Abstract

A precise method for evaluating the electro-optic coefficients of an optical fiber is introduced. The method was used to characterize the third-order nonlinearity of twin-hole silica fibers. The polarization dependence expected for isotropic materials and the Kleinmann symmetry condition was not observed. We explain the lack of polarization dependence of the third-order tensor by taking into account the electrostrictive contribution to the quadratic electro-optic effect.

© 2000 Optical Society of America

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References

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  1. R. A. Myers, N. Mukherjee, and S. R. J. Brueck, “Large second-order nonlinearity in poled fused silica,” Opt. Lett. 16, 1732–1734 (1991).
    [CrossRef] [PubMed]
  2. P. G. Kazansky, P. St. J. Russell, and H. Takebe, “Glass fiber poling and applications,” J. Lightwave Technol. 15, 1484–1493 (1997).
    [CrossRef]
  3. X.-C. Long and S. R. J. Brueck, “Large-signal phase retardation with a poled electrooptic fiber,” IEEE Photon. Technol. Lett. 9, 767–769 (1997).
    [CrossRef]
  4. R. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992).
  5. A. Liu, M. J. F. Digonnet, and G. S. Kino, “A dc Kerr measurement in a silica channel waveguide,” in Doped Fiber Devices, M. J. Digonnet and F. Ouellette, eds., Proc. SPIE 2841, 209–218 (1996).
    [CrossRef]
  6. Reference 2 and other publications by the same authors never stipulate whether there is a polarization dependence of the induced electro-optic effect.
  7. Y. Quiquempois, G. Martinelli, P. Bernage, M. Douay, P. Niay, E. Delevaque, H. Poignant, B. Loisel, and J. F. Bayon, “UV and thermal poling of germanosilicate fibre,” in Bragg Gratings, Photosensitivity, and Poling in Glass Fibers and Waveguides: Applications and Fundamentals, Vol. 17 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper BMG8.
  8. E. Buckland and R. Boyd, “Electrostrictive contribution to the intensity-dependent refractive index in optical fibers,” Opt. Lett. 21, 1117–1119 (1996).
    [CrossRef] [PubMed]
  9. 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]
  10. E. Buckland and R. Boyd, “Measurement of the frequency response of the electrostrictive nonlinearity in optical fibers,” Opt. Lett. 22, 676–678 (1997).
    [CrossRef] [PubMed]
  11. See, for example, E. J. Hearn, Mechanics of Materials, 2nd ed. (Pergamon, London, 1985).
  12. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
  13. R. C. Weast, ed., Handbook of Chemistry and Physics, 67th ed. (CRC Press, Boca Raton, Fla., 1986).
  14. M. Bass, ed., Handbook of Optics, 2nd ed. (McGraw-Hill, New York, 1994).
  15. W. Primak and D. Post, “Photoelastic constants of vitreous silica and its elastic coefficient of refractive index,” J. Appl. Phys. 30, 779–788 (1959).
    [CrossRef]
  16. C. J. F. Böttcher, Theory of Electric Polarization, 2nd ed. (Elsevier, Amsterdam, 1973), Vol. 1, p. 177.
  17. F. Agulló-López, J. M. Cabrera, and F. Agulló-Rueda, Electrooptics: Phenomena, Materials and Applications (Academic, San Diego, Calif., 1994), Sec. 4.11.2.
  18. R. Stolen, W. Reed, K. Kim, and G. Harvey, “Measurement of the nonlinear refractive index of long dispersion-shifted fibers by self-phase modulation at 1.55 m,” J. Lightwave Technol. 16, 1006–1012 (1998).
    [CrossRef]
  19. P. Mamyshev and S. Chernikov, “Recent developments in the ultrashort pulse Raman effect in optical fibers,” Sov. Lightwave Commun. 2, 97–111 (1992).

