zeghlache, and G. Martinelli, “Complete characterization of the nonlinear spatial distribution induced in poled silica glass with submicron resolution,” Appl. Phys. Lett. 83(17), 3623–3625 (2003).
[CrossRef]

Lepen’kin, Ya. A.

M. I. Petrov, Ya. A. Lepen’kin, and A. A. Lipovskii, “Polarization of glass containing fast and slow ions,” J. Appl. Phys. 112(4), 043101 (2012).
[CrossRef]

Lesche, B.

A. L. C. Triques, I. C. S. Carvalho, M. F. Moreira, H. R. Carvalho, R. Fischer, B. Lesche, and W. Margulis, “Time evolution of depletion region in poled silica,” Appl. Phys. Lett. 82(18), 2948–2950 (2003).
[CrossRef]

F. C. Garcia, I. C. S. Carvalho, E. Hering, W. Margulis, and B. Lesche, “Inducing a large second order optical nonlinearity in soft glasses by poling,” Appl. Phys. Lett. 72(25), 3252–3254 (1998).
[CrossRef]

Liegeois, F.

Lipovskii, A. A.

M. I. Petrov, Ya. A. Lepen’kin, and A. A. Lipovskii, “Polarization of glass containing fast and slow ions,” J. Appl. Phys. 112(4), 043101 (2012).
[CrossRef]

A. A. Lipovskii, V. G. Melehin, Y. P. Svirko, and V. V. Zhurikhina, “Bleaching versus poling: Comparison of electric field induced phenomena in glasses and in glass-metal nanocomposites,” J. Appl. Phys. 109(1), 011101 (2011).
[CrossRef]

Liu, A. C.

A. C. Liu, M. J. F. Digonnet, G. S. Kino, and E. J. Knystautas, “Improved nonlinear coefficient (0.7 pm/V) in silica thermally poled at high voltage and temperature,” Electron. Lett. 36(6), 555–556 (2000).
[CrossRef]

Lo, K.-M.

D. Wong, W. Xu, S. Fleming, M. Janos, and K.-M. Lo, “Frozen-in electrical field in thermally poled fibers,” Opt. Fiber Technol. 5(2), 235–241 (1999).
[CrossRef]

Long, X. C.

X. C. Long, R. A. Myers, and S. R. J. Brueck, “Measurement of linear electro-optic effect in temperature/electric-field poled optical fibres,” Electron. Lett. 30(25), 2162–2163 (1994).
[CrossRef]

Malmström, M.

Margulis, W.

M. Malmström, O. Tarasenko, and W. Margulis, “Pulse selection at 1 MHz with electrooptic fiber switch,” Opt. Express 20(9), 9465–9470 (2012).
[CrossRef] [PubMed]

W. Margulis, O. Tarasenko, and N. Myrén, “Who needs a cathode? Creating a second-order nonlinearity by charging glass fiber with two anodes,” Opt. Express 17(18), 15534–15540 (2009).
[CrossRef] [PubMed]

O. Tarasenko and W. Margulis, “Electro-optical fiber modulation in a Sagnac interferometer,” Opt. Lett. 32(11), 1356–1358 (2007).
[CrossRef] [PubMed]

Y. Quiquempois, A. Kudlinski, G. Martinelli, W. Margulis, and I. C. S. Carvalho, “Near-surface modification of the third-order nonlinear susceptibility in thermally poled Infrasil glasses,” Appl. Phys. Lett. 86(18), 181106 (2005).
[CrossRef]

N. Myrén, H. Olsson, L. Norin, N. Sjödin, P. Helander, J. Svennebrink, and W. Margulis, “Wide wedge-shaped depletion region in thermally poled fiber with alloy electrodes,” Opt. Express 12(25), 6093–6099 (2004).
[CrossRef] [PubMed]

A. L. C. Triques, I. C. S. Carvalho, M. F. Moreira, H. R. Carvalho, R. Fischer, B. Lesche, and W. Margulis, “Time evolution of depletion region in poled silica,” Appl. Phys. Lett. 82(18), 2948–2950 (2003).
[CrossRef]

