Abstract

We report, to our knowledge, the first polarization-resolved measurement of the frequency dependence of both the electronic and the electrostrictive contributions to the dc Kerr coefficient in silica. At the acoustic resonance the perpendicular polarization phase shift is a factor of 2.3 times greater than in the parallel polarization, confirming the presence of strong electrostriction. We find good agreement between the phase-shift measurements and theoretical models of both the polarization and frequency dependence. The analysis indicates the dc Kerr coefficient χ1111(3)(-ω;ω, 0, 0) to be 1.9×10-22 m2/V2. From these results the electrostrictive contribution to a poled-silica device near the device acoustic resonance is expected to be r33,Es=28 pm/V, over an order of magnitude greater than the electronic Kerr electro-optic coefficient r33,Kerr=0.2 pm/V.

© 2001 Optical Society of America

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  1. R. A. Myers, N. Mukherhee, and S. R. J. Brueck, “Large second-order nonlinearity in poled fused silica,” Opt. Lett. 16, 1732–1734 (1991).
    [CrossRef] [PubMed]
  2. N. Mukherjee, R. A. Myers, and S. R. J. Brueck, “Dynamics of second-harmonic generation in fused silica,” J. Opt. Soc. Am. B 11, 665–669 (1994).
    [CrossRef]
  3. A. Le Calvez, E. Freysz, and A. Ducasse, “A model for second harmonic generation in poled glasses,” Eur. Physical J. D 1, 223–226 (1998).
    [CrossRef]
  4. 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, 555–556 (2000).
    [CrossRef]
  5. M. C. Farries and A. J. Rogers, “Temperature dependence of the Kerr effect in a silica optical fibre,” Electron. Lett. 19, 890–891 (1983).
    [CrossRef]
  6. X. C. Long, R. A. Myers, and S. R. J. Brueck, “Measurement of the linear electro-optic coefficient in poled amorphous silica,” Opt. Lett. 19, 1819–1821 (1994).
    [CrossRef] [PubMed]
  7. E. L. Buckland and R. W. Boyd, “Measurement of the frequency response of the electrostrictive nonlinearity in optical fibers,” Opt. Lett. 22, 676–678 (1997).
    [CrossRef] [PubMed]
  8. A. Fellegara, A. Melloni, and M. Martinelli, “Measurement of the frequency response induced by electrostriction in optical fibers,” Opt. Lett. 22, 1615–1617 (1997).
    [CrossRef]
  9. P. J. Hardman, P. D. Townsend, A. J. Poustie, and K. J. Blow, “Experimental investigation of resonant enhancement of the acoustic interaction of optical pulses in an optical fiber,” Opt. Lett. 21, 393–395 (1996).
    [CrossRef] [PubMed]
  10. A. Melloni, M. Frasca, A. Garavaglia, A. Tonini, and M. Martinelli, “Direct measurement of electrostriction in optical fibers,” Opt. Lett. 23, 691–693 (1998).
    [CrossRef]
  11. A. Melloni, M. Martinelli, and A. Fellegara, “Frequency characterization of the nonlinear refractive index in optical fiber,” Fiber Integr. Opt. 18, 1–13 (1999).
    [CrossRef]
  12. T. Kato, Y. Suetsugu, M. Takagi, E. Sasaoka, and M. Nishimura, “Measurement of the nonlinear refractive index in optical fiber by the cross-phase-modulation method with depolarized pump light,” Opt. Lett. 20, 988–990 (1995).
    [CrossRef] [PubMed]
  13. K. S. Kim, R. H. Stolen, W. A. Reed, and K. W. Quoi, “Measurement of the nonlinear index of silica-core and dispersion-shifted fibers,” Opt. Lett. 19, 257–259 (1994).