1998 (2)

1997 (3)

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

P. G. Kazansky, P. St. J. Russell, and H. Takebe, “Glass fiber poling and applications,” J. Lightwave Technol. 15, 1484–1493 (1997).
[CrossRef]

X.-C. Long and S. R. J. Brueck, “Large-signal phase retardation with a poled electrooptic fiber,” IEEE Photon. Technol. Lett. 9, 767–769 (1997).
[CrossRef]

1996 (2)

A. Liu, M. J. F. Digonnet, and G. S. Kino, “A dc Kerr measurement in a silica channel waveguide,” in Doped Fiber Devices, M. J. Digonnet and F. Ouellette, eds., Proc. SPIE 2841, 209–218 (1996).
[CrossRef]

E. Buckland and R. Boyd, “Electrostrictive contribution to the intensity-dependent refractive index in optical fibers,” Opt. Lett. 21, 1117–1119 (1996).
[CrossRef] [PubMed]

1992 (1)

P. Mamyshev and S. Chernikov, “Recent developments in the ultrashort pulse Raman effect in optical fibers,” Sov. Lightwave Commun. 2, 97–111 (1992).

1991 (1)

1959 (1)

W. Primak and D. Post, “Photoelastic constants of vitreous silica and its elastic coefficient of refractive index,” J. Appl. Phys. 30, 779–788 (1959).
[CrossRef]

Boyd, R.

Brueck, S. R. J.

X.-C. Long and S. R. J. Brueck, “Large-signal phase retardation with a poled electrooptic fiber,” IEEE Photon. Technol. Lett. 9, 767–769 (1997).
[CrossRef]

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

Buckland, E.

Chernikov, S.

P. Mamyshev and S. Chernikov, “Recent developments in the ultrashort pulse Raman effect in optical fibers,” Sov. Lightwave Commun. 2, 97–111 (1992).

Digonnet, M. J. F.

A. Liu, M. J. F. Digonnet, and G. S. Kino, “A dc Kerr measurement in a silica channel waveguide,” in Doped Fiber Devices, M. J. Digonnet and F. Ouellette, eds., Proc. SPIE 2841, 209–218 (1996).
[CrossRef]

Frasca, M.

Garavaglia, A.

Harvey, G.

Kazansky, P. G.

P. G. Kazansky, P. St. J. Russell, and H. Takebe, “Glass fiber poling and applications,” J. Lightwave Technol. 15, 1484–1493 (1997).
[CrossRef]

Kim, K.

Kino, G. S.

A. Liu, M. J. F. Digonnet, and G. S. Kino, “A dc Kerr measurement in a silica channel waveguide,” in Doped Fiber Devices, M. J. Digonnet and F. Ouellette, eds., Proc. SPIE 2841, 209–218 (1996).
[CrossRef]

Liu, A.

A. Liu, M. J. F. Digonnet, and G. S. Kino, “A dc Kerr measurement in a silica channel waveguide,” in Doped Fiber Devices, M. J. Digonnet and F. Ouellette, eds., Proc. SPIE 2841, 209–218 (1996).
[CrossRef]

Long, X.-C.

X.-C. Long and S. R. J. Brueck, “Large-signal phase retardation with a poled electrooptic fiber,” IEEE Photon. Technol. Lett. 9, 767–769 (1997).
[CrossRef]

Mamyshev, P.

P. Mamyshev and S. Chernikov, “Recent developments in the ultrashort pulse Raman effect in optical fibers,” Sov. Lightwave Commun. 2, 97–111 (1992).

Martinelli, M.

Melloni, A.

Mukherjee, N.

Myers, R. A.

Post, D.

W. Primak and D. Post, “Photoelastic constants of vitreous silica and its elastic coefficient of refractive index,” J. Appl. Phys. 30, 779–788 (1959).
[CrossRef]

Primak, W.

W. Primak and D. Post, “Photoelastic constants of vitreous silica and its elastic coefficient of refractive index,” J. Appl. Phys. 30, 779–788 (1959).
[CrossRef]

Reed, W.

Russell, P. St. J.

P. G. Kazansky, P. St. J. Russell, and H. Takebe, “Glass fiber poling and applications,” J. Lightwave Technol. 15, 1484–1493 (1997).
[CrossRef]

Stolen, R.

Takebe, H.

P. G. Kazansky, P. St. J. Russell, and H. Takebe, “Glass fiber poling and applications,” J. Lightwave Technol. 15, 1484–1493 (1997).
[CrossRef]

Tonini, A.

