Abstract

A simple four-wave-mixing (FWM)-based method for measuring the ratio between the third- and the fourth-order dispersion coefficients (β3β4) in optical fibers is reported. The FWM interaction involves a low power laser and a low power amplified spontaneous emission noise source. The method is applied in several dispersion-shifted and non-zero-dispersion-shifted fibers with lengths varying from 0.03 to 25km, and we have obtained an error of less than 3% in measuring β3β4. In highly nonlinear fibers the error has presented a strong dependency with longitudinal variations of the zero-dispersion wavelength (λ0); an error less than 20% could be obtained in most of the tested fibers. Our method also allows for a fast estimation of the distribution of fluctuations of λ0 along the fiber.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. G. P. Agrawal, Applications of Nonlinear Fiber Optics (Academic, 2003).
  2. M. E. Marhic, Y. Park, F. S. Yang, and L. G. Kazovsky, "Broadband fiber optical parametric amplifiers and wavelength converters with low-ripple Chebyshev gain spectra," Opt. Lett. 21, 1354-1356 (1996).
    [CrossRef] [PubMed]
  3. J. M. Chavez Boggio, J. D. Marconi, and H. L. Fragnito, "Double-pumped fiber optical parametric amplifier with flat gain over 47-nm bandwidth using a conventional dispersion-shifted fiber," IEEE Photon. Technol. Lett. 17, 1842-1844 (2005).
    [CrossRef]
  4. M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, "Broadband wavelength conversion over 193-nm by HNL-DSF improving higher-order dispersion performance," in Proceedings of European Conference Optical Communication (ECOC) (ECOC, 2005), postdeadline paper Th 4.4.4.
    [CrossRef]
  5. F. Biancalana and D. V. Skryabin, "Vector modulation instabilities in ultra-small core optical fibres," J. Opt. A, Pure Appl. Opt. 6, 301-306 (2004).
    [CrossRef]
  6. S. Pitois and G. Millot, "Experimental observation of a new modulation instability spectral window induced by fourth-order dispersion in a normally dispersive single mode optical fiber," Opt. Commun. 226, 415-422 (2003).
    [CrossRef]
  7. J. D. Harvey, R. Leonhardt, S. Coen, G. K. L. Wong, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, "Scalar modulation instability in the normal dispersion regime by use of a photonic crystal fiber," Opt. Lett. 28, 2225-2227 (2003).
    [CrossRef] [PubMed]
  8. M. E. Marhic, K. K. Y. Wong, and L. G. Kazovsky, "Wide-band tuning of the gain spectra of one-pump fiber optical parametric amplifiers," IEEE J. Sel. Top. Quantum Electron. 10, 1133-1141 (2004).
    [CrossRef]
  9. A. Y. H. Chen, G. K. L. Wong, S. G. Murdoch, R. Leonhardt, J. D. Harvey, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, "Widely tunable optical parametric generation in a photonic crystal fiber," Opt. Lett. 30, 762-764 (2005).
    [CrossRef] [PubMed]
  10. P. K. A. Wai, C. R. Menyuk, H. H. Chen, and Y. C. Lee, "Soliton at the zero-dispersion wavelength of a single-mode fiber," Opt. Lett. 12, 628-630 (1987).
    [CrossRef] [PubMed]
  11. N. Akhmediev and M. Karlsson, "Cerenkov radiation emitted by solitons," Phys. Rev. A 51, 2602-2607 (1995).
    [CrossRef] [PubMed]
  12. W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A. J. Taylor, "Transformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibres," Nature 424, 511-515 (2003).
    [CrossRef] [PubMed]
  13. J. M. Dudley, G. Genty, and S. Coen, "Supercontinuum generation in photonic crystal fibres," Rev. Mod. Phys. 78, 1135-1184 (2006).
    [CrossRef]
  14. S. Coen, A. H. L. Chau, R. Leonhardt, J. D. Harvey, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, "Supercontinuum generation by stimulated Raman scattering and parametric four-wave mixing in photonic crystal fibres," J. Opt. Soc. Am. B 19, 753-764 (2002).
    [CrossRef]
  15. B. Auguié, A. Mussot, A. Boucon, E. Lantz, and T. Sylvestre, "Ultra low chromatic dispersion measurement of optical fibers with a tunable fiber laser," IEEE Photon. Technol. Lett. 18, 1825-1827 (2006).
    [CrossRef]
  16. G. K. L. Wong, A. Chen, S. Ha, R. Kruhlak, S. Murdoch, R. Leonhardt, J. Harvey, and N. Joly, "Characterization of chromatic dispersion in photonic crystal fiber using scalar modulation instability," Opt. Express 13, 8662-8670 (2005).
    [CrossRef] [PubMed]
  17. K. Inoue, "Four-wave mixing in an optical fiber in the zero-dispersion wavelength region," J. Lightwave Technol. 10, 1553-1561 (1992).
    [CrossRef]
  18. M. Eiselt, R. M. Jopson, and R. H. Stolen, "Nondestructive position-resolved measurement of the zero-dispersion wavelength in an optical fiber," J. Lightwave Technol. 15, 135-143 (1997).
    [CrossRef]
  19. I. Brener, P. P. Mitra, D. D. Lee, D. J. Thomson, and D. L. Philen, "High-resolution zero-dispersion wavelength mapping in single-mode fiber," Opt. Lett. 23, 1520-1522 (1998).
    [CrossRef]
  20. M. Gonzalez-Herraez, P. Corredera, M. L. Hernanz, and J. A. Mendez, "Enhanced method for the reconstruction of zero-dispersion wavelength maps of optical fibers by measurement of continuous-wave four-wave mixing efficiency," Appl. Opt. 41, 3796-3803 (2002).
    [CrossRef] [PubMed]
  21. J. Fatome, S. Pitois, and G. Millot, "Measurement of nonlinear and chromatic dispersion parameters of optical fibers using modulation instability," Opt. Fiber Technol. 12, 243-250 (2006).
    [CrossRef]
  22. J. M. Chavez Boggio, S. Tenenbaum, J. D. Marconi, and H. L. Fragnito, "A novel method for measuring longitudinal variations of the zero dispersion wavelength in optical fibers," in European Conference on Optical Communication (ECOC'06) (ECOC, 2006), paper Th1.5.2.
  23. C. Mazzali, D. F. Grosz, and H. L. Fragnito, "Simple method for measuring dispersion and nonlinear coefficient near the zero-dispersion wavelength of optical fibers," IEEE Photon. Technol. Lett. 11, 251-253 (1999).
    [CrossRef]
  24. D. Mogilevtsev, T. A. Birks, and P. St. J. Russell, "Group-velocity dispersion in photonic crystal fibres," Opt. Lett. 23, 1662-1664 (1998).
    [CrossRef]
  25. A. Ferrando, E. Silvestre, J. J. Miret, J. A. Monsoriu, M. V. Andres, and P. St. J. Russell, "Designing a photonic crystal fibre with flattened chromatic dispersion," Electron. Lett. 35, 325-327 (1999).
    [CrossRef]
  26. J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, "Anomalous dispersion in photonic crystal fibres," IEEE Photon. Technol. Lett. 12, 807-809 (2000).
    [CrossRef]
  27. W. H. Reeves, J. C. Knight, P. St. J. Russell, and P. J. Roberts, "Demonstration of ultra-flattened dispersion in photonic crystal fibres," Opt. Express 10, 609-613 (2002).
    [PubMed]