F. C. Garcia, I. C. S. Carvalho, E. Hering, W. Margulis, and B. Lesche, “Inducing a large second order optical nonlinearity in soft glasses by poling,” Appl. Phys. Lett. 72(25), 3252–3254 (1998).
[CrossRef]

M. Fokine, L. Kjellberg, P. Helander, N. Myren, L. Norin, H. Olsson, N. Sjodin, and W. Margulis, “A fibre-based kerr switch and modulator,” in 30th European Conference on Optical Communications ECOC 2004, Stockholm, Sweden (2004), Vol. 1, pp. 43–44.

Martinelli, G.

Y. Quiquempois, A. Kudlinski, G. Martinelli, W. Margulis, and I. C. S. Carvalho, “Near-surface modification of the third-order nonlinear susceptibility in thermally poled Infrasil glasses,” Appl. Phys. Lett. 86(18), 181106 (2005).
[CrossRef]

Y. Quiquempois, A. Kudlinski, and G. Martinelli, “Zero-potential condition in thermally poled silica samples: evidence of a negative electric field outside the depletion layer,” J. Opt. Soc. Am. B 22(3), 598–604 (2005).
[CrossRef]

A. Kudlinski, Y. Quiquempois, and G. Martinelli, “Modeling of the χ(2) susceptibility time-evolution in thermally poled fused silica,” Opt. Express 13(20), 8015–8024 (2005).
[CrossRef] [PubMed]

A. Kudlinski, Y. Quiquempois, M. Lelek, H. Zeghlache, and G. Martinelli, “Complete characterization of the nonlinear spatial distribution induced in poled silica glass with submicron resolution,” Appl. Phys. Lett. 83(17), 3623–3625 (2003).
[CrossRef]

A. Kudlinsk, Y. Quiquempois, and G. Martinelli, “Why the thermal poling could be innefficient in fibres,” in 30th European Conference on Optical Communications, Stockholm, Sweden (2004), Vol. 2, pp. 236–237.

Melehin, V. G.

A. A. Lipovskii, V. G. Melehin, Y. P. Svirko, and V. V. Zhurikhina, “Bleaching versus poling: Comparison of electric field induced phenomena in glasses and in glass-metal nanocomposites,” J. Appl. Phys. 109(1), 011101 (2011).
[CrossRef]

Mezzapesa, F.

F. Mezzapesa, I. C. S. Carvalho, C. Corbari, P. G. Kazansky, J. S. Wilkinson, and G. Chen, “Voltage assisted cooling: a new route to enhance χ(2) during poling,” in Conference on Lasers and Electro-Otics, CLEO 2005, Baltimore, USA (2005), 408–410.
[CrossRef]

Michie, A.

A. Michie, I. M. Bassett, J. H. Haywood, and J. Ingram, “Electric field and voltage sensing at 50 Hz using a thermally poled silica optical fiber,” Meas. Sci. Technol. 18(10), 3219–3222 (2007).
[CrossRef]

Moreira, M. F.

A. L. C. Triques, I. C. S. Carvalho, M. F. Moreira, H. R. Carvalho, R. Fischer, B. Lesche, and W. Margulis, “Time evolution of depletion region in poled silica,” Appl. Phys. Lett. 82(18), 2948–2950 (2003).
[CrossRef]

Morinaga, K.

Mukherjee, N.

R. A. Myers, N. Mukherjee, and S. R. J. Brueck, “Temporal and spectral studies of large χ(2) in fused silica,” Proc. SPIE 2044, 2–10 (1993).
[CrossRef]

R. A. Myers, N. Mukherjee, and S. R. J. Brueck, “Large second-order nonlinearity in poled fused silica,” Opt. Lett. 16(22), 1732–1734 (1991).
[CrossRef] [PubMed]

Myers, R. A.

