Abstract

The optical Kerr effect in coiled high-birefringent fibers was measured based on a double-beam polarimetric method. A Q-switched Nd:YAG laser, operating at 1.064 μm (FWHM of 80 ns at 1 kHz), was used as the pump beam and a cw 0.633-μm He–Ne laser was used as the probe beam with its polarization fixed at 45° with respect to the birefringent axis whereas orientation of the linearly polarized pump light varied. The phase shifts induced by an intense pump beam in a short bow-tie high-birefringent fiber were determined for different fiber lengths coiled into 15- and 30-cm-diameter drums. It was found that the induced phase shift changes drastically with the state of polarization of the pump light. A strong dependence of the phase shift on orientations of linear pump polarization is attributed to differential losses of eigenmodes peculiar to birefringent axes. Therefore, optical Kerr coefficients remain unchanged regardless of the dependence of the nonlinear response of the coiled high-birefringent fibers on pump polarization.

© 1998 Optical Society of America

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References

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  1. R. H. Stolen, C. Lin, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A 17, 1448–1453 (1978).
    [CrossRef]
  2. J. M. Dziedzic, R. H. Stolen, A. Ashkin, “Optical Kerr effect in long fibers,” Appl. Opt. 20, 1403–1406 (1981).
    [CrossRef] [PubMed]
  3. J. L. Ayral, J. P. Pocholle, J. Raffy, M. Papuchon, “Optical Kerr coefficient measurement at 1.15 μm in single mode optical fibers,” Opt. Commun. 49, 405–408 (1984).
    [CrossRef]
  4. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989), Chap. 7.2.
  5. K. S. Kim, R. H. Stolen, W. A. Reed, K. W. Quoi, “Measurement of the nonlinear index of silica-core and dispersion-shifted fibers,” Opt. Lett. 19, 257–259 (1994).
    [CrossRef] [PubMed]
  6. Y. Namihira, A. Miyata, N. Tanahashi, “Nonlinear Kerr coefficient measurements for dispersion shifted fibers using self-phase modulation method at 1.55 μm,” in Technical Digest of the Fifth Optoelectronics Conference (Institute of Electronics, Information, and Communication Engineers, Tokyo, 1994), pp. 136–137.
  7. A. Wada, T. O. Tsun, R. Yamauchi, “Measurement of nonlinear-index coefficients of optical fibers through the cross-phase modulation using delayed-self-heterodyne technique,” in Proceedings of the 18th European Conference on Optical Communication (VDE-Verlag, Berlin, 1992), pp. 45–48.
  8. T. Kato, Y. Suetsugu, M. Takagi, E. Sasaoka, M. Nishimura, “Accurate measurement of nonlinear refractive index in optical fiber by cross phase modulation method using depolarized pump light,” Trans. IEICE J78C-I, 194–196 (1995), in Japanese.
  9. L. Amato, A. Fellegara, P. Sacchetto, P. Boffi, A. Melloni, M. Martinelli, “Polarization-independent Kerr coefficient measurement in optical fibers,” Opt. Lett. 21, 612–614 (1996).
    [CrossRef] [PubMed]
  10. L. Prigent, J. P. Hamaide, “Measurement of fiber nonlinear Kerr coefficient by four-wave mixing,” IEEE Photon. Technol. Lett. 5, 1092–1095 (1993).
    [CrossRef]
  11. M. P. Varnham, D. N. Payne, R. D. Birch, E. J. Tarbox, “Bend behavior of polarizing optical fibers,” Electron. Lett. 19, 679–680 (1983).
    [CrossRef]
  12. M. P. Varnham, D. N. Payne, R. D. Birch, E. J. Tarbox, “Single-polarization operation of highly birefringent Bow-Tie optical fibers,” Electron. Lett. 19, 246–247 (1983).
    [CrossRef]
  13. J. R. Simpson, R. H. Stolen, F. M. Sears, W. Pleibel, J. B. MacChesney, R. E. Howard, “A single-polarization fiber,” J. Lightwave Technol. LT-1, 370–374 (1983).
    [CrossRef]
  14. M. Imai, Y. Tsuji, T. Iwamoto, “The optical Kerr effect in polarization-maintaining optical fibers and its polarization dependence,” in Technical Digest of the First Optoelectronics and Communications Conference (Institute of Electronics, Information, and Communication Engineers, Tokyo, 1996), pp. 284–285.
  15. W. T. Anderson, D. L. Philen, “Spot size measurements for single-mode fibers: a comparison of four techniques,” J. Lightwave Technol. LT-1, 20–26 (1983).
    [CrossRef]
  16. W. T. Anderson, “Consistency of measurement methods for the mode field radius in a single-mode fiber,” J. Lightwave Technol. LT-2, 191–197 (1984).
    [CrossRef]
  17. R. H. Stolen, A. Ashkin, “Optical Kerr effect in glass waveguide,” Appl. Phys. Lett. 22, 294–296 (1973).
    [CrossRef]

