Abstract

We have used the photorefractive two-beam-coupling technique to measure the nonlinear coefficient (n2Aeff) of several telecommunication fibers and investigated the dependence of n2Aeff on Er, Al, and Ge doping profiles in single-mode fibers, where n2 is the nonlinear refractive index and Aeff is the effective area of the LP01 mode. A semiempirical relation is derived for predicting the value of n2Aeff as a function of Er, Al, and Ge content in optical fibers. We have further examined the wavelength dependence of Aeff in pure and doped silica fibers between 1064 and 1552nm and found that the Aeff value of doped fibers changes more markedly with wavelength than that of pure-silica fibers.

© 2005 Optical Society of America

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  1. D. Marcuse, A. R. Chraplyvy, and R. W. Tkach, "Effect of fiber nonlinearity on long-distance transmission," J. Lightwave Technol. 9, 121-128 (1991).
    [CrossRef]
  2. P. C. Becker, N. A. Olson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers--Fundamentals and Technology (Academic, 1999), p. 13.
    [CrossRef]
  3. S. B. Poole, "Fabrication of Al2O3 co-doped optical fibers by a solution doping technique," in Proceedings of the Fourteenth European Conference on Optical Fiber Communications, Part 1 (1988), pp. 433-436.
  4. R. H. Stolen and C. Lin, "Self-phase modulation in silica optical fibers," Phys. Rev. A 4, 1448-1453 (1978).
    [CrossRef]
  5. K. S. Kim, W. A. Reed, R. H. Stolen, and K. W. Quoi, "Measurement of the nonlinear refractive index of silica-core and dispersion-shifted fibers," Opt. Lett. 19, 257-259 (1994).
    [CrossRef] [PubMed]
  6. R. H. Stolen, W. A. Reed, K. S. Kim, and G. T. Harvey, "Measurement of the nonlinear refractive index of long dispersion-shifted fibers by self-phase modulation at 1.55 µm," J. Lightwave Technol. 16, 1006-1012 (1998).
    [CrossRef]
  7. A. Wada, T. O. Tsun, and R. Yamauchi, "Measurement of nonlinear index coefficient of optical fibers through the cross-phase modulation using delayed self-heterodyne technique," Proceedings of the European Conference on Optical Communication (ECOC, 1992), pp. 42-48.
  8. L. Prigent and J. P. Hamaide, "Measurement of fiber nonlinear Kerr coefficient by four-wave mixing," IEEE Photonics Technol. Lett. 5, 1092-1095 (1993).
    [CrossRef]
  9. M. Artiglia, E. Ciaramella, and B. Sordo, "Using modulation instability to determine Kerr coefficient in optical fibers," Electron. Lett. 31, 1012-1013 (1995).
    [CrossRef]
  10. A. Boskovic, S. V. Chenikov, J. R. Taylor, L. Gruner-Nielson, and O. A. Levring, "Direct continuous-wave measurement of n2 in various types of telecommunication fiber at 1.55 µm," Opt. Lett. 21, 1966-1968 (1996).
    [CrossRef]
  11. H. Garcia, A. M. Johnson, F. A. Oguama, and S. Trivedi, "New approach to the measurement of the nonlinear refractive index of short (<25 m) lengths of silica and erbium-doped fibers," Opt. Lett. 28, 1796-1798 (2003).
    [CrossRef]
  12. A. M. Levine, E. Ozizmir, R. Trebino, C. C. Hayden, A. M. Johnson, and K. L. Tokuda, "Induced-grating autocorrelation of ultrashort pulses in slowly responding medium," J. Opt. Soc. Am. B 11, 1609-1618 (1994).
    [CrossRef]
  13. F. A. Oguama, H. Garcia, A. M. Johnson, and S. Trivedi, "Photorefractive beam coupling measurement of the nonlinear refractive index (n2) of erbium-doped fibers as a function of germania and aluminum content," in Conference on Lasers and Electro-Optics, Vol. 56 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2001).
  14. T. Nakashima, S. Seikai, and M. Nakazawa, "Dependence of Raman gain on relative index difference for GeO2-doped single-mode fibers," Opt. Lett. 10, 420-422 (1985).
    [CrossRef]
  15. F. A. Oguama, "Measurement of the nonlinear refractive index and stimulated Raman scattering in optical fibers as a function of germania content, using the photorefractive beam-coupling technique," Ph.D. thesis (New Jersey Institute of Technology, Newark, N.J., 2003).
  16. R. Billington, "Effective area of optical fibres--definition and measurement techniques," Tech. Rep. (National Physical Laboratory, Teddington, Middlesex, UK, 2003).
  17. M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, and A. Sharma, "Mode-field diameter measurements in single mode optical fibers," J. Lightwave Technol. 7, 1139-1152 (1989).
    [CrossRef]
  18. Y. Namihira, "Wavelength dependence of the correction factor on effective area and mode field diameter for various single-mode optical fibers," Electron. Lett. 33, 1483-1485 (1997).
    [CrossRef]
  19. N. L. Boling, A. J. Glass, and A. Owyoung, "Empirical relationships for predicting nonlinear refractive index changes in optical solids," IEEE J. Quantum Electron. QE-14, 601-608 (1978).
    [CrossRef]
  20. A. Ghatak and A. Sharma, "Single mode fiber characteristics," J. Inst. Electronics Telecom. Engrs. 32, 213-223 (1986).
  21. A. Ghatak and K. Thyagarajan, Introduction to Fiber Optics (Cambridge U. Press, 1998).
    [CrossRef]

