Abstract

A novel method for measuring optical fiber’s nonlinear coefficient, based on phase mismatching four-wave mixing is proposed. Measurements for both high nonlinearity dispersion shifted fiber and low nonlinearity standard single mode fiber are demonstrated with simple setup. Chromatic dispersion is also measured with high precision simultaneously, and therefore its effect to the nonlinear coefficient measurement can be removed.

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References

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  1. M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, “Silica-based highly nonlinear fibers and their application,” IEEE J. Sel. Top. Quant.15(1), 103–113 (2009).
    [CrossRef]
  2. R. H. Stolen and L. Chinlon, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A17(4), 1448–1453 (1978).
    [CrossRef]
  3. M. Monerie and Y. Durteste, “Direct interferometric measurement of nonlinear refractive index of optical fiber by cross-phase modulation,” Electron. Lett.23(18), 961–963 (1987).
    [CrossRef]
  4. F. Wittl, “Interferometric determination of the nonlinear refractive index n2 of optical fibers,” Proc. Symposium on Optical Fiber Measurements’96, 71–74 (1996).
  5. C. Vinegoni, M. Wegmuller, and N. Gisin, “Measurement of the nonlinear coefficient of standard SMF, DSF, and DCF fiber using a self-aligned interferometer and a Faraday Mirror,” IEEE Photon. Technol. Lett.13(12), 1337–1339 (2001).
    [CrossRef]
  6. A. Boskovic, S. V. Chernikov, J. R. Taylor, L. Gruner-Nielsen, and O. A. Levring, “Direct continuous-wave measurement of n2 in various types of telecommunication fiber at 155 µm,” Opt. Lett.21(24), 1966–1968 (1996).
    [CrossRef] [PubMed]
  7. L. Prigent and J.-P. Hamaide, “Measurement of fiber nonlinear Kerr coefficient by Four-Wave Mixing,” IEEE Photon. Technol. Lett.5(9), 1062–1065 (1993).
    [CrossRef]
  8. O. Aso, M. Tadakuma, and S. Namiki, “Four-Wave Mixing in Optical Fibers and Its Applications,” Furukawa Review, No.19, 63–68 (2000).
  9. M. Hirano and T. Sasaki, “Straightforward chromatic dispersion measurement based on phase mismatching FWM,” Proc. ECOC’2009, Vienna, Austria, .
  10. G. P. Agrawal, Nonlinear Fiber Optics, 4th Edition, Academic Press, (2007).
  11. T. Dennis and P. A. Williams, “Achieving high absolute accuracy for group-delay measurements using the modulation phase-shift technique,” J. Lightwave Technol.23(11), 3748–3754 (2005).
    [CrossRef]

2009 (1)

M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, “Silica-based highly nonlinear fibers and their application,” IEEE J. Sel. Top. Quant.15(1), 103–113 (2009).
[CrossRef]

2005 (1)

2001 (1)

C. Vinegoni, M. Wegmuller, and N. Gisin, “Measurement of the nonlinear coefficient of standard SMF, DSF, and DCF fiber using a self-aligned interferometer and a Faraday Mirror,” IEEE Photon. Technol. Lett.13(12), 1337–1339 (2001).
[CrossRef]

2000 (1)

O. Aso, M. Tadakuma, and S. Namiki, “Four-Wave Mixing in Optical Fibers and Its Applications,” Furukawa Review, No.19, 63–68 (2000).

1996 (1)

1993 (1)

L. Prigent and J.-P. Hamaide, “Measurement of fiber nonlinear Kerr coefficient by Four-Wave Mixing,” IEEE Photon. Technol. Lett.5(9), 1062–1065 (1993).
[CrossRef]

1987 (1)

M. Monerie and Y. Durteste, “Direct interferometric measurement of nonlinear refractive index of optical fiber by cross-phase modulation,” Electron. Lett.23(18), 961–963 (1987).
[CrossRef]

1978 (1)

R. H. Stolen and L. Chinlon, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A17(4), 1448–1453 (1978).
[CrossRef]

Aso, O.

O. Aso, M. Tadakuma, and S. Namiki, “Four-Wave Mixing in Optical Fibers and Its Applications,” Furukawa Review, No.19, 63–68 (2000).

