Abstract

The zero-dispersion wavelength map of an optical fiber can be obtained from measurement of end-to-end four-wave mixing efficiency at various wavelengths. A fast and unambiguous algorithm for reconstruction of the zero-dispersion wavelength map of an optical fiber by measurement of four-wave mixing efficiency is proposed. This method can produce high-resolution results in a few seconds. We also study the limitations of this technique that are due to polarization-mode dispersion (PMD). Simple practical rules to avoid the effects of PMD in such measurements are established.

© 2002 Optical Society of America

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References

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  1. S. Nishi, M. Saruwatari, “Technique for measuring the distributed zero dispersion wavelength of optical fibers using pulse amplification caused by modulation instability,” Electron. Lett. 31, 225–226 (1995).
    [CrossRef]
  2. L. F. Mollenauer, P. V. Mamyshev, M. J. Neubelt, “Method for facile and accurate measurement of optical fiber dispersion maps,” Opt. Lett. 21, 1724–1726 (1996).
    [CrossRef] [PubMed]
  3. I. Brener, P. P. Mitra, D. D. Lee, D. J. Thomson, D. L. Philen, “High-resolution zero-dispersion wavelength mapping in single-mode fiber,” Opt. Lett. 23, 1520–1522 (1998).
    [CrossRef]
  4. M. Eiselt, R. M. Jopson, R. H. Stolen, “Nondestructive position-resolved measurement of the zero-dispersion wavelength in an optical fiber,” J. Lightwave Technol. 15, 135–143 (1997).
    [CrossRef]
  5. J. B. Schlager, “Zero-dispersion in optical fibers from cw four-wave mixing efficiency,” in LEOS ’98 (Institute of Electrical and Electronic Engineers, Orlando, Fla., 1998), Vol. 2, pp. 309–331.
  6. M. L. Hernanz, M. Gonzalez-Herraez, P. Corredera, “Zero-dispersion wavelength mapping in single-mode optical fibers using cw four-wave mixing,” in 6th Optical Fibre Measurement Conference (OFMC ’01) Proceedings (National Physical Laboratory, Teddington, Middlesex, UK, 2001), pp. 225–229.
  7. M. L. Hernanz, P. Corredera, M. Gonzalez-Herraez, “Selection of uniform fibers as standards for chromatic dispersion using cw four-wave mixing,” in 6th Optical Fibre Measurement Conference (OFMC ’01) Proceedings (National Physical Laboratory, Teddington, Middlesex, UK, 2001), pp. 235–239.
  8. K. Inoue, “Four-wave mixing in an optical fiber in the zero-dispersion wavelength region,” J. Lightwave Technol. 10, 1553–1561 (1992).
    [CrossRef]
  9. S. Song, C. T. Allen, K. R. Demarest, R. Hui, “Intensity-dependent phase-matching effects on four-wave mixing in optical fibers,” J. Lightwave Technol. 17, 2285–2290 (1999).
    [CrossRef]
  10. H. Onaka, K. Otsuka, H. Miyata, T. Chikama, “Measuring the longitudinal distribution of four-wave mixing efficiency in dispersion-shifted fibers,” IEEE Photon. Technol. Lett. 6, 1454–1456 (1994).
    [CrossRef]
  11. M. Karlsson, “Four-wave mixing in fibers with randomly varying zero-dispersion wavelength,” J. Opt. Soc. Am. B 15, 2269–2275 (1998).
    [CrossRef]
  12. J. R. Fienup, “Reconstruction of an object from the modulus of its Fourier transform,” Opt. Lett. 3, 27–29 (1978).
    [CrossRef] [PubMed]
  13. M. Nieto-Vesperinas, J. A. Mendez, “Phase retrieval by Monte Carlo methods,” Opt. Commun. 59, 249–254 (1986).
    [CrossRef]
  14. M. Karlsson, J. Brentel, “Autocorrelation function of the polarization-mode dispersion vector,” Opt. Lett. 24, 939–941 (1999).
    [CrossRef]

1999 (2)

1998 (2)

1997 (1)

M. Eiselt, R. M. Jopson, R. H. Stolen, “Nondestructive position-resolved measurement of the zero-dispersion wavelength in an optical fiber,” J. Lightwave Technol. 15, 135–143 (1997).
[CrossRef]