1996 (1)

1995 (1)

T. Kato, Y. Suetsugu, M. Takagi, E. Sasaoka, M. Nishimura, “Accurate measurement of nonlinear refractive index in optical fiber by cross phase modulation method using depolarized pump light,” Trans. IEICE J78C-I, 194–196 (1995), in Japanese.

1994 (1)

1993 (1)

L. Prigent, J. P. Hamaide, “Measurement of fiber nonlinear Kerr coefficient by four-wave mixing,” IEEE Photon. Technol. Lett. 5, 1092–1095 (1993).
[CrossRef]

1984 (2)

J. L. Ayral, J. P. Pocholle, J. Raffy, M. Papuchon, “Optical Kerr coefficient measurement at 1.15 μm in single mode optical fibers,” Opt. Commun. 49, 405–408 (1984).
[CrossRef]

W. T. Anderson, “Consistency of measurement methods for the mode field radius in a single-mode fiber,” J. Lightwave Technol. LT-2, 191–197 (1984).
[CrossRef]

1983 (4)

M. P. Varnham, D. N. Payne, R. D. Birch, E. J. Tarbox, “Bend behavior of polarizing optical fibers,” Electron. Lett. 19, 679–680 (1983).
[CrossRef]

M. P. Varnham, D. N. Payne, R. D. Birch, E. J. Tarbox, “Single-polarization operation of highly birefringent Bow-Tie optical fibers,” Electron. Lett. 19, 246–247 (1983).
[CrossRef]

J. R. Simpson, R. H. Stolen, F. M. Sears, W. Pleibel, J. B. MacChesney, R. E. Howard, “A single-polarization fiber,” J. Lightwave Technol. LT-1, 370–374 (1983).
[CrossRef]

W. T. Anderson, D. L. Philen, “Spot size measurements for single-mode fibers: a comparison of four techniques,” J. Lightwave Technol. LT-1, 20–26 (1983).
[CrossRef]

1981 (1)

1978 (1)

R. H. Stolen, C. Lin, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A 17, 1448–1453 (1978).
[CrossRef]

1973 (1)

R. H. Stolen, A. Ashkin, “Optical Kerr effect in glass waveguide,” Appl. Phys. Lett. 22, 294–296 (1973).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989), Chap. 7.2.

Amato, L.

Anderson, W. T.

W. T. Anderson, “Consistency of measurement methods for the mode field radius in a single-mode fiber,” J. Lightwave Technol. LT-2, 191–197 (1984).
[CrossRef]

W. T. Anderson, D. L. Philen, “Spot size measurements for single-mode fibers: a comparison of four techniques,” J. Lightwave Technol. LT-1, 20–26 (1983).
[CrossRef]

Ashkin, A.

J. M. Dziedzic, R. H. Stolen, A. Ashkin, “Optical Kerr effect in long fibers,” Appl. Opt. 20, 1403–1406 (1981).
[CrossRef] [PubMed]

R. H. Stolen, A. Ashkin, “Optical Kerr effect in glass waveguide,” Appl. Phys. Lett. 22, 294–296 (1973).
[CrossRef]

Ayral, J. L.