    [CrossRef] [PubMed]
  14. P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics, Vol. 9 of Cambridge Studies in Modern Optics (Cambridge University, Cambridge, UK, 1990).
  15. J. F. Nye, Physical Properties of Crystals; 2nd ed. (Clarendon, Oxford, 1985).
  16. G. S. Kino, Acoustic Waves: Devices, Imaging, and Analog Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1987).
  17. R. W. Dixon, “Photoelastic properties of selected materials and their relevance for applications to acoustic light modulators and scanners,” J. Appl. Phys. 38, 5149–5153 (1967).
    [CrossRef]
  18. M. Paillette, “Kerr effect and electrostriction in lead silicate glasses,” J. Phys. (France) 37, 855–864 (1976).
    [CrossRef]
  19. A. R. Selfridge, “Approximate material properties in isotropic materials,” IEEE Trans. Sonics Ultrason. SU-32, 381–394 (1985).
    [CrossRef]
  20. Y. Sun, W. W. Cao, and L. E. Cross, “Electrostriction effect in glass,” Mater. Lett. 4, 329–336 (1986).
    [CrossRef]
  21. R. E. Newnham, V. Sundar, R. Yimnirun, J. Su, and Q. M. Zhang, “Electrostriction: nonlinear electromechanical coupling in solid dielectrics,” J. Phys. Chem. B 101, 10141–10150 (1997).
    [CrossRef]
  22. V. Sundar, R. Yimnirun, B. G. Aitken, and R. E. Newnham, “Structure-property relationships in the electrostriction response of low dielectric permittivity silicate glasses,” Mater. Res. Bull. 33, 1307–1314 (1998).
    [CrossRef]
  23. M. Khoshnevisan and P. Yeh, “Relationship between nonlinear electrostrictive Kerr effects and acousto-optics,” Proc. SPIE 739, 82–86 (1987).
    [CrossRef]
  24. A. C. Liu, “Poled silica: material and device characterization,” Ph.D. dissertation (Stanford University, Stanford, Calif., 1999).
  25. A. Yariv and P. Yeh, Optical Waves in Crystal, Wiley Series in Pure and Applied Optics (Wiley, New York, 1984).
  26. F. Haberl, H. Hochreiter, J. Zehetner, A. J. Schmidt, M. E. Fermann, and L. Luksun, “Electrical breakdown in Ge-doped silica glass fibres,” Int. J. Optoelectron. 5, 363–366 (1990).
  27. 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, 2162–2163 (1994).
    [CrossRef]
  28. P. G. Kazansky, L. Dong, and P. S. J. Russell, “High second-order nonlinearities in poled silicate fibers,” Opt. Lett. 19, 701–703 (1994).
    [CrossRef] [PubMed]
  29. P. G. Kazansky, P. S. J. Russell, L. Dong, and C. N. Pannell, “Pockels effect in thermally poled silica optical fibres,” Electron. Lett. 31, 62–63 (1995).
    [CrossRef]
  30. T. Fujiwara, D. Wong, and S. Fleming, “Large electrooptic modulation in a thermally-poled germanosilicate fiber,” IEEE Photon. Technol. Lett. 7, 1177–1179 (1995).
    [CrossRef]
  31. P. G. Kazansky and P. S. J. Russell, “Thermally poled glass: frozen-in electric field or oriented dipoles?,” Opt. Commun. 110, 611–614 (1994).
    [CrossRef]
  32. I. Abdulhalim and C. N. Pannell, “Photoelastic in-fiber birefringence modulator operating at the fundamental transverse acoustic resonance,” IEEE Photon. Technol. Lett. 5, 1197–1199 (1993).
    [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, 555–556 (2000).
[CrossRef]

1999 (1)

A. Melloni, M. Martinelli, and A. Fellegara, “Frequency characterization of the nonlinear refractive index in optical fiber,” Fiber Integr. Opt. 18, 1–13 (1999).
[CrossRef]

1998 (3)