2006

J. M. Dudley, G. Genty, and S. Coen, "Supercontinuum generation in photonic crystal fibres," Rev. Mod. Phys. 78, 1135-1184 (2006).
[CrossRef]

B. Auguié, A. Mussot, A. Boucon, E. Lantz, and T. Sylvestre, "Ultra low chromatic dispersion measurement of optical fibers with a tunable fiber laser," IEEE Photon. Technol. Lett. 18, 1825-1827 (2006).
[CrossRef]

J. Fatome, S. Pitois, and G. Millot, "Measurement of nonlinear and chromatic dispersion parameters of optical fibers using modulation instability," Opt. Fiber Technol. 12, 243-250 (2006).
[CrossRef]

2005

2004

M. E. Marhic, K. K. Y. Wong, and L. G. Kazovsky, "Wide-band tuning of the gain spectra of one-pump fiber optical parametric amplifiers," IEEE J. Sel. Top. Quantum Electron. 10, 1133-1141 (2004).
[CrossRef]

F. Biancalana and D. V. Skryabin, "Vector modulation instabilities in ultra-small core optical fibres," J. Opt. A, Pure Appl. Opt. 6, 301-306 (2004).
[CrossRef]

2003

S. Pitois and G. Millot, "Experimental observation of a new modulation instability spectral window induced by fourth-order dispersion in a normally dispersive single mode optical fiber," Opt. Commun. 226, 415-422 (2003).
[CrossRef]