2003 (1)

1998 (1)

1997 (1)

Y. Namihira, "Wavelength dependence of the correction factor on effective area and mode field diameter for various single-mode optical fibers," Electron. Lett. 33, 1483-1485 (1997).
[CrossRef]

1996 (1)

1995 (1)

M. Artiglia, E. Ciaramella, and B. Sordo, "Using modulation instability to determine Kerr coefficient in optical fibers," Electron. Lett. 31, 1012-1013 (1995).
[CrossRef]

1994 (2)

1993 (1)

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

1991 (1)

D. Marcuse, A. R. Chraplyvy, and R. W. Tkach, "Effect of fiber nonlinearity on long-distance transmission," J. Lightwave Technol. 9, 121-128 (1991).
[CrossRef]

1989 (1)

M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, and A. Sharma, "Mode-field diameter measurements in single mode optical fibers," J. Lightwave Technol. 7, 1139-1152 (1989).
[CrossRef]

1986 (1)

A. Ghatak and A. Sharma, "Single mode fiber characteristics," J. Inst. Electronics Telecom. Engrs. 32, 213-223 (1986).

1985 (1)

1978 (2)

N. L. Boling, A. J. Glass, and A. Owyoung, "Empirical relationships for predicting nonlinear refractive index changes in optical solids," IEEE J. Quantum Electron. QE-14, 601-608 (1978).
[CrossRef]

R. H. Stolen and C. Lin, "Self-phase modulation in silica optical fibers," Phys. Rev. A 4, 1448-1453 (1978).
[CrossRef]

Artiglia, M.

M. Artiglia, E. Ciaramella, and B. Sordo, "Using modulation instability to determine Kerr coefficient in optical fibers," Electron. Lett. 31, 1012-1013 (1995).
[CrossRef]

M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, and A. Sharma, "Mode-field diameter measurements in single mode optical fibers," J. Lightwave Technol. 7, 1139-1152 (1989).
[CrossRef]

Becker, P. C.

P. C. Becker, N. A. Olson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers--Fundamentals and Technology (Academic, 1999), p. 13.
[CrossRef]

Billington, R.

R. Billington, "Effective area of optical fibres--definition and measurement techniques," Tech. Rep. (National Physical Laboratory, Teddington, Middlesex, UK, 2003).

Boling, N. L.

N. L. Boling, A. J. Glass, and A. Owyoung, "Empirical relationships for predicting nonlinear refractive index changes in optical solids," IEEE J. Quantum Electron. QE-14, 601-608 (1978).
[CrossRef]

Boskovic, A.

Chenikov, S. V.

Chraplyvy, A. R.

D. Marcuse, A. R. Chraplyvy, and R. W. Tkach, "Effect of fiber nonlinearity on long-distance transmission," J. Lightwave Technol. 9, 121-128 (1991).
[CrossRef]

Ciaramella, E.

M. Artiglia, E. Ciaramella, and B. Sordo, "Using modulation instability to determine Kerr coefficient in optical fibers," Electron. Lett. 31, 1012-1013 (1995).
[CrossRef]

Coppa, G.

M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, and A. Sharma, "Mode-field diameter measurements in single mode optical fibers," J. Lightwave Technol. 7, 1139-1152 (1989).
[CrossRef]

Di Vita, P.

M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, and A. Sharma, "Mode-field diameter measurements in single mode optical fibers," J. Lightwave Technol. 7, 1139-1152 (1989).
[CrossRef]

Garcia, H.