1996 (1)

1995 (1)

S. Nishi, M. Saruwatari, “Technique for measuring the distributed zero dispersion wavelength of optical fibers using pulse amplification caused by modulation instability,” Electron. Lett. 31, 225–226 (1995).
[CrossRef]

1994 (1)

H. Onaka, K. Otsuka, H. Miyata, T. Chikama, “Measuring the longitudinal distribution of four-wave mixing efficiency in dispersion-shifted fibers,” IEEE Photon. Technol. Lett. 6, 1454–1456 (1994).
[CrossRef]

1992 (1)

K. Inoue, “Four-wave mixing in an optical fiber in the zero-dispersion wavelength region,” J. Lightwave Technol. 10, 1553–1561 (1992).
[CrossRef]

1986 (1)

M. Nieto-Vesperinas, J. A. Mendez, “Phase retrieval by Monte Carlo methods,” Opt. Commun. 59, 249–254 (1986).
[CrossRef]

1978 (1)

Allen, C. T.

Brener, I.

Brentel, J.

Chikama, T.

H. Onaka, K. Otsuka, H. Miyata, T. Chikama, “Measuring the longitudinal distribution of four-wave mixing efficiency in dispersion-shifted fibers,” IEEE Photon. Technol. Lett. 6, 1454–1456 (1994).
[CrossRef]

Corredera, P.

M. L. Hernanz, P. Corredera, M. Gonzalez-Herraez, “Selection of uniform fibers as standards for chromatic dispersion using cw four-wave mixing,” in 6th Optical Fibre Measurement Conference (OFMC ’01) Proceedings (National Physical Laboratory, Teddington, Middlesex, UK, 2001), pp. 235–239.

M. L. Hernanz, M. Gonzalez-Herraez, P. Corredera, “Zero-dispersion wavelength mapping in single-mode optical fibers using cw four-wave mixing,” in 6th Optical Fibre Measurement Conference (OFMC ’01) Proceedings (National Physical Laboratory, Teddington, Middlesex, UK, 2001), pp. 225–229.

Demarest, K. R.

Eiselt, M.

M. Eiselt, R. M. Jopson, R. H. Stolen, “Nondestructive position-resolved measurement of the zero-dispersion wavelength in an optical fiber,” J. Lightwave Technol. 15, 135–143 (1997).
[CrossRef]

Fienup, J. R.

Gonzalez-Herraez, M.

M. L. Hernanz, M. Gonzalez-Herraez, P. Corredera, “Zero-dispersion wavelength mapping in single-mode optical fibers using cw four-wave mixing,” in 6th Optical Fibre Measurement Conference (OFMC ’01) Proceedings (National Physical Laboratory, Teddington, Middlesex, UK, 2001), pp. 225–229.

M. L. Hernanz, P. Corredera, M. Gonzalez-Herraez, “Selection of uniform fibers as standards for chromatic dispersion using cw four-wave mixing,” in 6th Optical Fibre Measurement Conference (OFMC ’01) Proceedings (National Physical Laboratory, Teddington, Middlesex, UK, 2001), pp. 235–239.

Hernanz, M. L.

M. L. Hernanz, P. Corredera, M. Gonzalez-Herraez, “Selection of uniform fibers as standards for chromatic dispersion using cw four-wave mixing,” in 6th Optical Fibre Measurement Conference (OFMC ’01) Proceedings (National Physical Laboratory, Teddington, Middlesex, UK, 2001), pp. 235–239.

M. L. Hernanz, M. Gonzalez-Herraez, P. Corredera, “Zero-dispersion wavelength mapping in single-mode optical fibers using cw four-wave mixing,” in 6th Optical Fibre Measurement Conference (OFMC ’01) Proceedings (National Physical Laboratory, Teddington, Middlesex, UK, 2001), pp. 225–229.

Hui, R.

Inoue, K.

K. Inoue, “Four-wave mixing in an optical fiber in the zero-dispersion wavelength region,” J. Lightwave Technol. 10, 1553–1561 (1992).
[CrossRef]

Jopson, R. M.