J. L. Ayral, J. P. Pocholle, J. Raffy, M. Papuchon, “Optical Kerr coefficient measurement at 1.15 μm in single mode optical fibers,” Opt. Commun. 49, 405–408 (1984).
[CrossRef]

Birch, R. D.

M. P. Varnham, D. N. Payne, R. D. Birch, E. J. Tarbox, “Single-polarization operation of highly birefringent Bow-Tie optical fibers,” Electron. Lett. 19, 246–247 (1983).
[CrossRef]

M. P. Varnham, D. N. Payne, R. D. Birch, E. J. Tarbox, “Bend behavior of polarizing optical fibers,” Electron. Lett. 19, 679–680 (1983).
[CrossRef]

Boffi, P.

Dziedzic, J. M.

Fellegara, A.

Hamaide, J. P.

L. Prigent, J. P. Hamaide, “Measurement of fiber nonlinear Kerr coefficient by four-wave mixing,” IEEE Photon. Technol. Lett. 5, 1092–1095 (1993).
[CrossRef]

Howard, R. E.

J. R. Simpson, R. H. Stolen, F. M. Sears, W. Pleibel, J. B. MacChesney, R. E. Howard, “A single-polarization fiber,” J. Lightwave Technol. LT-1, 370–374 (1983).
[CrossRef]

Imai, M.

M. Imai, Y. Tsuji, T. Iwamoto, “The optical Kerr effect in polarization-maintaining optical fibers and its polarization dependence,” in Technical Digest of the First Optoelectronics and Communications Conference (Institute of Electronics, Information, and Communication Engineers, Tokyo, 1996), pp. 284–285.

Iwamoto, T.

M. Imai, Y. Tsuji, T. Iwamoto, “The optical Kerr effect in polarization-maintaining optical fibers and its polarization dependence,” in Technical Digest of the First Optoelectronics and Communications Conference (Institute of Electronics, Information, and Communication Engineers, Tokyo, 1996), pp. 284–285.

Kato, T.

T. Kato, Y. Suetsugu, M. Takagi, E. Sasaoka, M. Nishimura, “Accurate measurement of nonlinear refractive index in optical fiber by cross phase modulation method using depolarized pump light,” Trans. IEICE J78C-I, 194–196 (1995), in Japanese.

Kim, K. S.

Lin, C.

R. H. Stolen, C. Lin, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A 17, 1448–1453 (1978).
[CrossRef]

MacChesney, J. B.

J. R. Simpson, R. H. Stolen, F. M. Sears, W. Pleibel, J. B. MacChesney, R. E. Howard, “A single-polarization fiber,” J. Lightwave Technol. LT-1, 370–374 (1983).
[CrossRef]

Martinelli, M.

Melloni, A.

Miyata, A.

Y. Namihira, A. Miyata, N. Tanahashi, “Nonlinear Kerr coefficient measurements for dispersion shifted fibers using self-phase modulation method at 1.55 μm,” in Technical Digest of the Fifth Optoelectronics Conference (Institute of Electronics, Information, and Communication Engineers, Tokyo, 1994), pp. 136–137.

Namihira, Y.

Y. Namihira, A. Miyata, N. Tanahashi, “Nonlinear Kerr coefficient measurements for dispersion shifted fibers using self-phase modulation method at 1.55 μm,” in Technical Digest of the Fifth Optoelectronics Conference (Institute of Electronics, Information, and Communication Engineers, Tokyo, 1994), pp. 136–137.

Nishimura, M.

T. Kato, Y. Suetsugu, M. Takagi, E. Sasaoka, M. Nishimura, “Accurate measurement of nonlinear refractive index in optical fiber by cross phase modulation method using depolarized pump light,” Trans. IEICE J78C-I, 194–196 (1995), in Japanese.

Papuchon, M.

J. L. Ayral, J. P. Pocholle, J. Raffy, M. Papuchon, “Optical Kerr coefficient measurement at 1.15 μm in single mode optical fibers,” Opt. Commun. 49, 405–408 (1984).
[CrossRef]

Payne, D. N.