H. Garcia, A. M. Johnson, F. A. Oguama, and S. Trivedi, "New approach to the measurement of the nonlinear refractive index of short (<25 m) lengths of silica and erbium-doped fibers," Opt. Lett. 28, 1796-1798 (2003).
[CrossRef]

F. A. Oguama, H. Garcia, A. M. Johnson, and S. Trivedi, "Photorefractive beam coupling measurement of the nonlinear refractive index (n2) of erbium-doped fibers as a function of germania and aluminum content," in Conference on Lasers and Electro-Optics, Vol. 56 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2001).

Ghatak, A.

A. Ghatak and A. Sharma, "Single mode fiber characteristics," J. Inst. Electronics Telecom. Engrs. 32, 213-223 (1986).

A. Ghatak and K. Thyagarajan, Introduction to Fiber Optics (Cambridge U. Press, 1998).
[CrossRef]

Glass, A. J.

N. L. Boling, A. J. Glass, and A. Owyoung, "Empirical relationships for predicting nonlinear refractive index changes in optical solids," IEEE J. Quantum Electron. QE-14, 601-608 (1978).
[CrossRef]

Gruner-Nielson, L.

Hamaide, J. P.

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

Harvey, G. T.

Hayden, C. C.

Johnson, A. M.

H. Garcia, A. M. Johnson, F. A. Oguama, and S. Trivedi, "New approach to the measurement of the nonlinear refractive index of short (<25 m) lengths of silica and erbium-doped fibers," Opt. Lett. 28, 1796-1798 (2003).
[CrossRef]

A. M. Levine, E. Ozizmir, R. Trebino, C. C. Hayden, A. M. Johnson, and K. L. Tokuda, "Induced-grating autocorrelation of ultrashort pulses in slowly responding medium," J. Opt. Soc. Am. B 11, 1609-1618 (1994).
[CrossRef]

F. A. Oguama, H. Garcia, A. M. Johnson, and S. Trivedi, "Photorefractive beam coupling measurement of the nonlinear refractive index (n2) of erbium-doped fibers as a function of germania and aluminum content," in Conference on Lasers and Electro-Optics, Vol. 56 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2001).

Kim, K. S.

Levine, A. M.

Levring, O. A.

Lin, C.

R. H. Stolen and C. Lin, "Self-phase modulation in silica optical fibers," Phys. Rev. A 4, 1448-1453 (1978).
[CrossRef]

Marcuse, D.

D. Marcuse, A. R. Chraplyvy, and R. W. Tkach, "Effect of fiber nonlinearity on long-distance transmission," J. Lightwave Technol. 9, 121-128 (1991).
[CrossRef]

Nakashima, T.

Nakazawa, M.

Namihira, Y.

Y. Namihira, "Wavelength dependence of the correction factor on effective area and mode field diameter for various single-mode optical fibers," Electron. Lett. 33, 1483-1485 (1997).
[CrossRef]

Oguama, F. A.

H. Garcia, A. M. Johnson, F. A. Oguama, and S. Trivedi, "New approach to the measurement of the nonlinear refractive index of short (<25 m) lengths of silica and erbium-doped fibers," Opt. Lett. 28, 1796-1798 (2003).
[CrossRef]

F. A. Oguama, "Measurement of the nonlinear refractive index and stimulated Raman scattering in optical fibers as a function of germania content, using the photorefractive beam-coupling technique," Ph.D. thesis (New Jersey Institute of Technology, Newark, N.J., 2003).

F. A. Oguama, H. Garcia, A. M. Johnson, and S. Trivedi, "Photorefractive beam coupling measurement of the nonlinear refractive index (n2) of erbium-doped fibers as a function of germania and aluminum content," in Conference on Lasers and Electro-Optics, Vol. 56 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2001).

Olson, N. A.

P. C. Becker, N. A. Olson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers--Fundamentals and Technology (Academic, 1999), p. 13.
[CrossRef]

Owyoung, A.

N. L. Boling, A. J. Glass, and A. Owyoung, "Empirical relationships for predicting nonlinear refractive index changes in optical solids," IEEE J. Quantum Electron. QE-14, 601-608 (1978).
[CrossRef]

Ozizmir, E.

Poole, S. B.

S. B. Poole, "Fabrication of Al2O3 co-doped optical fibers by a solution doping technique," in Proceedings of the Fourteenth European Conference on Optical Fiber Communications, Part 1 (1988), pp. 433-436.

Potenza, M.

M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, and A. Sharma, "Mode-field diameter measurements in single mode optical fibers," J. Lightwave Technol. 7, 1139-1152 (1989).
[CrossRef]

Prigent, L.

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

Quoi, K. W.

Reed, W. A.

Seikai, S.

Sharma, A.