Boskovic, A.

Chernikov, S. V.

Chinlon, L.

R. H. Stolen and L. Chinlon, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A17(4), 1448–1453 (1978).
[CrossRef]

Dennis, T.

Durteste, Y.

M. Monerie and Y. Durteste, “Direct interferometric measurement of nonlinear refractive index of optical fiber by cross-phase modulation,” Electron. Lett.23(18), 961–963 (1987).
[CrossRef]

Gisin, N.

C. Vinegoni, M. Wegmuller, and N. Gisin, “Measurement of the nonlinear coefficient of standard SMF, DSF, and DCF fiber using a self-aligned interferometer and a Faraday Mirror,” IEEE Photon. Technol. Lett.13(12), 1337–1339 (2001).
[CrossRef]

Gruner-Nielsen, L.

Hamaide, J.-P.

L. Prigent and J.-P. Hamaide, “Measurement of fiber nonlinear Kerr coefficient by Four-Wave Mixing,” IEEE Photon. Technol. Lett.5(9), 1062–1065 (1993).
[CrossRef]

Hirano, M.

M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, “Silica-based highly nonlinear fibers and their application,” IEEE J. Sel. Top. Quant.15(1), 103–113 (2009).
[CrossRef]

M. Hirano and T. Sasaki, “Straightforward chromatic dispersion measurement based on phase mismatching FWM,” Proc. ECOC’2009, Vienna, Austria, .

Levring, O. A.

Monerie, M.

M. Monerie and Y. Durteste, “Direct interferometric measurement of nonlinear refractive index of optical fiber by cross-phase modulation,” Electron. Lett.23(18), 961–963 (1987).
[CrossRef]

Nakanishi, T.

M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, “Silica-based highly nonlinear fibers and their application,” IEEE J. Sel. Top. Quant.15(1), 103–113 (2009).
[CrossRef]

Namiki, S.

O. Aso, M. Tadakuma, and S. Namiki, “Four-Wave Mixing in Optical Fibers and Its Applications,” Furukawa Review, No.19, 63–68 (2000).

Okuno, T.

M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, “Silica-based highly nonlinear fibers and their application,” IEEE J. Sel. Top. Quant.15(1), 103–113 (2009).
[CrossRef]

Onishi, M.

M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, “Silica-based highly nonlinear fibers and their application,” IEEE J. Sel. Top. Quant.15(1), 103–113 (2009).
[CrossRef]

Prigent, L.

L. Prigent and J.-P. Hamaide, “Measurement of fiber nonlinear Kerr coefficient by Four-Wave Mixing,” IEEE Photon. Technol. Lett.5(9), 1062–1065 (1993).
[CrossRef]

Sasaki, T.

M. Hirano and T. Sasaki, “Straightforward chromatic dispersion measurement based on phase mismatching FWM,” Proc. ECOC’2009, Vienna, Austria, .

Stolen, R. H.

R. H. Stolen and L. Chinlon, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A17(4), 1448–1453 (1978).
[CrossRef]

Tadakuma, M.

O. Aso, M. Tadakuma, and S. Namiki, “Four-Wave Mixing in Optical Fibers and Its Applications,” Furukawa Review, No.19, 63–68 (2000).

Taylor, J. R.

Vinegoni, C.

C. Vinegoni, M. Wegmuller, and N. Gisin, “Measurement of the nonlinear coefficient of standard SMF, DSF, and DCF fiber using a self-aligned interferometer and a Faraday Mirror,” IEEE Photon. Technol. Lett.13(12), 1337–1339 (2001).
[CrossRef]

Wegmuller, M.

C. Vinegoni, M. Wegmuller, and N. Gisin, “Measurement of the nonlinear coefficient of standard SMF, DSF, and DCF fiber using a self-aligned interferometer and a Faraday Mirror,” IEEE Photon. Technol. Lett.13(12), 1337–1339 (2001).
[CrossRef]

Williams, P. A.

Wittl, F.

F. Wittl, “Interferometric determination of the nonlinear refractive index n2 of optical fibers,” Proc. Symposium on Optical Fiber Measurements’96, 71–74 (1996).