M. P. Varnham, D. N. Payne, R. D. Birch, E. J. Tarbox, “Bend behavior of polarizing optical fibers,” Electron. Lett. 19, 679–680 (1983).
[CrossRef]

M. P. Varnham, D. N. Payne, R. D. Birch, E. J. Tarbox, “Single-polarization operation of highly birefringent Bow-Tie optical fibers,” Electron. Lett. 19, 246–247 (1983).
[CrossRef]

Philen, D. L.

W. T. Anderson, D. L. Philen, “Spot size measurements for single-mode fibers: a comparison of four techniques,” J. Lightwave Technol. LT-1, 20–26 (1983).
[CrossRef]

Pleibel, W.

J. R. Simpson, R. H. Stolen, F. M. Sears, W. Pleibel, J. B. MacChesney, R. E. Howard, “A single-polarization fiber,” J. Lightwave Technol. LT-1, 370–374 (1983).
[CrossRef]

Pocholle, J. P.

J. L. Ayral, J. P. Pocholle, J. Raffy, M. Papuchon, “Optical Kerr coefficient measurement at 1.15 μm in single mode optical fibers,” Opt. Commun. 49, 405–408 (1984).
[CrossRef]

Prigent, L.

L. Prigent, J. P. Hamaide, “Measurement of fiber nonlinear Kerr coefficient by four-wave mixing,” IEEE Photon. Technol. Lett. 5, 1092–1095 (1993).
[CrossRef]

Quoi, K. W.

Raffy, J.

J. L. Ayral, J. P. Pocholle, J. Raffy, M. Papuchon, “Optical Kerr coefficient measurement at 1.15 μm in single mode optical fibers,” Opt. Commun. 49, 405–408 (1984).
[CrossRef]

Reed, W. A.

Sacchetto, P.

Sasaoka, E.

T. Kato, Y. Suetsugu, M. Takagi, E. Sasaoka, M. Nishimura, “Accurate measurement of nonlinear refractive index in optical fiber by cross phase modulation method using depolarized pump light,” Trans. IEICE J78C-I, 194–196 (1995), in Japanese.

Sears, F. M.

J. R. Simpson, R. H. Stolen, F. M. Sears, W. Pleibel, J. B. MacChesney, R. E. Howard, “A single-polarization fiber,” J. Lightwave Technol. LT-1, 370–374 (1983).
[CrossRef]

Simpson, J. R.

J. R. Simpson, R. H. Stolen, F. M. Sears, W. Pleibel, J. B. MacChesney, R. E. Howard, “A single-polarization fiber,” J. Lightwave Technol. LT-1, 370–374 (1983).
[CrossRef]

Stolen, R. H.

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

J. R. Simpson, R. H. Stolen, F. M. Sears, W. Pleibel, J. B. MacChesney, R. E. Howard, “A single-polarization fiber,” J. Lightwave Technol. LT-1, 370–374 (1983).
[CrossRef]

J. M. Dziedzic, R. H. Stolen, A. Ashkin, “Optical Kerr effect in long fibers,” Appl. Opt. 20, 1403–1406 (1981).
[CrossRef] [PubMed]

R. H. Stolen, C. Lin, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A 17, 1448–1453 (1978).
[CrossRef]

R. H. Stolen, A. Ashkin, “Optical Kerr effect in glass waveguide,” Appl. Phys. Lett. 22, 294–296 (1973).
[CrossRef]

Suetsugu, Y.

T. Kato, Y. Suetsugu, M. Takagi, E. Sasaoka, M. Nishimura, “Accurate measurement of nonlinear refractive index in optical fiber by cross phase modulation method using depolarized pump light,” Trans. IEICE J78C-I, 194–196 (1995), in Japanese.

Takagi, M.

T. Kato, Y. Suetsugu, M. Takagi, E. Sasaoka, M. Nishimura, “Accurate measurement of nonlinear refractive index in optical fiber by cross phase modulation method using depolarized pump light,” Trans. IEICE J78C-I, 194–196 (1995), in Japanese.