A. Le Calvez, E. Freysz, and A. Ducasse, “A model for second harmonic generation in poled glasses,” Eur. Physical J. D 1, 223–226 (1998).
[CrossRef]

V. Sundar, R. Yimnirun, B. G. Aitken, and R. E. Newnham, “Structure-property relationships in the electrostriction response of low dielectric permittivity silicate glasses,” Mater. Res. Bull. 33, 1307–1314 (1998).
[CrossRef]

A. Melloni, M. Frasca, A. Garavaglia, A. Tonini, and M. Martinelli, “Direct measurement of electrostriction in optical fibers,” Opt. Lett. 23, 691–693 (1998).
[CrossRef]

1997 (3)

1996 (1)

1995 (3)

T. Kato, Y. Suetsugu, M. Takagi, E. Sasaoka, and M. Nishimura, “Measurement of the nonlinear refractive index in optical fiber by the cross-phase-modulation method with depolarized pump light,” Opt. Lett. 20, 988–990 (1995).
[CrossRef] [PubMed]

P. G. Kazansky, P. S. J. Russell, L. Dong, and C. N. Pannell, “Pockels effect in thermally poled silica optical fibres,” Electron. Lett. 31, 62–63 (1995).
[CrossRef]

T. Fujiwara, D. Wong, and S. Fleming, “Large electrooptic modulation in a thermally-poled germanosilicate fiber,” IEEE Photon. Technol. Lett. 7, 1177–1179 (1995).
[CrossRef]

1994 (6)

1993 (1)

I. Abdulhalim and C. N. Pannell, “Photoelastic in-fiber birefringence modulator operating at the fundamental transverse acoustic resonance,” IEEE Photon. Technol. Lett. 5, 1197–1199 (1993).
[CrossRef]

1991 (1)

1990 (1)

F. Haberl, H. Hochreiter, J. Zehetner, A. J. Schmidt, M. E. Fermann, and L. Luksun, “Electrical breakdown in Ge-doped silica glass fibres,” Int. J. Optoelectron. 5, 363–366 (1990).

1987 (1)

M. Khoshnevisan and P. Yeh, “Relationship between nonlinear electrostrictive Kerr effects and acousto-optics,” Proc. SPIE 739, 82–86 (1987).
[CrossRef]

1986 (1)

Y. Sun, W. W. Cao, and L. E. Cross, “Electrostriction effect in glass,” Mater. Lett. 4, 329–336 (1986).
[CrossRef]

1985 (1)

A. R. Selfridge, “Approximate material properties in isotropic materials,” IEEE Trans. Sonics Ultrason. SU-32, 381–394 (1985).
[CrossRef]

1983 (1)

M. C. Farries and A. J. Rogers, “Temperature dependence of the Kerr effect in a silica optical fibre,” Electron. Lett. 19, 890–891 (1983).
[CrossRef]

1976 (1)

M. Paillette, “Kerr effect and electrostriction in lead silicate glasses,” J. Phys. (France) 37, 855–864 (1976).
[CrossRef]

1967 (1)

R. W. Dixon, “Photoelastic properties of selected materials and their relevance for applications to acoustic light modulators and scanners,” J. Appl. Phys. 38, 5149–5153 (1967).
[CrossRef]

Abdulhalim, I.

I. Abdulhalim and C. N. Pannell, “Photoelastic in-fiber birefringence modulator operating at the fundamental transverse acoustic resonance,” IEEE Photon. Technol. Lett. 5, 1197–1199 (1993).
[CrossRef]

Aitken, B. G.

V. Sundar, R. Yimnirun, B. G. Aitken, and R. E. Newnham, “Structure-property relationships in the electrostriction response of low dielectric permittivity silicate glasses,” Mater. Res. Bull. 33, 1307–1314 (1998).
[CrossRef]

Blow, K. J.

Boyd, R. W.

Brueck, S. R. J.

Buckland, E. L.

Cao, W. W.