T. G. Alley, S. R. J. Brueck, and R. A. Myers, “Space-charge dynamics in thermally poled fused silica,” J. Non-Cryst. Solids 242(2–3), 165–176 (1998).
[CrossRef]

X. C. Long, R. A. Myers, and S. R. J. Brueck, “Measurement of linear electro-optic effect in temperature/electric-field poled optical fibres,” Electron. Lett. 30(25), 2162–2163 (1994).
[CrossRef]

R. A. Myers, N. Mukherjee, and S. R. J. Brueck, “Temporal and spectral studies of large χ(2) in fused silica,” Proc. SPIE 2044, 2–10 (1993).
[CrossRef]

R. A. Myers, N. Mukherjee, and S. R. J. Brueck, “Large second-order nonlinearity in poled fused silica,” Opt. Lett. 16(22), 1732–1734 (1991).
[CrossRef] [PubMed]

Myren, N.

M. Fokine, L. Kjellberg, P. Helander, N. Myren, L. Norin, H. Olsson, N. Sjodin, and W. Margulis, “A fibre-based kerr switch and modulator,” in 30th European Conference on Optical Communications ECOC 2004, Stockholm, Sweden (2004), Vol. 1, pp. 43–44.

Myrén, N.

Norin, L.

N. Myrén, H. Olsson, L. Norin, N. Sjödin, P. Helander, J. Svennebrink, and W. Margulis, “Wide wedge-shaped depletion region in thermally poled fiber with alloy electrodes,” Opt. Express 12(25), 6093–6099 (2004).
[CrossRef] [PubMed]

M. Fokine, L. Kjellberg, P. Helander, N. Myren, L. Norin, H. Olsson, N. Sjodin, and W. Margulis, “A fibre-based kerr switch and modulator,” in 30th European Conference on Optical Communications ECOC 2004, Stockholm, Sweden (2004), Vol. 1, pp. 43–44.

Olsson, H.

N. Myrén, H. Olsson, L. Norin, N. Sjödin, P. Helander, J. Svennebrink, and W. Margulis, “Wide wedge-shaped depletion region in thermally poled fiber with alloy electrodes,” Opt. Express 12(25), 6093–6099 (2004).
[CrossRef] [PubMed]

M. Fokine, L. Kjellberg, P. Helander, N. Myren, L. Norin, H. Olsson, N. Sjodin, and W. Margulis, “A fibre-based kerr switch and modulator,” in 30th European Conference on Optical Communications ECOC 2004, Stockholm, Sweden (2004), Vol. 1, pp. 43–44.

Petrov, M. I.

M. I. Petrov, Ya. A. Lepen’kin, and A. A. Lipovskii, “Polarization of glass containing fast and slow ions,” J. Appl. Phys. 112(4), 043101 (2012).
[CrossRef]

Pruneri, V.

D. Faccio, V. Pruneri, and P. G. Kazansky, “Dynamics of the second-order nonlinearity in thermally poled silica glass,” Appl. Phys. Lett. 79(17), 2687–2689 (2001).
[CrossRef]

Quiquempois, Y.

Y. Quiquempois, A. Kudlinski, G. Martinelli, W. Margulis, and I. C. S. Carvalho, “Near-surface modification of the third-order nonlinear susceptibility in thermally poled Infrasil glasses,” Appl. Phys. Lett. 86(18), 181106 (2005).
[CrossRef]

Y. Quiquempois, A. Kudlinski, and G. Martinelli, “Zero-potential condition in thermally poled silica samples: evidence of a negative electric field outside the depletion layer,” J. Opt. Soc. Am. B 22(3), 598–604 (2005).
[CrossRef]

A. Kudlinski, Y. Quiquempois, and G. Martinelli, “Modeling of the χ(2) susceptibility time-evolution in thermally poled fused silica,” Opt. Express 13(20), 8015–8024 (2005).
[CrossRef] [PubMed]

A. Kudlinski, Y. Quiquempois, M. Lelek, H. Zeghlache, and G. Martinelli, “Complete characterization of the nonlinear spatial distribution induced in poled silica glass with submicron resolution,” Appl. Phys. Lett. 83(17), 3623–3625 (2003).
[CrossRef]

A. Kudlinsk, Y. Quiquempois, and G. Martinelli, “Why the thermal poling could be innefficient in fibres,” in 30th European Conference on Optical Communications, Stockholm, Sweden (2004), Vol. 2, pp. 236–237.