J. D. Harvey, R. Leonhardt, S. Coen, G. K. L. Wong, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, "Scalar modulation instability in the normal dispersion regime by use of a photonic crystal fiber," Opt. Lett. 28, 2225-2227 (2003).
[CrossRef] [PubMed]

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A. J. Taylor, "Transformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibres," Nature 424, 511-515 (2003).
[CrossRef] [PubMed]

2002

2000

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, "Anomalous dispersion in photonic crystal fibres," IEEE Photon. Technol. Lett. 12, 807-809 (2000).
[CrossRef]

1999

A. Ferrando, E. Silvestre, J. J. Miret, J. A. Monsoriu, M. V. Andres, and P. St. J. Russell, "Designing a photonic crystal fibre with flattened chromatic dispersion," Electron. Lett. 35, 325-327 (1999).
[CrossRef]

C. Mazzali, D. F. Grosz, and H. L. Fragnito, "Simple method for measuring dispersion and nonlinear coefficient near the zero-dispersion wavelength of optical fibers," IEEE Photon. Technol. Lett. 11, 251-253 (1999).
[CrossRef]

1998

1997

M. Eiselt, R. M. Jopson, and 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

1995

N. Akhmediev and M. Karlsson, "Cerenkov radiation emitted by solitons," Phys. Rev. A 51, 2602-2607 (1995).
[CrossRef] [PubMed]

1992

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

1987

Appl. Opt.

Electron. Lett.

A. Ferrando, E. Silvestre, J. J. Miret, J. A. Monsoriu, M. V. Andres, and P. St. J. Russell, "Designing a photonic crystal fibre with flattened chromatic dispersion," Electron. Lett. 35, 325-327 (1999).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

M. E. Marhic, K. K. Y. Wong, and L. G. Kazovsky, "Wide-band tuning of the gain spectra of one-pump fiber optical parametric amplifiers," IEEE J. Sel. Top. Quantum Electron. 10, 1133-1141 (2004).
[CrossRef]

IEEE Photon. Technol. Lett.

J. M. Chavez Boggio, J. D. Marconi, and H. L. Fragnito, "Double-pumped fiber optical parametric amplifier with flat gain over 47-nm bandwidth using a conventional dispersion-shifted fiber," IEEE Photon. Technol. Lett. 17, 1842-1844 (2005).
[CrossRef]

B. Auguié, A. Mussot, A. Boucon, E. Lantz, and T. Sylvestre, "Ultra low chromatic dispersion measurement of optical fibers with a tunable fiber laser," IEEE Photon. Technol. Lett. 18, 1825-1827 (2006).
[CrossRef]

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, "Anomalous dispersion in photonic crystal fibres," IEEE Photon. Technol. Lett. 12, 807-809 (2000).
[CrossRef]

C. Mazzali, D. F. Grosz, and H. L. Fragnito, "Simple method for measuring dispersion and nonlinear coefficient near the zero-dispersion wavelength of optical fibers," IEEE Photon. Technol. Lett. 11, 251-253 (1999).
[CrossRef]

J. Lightwave Technol.

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

M. Eiselt, R. M. Jopson, and 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. A, Pure Appl. Opt.

F. Biancalana and D. V. Skryabin, "Vector modulation instabilities in ultra-small core optical fibres," J. Opt. A, Pure Appl. Opt. 6, 301-306 (2004).
[CrossRef]

J. Opt. Soc. Am. B

Nature

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A. J. Taylor, "Transformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibres," Nature 424, 511-515 (2003).
[CrossRef] [PubMed]

Opt. Commun.

S. Pitois and G. Millot, "Experimental observation of a new modulation instability spectral window induced by fourth-order dispersion in a normally dispersive single mode optical fiber," Opt. Commun. 226, 415-422 (2003).
[CrossRef]

Opt. Express

Opt. Fiber Technol.

J. Fatome, S. Pitois, and G. Millot, "Measurement of nonlinear and chromatic dispersion parameters of optical fibers using modulation instability," Opt. Fiber Technol. 12, 243-250 (2006).
[CrossRef]

Opt. Lett.

Phys. Rev. A

N. Akhmediev and M. Karlsson, "Cerenkov radiation emitted by solitons," Phys. Rev. A 51, 2602-2607 (1995).
[CrossRef] [PubMed]

Rev. Mod. Phys.