Y. Sun, W. W. Cao, and L. E. Cross, “Electrostriction effect in glass,” Mater. Lett. 4, 329–336 (1986).
[CrossRef]

Cross, L. E.

Y. Sun, W. W. Cao, and L. E. Cross, “Electrostriction effect in glass,” Mater. Lett. 4, 329–336 (1986).
[CrossRef]

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, 555–556 (2000).
[CrossRef]

Dixon, R. W.

R. W. Dixon, “Photoelastic properties of selected materials and their relevance for applications to acoustic light modulators and scanners,” J. Appl. Phys. 38, 5149–5153 (1967).
[CrossRef]

Dong, L.

P. G. Kazansky, P. S. J. Russell, L. Dong, and C. N. Pannell, “Pockels effect in thermally poled silica optical fibres,” Electron. Lett. 31, 62–63 (1995).
[CrossRef]

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

Ducasse, A.

A. Le Calvez, E. Freysz, and A. Ducasse, “A model for second harmonic generation in poled glasses,” Eur. Physical J. D 1, 223–226 (1998).
[CrossRef]

Farries, M. C.

M. C. Farries and A. J. Rogers, “Temperature dependence of the Kerr effect in a silica optical fibre,” Electron. Lett. 19, 890–891 (1983).
[CrossRef]

Fellegara, A.

A. Melloni, M. Martinelli, and A. Fellegara, “Frequency characterization of the nonlinear refractive index in optical fiber,” Fiber Integr. Opt. 18, 1–13 (1999).
[CrossRef]

A. Fellegara, A. Melloni, and M. Martinelli, “Measurement of the frequency response induced by electrostriction in optical fibers,” Opt. Lett. 22, 1615–1617 (1997).
[CrossRef]

Fermann, M. E.

F. Haberl, H. Hochreiter, J. Zehetner, A. J. Schmidt, M. E. Fermann, and L. Luksun, “Electrical breakdown in Ge-doped silica glass fibres,” Int. J. Optoelectron. 5, 363–366 (1990).

Fleming, S.

T. Fujiwara, D. Wong, and S. Fleming, “Large electrooptic modulation in a thermally-poled germanosilicate fiber,” IEEE Photon. Technol. Lett. 7, 1177–1179 (1995).
[CrossRef]

Frasca, M.

Freysz, E.

A. Le Calvez, E. Freysz, and A. Ducasse, “A model for second harmonic generation in poled glasses,” Eur. Physical J. D 1, 223–226 (1998).
[CrossRef]

Fujiwara, T.

T. Fujiwara, D. Wong, and S. Fleming, “Large electrooptic modulation in a thermally-poled germanosilicate fiber,” IEEE Photon. Technol. Lett. 7, 1177–1179 (1995).
[CrossRef]

Garavaglia, A.

Haberl, F.

F. Haberl, H. Hochreiter, J. Zehetner, A. J. Schmidt, M. E. Fermann, and L. Luksun, “Electrical breakdown in Ge-doped silica glass fibres,” Int. J. Optoelectron. 5, 363–366 (1990).

Hardman, P. J.

Hochreiter, H.

F. Haberl, H. Hochreiter, J. Zehetner, A. J. Schmidt, M. E. Fermann, and L. Luksun, “Electrical breakdown in Ge-doped silica glass fibres,” Int. J. Optoelectron. 5, 363–366 (1990).

Kato, T.

Kazansky, P. G.

P. G. Kazansky, P. S. J. Russell, L. Dong, and C. N. Pannell, “Pockels effect in thermally poled silica optical fibres,” Electron. Lett. 31, 62–63 (1995).
[CrossRef]

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

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

Khoshnevisan, M.

M. Khoshnevisan and P. Yeh, “Relationship between nonlinear electrostrictive Kerr effects and acousto-optics,” Proc. SPIE 739, 82–86 (1987).
[CrossRef]

Kim, K. S.