Roberts, J. P.

T. Drury and J. P. Roberts, “Diffusion in silica glass following reaction with tritiated water vapor,” Phys. Chem. Glasses 4, 79–90 (1963).

Russel, P. St. J.

P. G. Kazansky and P. St. J. Russel, “Thermally poled glass: Frozen-in electric field or oriented dipoles?” Opt. Commun. 110(5–6), 611–614 (1994).
[CrossRef]

Russell, P. S.

Russell, P. St. J.

Shin, D. W.

D. W. Shin and M. Tomozawa, “Electrical resistivity of silica glasses,” J. Non-Cryst. Solids 163(2), 203–210 (1993).
[CrossRef]

Sjodin, N.

M. Fokine, L. Kjellberg, P. Helander, N. Myren, L. Norin, H. Olsson, N. Sjodin, and W. Margulis, “A fibre-based kerr switch and modulator,” in 30th European Conference on Optical Communications ECOC 2004, Stockholm, Sweden (2004), Vol. 1, pp. 43–44.

Sjödin, N.

Smelser, C. W.

Stockdale, G. F.

D. E. Carlson, K. W. Hang, and G. F. Stockdale, “Ion depletion of glass at a blocking anode: II, properties of ion-depleted glasses,” J. Am. Ceram. Soc. 57(7), 295–300 (1974).
[CrossRef]

Svennebrink, J.

Svirko, Y. P.

A. A. Lipovskii, V. G. Melehin, Y. P. Svirko, and V. V. Zhurikhina, “Bleaching versus poling: Comparison of electric field induced phenomena in glasses and in glass-metal nanocomposites,” J. Appl. Phys. 109(1), 011101 (2011).
[CrossRef]

Takebe, H.

Tarasenko, O.

Tomozawa, M.

D. W. Shin and M. Tomozawa, “Electrical resistivity of silica glasses,” J. Non-Cryst. Solids 163(2), 203–210 (1993).
[CrossRef]

Town, G. E.

A. De Francesco and G. E. Town, “Modeling the electrooptic evolution in thermally poled germanosilicate fibers,” IEEE J. Quantum Electron. 37(10), 1312–1320 (2001).
[CrossRef]

Triques, A. L. C.

A. L. C. Triques, I. C. S. Carvalho, M. F. Moreira, H. R. Carvalho, R. Fischer, B. Lesche, and W. Margulis, “Time evolution of depletion region in poled silica,” Appl. Phys. Lett. 82(18), 2948–2950 (2003).
[CrossRef]

Vogelaar, L.

von Hippel, A.

A. von Hippel, E. P. Gross, J. G. Jelatis, and M. Geller, “Photocurrent, space-charge buildup and field emission in alkali halide crystals,” Phys. Rev. 91(3), 568–579 (1953).
[CrossRef]

Wiedenbeck, M.

T. G. Alley, S. R. J. Brueck, and M. Wiedenbeck, “Secondary ion mass spectrometry study of space-charge formation in thermally poled fused silica,” J. Appl. Phys. 86, 6634–6640 (1999).
[CrossRef]

Wilkinson, J. S.

F. Mezzapesa, I. C. S. Carvalho, C. Corbari, P. G. Kazansky, J. S. Wilkinson, and G. Chen, “Voltage assisted cooling: a new route to enhance χ(2) during poling,” in Conference on Lasers and Electro-Otics, CLEO 2005, Baltimore, USA (2005), 408–410.
[CrossRef]

Wong, D.

D. Wong, W. Xu, S. Fleming, M. Janos, and K.-M. Lo, “Frozen-in electrical field in thermally poled fibers,” Opt. Fiber Technol. 5(2), 235–241 (1999).
[CrossRef]

Xu, W.

D. Wong, W. Xu, S. Fleming, M. Janos, and K.-M. Lo, “Frozen-in electrical field in thermally poled fibers,” Opt. Fiber Technol. 5(2), 235–241 (1999).
[CrossRef]

Yadav, K.

