Abstract

The effect of dispersion fluctuations on the conversion efficiency of large frequency shift parametric sidebands is studied by numerical simulation and experiment. Numerical results based on periodic and random dispersion models are used to fit the experimental results. The fitting parameters provide a measure of the uniformity of the photonic crystal fiber used in the experiment. This allows us to place limits on the required uniformity of a photonic crystal fiber for strong frequency conversion.

© 2006 Optical Society of America

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  1. C. Lin, W. A. Reed, A. D. Pearson, and H. T. Sbang, "Phase matching in the minimum-chromatic-dispersion region of single-mode fibers for stimulated four-photon mixing," Opt. Lett. 6, 493-5 (1981).
    [CrossRef] [PubMed]
  2. 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, 2225-7 (2003).
    [CrossRef] [PubMed]
  3. A. Y. H. Chen, G. K. L. Wong, S. G. Murdoch, R. Leonhardt, J. D. Harvey, J. C. Knight, W. J. Wadsworth, and P. S. J. Russell, "Widely tunable optical parametric generation in a photonic crystal fiber," Opt. Lett. 30, 762-764 (2005).
    [CrossRef] [PubMed]
  4. S. Pitois and G. Millot, "Experimental observation of a new modulational instability spectral window induced by fourth-order dispersion in a normally dispersive single-mode optical fiber," Opt. Commun. 226, 415-22 (2003).
    [CrossRef]
  5. M. E. Marhic, K. K. Y. Wong, and L. G. Kazovsky, "Wideband tuning of the gain spectra of one-pump fiber optical parametric amplifiers," J. Sel. Top. Quantum. Electron. 10, 1133-1141 (2004).
    [CrossRef]
  6. G. K. L. Wong, A. Y. H. Chen, S. G. Murdoch, R. Leonhardt, J. D. Harvey, N. Y. Joly, J. C. Knight, W. J. Wadsworth, and P. S. J. Russell, "Continuous-wave tunable optical parametric generation in a photonic-crystal fiber," J. Opt. Soc. Am. B 22, 2505-2511 (2005).
    [CrossRef]
  7. N. J. Smith and N. J. Doran, "Modulational instabilities in fibers with periodic dispersion management," Opt. Lett. 21, 570-2 (1996).
    [CrossRef] [PubMed]
  8. J. C. Bronski and J. N. Kutz, "Modulational stability of plane waves in nonreturn-to-zero communications systems with dispersion management," Opt. Lett. 21, 937-9 (1996).
    [CrossRef] [PubMed]
  9. S. G. Murdoch, R. Leonhardt, J. D. Harvey, and T. A. B. Kennedy, "Quasi-phase matching in an optical fiber with periodic birefringence," J. Opt. Soc. Am. B 14, 1816-1822 (1997).
    [CrossRef]
  10. E. Ciaramella and M. Tamburrini, "Modulation instability in long amplified links with strong dispersion compensation," IEEE Photon. Technol. Lett. 11, 1608-1610 (1999).
    [CrossRef]
  11. A. Kumar, A. Labruyere, and P. Tchofo Dinda, "Modulational instability in fiber systems with periodic loss compensation and dispersion management," Opt. Commun. 219, 221-239 (2003).
    [CrossRef]
  12. F. K. Abdullaev, S. A. Darmanyan, A. Kobyakov, and F. Lederer, "Modulational instability in optical fibers with variable dispersion," Phys. Lett. A 220, 213-218 (1996).
    [CrossRef]
  13. M. Karlsson, "Four-wave mixing in fibers with randomly varying zero-dispersion wavelength," J. Opt. Soc. Am. B 15, 2269-2275 (1998).
    [CrossRef]
  14. M. Farahmand and M. de Sterke, "Parametric amplification in presence of dispersion fluctuations," Opt. Express 12, 136-142 (2004).
    [CrossRef] [PubMed]
  15. B. Kibler, C. Billet, J. M. Dudley, R. S. Windeler, and G. Millot, "Effects of structural irregularities on modulational instability phase matching in photonic crystal fibers," Opt. Lett. 29, 1903-1905 (2004).
    [CrossRef] [PubMed]
  16. G. Cappellini and S. Trillo, "Third-order three-wave mixing in single-mode fibers: exact solutions and spatial instability effects," J. Opt. Soc. Am. B 8, 824-838 (1991).
    [CrossRef]
  17. K. L. Reichenbach and C. Xu, "The effects of randomly occurring nonuniformities on propagation in photonic crystal fibers," Opt. Express 13, 2799-2807 (2005).
    [CrossRef] [PubMed]
  18. D. Derickson, Fiber Optic Test and Measurement, 1st ed. (Prentice Hall, Upper Saddle River, NJ, 1998).
  19. A. Mussot, E. Lantz, A. Durecu-Legrand, C. Simonneau, D. Bayart, T. Sylvestre, and H. Maillotte, "Zerodispersion wavelength mapping in short single-mode optical fibers using parametric amplification," IEEE Photon. Technol. Lett. 18, 22-4 (2006).
    [CrossRef]
  20. G. K. L. Wong, A. Y. H. Chen, S. W. Ha, R. J. Kruhlak, S. G. Murdoch, R. Leonhardt, J. D. Harvey, and N. Y. Joly, "Characterization of chromatic dispersion in photonic crystal fibers using scalar modulation instability," Opt. Express 13, 8662-8670 (2005).
    [CrossRef] [PubMed]