M. Eiselt, R. M. Jopson, R. H. Stolen, “Nondestructive position-resolved measurement of the zero-dispersion wavelength in an optical fiber,” J. Lightwave Technol. 15, 135–143 (1997).
[CrossRef]

Karlsson, M.

Lee, D. D.

Mamyshev, P. V.

Mendez, J. A.

M. Nieto-Vesperinas, J. A. Mendez, “Phase retrieval by Monte Carlo methods,” Opt. Commun. 59, 249–254 (1986).
[CrossRef]

Mitra, P. P.

Miyata, H.

H. Onaka, K. Otsuka, H. Miyata, T. Chikama, “Measuring the longitudinal distribution of four-wave mixing efficiency in dispersion-shifted fibers,” IEEE Photon. Technol. Lett. 6, 1454–1456 (1994).
[CrossRef]

Mollenauer, L. F.

Neubelt, M. J.

Nieto-Vesperinas, M.

M. Nieto-Vesperinas, J. A. Mendez, “Phase retrieval by Monte Carlo methods,” Opt. Commun. 59, 249–254 (1986).
[CrossRef]

Nishi, S.

S. Nishi, M. Saruwatari, “Technique for measuring the distributed zero dispersion wavelength of optical fibers using pulse amplification caused by modulation instability,” Electron. Lett. 31, 225–226 (1995).
[CrossRef]

Onaka, H.

H. Onaka, K. Otsuka, H. Miyata, T. Chikama, “Measuring the longitudinal distribution of four-wave mixing efficiency in dispersion-shifted fibers,” IEEE Photon. Technol. Lett. 6, 1454–1456 (1994).
[CrossRef]

Otsuka, K.

H. Onaka, K. Otsuka, H. Miyata, T. Chikama, “Measuring the longitudinal distribution of four-wave mixing efficiency in dispersion-shifted fibers,” IEEE Photon. Technol. Lett. 6, 1454–1456 (1994).
[CrossRef]

Philen, D. L.

Saruwatari, M.

S. Nishi, M. Saruwatari, “Technique for measuring the distributed zero dispersion wavelength of optical fibers using pulse amplification caused by modulation instability,” Electron. Lett. 31, 225–226 (1995).
[CrossRef]

Schlager, J. B.

J. B. Schlager, “Zero-dispersion in optical fibers from cw four-wave mixing efficiency,” in LEOS ’98 (Institute of Electrical and Electronic Engineers, Orlando, Fla., 1998), Vol. 2, pp. 309–331.

Song, S.

Stolen, R. H.

M. Eiselt, R. M. Jopson, R. H. Stolen, “Nondestructive position-resolved measurement of the zero-dispersion wavelength in an optical fiber,” J. Lightwave Technol. 15, 135–143 (1997).
[CrossRef]

Thomson, D. J.

Electron. Lett. (1)

S. Nishi, M. Saruwatari, “Technique for measuring the distributed zero dispersion wavelength of optical fibers using pulse amplification caused by modulation instability,” Electron. Lett. 31, 225–226 (1995).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

H. Onaka, K. Otsuka, H. Miyata, T. Chikama, “Measuring the longitudinal distribution of four-wave mixing efficiency in dispersion-shifted fibers,” IEEE Photon. Technol. Lett. 6, 1454–1456 (1994).
[CrossRef]

J. Lightwave Technol. (3)

K. Inoue, “Four-wave mixing in an optical fiber in the zero-dispersion wavelength region,” J. Lightwave Technol. 10, 1553–1561 (1992).
[CrossRef]

S. Song, C. T. Allen, K. R. Demarest, R. Hui, “Intensity-dependent phase-matching effects on four-wave mixing in optical fibers,” J. Lightwave Technol. 17, 2285–2290 (1999).
[CrossRef]

M. Eiselt, R. M. Jopson, R. H. Stolen, “Nondestructive position-resolved measurement of the zero-dispersion wavelength in an optical fiber,” J. Lightwave Technol. 15, 135–143 (1997).
[CrossRef]

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

Opt. Commun. (1)

M. Nieto-Vesperinas, J. A. Mendez, “Phase retrieval by Monte Carlo methods,” Opt. Commun. 59, 249–254 (1986).
[CrossRef]

Opt. Lett. (4)

Other (3)

J. B. Schlager, “Zero-dispersion in optical fibers from cw four-wave mixing efficiency,” in LEOS ’98 (Institute of Electrical and Electronic Engineers, Orlando, Fla., 1998), Vol. 2, pp. 309–331.