Tanahashi, N.

Y. Namihira, A. Miyata, N. Tanahashi, “Nonlinear Kerr coefficient measurements for dispersion shifted fibers using self-phase modulation method at 1.55 μm,” in Technical Digest of the Fifth Optoelectronics Conference (Institute of Electronics, Information, and Communication Engineers, Tokyo, 1994), pp. 136–137.

Tarbox, E. J.

M. P. Varnham, D. N. Payne, R. D. Birch, E. J. Tarbox, “Bend behavior of polarizing optical fibers,” Electron. Lett. 19, 679–680 (1983).
[CrossRef]

M. P. Varnham, D. N. Payne, R. D. Birch, E. J. Tarbox, “Single-polarization operation of highly birefringent Bow-Tie optical fibers,” Electron. Lett. 19, 246–247 (1983).
[CrossRef]

Tsuji, Y.

M. Imai, Y. Tsuji, T. Iwamoto, “The optical Kerr effect in polarization-maintaining optical fibers and its polarization dependence,” in Technical Digest of the First Optoelectronics and Communications Conference (Institute of Electronics, Information, and Communication Engineers, Tokyo, 1996), pp. 284–285.

Tsun, T. O.

A. Wada, T. O. Tsun, R. Yamauchi, “Measurement of nonlinear-index coefficients of optical fibers through the cross-phase modulation using delayed-self-heterodyne technique,” in Proceedings of the 18th European Conference on Optical Communication (VDE-Verlag, Berlin, 1992), pp. 45–48.

Varnham, M. P.

M. P. Varnham, D. N. Payne, R. D. Birch, E. J. Tarbox, “Single-polarization operation of highly birefringent Bow-Tie optical fibers,” Electron. Lett. 19, 246–247 (1983).
[CrossRef]

M. P. Varnham, D. N. Payne, R. D. Birch, E. J. Tarbox, “Bend behavior of polarizing optical fibers,” Electron. Lett. 19, 679–680 (1983).
[CrossRef]

Wada, A.

A. Wada, T. O. Tsun, R. Yamauchi, “Measurement of nonlinear-index coefficients of optical fibers through the cross-phase modulation using delayed-self-heterodyne technique,” in Proceedings of the 18th European Conference on Optical Communication (VDE-Verlag, Berlin, 1992), pp. 45–48.

Yamauchi, R.

A. Wada, T. O. Tsun, R. Yamauchi, “Measurement of nonlinear-index coefficients of optical fibers through the cross-phase modulation using delayed-self-heterodyne technique,” in Proceedings of the 18th European Conference on Optical Communication (VDE-Verlag, Berlin, 1992), pp. 45–48.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

R. H. Stolen, A. Ashkin, “Optical Kerr effect in glass waveguide,” Appl. Phys. Lett. 22, 294–296 (1973).
[CrossRef]

Electron. Lett. (2)

M. P. Varnham, D. N. Payne, R. D. Birch, E. J. Tarbox, “Bend behavior of polarizing optical fibers,” Electron. Lett. 19, 679–680 (1983).
[CrossRef]

M. P. Varnham, D. N. Payne, R. D. Birch, E. J. Tarbox, “Single-polarization operation of highly birefringent Bow-Tie optical fibers,” Electron. Lett. 19, 246–247 (1983).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

L. Prigent, J. P. Hamaide, “Measurement of fiber nonlinear Kerr coefficient by four-wave mixing,” IEEE Photon. Technol. Lett. 5, 1092–1095 (1993).
[CrossRef]

J. Lightwave Technol. (3)

J. R. Simpson, R. H. Stolen, F. M. Sears, W. Pleibel, J. B. MacChesney, R. E. Howard, “A single-polarization fiber,” J. Lightwave Technol. LT-1, 370–374 (1983).
[CrossRef]

W. T. Anderson, D. L. Philen, “Spot size measurements for single-mode fibers: a comparison of four techniques,” J. Lightwave Technol. LT-1, 20–26 (1983).
[CrossRef]