M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, and A. Sharma, "Mode-field diameter measurements in single mode optical fibers," J. Lightwave Technol. 7, 1139-1152 (1989).
[CrossRef]

A. Ghatak and A. Sharma, "Single mode fiber characteristics," J. Inst. Electronics Telecom. Engrs. 32, 213-223 (1986).

Simpson, J. R.

P. C. Becker, N. A. Olson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers--Fundamentals and Technology (Academic, 1999), p. 13.
[CrossRef]

Sordo, B.

M. Artiglia, E. Ciaramella, and B. Sordo, "Using modulation instability to determine Kerr coefficient in optical fibers," Electron. Lett. 31, 1012-1013 (1995).
[CrossRef]

Stolen, R. H.

Taylor, J. R.

Thyagarajan, K.

A. Ghatak and K. Thyagarajan, Introduction to Fiber Optics (Cambridge U. Press, 1998).
[CrossRef]

Tkach, R. W.

D. Marcuse, A. R. Chraplyvy, and R. W. Tkach, "Effect of fiber nonlinearity on long-distance transmission," J. Lightwave Technol. 9, 121-128 (1991).
[CrossRef]

Tokuda, K. L.

Trebino, R.

Trivedi, S.

H. Garcia, A. M. Johnson, F. A. Oguama, and S. Trivedi, "New approach to the measurement of the nonlinear refractive index of short (<25 m) lengths of silica and erbium-doped fibers," Opt. Lett. 28, 1796-1798 (2003).
[CrossRef]

F. A. Oguama, H. Garcia, A. M. Johnson, and S. Trivedi, "Photorefractive beam coupling measurement of the nonlinear refractive index (n2) of erbium-doped fibers as a function of germania and aluminum content," in Conference on Lasers and Electro-Optics, Vol. 56 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2001).

Tsun, T. O.

A. Wada, T. O. Tsun, and R. Yamauchi, "Measurement of nonlinear index coefficient of optical fibers through the cross-phase modulation using delayed self-heterodyne technique," Proceedings of the European Conference on Optical Communication (ECOC, 1992), pp. 42-48.

Wada, A.

A. Wada, T. O. Tsun, and R. Yamauchi, "Measurement of nonlinear index coefficient of optical fibers through the cross-phase modulation using delayed self-heterodyne technique," Proceedings of the European Conference on Optical Communication (ECOC, 1992), pp. 42-48.

Yamauchi, R.

A. Wada, T. O. Tsun, and R. Yamauchi, "Measurement of nonlinear index coefficient of optical fibers through the cross-phase modulation using delayed self-heterodyne technique," Proceedings of the European Conference on Optical Communication (ECOC, 1992), pp. 42-48.

Electron. Lett. (2)

M. Artiglia, E. Ciaramella, and B. Sordo, "Using modulation instability to determine Kerr coefficient in optical fibers," Electron. Lett. 31, 1012-1013 (1995).
[CrossRef]

Y. Namihira, "Wavelength dependence of the correction factor on effective area and mode field diameter for various single-mode optical fibers," Electron. Lett. 33, 1483-1485 (1997).
[CrossRef]

IEEE J. Quantum Electron. (1)

N. L. Boling, A. J. Glass, and A. Owyoung, "Empirical relationships for predicting nonlinear refractive index changes in optical solids," IEEE J. Quantum Electron. QE-14, 601-608 (1978).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

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

J. Inst. Electronics Telecom. Engrs. (1)

A. Ghatak and A. Sharma, "Single mode fiber characteristics," J. Inst. Electronics Telecom. Engrs. 32, 213-223 (1986).

J. Lightwave Technol. (3)

R. H. Stolen, W. A. Reed, K. S. Kim, and G. T. Harvey, "Measurement of the nonlinear refractive index of long dispersion-shifted fibers by self-phase modulation at 1.55 µm," J. Lightwave Technol. 16, 1006-1012 (1998).
[CrossRef]

D. Marcuse, A. R. Chraplyvy, and R. W. Tkach, "Effect of fiber nonlinearity on long-distance transmission," J. Lightwave Technol. 9, 121-128 (1991).
[CrossRef]

M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, and A. Sharma, "Mode-field diameter measurements in single mode optical fibers," J. Lightwave Technol. 7, 1139-1152 (1989).
[CrossRef]

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

Opt. Lett. (4)

Phys. Rev. A (1)

R. H. Stolen and C. Lin, "Self-phase modulation in silica optical fibers," Phys. Rev. A 4, 1448-1453 (1978).
[CrossRef]

Other (7)

P. C. Becker, N. A. Olson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers--Fundamentals and Technology (Academic, 1999), p. 13.
[CrossRef]

S. B. Poole, "Fabrication of Al2O3 co-doped optical fibers by a solution doping technique," in Proceedings of the Fourteenth European Conference on Optical Fiber Communications, Part 1 (1988), pp. 433-436.