IEEE Photon. Technol. Lett. (1)

X.-C. Long and S. R. J. Brueck, “Large-signal phase retardation with a poled electrooptic fiber,” IEEE Photon. Technol. Lett. 9, 767–769 (1997).
[CrossRef]

J. Appl. Phys. (1)

W. Primak and D. Post, “Photoelastic constants of vitreous silica and its elastic coefficient of refractive index,” J. Appl. Phys. 30, 779–788 (1959).
[CrossRef]

J. Lightwave Technol. (2)

Opt. Lett. (4)

Proc. SPIE (1)

A. Liu, M. J. F. Digonnet, and G. S. Kino, “A dc Kerr measurement in a silica channel waveguide,” in Doped Fiber Devices, M. J. Digonnet and F. Ouellette, eds., Proc. SPIE 2841, 209–218 (1996).
[CrossRef]

Sov. Lightwave Commun. (1)

P. Mamyshev and S. Chernikov, “Recent developments in the ultrashort pulse Raman effect in optical fibers,” Sov. Lightwave Commun. 2, 97–111 (1992).

Other (9)

Reference 2 and other publications by the same authors never stipulate whether there is a polarization dependence of the induced electro-optic effect.

Y. Quiquempois, G. Martinelli, P. Bernage, M. Douay, P. Niay, E. Delevaque, H. Poignant, B. Loisel, and J. F. Bayon, “UV and thermal poling of germanosilicate fibre,” in Bragg Gratings, Photosensitivity, and Poling in Glass Fibers and Waveguides: Applications and Fundamentals, Vol. 17 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper BMG8.

C. J. F. Böttcher, Theory of Electric Polarization, 2nd ed. (Elsevier, Amsterdam, 1973), Vol. 1, p. 177.

F. Agulló-López, J. M. Cabrera, and F. Agulló-Rueda, Electrooptics: Phenomena, Materials and Applications (Academic, San Diego, Calif., 1994), Sec. 4.11.2.

R. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992).

See, for example, E. J. Hearn, Mechanics of Materials, 2nd ed. (Pergamon, London, 1985).

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).

R. C. Weast, ed., Handbook of Chemistry and Physics, 67th ed. (CRC Press, Boca Raton, Fla., 1986).

M. Bass, ed., Handbook of Optics, 2nd ed. (McGraw-Hill, New York, 1994).

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Figures (3)

Fig. 1
Fig. 1

Placement of electrodes in the twin-hole fiber.

Fig. 2
Fig. 2

Experimentally measured (filled circles) wavelength shift of the FP resonance for polarization (a) parallel and (b) perpendicular to the applied field as a function of voltage applied to the internal electrodes. Continuous lines, quadratic fits.

Fig. 3
Fig. 3

(a) Geometry of the fiber used in the experiment. (b) Equivalent model used in the evaluation of the electrostrictive effect to χ(3).

Tables (1)

Tables Icon

Table 1 Numerical Values Used for the Computation of χ(3)ES

Equations (27)

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χijk(2)(ω1, ω2)=3χijkx(3)(ω1, ω2, 0)Ex,
Δλ=bV2.
b=(5.0±0.3)×10-6 pm/V2,
b=(5.0±0.3)×10-6 pm/V2.
χ(3)=2n2d2b3λ,
χxxxx(3)(0, 0, ω)=χxyyx(3)(0, 0, ω)=(2.3±0.4)×10-22 m2/V2.
UE=02VrE2dV,
Fi=-UEqi,
F=-0A2d(rE2d)
=-0A2rE2+E2d rd+rd E2rrd,
E2r=-2E2r.
σ=-0E22(γES0+r),
γES-V drdV
ε=σ/Y,
Δn=-n32p11ε,
Δn=-n32p12ε,
χxxxx(3)ES(0, 0, ω)=2nΔn3E2,
χxyyx(3)ES(0, 0, ω)=2nΔn3E2.
γES0=r(r-1)(2r+1)2r2+1,
χxxxx(3)ES(0, 0, ω)=0.77×10-22 m2/V2,
χxyyx(3)ES(0, 0, ω)=1.70×10-22 m2/V2.
n2I=2.76×10-20 m2/W
χxxxx(3)fast(ω, ω,-ω)=2.07×10-22 m2/V2.
χ(3)el(0, 0, ω)=r(n2+2)2r+n23n2+22χ(3)el(ω, ω,-ω).
χxxxx(3)el(0, 0, ω)=3χxxyy(3)el(0, 0, ω)=3χxyxy(3)el(0, 0, ω)=3χxyyx(3)el(0, 0, ω)=2.30×10-22 m2/V2.
χxxxx(3)tot(0, 0, ω)=3.07×10-22 m2/V2,
χxyyx(3)tot(0, 0, ω)=2.47×10-22 m2/V2.

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