W. T. Anderson, “Consistency of measurement methods for the mode field radius in a single-mode fiber,” J. Lightwave Technol. LT-2, 191–197 (1984).
[CrossRef]

Opt. Commun. (1)

J. L. Ayral, J. P. Pocholle, J. Raffy, M. Papuchon, “Optical Kerr coefficient measurement at 1.15 μm in single mode optical fibers,” Opt. Commun. 49, 405–408 (1984).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (1)

R. H. Stolen, C. Lin, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A 17, 1448–1453 (1978).
[CrossRef]

Trans. IEICE (1)

T. Kato, Y. Suetsugu, M. Takagi, E. Sasaoka, M. Nishimura, “Accurate measurement of nonlinear refractive index in optical fiber by cross phase modulation method using depolarized pump light,” Trans. IEICE J78C-I, 194–196 (1995), in Japanese.

Other (4)

Y. Namihira, A. Miyata, N. Tanahashi, “Nonlinear Kerr coefficient measurements for dispersion shifted fibers using self-phase modulation method at 1.55 μm,” in Technical Digest of the Fifth Optoelectronics Conference (Institute of Electronics, Information, and Communication Engineers, Tokyo, 1994), pp. 136–137.

A. Wada, T. O. Tsun, R. Yamauchi, “Measurement of nonlinear-index coefficients of optical fibers through the cross-phase modulation using delayed-self-heterodyne technique,” in Proceedings of the 18th European Conference on Optical Communication (VDE-Verlag, Berlin, 1992), pp. 45–48.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989), Chap. 7.2.

M. Imai, Y. Tsuji, T. Iwamoto, “The optical Kerr effect in polarization-maintaining optical fibers and its polarization dependence,” in Technical Digest of the First Optoelectronics and Communications Conference (Institute of Electronics, Information, and Communication Engineers, Tokyo, 1996), pp. 284–285.

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Figures (5)

Fig. 1
Fig. 1

Experimental setup for measuring the optical Kerr effect: Pol., polarizer; H.M., half-mirror; Obj., objective lens; λ/2, half-wave plate; λ/4, quarter-wave plate; A.P.D., avalanche photodiode.

Fig. 2
Fig. 2

Bending loss of a coiled bow-tie HB fiber for various polarization orientations (see inset).

Fig. 3
Fig. 3

Far-field pattern plots and Gaussian fits (solid curve) of a bow-tie HB fiber illuminated by (a) a He–Ne laser and (b) a YAG laser.

Fig. 4
Fig. 4

Phase retardation versus incident pump power for a coiled bow-tie HB fiber wound loosely into a 35-cm-diameter drum at different orientations.

Fig. 5
Fig. 5

Phase retardation versus incident pump power for a coiled bow-tie HB fiber wound under tension into a 15-cm-diameter drum at different orientations.

Tables (3)

Tables Icon

Table 1 Specifications of HB Optical Fibers

Tables Icon

Table 2 Measured Kerr Coefficients of a Coiled Bow-Tie Fiber Wound Loosely Into a 35-cm-Diameter Drum

Tables Icon

Table 3 Measured Kerr Coefficients of a Coiled Bow-Tie Fiber Wound Under Tension into a 15-cm-Diameter Drum

Equations (6)

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

Δ ϕ NL = 0 L 2 π λ   | E p | 2 n 2 B d z = 2 π λ   n 2 B | E po | 2 L eff ,
Δ ϕ NL = 2 π λ   n 2 B P A eff ( L x eff cos 2   θ - L y eff sin 2   θ ) ,
L eff = L x eff cos 2   θ - L y eff sin 2   θ
A eff = π ( w s 2 + w p 2 ) 2 .
w = 2   0   r 3 ϕ 2 ( r ) d r 0   r ϕ 2 ( r ) d r 1 / 2 .
Δ ϕ = 2 π λ   n 2 B | E x | 2 0 L exp ( - α x z ) d z - | E y | 2 0 L exp ( - α y z ) d z ,

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