A. Wada, T. O. Tsun, and R. Yamauchi, "Measurement of nonlinear index coefficient of optical fibers through the cross-phase modulation using delayed self-heterodyne technique," Proceedings of the European Conference on Optical Communication (ECOC, 1992), pp. 42-48.

F. A. Oguama, "Measurement of the nonlinear refractive index and stimulated Raman scattering in optical fibers as a function of germania content, using the photorefractive beam-coupling technique," Ph.D. thesis (New Jersey Institute of Technology, Newark, N.J., 2003).

R. Billington, "Effective area of optical fibres--definition and measurement techniques," Tech. Rep. (National Physical Laboratory, Teddington, Middlesex, UK, 2003).

F. A. Oguama, H. Garcia, A. M. Johnson, and S. Trivedi, "Photorefractive beam coupling measurement of the nonlinear refractive index (n2) of erbium-doped fibers as a function of germania and aluminum content," in Conference on Lasers and Electro-Optics, Vol. 56 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2001).

A. Ghatak and K. Thyagarajan, Introduction to Fiber Optics (Cambridge U. Press, 1998).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Typical measured IGA traces fitted to expression (1) at different power levels in the fiber for a 56 ps input pulse (fiber 6 in Table 1, L = 20 m ). (a) IGA trace at 0.04 W average power ( ω 0 τ p Q = 5.5 ) . (b) IGA trace at 0.1 W average power ( ω 0 τ p Q = 13.5 ) .

Fig. 2
Fig. 2

Plot of ω 0 τ p Q versus average power for an Er–Al–Ge-doped silica fiber (fiber 6 in Table 1). The slope is proportional to n 2 A eff .

Fig. 3
Fig. 3

Typical extrapolation curves showing the wavelength dependence of MFD based on Eq. (17), for some of the fibers.

Tables (1)

Tables Icon

Table 1 Measured Values of n 2 A eff and n 2 at 1064 nm as a Function of Al, Ge, and Er Content and A eff Values Determined at 1064, 1314, and 1552 nm for Different Fibers

Equations (17)

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

W det. K ( τ ) 2 = + E ( t ) E * ( t + τ ) d t 2 ,
E ( t ) = E 0 exp ( 2 ln 2 ( t 2 τ p 2 ) i { ω 0 t + ω 0 τ p Q exp [ 4 ln 2 ( t 2 τ 2 ) ] } ) .
n 2 ( esu ) = A eff τ p n c λ t r , L [ 32 π 2 ( ln 2 π ) 1 2 × 10 7 ] 1 ω 0 τ p Q P avg ,
n 2 A eff = ( n 2 A eff ) ( Si O 2 ) + K ( Al 2 O 3 ) X ( Al 2 O 3 ) + K ( Er 2 O 3 ) X ( Er 2 O 3 ) + K ( Ge O 2 ) X ( Ge O 2 ) ,
MFD = 2 2 { [ 0 Ψ ( r ) 2 r d r ] 0 [ d Ψ ( r ) d r ] 2 r d r } 1 2 ,
A eff = k [ π ( MFD ) 2 4 ] ,
1 r d d r ( r d Ψ d r ) + [ k 2 n 2 ( r ) β 2 ] Ψ ( r ) = 0 ,
0 Ψ ( r ) d d r ( r d Ψ d r ) d r + 0 r [ k 2 n 2 ( r ) β 2 ] Ψ 2 ( r ) d r = 0 .
β 2 = k 2 0 n 2 ( r ) Ψ 2 ( r ) r d r 0 ( d Ψ d r ) 2 r d r 0 Ψ 2 ( r ) r d r .
d β d k = k β 2 β [ 1 k 2 + 0 ( d Ψ d r ) 2 r d r k 2 0 Ψ 2 ( r ) r d r ] .
w p = { 2 [ 0 Ψ ( r ) 2 r d r ] 0 d Ψ d r 2 r d r } 1 2 ,
d β d k = k β ( β 2 k 2 + 2 k 2 w p 2 ) ,
d β d λ = β λ 2 λ w p 2 β .
β 2 = 4 π 2 λ 2 [ n 2 + δ exp ( α λ h ) ] ,
d β d λ = β λ ( 2 π 2 δ λ 2 β ) α h λ h 1 exp ( α λ h ) .
w p 2 = exp ( α λ h ) π 2 α h λ h 2 δ .
MFD = 2 w p = 2 [ exp ( α λ h ) π 2 α h λ h 2 δ ] 1 2 .

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