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, 555–556 (2000).
[CrossRef]

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, 555–556 (2000).
[CrossRef]

Le Calvez, A.

A. Le Calvez, E. Freysz, and A. Ducasse, “A model for second harmonic generation in poled glasses,” Eur. Physical J. D 1, 223–226 (1998).
[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, 555–556 (2000).
[CrossRef]

Long, X. C.

X. C. Long, R. A. Myers, and S. R. J. Brueck, “Measurement of the linear electro-optic coefficient in poled amorphous silica,” Opt. Lett. 19, 1819–1821 (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, 2162–2163 (1994).
[CrossRef]

Luksun, L.

F. Haberl, H. Hochreiter, J. Zehetner, A. J. Schmidt, M. E. Fermann, and L. Luksun, “Electrical breakdown in Ge-doped silica glass fibres,” Int. J. Optoelectron. 5, 363–366 (1990).

Martinelli, M.

Melloni, A.

Mukherhee, N.

Mukherjee, N.

Myers, R. A.

Newnham, R. E.

V. Sundar, R. Yimnirun, B. G. Aitken, and R. E. Newnham, “Structure-property relationships in the electrostriction response of low dielectric permittivity silicate glasses,” Mater. Res. Bull. 33, 1307–1314 (1998).
[CrossRef]

R. E. Newnham, V. Sundar, R. Yimnirun, J. Su, and Q. M. Zhang, “Electrostriction: nonlinear electromechanical coupling in solid dielectrics,” J. Phys. Chem. B 101, 10141–10150 (1997).
[CrossRef]

Nishimura, M.

Paillette, M.

M. Paillette, “Kerr effect and electrostriction in lead silicate glasses,” J. Phys. (France) 37, 855–864 (1976).
[CrossRef]

Pannell, C. N.

P. G. Kazansky, P. S. J. Russell, L. Dong, and C. N. Pannell, “Pockels effect in thermally poled silica optical fibres,” Electron. Lett. 31, 62–63 (1995).
[CrossRef]

I. Abdulhalim and C. N. Pannell, “Photoelastic in-fiber birefringence modulator operating at the fundamental transverse acoustic resonance,” IEEE Photon. Technol. Lett. 5, 1197–1199 (1993).
[CrossRef]

Poustie, A. J.

Quoi, K. W.

Reed, W. A.

Rogers, A. J.

M. C. Farries and A. J. Rogers, “Temperature dependence of the Kerr effect in a silica optical fibre,” Electron. Lett. 19, 890–891 (1983).
[CrossRef]

Russell, P. S. J.

P. G. Kazansky, P. S. J. Russell, L. Dong, and C. N. Pannell, “Pockels effect in thermally poled silica optical fibres,” Electron. Lett. 31, 62–63 (1995).
[CrossRef]

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

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

Sasaoka, E.

Schmidt, A. J.

F. Haberl, H. Hochreiter, J. Zehetner, A. J. Schmidt, M. E. Fermann, and L. Luksun, “Electrical breakdown in Ge-doped silica glass fibres,” Int. J. Optoelectron. 5, 363–366 (1990).

Selfridge, A. R.

A. R. Selfridge, “Approximate material properties in isotropic materials,” IEEE Trans. Sonics Ultrason. SU-32, 381–394 (1985).
[CrossRef]

Stolen, R. H.

Su, J.

R. E. Newnham, V. Sundar, R. Yimnirun, J. Su, and Q. M. Zhang, “Electrostriction: nonlinear electromechanical coupling in solid dielectrics,” J. Phys. Chem. B 101, 10141–10150 (1997).
[CrossRef]

Suetsugu, Y.

Sun, Y.

Y. Sun, W. W. Cao, and L. E. Cross, “Electrostriction effect in glass,” Mater. Lett. 4, 329–336 (1986).
[CrossRef]

Sundar, V.