2006 (1)

A. Mussot, E. Lantz, A. Durecu-Legrand, C. Simonneau, D. Bayart, T. Sylvestre, and H. Maillotte, "Zerodispersion wavelength mapping in short single-mode optical fibers using parametric amplification," IEEE Photon. Technol. Lett. 18, 22-4 (2006).
[CrossRef]

2005 (4)

2004 (3)

2003 (3)

A. Kumar, A. Labruyere, and P. Tchofo Dinda, "Modulational instability in fiber systems with periodic loss compensation and dispersion management," Opt. Commun. 219, 221-239 (2003).
[CrossRef]

S. Pitois and G. Millot, "Experimental observation of a new modulational instability spectral window induced by fourth-order dispersion in a normally dispersive single-mode optical fiber," Opt. Commun. 226, 415-22 (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, 2225-7 (2003).
[CrossRef] [PubMed]

1999 (1)

E. Ciaramella and M. Tamburrini, "Modulation instability in long amplified links with strong dispersion compensation," IEEE Photon. Technol. Lett. 11, 1608-1610 (1999).
[CrossRef]

1998 (1)

1997 (1)

1996 (3)

1991 (1)

1981 (1)

Abdullaev, F. K.

F. K. Abdullaev, S. A. Darmanyan, A. Kobyakov, and F. Lederer, "Modulational instability in optical fibers with variable dispersion," Phys. Lett. A 220, 213-218 (1996).
[CrossRef]

Bayart, D.

A. Mussot, E. Lantz, A. Durecu-Legrand, C. Simonneau, D. Bayart, T. Sylvestre, and H. Maillotte, "Zerodispersion wavelength mapping in short single-mode optical fibers using parametric amplification," IEEE Photon. Technol. Lett. 18, 22-4 (2006).
[CrossRef]

Billet, C.

Bronski, J. C.

Cappellini, G.

Chen, A. Y. H.

Ciaramella, E.

E. Ciaramella and M. Tamburrini, "Modulation instability in long amplified links with strong dispersion compensation," IEEE Photon. Technol. Lett. 11, 1608-1610 (1999).
[CrossRef]

Coen, S.

Darmanyan, S. A.

F. K. Abdullaev, S. A. Darmanyan, A. Kobyakov, and F. Lederer, "Modulational instability in optical fibers with variable dispersion," Phys. Lett. A 220, 213-218 (1996).
[CrossRef]

de Sterke, M.

Doran, N. J.

Dudley, J. M.

Durecu-Legrand, A.

A. Mussot, E. Lantz, A. Durecu-Legrand, C. Simonneau, D. Bayart, T. Sylvestre, and H. Maillotte, "Zerodispersion wavelength mapping in short single-mode optical fibers using parametric amplification," IEEE Photon. Technol. Lett. 18, 22-4 (2006).
[CrossRef]

Farahmand, M.

Ha, S. W.

Harvey, J. D.

Joly, N. Y.

Karlsson, M.

Kazovsky, L. G.

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

Kennedy, T. A. B.

Kibler, B.

Knight, J. C.

Kobyakov, A.

F. K. Abdullaev, S. A. Darmanyan, A. Kobyakov, and F. Lederer, "Modulational instability in optical fibers with variable dispersion," Phys. Lett. A 220, 213-218 (1996).
[CrossRef]

Kruhlak, R. J.

Kumar, A.

A. Kumar, A. Labruyere, and P. Tchofo Dinda, "Modulational instability in fiber systems with periodic loss compensation and dispersion management," Opt. Commun. 219, 221-239 (2003).
[CrossRef]

Kutz, J. N.

Labruyere, A.

A. Kumar, A. Labruyere, and P. Tchofo Dinda, "Modulational instability in fiber systems with periodic loss compensation and dispersion management," Opt. Commun. 219, 221-239 (2003).
[CrossRef]

Lantz, E.