Electron. Lett. (1)

M. Monerie and Y. Durteste, “Direct interferometric measurement of nonlinear refractive index of optical fiber by cross-phase modulation,” Electron. Lett.23(18), 961–963 (1987).
[CrossRef]

Furukawa Review, No. (1)

O. Aso, M. Tadakuma, and S. Namiki, “Four-Wave Mixing in Optical Fibers and Its Applications,” Furukawa Review, No.19, 63–68 (2000).

IEEE J. Sel. Top. Quant. (1)

M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, “Silica-based highly nonlinear fibers and their application,” IEEE J. Sel. Top. Quant.15(1), 103–113 (2009).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

C. Vinegoni, M. Wegmuller, and N. Gisin, “Measurement of the nonlinear coefficient of standard SMF, DSF, and DCF fiber using a self-aligned interferometer and a Faraday Mirror,” IEEE Photon. Technol. Lett.13(12), 1337–1339 (2001).
[CrossRef]

L. Prigent and J.-P. Hamaide, “Measurement of fiber nonlinear Kerr coefficient by Four-Wave Mixing,” IEEE Photon. Technol. Lett.5(9), 1062–1065 (1993).
[CrossRef]

J. Lightwave Technol. (1)

Opt. Lett. (1)

Phys. Rev. A (1)

R. H. Stolen and L. Chinlon, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A17(4), 1448–1453 (1978).
[CrossRef]

Other (3)

F. Wittl, “Interferometric determination of the nonlinear refractive index n2 of optical fibers,” Proc. Symposium on Optical Fiber Measurements’96, 71–74 (1996).

M. Hirano and T. Sasaki, “Straightforward chromatic dispersion measurement based on phase mismatching FWM,” Proc. ECOC’2009, Vienna, Austria, .

G. P. Agrawal, Nonlinear Fiber Optics, 4th Edition, Academic Press, (2007).

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Figures (4)

Fig. 1
Fig. 1

Idler output power as a function of (a) pump angular frequency with a constant frequency difference, and (b) squared angular frequency difference with a constant pump frequency.

Fig. 2
Fig. 2

Measurement Setup of PM-FWM Method

Fig. 3
Fig. 3

Experimental results for HNLDSFs. (a): Examples of generated idler power Pidler against pump frequency with Δω = 7.8 × 1012 rad/s for 1km-long HNLDSF. (b)-(d): Pump angle frequency providing the minimal idler power against pump power with (b) N = 1 and (c) N = 2 for 1.0km-long HNLDSF, and (d) N = 1 for 0.14km-long HNLDSF.

Fig. 4
Fig. 4

Experimental results for 1km-long SSMF. (a) The generated idler power Pidler against squared frequency difference. (b) Squared frequency difference [ΔωP(N)]2 providing the minimal idler power against pump power Ppump with N = −1.

Tables (2)

Tables Icon

Table 1 Definitions of β

Tables Icon

Table 2 Measured results of n2

Equations (13)

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P idler = ( γ P pump L ) 2 P probe sin c 2 ( ΔβL 2 ),
Δβ= β 2 ( Δω ) 2 +2γ P pump ,
ΔβL 2 =Nπ ( N:integer ).
β 2Z ( N ) = 2Nπ ( Δω ) 2 L .
β 2P ( N ) = β 3Z ( N ) ( ω P ( N ) ω Z ( N ) )+ β 2Z ( N ) .
ω P ( N ) = 2γ β 3Z ( N ) ( Δω ) 2 P pump + ω Z ( N ) ,
γ= β 3Z ( N ) 2 ( Δω ) 2 ω P ( N ) P pump .
β 2 [ Δ ω P ( N ) ] 2 +2γ P pump = 2Nπ L ,
β 2 [ Δ ω P ( N1 ) ] 2 +2γ P pump = 2( N1 )π L ,
β 2 = 2π { [ Δ ω P ( N1 ) ] 2 [ Δ ω P ( N ) ] 2 }L .
[ Δ ω Z ( N ) ] 2 = 2Nπ β 2 L .
[ Δ ω P ( N ) ] 2 = 2γ β 2 P pump + [ Δ ω Z ( N ) ] 2 .
γ= β 2 2 [ Δ ω P ( N ) ] 2 P pump ,

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