V. Sundar, R. Yimnirun, B. G. Aitken, and R. E. Newnham, “Structure-property relationships in the electrostriction response of low dielectric permittivity silicate glasses,” Mater. Res. Bull. 33, 1307–1314 (1998).
[CrossRef]

R. E. Newnham, V. Sundar, R. Yimnirun, J. Su, and Q. M. Zhang, “Electrostriction: nonlinear electromechanical coupling in solid dielectrics,” J. Phys. Chem. B 101, 10141–10150 (1997).
[CrossRef]

Takagi, M.

Tonini, A.

Townsend, P. D.

Wong, D.

T. Fujiwara, D. Wong, and S. Fleming, “Large electrooptic modulation in a thermally-poled germanosilicate fiber,” IEEE Photon. Technol. Lett. 7, 1177–1179 (1995).
[CrossRef]

Yeh, P.

M. Khoshnevisan and P. Yeh, “Relationship between nonlinear electrostrictive Kerr effects and acousto-optics,” Proc. SPIE 739, 82–86 (1987).
[CrossRef]

Yimnirun, R.

V. Sundar, R. Yimnirun, B. G. Aitken, and R. E. Newnham, “Structure-property relationships in the electrostriction response of low dielectric permittivity silicate glasses,” Mater. Res. Bull. 33, 1307–1314 (1998).
[CrossRef]

R. E. Newnham, V. Sundar, R. Yimnirun, J. Su, and Q. M. Zhang, “Electrostriction: nonlinear electromechanical coupling in solid dielectrics,” J. Phys. Chem. B 101, 10141–10150 (1997).
[CrossRef]

Zehetner, J.

F. Haberl, H. Hochreiter, J. Zehetner, A. J. Schmidt, M. E. Fermann, and L. Luksun, “Electrical breakdown in Ge-doped silica glass fibres,” Int. J. Optoelectron. 5, 363–366 (1990).

Zhang, Q. M.

R. E. Newnham, V. Sundar, R. Yimnirun, J. Su, and Q. M. Zhang, “Electrostriction: nonlinear electromechanical coupling in solid dielectrics,” J. Phys. Chem. B 101, 10141–10150 (1997).
[CrossRef]

Electron. Lett. (4)

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, 555–556 (2000).
[CrossRef]

M. C. Farries and A. J. Rogers, “Temperature dependence of the Kerr effect in a silica optical fibre,” Electron. Lett. 19, 890–891 (1983).
[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, 2162–2163 (1994).
[CrossRef]

P. G. Kazansky, P. S. J. Russell, L. Dong, and C. N. Pannell, “Pockels effect in thermally poled silica optical fibres,” Electron. Lett. 31, 62–63 (1995).
[CrossRef]

Eur. Physical J. D (1)

A. Le Calvez, E. Freysz, and A. Ducasse, “A model for second harmonic generation in poled glasses,” Eur. Physical J. D 1, 223–226 (1998).
[CrossRef]

Fiber Integr. Opt. (1)

A. Melloni, M. Martinelli, and A. Fellegara, “Frequency characterization of the nonlinear refractive index in optical fiber,” Fiber Integr. Opt. 18, 1–13 (1999).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

T. Fujiwara, D. Wong, and S. Fleming, “Large electrooptic modulation in a thermally-poled germanosilicate fiber,” IEEE Photon. Technol. Lett. 7, 1177–1179 (1995).
[CrossRef]

I. Abdulhalim and C. N. Pannell, “Photoelastic in-fiber birefringence modulator operating at the fundamental transverse acoustic resonance,” IEEE Photon. Technol. Lett. 5, 1197–1199 (1993).
[CrossRef]

IEEE Trans. Sonics Ultrason. (1)

A. R. Selfridge, “Approximate material properties in isotropic materials,” IEEE Trans. Sonics Ultrason. SU-32, 381–394 (1985).
[CrossRef]

Int. J. Optoelectron. (1)

F. Haberl, H. Hochreiter, J. Zehetner, A. J. Schmidt, M. E. Fermann, and L. Luksun, “Electrical breakdown in Ge-doped silica glass fibres,” Int. J. Optoelectron. 5, 363–366 (1990).