Yashkov, M. V.

Zeghlache, H.

A. Kudlinski, Y. Quiquempois, M. Lelek, H. Zeghlache, and G. Martinelli, “Complete characterization of the nonlinear spatial distribution induced in poled silica glass with submicron resolution,” Appl. Phys. Lett. 83(17), 3623–3625 (2003).
[CrossRef]

Zhurikhina, V. V.

A. A. Lipovskii, V. G. Melehin, Y. P. Svirko, and V. V. Zhurikhina, “Bleaching versus poling: Comparison of electric field induced phenomena in glasses and in glass-metal nanocomposites,” J. Appl. Phys. 109(1), 011101 (2011).
[CrossRef]

Appl. Phys. Lett. (5)

D. Faccio, V. Pruneri, and P. G. Kazansky, “Dynamics of the second-order nonlinearity in thermally poled silica glass,” Appl. Phys. Lett. 79(17), 2687–2689 (2001).
[CrossRef]

A. L. C. Triques, I. C. S. Carvalho, M. F. Moreira, H. R. Carvalho, R. Fischer, B. Lesche, and W. Margulis, “Time evolution of depletion region in poled silica,” Appl. Phys. Lett. 82(18), 2948–2950 (2003).
[CrossRef]

A. Kudlinski, Y. Quiquempois, M. Lelek, H. Zeghlache, and G. Martinelli, “Complete characterization of the nonlinear spatial distribution induced in poled silica glass with submicron resolution,” Appl. Phys. Lett. 83(17), 3623–3625 (2003).
[CrossRef]

Y. Quiquempois, A. Kudlinski, G. Martinelli, W. Margulis, and I. C. S. Carvalho, “Near-surface modification of the third-order nonlinear susceptibility in thermally poled Infrasil glasses,” Appl. Phys. Lett. 86(18), 181106 (2005).
[CrossRef]

F. C. Garcia, I. C. S. Carvalho, E. Hering, W. Margulis, and B. Lesche, “Inducing a large second order optical nonlinearity in soft glasses by poling,” Appl. Phys. Lett. 72(25), 3252–3254 (1998).
[CrossRef]

Electron. Lett. (2)

X. C. Long, R. A. Myers, and S. R. J. Brueck, “Measurement of linear electro-optic effect in temperature/electric-field poled optical fibres,” Electron. Lett. 30(25), 2162–2163 (1994).
[CrossRef]

A. C. Liu, M. J. F. Digonnet, G. S. Kino, and E. J. Knystautas, “Improved nonlinear coefficient (0.7 pm/V) in silica thermally poled at high voltage and temperature,” Electron. Lett. 36(6), 555–556 (2000).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. De Francesco and G. E. Town, “Modeling the electrooptic evolution in thermally poled germanosilicate fibers,” IEEE J. Quantum Electron. 37(10), 1312–1320 (2001).
[CrossRef]

J. Am. Ceram. Soc. (2)

G. Frischat, “Sodium diffusion in SiO2 glass,” J. Am. Ceram. Soc. 51(9), 528–530 (1968).
[CrossRef]

D. E. Carlson, K. W. Hang, and G. F. Stockdale, “Ion depletion of glass at a blocking anode: II, properties of ion-depleted glasses,” J. Am. Ceram. Soc. 57(7), 295–300 (1974).
[CrossRef]

J. Appl. Phys. (3)

M. I. Petrov, Ya. A. Lepen’kin, and A. A. Lipovskii, “Polarization of glass containing fast and slow ions,” J. Appl. Phys. 112(4), 043101 (2012).
[CrossRef]

A. A. Lipovskii, V. G. Melehin, Y. P. Svirko, and V. V. Zhurikhina, “Bleaching versus poling: Comparison of electric field induced phenomena in glasses and in glass-metal nanocomposites,” J. Appl. Phys. 109(1), 011101 (2011).
[CrossRef]