J. M. Dudley, G. Genty, and S. Coen, "Supercontinuum generation in photonic crystal fibres," Rev. Mod. Phys. 78, 1135-1184 (2006).
[CrossRef]

Other

G. P. Agrawal, Applications of Nonlinear Fiber Optics (Academic, 2003).

M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, "Broadband wavelength conversion over 193-nm by HNL-DSF improving higher-order dispersion performance," in Proceedings of European Conference Optical Communication (ECOC) (ECOC, 2005), postdeadline paper Th 4.4.4.
[CrossRef]

J. M. Chavez Boggio, S. Tenenbaum, J. D. Marconi, and H. L. Fragnito, "A novel method for measuring longitudinal variations of the zero dispersion wavelength in optical fibers," in European Conference on Optical Communication (ECOC'06) (ECOC, 2006), paper Th1.5.2.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

(a) Schematic of the proposed FWM process for measuring β 3 β 4 . The narrowband ASE noise source, located near to ω 0 , interact by FWM with a low power laser. (b) Continuum of pairs of noise Fourier components at ω and ω interact with the laser through the FWM process that satisfy the relationship ω = ω 1 + ω 1 ω l .

Fig. 2
Fig. 2

Experimental setup. With the polarization controller (PC) we analyzed how the generation of the FWM product depends on the laser polarization. We used a WDM coupler as optical filter (OF) to filter out the laser and the noise.

Fig. 3
Fig. 3

(a) Typical output spectrum. The noise source located near λ 0 interacts with the laser, at λ l , and generates a FWM product at λ F W M . The laser is located far from λ 0 in order to have a narrow FWM product. The spectrum was taken with a WDM coupler at the fiber output, which attenuated the laser (by 20 dB ) and the ASE source (by 22 dB ). This is to prevent strong stray light in our OSA. (b) Zoom of the FWM product at λ F W M after further filtering out the noise and the laser.

Fig. 4
Fig. 4

Continuous curves: Spectrum of the FWM product for (a) λ l = 1646.93 nm and (b) λ l = 1626.93 nm . The value of λ pm can be measured with error smaller than 0.01 nm . Dotted curves: Fitting of experimental spectrum using Eq. (2). The fitting parameters were obtained from the measurement of β 30 and β 30 β 4 . We used for (a) β 30 = 0.123 ps 3 km and β 4 = 5.71 × 10 4 ps 4 km and for (b) β 30 = 0.124 ps 3 km and β 4 = 5.71 × 10 4 ps 4 km .

Fig. 5
Fig. 5

Output spectrum for a DSF with L = 25 km . The noise source located near λ 0 interacts with the laser at λ l and generates an FWM product at λ F W M . The spectrum was taken with a WDM at the fiber output, which attenuated the laser (by 20 dB ) and the ASE source (by 22 dB ) to prevent strong stray light in our OSA.

Fig. 6
Fig. 6

Spectrum of the FWM product for a DSF with L = 25 km . (a) λ l = 1632.1 nm and (b) λ l = 1646.97 nm . The value of λ pm , measured at the strongest peak, can be obtained with an error smaller than 0.05 nm .

Fig. 7
Fig. 7

Spectrum of the FWM product for an HNLF with L = 0.15 km . The value of λ pm in the strongest FWM peak can be measured with an error smaller than 0.03 nm . By maximizing this 1 st peak we obtain β 30 β 4 = ( 457 ± 12 ) ps 1 . Note that the maximized peaks in the spectra depicted in continuous and dotted–dashed curves are rather weak.

Fig. 8
Fig. 8

Spectrum of the FWM product for an HNLF with L = 0.3 km . The noise source was tuned at seven locations in order to maximize FWM peaks indicated with arrows. The value of λ pm in the strongest FWM peak (called 1 st ) can be measured with an error smaller than 0.05 nm and leads to β 30 β 4 = ( 401 ± 14 ) ps 1 .

Fig. 9
Fig. 9

Spectrum of the FWM product for an HNLF with L = 0.21 km . The value of λ A was tuned at (a) 1555.9, 1556.5, 1557, 1557.6 nm , and 1558.1, and we obtained the FWM spectra shown in continuous, dotted–dashed, dashed, dotted, and long dashed curves, respectively. (b) shows the FWM spectra for λ A = 1558.5 , 1558.9, 1559.3, and 1559.6 nm in continuous, dotted–dashed, dashed, and dotted curves, respectively. (c) λ A = 1560 , 1560.75, 1561.2, and 1562.7 nm and the respective FWM spectra are shown in continuous, dashed, dotted, and long dashed curves.