J. Appl. Phys. (1)

R. W. Dixon, “Photoelastic properties of selected materials and their relevance for applications to acoustic light modulators and scanners,” J. Appl. Phys. 38, 5149–5153 (1967).
[CrossRef]

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

J. Phys. (France) (1)

M. Paillette, “Kerr effect and electrostriction in lead silicate glasses,” J. Phys. (France) 37, 855–864 (1976).
[CrossRef]

J. Phys. Chem. B (1)

R. E. Newnham, V. Sundar, R. Yimnirun, J. Su, and Q. M. Zhang, “Electrostriction: nonlinear electromechanical coupling in solid dielectrics,” J. Phys. Chem. B 101, 10141–10150 (1997).
[CrossRef]

Mater. Lett. (1)

Y. Sun, W. W. Cao, and L. E. Cross, “Electrostriction effect in glass,” Mater. Lett. 4, 329–336 (1986).
[CrossRef]

Mater. Res. Bull. (1)

V. Sundar, R. Yimnirun, B. G. Aitken, and R. E. Newnham, “Structure-property relationships in the electrostriction response of low dielectric permittivity silicate glasses,” Mater. Res. Bull. 33, 1307–1314 (1998).
[CrossRef]

Opt. Commun. (1)

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

Opt. Lett. (9)

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

K. S. Kim, R. H. Stolen, W. A. Reed, and K. W. Quoi, “Measurement of the nonlinear index of silica-core and dispersion-shifted fibers,” Opt. Lett. 19, 257–259 (1994).
[CrossRef] [PubMed]

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

X. C. Long, R. A. Myers, and S. R. J. Brueck, “Measurement of the linear electro-optic coefficient in poled amorphous silica,” Opt. Lett. 19, 1819–1821 (1994).
[CrossRef] [PubMed]

T. Kato, Y. Suetsugu, M. Takagi, E. Sasaoka, and M. Nishimura, “Measurement of the nonlinear refractive index in optical fiber by the cross-phase-modulation method with depolarized pump light,” Opt. Lett. 20, 988–990 (1995).
[CrossRef] [PubMed]

E. L. Buckland and R. W. Boyd, “Measurement of the frequency response of the electrostrictive nonlinearity in optical fibers,” Opt. Lett. 22, 676–678 (1997).
[CrossRef] [PubMed]

A. Fellegara, A. Melloni, and M. Martinelli, “Measurement of the frequency response induced by electrostriction in optical fibers,” Opt. Lett. 22, 1615–1617 (1997).
[CrossRef]

A. Melloni, M. Frasca, A. Garavaglia, A. Tonini, and M. Martinelli, “Direct measurement of electrostriction in optical fibers,” Opt. Lett. 23, 691–693 (1998).
[CrossRef]

P. J. Hardman, P. D. Townsend, A. J. Poustie, and K. J. Blow, “Experimental investigation of resonant enhancement of the acoustic interaction of optical pulses in an optical fiber,” Opt. Lett. 21, 393–395 (1996).
[CrossRef] [PubMed]

Proc. SPIE (1)

M. Khoshnevisan and P. Yeh, “Relationship between nonlinear electrostrictive Kerr effects and acousto-optics,” Proc. SPIE 739, 82–86 (1987).
[CrossRef]

Other (5)

A. C. Liu, “Poled silica: material and device characterization,” Ph.D. dissertation (Stanford University, Stanford, Calif., 1999).

A. Yariv and P. Yeh, Optical Waves in Crystal, Wiley Series in Pure and Applied Optics (Wiley, New York, 1984).

P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics, Vol. 9 of Cambridge Studies in Modern Optics (Cambridge University, Cambridge, UK, 1990).