M. L. Hernanz, M. Gonzalez-Herraez, P. Corredera, “Zero-dispersion wavelength mapping in single-mode optical fibers using cw four-wave mixing,” in 6th Optical Fibre Measurement Conference (OFMC ’01) Proceedings (National Physical Laboratory, Teddington, Middlesex, UK, 2001), pp. 225–229.

M. L. Hernanz, P. Corredera, M. Gonzalez-Herraez, “Selection of uniform fibers as standards for chromatic dispersion using cw four-wave mixing,” in 6th Optical Fibre Measurement Conference (OFMC ’01) Proceedings (National Physical Laboratory, Teddington, Middlesex, UK, 2001), pp. 235–239.

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Figures (6)

Fig. 1
Fig. 1

(a) Zero-dispersion wavelength map of a nonuniform fiber, including and excluding short-term variations. (b) FWM efficiency curve (Δλ = 4 nm) for the simulated fiber including and neglecting short-term fluctuations versus the efficiency curve for a fiber with constant zero-dispersion wavelength (dotted curve). The slight differences that appear between the two cases are due to small long-term perturbations induced by the simulated short-term perturbations. Note the wavelength shift of the peak FWM efficiency and the decrease of ∼5 dB in the peak gain.

Fig. 2
Fig. 2

(a) Zero-dispersion wavelength map of nonuniform fiber with L c ∼ 3 km and profile reconstructed by the new algorithm and by the Gauss–Newton algorithm. (b) FWM efficiency curve for the simulated fiber and FWM efficiency of the fiber reconstructed by both methods.

Fig. 3
Fig. 3

(a) Zero-dispersion wavelength map of nonuniform fiber with L c ∼ 1 km and profile reconstructed by the new algorithm and by the Gauss–Newton algorithm. (b) FWM efficiency curve for the simulated fiber and FWM efficiency of the fiber reconstructed by both methods.

Fig. 4
Fig. 4

(a) Zero-dispersion wavelength map of nonuniform fiber with L c ∼ 1 km in the 1550-nm window and profile reconstructed with the new algorithm. (b) FWM efficiency curve for the simulated fiber and FWM efficiency of the reconstructed fiber.

Fig. 5
Fig. 5

(a) Zero-dispersion wavelength map of nonuniform fiber with L c ∼ 1 km in the 1550-nm window and profile reconstructed with the new algorithm for various levels of noise. (b) Original FWM efficiency curve of the simulated fiber with no noise; measured FWM efficiency including noise and reconstructed efficiency.

Fig. 6
Fig. 6

Reconstruction under conditions of noise in the fiber parameters. The attenuation has an 11% underestimation, the length has a 5% overestimation, and the dispersion slope has a 10% overestimation (all these conditions are labeled as C1 in the figure). Results were obtained with noisy and nonnoisy FWM efficiency data.

Equations (15)

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Pw=FPγ, α, Pi, Pk, LηDc, Δλ, α, Pi, Pk, L×Tpolsi, sk.
η=α2α2+Δβ21+4 exp-αLsin2ΔβL/21-exp-αL2,
Δβ=βλw+βλk-2βλi=-2πcλ2dDcdλ 2λi-λk2λi-λ0.
Tpolsi, sk=1/21+si · sk,
λ0z=λ0const+λ0randz.
Lc=0 RλζdζRλ0,
IFWMλ1  0Lexpiϕzexp-iκλ1zexp-αzdz2,
ϕz=κ 0z λ0ydy, κ=2πcΔλλ2dDdλ,
IFWMq  0L gzexp-iqzdz2,
gk+1z=gkzzγ0zγ,
gk+1z=gkzzγgkz-βgkzzγ,
gk+1z=exp-αzexpjϕkzz0, L0z0, L,
ΔξL, ΔωΔτωΔω,
Δω0.3Δτ2  Δλ0.3λ22πcΔτ2.
Δω0.6Δτ2  Δλ0.6λ22πcΔτ2.

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