Fig. 10
Fig. 10

Δ β as a function of λ for 15 values of δ ν ranging from 0.1 to 0.1 THz . λ c = 1546.8 nm , λ 0 = 1549.8 nm , λ l = 1646.93 nm , β 30 = 0.0123 ps 3 km , and β 4 = 5.71 × 10 4 ps 4 km . All 15 curves are superimposed, demonstrating that Δ β is independent of δ ν (for δ ν ν ν 0 ).

Tables (3)

Tables Icon

Table 1 Results of Four Measurements of β 30 β 4 with a DSF Having L = 0.58 km

Tables Icon

Table 2 Results of Measurements of β 30 β 4 with DSFs and NZ-DSFs

Tables Icon

Table 3 Results of Measurements of β 30 β 4 with Several HNLFs from a Coil of 2 km

Equations (17)

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

P F W M ( ω ) = γ 2 P l S 0 2 L 2 Δ ω A 2 1 1 d x rect ( x ) rect ( x ) sinc 2 ( Δ β L 2 ) ,
P F W M ( ω ) = γ 2 P l S 0 2 L 2 Δ ω A 2 sinc 2 ( Δ β C L 2 ) ,
β 30 ( ω A ω 0 ) ( ω A ω l ) 2 + β 4 ( ω A ω l ) 4 12 = 0 ,
β 30 β 4 = ( ω pm ( a ) ω l ( a ) ) 2 ( ω pm ( b ) ω l ( b ) ) 2 2 ( ω pm ( b ) + ω l ( b ) ω pm ( a ) ω l ( a ) ) ,
δ x x = 2 2 δ ω pm ω pm ( a ) + ω l ( a ) ω pm ( b ) ω l ( b ) ,
( ω ) = 3 4 ε 0 χ ( 3 ) 0 0 d ω 1 2 π d ω 2 2 π A ( ω 1 ) A ( ω 2 ) A * ( ω 3 ) ,
( ω ) = 2 3 ε 0 χ ( 3 ) 2 π E ̃ l * 4 ( 2 π ) 2 0 d ω 1 A 0 ( ω 1 ) A 0 ( ω + ω l ω 1 ) .
A ̃ F W M ( ω , z ) z = i ω c μ 0 2 n ( ω ) e i β ( ω ) z + α z 2 .
A ̃ F W M ( ω , L ) = i ω 2 n c 3 χ ( 3 ) E ̃ l * 4 0 d ω 1 A r ( ω 1 ) A r ( ω + ω l ω 1 ) 0 L d z e i Δ β z α z ,
A ̃ F W M ( ω ) 2 = K sinc ( Δ β L 2 ) sinc ( Δ β L 2 ) 0 d ω 1 d ω 2 A r ( ω 1 ) A r ( ω 2 ) A r ( ω 1 ) A r ( ω 2 ) ,
K = ( ω 2 n c 3 χ ( 3 ) 4 ) 2 E ̃ l 2 L 2 ,
A r ( ω 1 ) A r * ( ω 2 ) A r ( ω 1 ) A r * ( ω 2 ) = A r ( ω 1 ) 2 A r ( ω 1 ) 2 [ δ ( ω 2 ω 1 ) + δ ( ω 2 ω 1 ) ] .
A ̃ F W M ( ω ) 2 = ( 3 χ ( 3 ) ω 2 n c ) 2 E ̃ l 2 L 2 0 d ω 1 S 0 ( ω 1 ) S 0 ( ω 1 ) sinc 2 ( Δ β L 2 ) .
γ ω = 3 ω χ ( 3 ) ω 4 ε 0 n 2 c 2 A e f f ,
P F W M ( ω ) = 2 γ 2 P l S 0 2 Δ ω A 2 L 2 0 d ω 1 rect ( ω 1 ) rect ( ω 1 ) sinc 2 ( Δ β L 2 ) ,
Δ β = β 2 c [ ( ω ω 1 ) ( ω 1 ω l ) ] + β 4 c [ ( ω ω 1 ) ( ω + ω 1 2 ω c ) ] [ ( ω ω c ) 2 + ( ω 1 ω c ) 2 ] 12 ,
Δ β = β 30 [ ( ω c ω 0 ) ] [ ( ω ω c δ ω ) ( ω c ω l + δ ω ) ] + β 4 c [ ( ω ω c δ ω ) ( ω ω c + δ ω ) ] [ ( ω ω c ) 2 + ( δ ω ) 2 ] 12 .

Metrics