J. F. Nye, Physical Properties of Crystals; 2nd ed. (Clarendon, Oxford, 1985).

G. S. Kino, Acoustic Waves: Devices, Imaging, and Analog Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1987).

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Figures (5)

Fig. 1
Fig. 1

Rectangular silica-slab (thickness d=406 µm, L=25 mm) geometry employed in the electric-field-induced refractive-index-modulation measurement.

Fig. 2
Fig. 2

Schematic of the phase-shift measurement setup with a Mach–Zehnder interferometer.

Fig. 3
Fig. 3

Measured phase shift versus modulation frequency in the unpoled silica slab. The open and closed diamonds represent the phase shift measured for the parallel and perpendicular polarization, respectively. (a) Modulation frequency: f=0.519 MHz. (b) Modulation frequency: f=7.07.6 MHz.

Fig. 4
Fig. 4

Comparison between the experimental (curve with diamonds) and the theoretical magnitude of the phase shift (solid curve) for (a) the parallel polarization and (b) the perpendicular polarization. The separate contribution of electrostriction and electronic Kerr are depicted by the dashed and dotted curves, respectively. Fitting parameters: χ(3)(-ω;ω, 0, 0)=1.94×10-22 m2/V2, α=0.3f2×10-12 m-1.

Fig. 5
Fig. 5

Calculated electro-optic coefficient (a) r33 and (b) r13 based on electrostriction (solid curve) and the Kerr effect (dashed line) in a poled-silica device assuming a built-in dc electric field Edc=800 V/µm.

Tables (2)

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Table 1 Third-Order Nonlinear Susceptibility in Silica

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Table 2 Comparison of the Electrostrictive Coefficient Γ33 in Silica

Equations (28)

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Δn(ωm)=Δn,Kerr+Δn,Es(ωm),
Δn(ωm)=bkΔn,Kerr+besΔn,Es(ωm),
Δn,Kerr=3nχ1111(3)(-ω; ω, 0, 0)EdcEm,
Δn,Kerr=3nχ1122(3)(-ω; ω, 0, 0)EdcEm,
ΔT3=-12Γ33E2.
ΔT3=-Γ33EdcEm,
T3=c33S33+η33 S33t-Γ33EdcEm,
Δnij,Es=12n3pijrsSrs,
Δn,Es=12n3[2p12S11+p11S33],
Δn,Es=12n3[(p12+p11)S11+p12S33],
Δn,Es(ωm)12n3p11S33(ωm),
Δn,Es(ωm)12n3p12S33(ωm),
beΔn,EsΔn,Esp12p11=2.23,
T3z=ρ0 vt=ρ0 2uzt2,
2T3z2=-ωm2ρ0S33,
T3=(c33+jωmη33)S33-Γ33EdcEm,
2T3z2+ωm2ρ0c33+jωmη33T3=-Γ33ωm2ρ0c33+jωmη33EdcEm.
β2=ωm2ρ0c33+jωmη33.
βωmv-j ωm2η332v3ρ0=β0-jα,
v2=c332+ω2η332ρ0c33
=c33/ρ0.
T3(z, ωm)=Γ33cos[β(z-d/2)]cos(βd/2)-1EdcEm.
S33(z, ωm)=Γ33c33+jωmη33 cos[β(z-d/2)]cos(βd/2)EdcEm.
Δn(ωm)=3nχ1111(3)+n3p11Γ332(c33+jωmη33) cos[β(z-d/2)]cos(βd/2)EdcEm,
Δn(ωm)=3nχ1122(3)+n3p12Γ332(c33+jωmη33) cos[β(z-d/2)]cos(βd/2)EdcEm.
r=6χ(3)(-ω;ω, 0, 0)n4Edc,
Δn=12n3(r33,Kerr+r33,Es)Em,
Δn=12n3(r13,Kerr+r13,Es)Em,

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