T. G. Alley, S. R. J. Brueck, and M. Wiedenbeck, “Secondary ion mass spectrometry study of space-charge formation in thermally poled fused silica,” J. Appl. Phys. 86, 6634–6640 (1999).
[CrossRef]

J. Ceram. Soc. Jpn. (1)

S. Fleming and H. An, “Poled glasses and poled fiber devices,” J. Ceram. Soc. Jpn. 116(1358), 1007–1023 (2008).
[CrossRef]

J. Non-Cryst. Solids (2)

T. G. Alley, S. R. J. Brueck, and R. A. Myers, “Space-charge dynamics in thermally poled fused silica,” J. Non-Cryst. Solids 242(2–3), 165–176 (1998).
[CrossRef]

D. W. Shin and M. Tomozawa, “Electrical resistivity of silica glasses,” J. Non-Cryst. Solids 163(2), 203–210 (1993).
[CrossRef]

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

Meas. Sci. Technol. (1)

A. Michie, I. M. Bassett, J. H. Haywood, and J. Ingram, “Electric field and voltage sensing at 50 Hz using a thermally poled silica optical fiber,” Meas. Sci. Technol. 18(10), 3219–3222 (2007).
[CrossRef]

Opt. Commun. (1)

P. G. Kazansky and P. St. J. Russel, “Thermally poled glass: Frozen-in electric field or oriented dipoles?” Opt. Commun. 110(5–6), 611–614 (1994).
[CrossRef]

Opt. Express (7)

Opt. Fiber Technol. (1)

D. Wong, W. Xu, S. Fleming, M. Janos, and K.-M. Lo, “Frozen-in electrical field in thermally poled fibers,” Opt. Fiber Technol. 5(2), 235–241 (1999).
[CrossRef]

Opt. Lett. (5)

Phys. Chem. Glasses (2)

T. Drury and J. P. Roberts, “Diffusion in silica glass following reaction with tritiated water vapor,” Phys. Chem. Glasses 4, 79–90 (1963).

R. H. Doremus, “Electrolysis of alkali ions in silica glass,” Phys. Chem. Glasses 10, 28 (1969).

Phys. Rev. (1)

A. von Hippel, E. P. Gross, J. G. Jelatis, and M. Geller, “Photocurrent, space-charge buildup and field emission in alkali halide crystals,” Phys. Rev. 91(3), 568–579 (1953).
[CrossRef]

Proc. SPIE (1)

R. A. Myers, N. Mukherjee, and S. R. J. Brueck, “Temporal and spectral studies of large χ(2) in fused silica,” Proc. SPIE 2044, 2–10 (1993).
[CrossRef]

Other (5)

F. Mezzapesa, I. C. S. Carvalho, C. Corbari, P. G. Kazansky, J. S. Wilkinson, and G. Chen, “Voltage assisted cooling: a new route to enhance χ(2) during poling,” in Conference on Lasers and Electro-Otics, CLEO 2005, Baltimore, USA (2005), 408–410.
[CrossRef]

ILMASIL PN contamination levels are specified at http://www.qsil.com/en/material.html

W. Xu, PhD thesis, University of Sydney, Chapter 4 (2004).

M. Fokine, L. Kjellberg, P. Helander, N. Myren, L. Norin, H. Olsson, N. Sjodin, and W. Margulis, “A fibre-based kerr switch and modulator,” in 30th European Conference on Optical Communications ECOC 2004, Stockholm, Sweden (2004), Vol. 1, pp. 43–44.

A. Kudlinsk, Y. Quiquempois, and G. Martinelli, “Why the thermal poling could be innefficient in fibres,” in 30th European Conference on Optical Communications, Stockholm, Sweden (2004), Vol. 2, pp. 236–237.

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Figures (13)

Fig. 1
Fig. 1

Map of electric field (a) and potential (b) across a fiber at the start of poling. The left electrode is the anode biased at 5 kV and the right electrode is the grounded (Gnd) cathode. The field has a wedged-shape [27]. Map of electric field (c) and potential (d) when both electrodes are anodes at + 5 kV. The arrows indicate direction and field strength.

Fig. 2
Fig. 2

Time evolution of the distribution of mobile cations, their sum and the potential map at four representative times for fiber F1 with both electrodes biased at positive high-voltage. Here, the injection of H3O+ is assumed to be inexhaustible and capable of neutralizing the unpaired electrons created by the displacement of Na+ and Li+.

Fig. 3
Fig. 3

2D map of electric field (a) and potential (b) across a fiber poled in a conventional (+/−) configuration when the field recorded at the center of the core reaches its maximum (8800 s). When the 5 kV voltage bias is switched off, the electric field distribution (c) and the potential (d) change significantly and the maximum recorded field is Erec = 1.6 × 108 V/m .

Fig. 4
Fig. 4

2D map of electric field (a) and potential (b) across a fiber poled in a two-anode (+/+) configuration when the field recorded at the center of the core reaches its maximum (8800 s). When the 5 kV voltage bias is switched off, the electric field distribution (c) and the potential (d) change significantly. The maximum recorded field at the center of the core after the process is completed is Erec = 3.1 × 108 V/m .

Fig. 5
Fig. 5

Simulation of the dynamics of poling associated to different cations in a fiber poled with internal electrodes on a linear time-scale (left) and a log time-scale (right). The apparent second-order nonlinearity here is determined at the core center and in the presence of the HV poling bias, i.e., it is partly induced by the applied voltage. The poling voltage assumed is 5 kV and the temperature 265 °C.

Fig. 6
Fig. 6

Simulation of the dynamics of electrostatic charging with two anodes associated to different cations in a fiber with internal electrodes on a linear time-scale (left) and on a log time-scale (right). The apparent second-order nonlinearity here is determined at the core center and in the presence of the HV poling bias.

Fig. 7
Fig. 7

Time evolution of the absolute value of the recorded field at the centre of the core for fiber 1 (left) and fiber 2 (right). The bias is 5 kV and the temperature 265 °C. The cation concentrations are those in section 2, and the mobility values from ref [17]. Both configurations are studied, (+/−) in blue and (+/+) in red. At the end of poling, the fiber is assumed to be cooled off and then the voltage switched off, when the residual electric field becomes constant. The onset of the nonlinearity in fiber 1 is slow because of the long distance from the electrodes to the core.

Fig. 8
Fig. 8

Qualitative identification of the rings associated with the three cations considered in the model. After electrostatic charging at 4.3 kV, the sample was cleaved and etched for 45 seconds in 40% HF and photographed with a phase-contrast microscope with 500 × magnification. In consonance with the model here, the red arrows indicate the boundary of the depletion region of Na+, the turquoise arrows point to the edge of the accumulation region of Li+ and the yellow arrows show the extent of the region with injection of H3O+.

Fig. 9
Fig. 9

Comparison of experimental data to the results of the simulation for fiber F2. Individual pieces of fiber are electrostatic charged at 5 kV and 265 °C.

Fig. 10
Fig. 10

Simulation of the time evolution of the effective nonlinearity for different applied voltages for (a) the poling configuration; (b) electrostatic charging; and (c) bias voltage dependence of the value of the nonlinearity recorded after the voltage is switched off. The recorded field is the residual field when the voltage is switched off at the maximum of poling/electrostatic charging, when the field becomes constant in time.

Fig. 11
Fig. 11

Simulation of the time evolution of the effective nonlinearity for different applied voltages when the carrier concentration is halved from that in Fig. 10.

Fig. 12
Fig. 12

Simulation of the time evolution of the effective nonlinearity for different carrier concentrations. The χ(2) induced saturates for higher concentrations (~0.5-1 ppm).

Fig. 13
Fig. 13

Simulation of the time evolution of the effective nonlinearity for different temperatures. The time can be shortened with a temperature increase but the nonlinearity induced does not change if the carrier concentrations are assumed to be constant.

Tables (1)

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Table 1 Parameters of the fibers used for model validation and in variational studies.

Equations (1)

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c i / t + ( D i c i z i μ   F c i V ) = R i

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