A. Mussot, E. Lantz, A. Durecu-Legrand, C. Simonneau, D. Bayart, T. Sylvestre, and H. Maillotte, "Zerodispersion wavelength mapping in short single-mode optical fibers using parametric amplification," IEEE Photon. Technol. Lett. 18, 22-4 (2006).
[CrossRef]

Lederer, F.

F. K. Abdullaev, S. A. Darmanyan, A. Kobyakov, and F. Lederer, "Modulational instability in optical fibers with variable dispersion," Phys. Lett. A 220, 213-218 (1996).
[CrossRef]

Leonhardt, R.

Lin, C.

Maillotte, H.

A. Mussot, E. Lantz, A. Durecu-Legrand, C. Simonneau, D. Bayart, T. Sylvestre, and H. Maillotte, "Zerodispersion wavelength mapping in short single-mode optical fibers using parametric amplification," IEEE Photon. Technol. Lett. 18, 22-4 (2006).
[CrossRef]

Marhic, M. E.

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

Millot, G.

B. Kibler, C. Billet, J. M. Dudley, R. S. Windeler, and G. Millot, "Effects of structural irregularities on modulational instability phase matching in photonic crystal fibers," Opt. Lett. 29, 1903-1905 (2004).
[CrossRef] [PubMed]

S. Pitois and G. Millot, "Experimental observation of a new modulational instability spectral window induced by fourth-order dispersion in a normally dispersive single-mode optical fiber," Opt. Commun. 226, 415-22 (2003).
[CrossRef]

Murdoch, S. G.

Mussot, A.

A. Mussot, E. Lantz, A. Durecu-Legrand, C. Simonneau, D. Bayart, T. Sylvestre, and H. Maillotte, "Zerodispersion wavelength mapping in short single-mode optical fibers using parametric amplification," IEEE Photon. Technol. Lett. 18, 22-4 (2006).
[CrossRef]

Pearson, A. D.

Pitois, S.

S. Pitois and G. Millot, "Experimental observation of a new modulational instability spectral window induced by fourth-order dispersion in a normally dispersive single-mode optical fiber," Opt. Commun. 226, 415-22 (2003).
[CrossRef]

Reed, W. A.

Reichenbach, K. L.

Russell, P. S. J.

Russell, P. St. J.

Sbang, H. T.

Simonneau, C.

A. Mussot, E. Lantz, A. Durecu-Legrand, C. Simonneau, D. Bayart, T. Sylvestre, and H. Maillotte, "Zerodispersion wavelength mapping in short single-mode optical fibers using parametric amplification," IEEE Photon. Technol. Lett. 18, 22-4 (2006).
[CrossRef]

Smith, N. J.

Sylvestre, T.

A. Mussot, E. Lantz, A. Durecu-Legrand, C. Simonneau, D. Bayart, T. Sylvestre, and H. Maillotte, "Zerodispersion wavelength mapping in short single-mode optical fibers using parametric amplification," IEEE Photon. Technol. Lett. 18, 22-4 (2006).
[CrossRef]

Tamburrini, M.

E. Ciaramella and M. Tamburrini, "Modulation instability in long amplified links with strong dispersion compensation," IEEE Photon. Technol. Lett. 11, 1608-1610 (1999).
[CrossRef]

Tchofo Dinda, P.

A. Kumar, A. Labruyere, and P. Tchofo Dinda, "Modulational instability in fiber systems with periodic loss compensation and dispersion management," Opt. Commun. 219, 221-239 (2003).
[CrossRef]

Trillo, S.

Wadsworth, W. J.

Windeler, R. S.

Wong, G. K. L.

Wong, K. K. Y.

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

Xu, C.

IEEE Photon. Technol. Lett. (2)

E. Ciaramella and M. Tamburrini, "Modulation instability in long amplified links with strong dispersion compensation," IEEE Photon. Technol. Lett. 11, 1608-1610 (1999).
[CrossRef]

A. Mussot, E. Lantz, A. Durecu-Legrand, C. Simonneau, D. Bayart, T. Sylvestre, and H. Maillotte, "Zerodispersion wavelength mapping in short single-mode optical fibers using parametric amplification," IEEE Photon. Technol. Lett. 18, 22-4 (2006).
[CrossRef]

J. Opt. Soc. Am. B (4)

J. Sel. Top. Quantum. Electron. (1)

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

Opt. Commun. (2)

S. Pitois and G. Millot, "Experimental observation of a new modulational instability spectral window induced by fourth-order dispersion in a normally dispersive single-mode optical fiber," Opt. Commun. 226, 415-22 (2003).
[CrossRef]

A. Kumar, A. Labruyere, and P. Tchofo Dinda, "Modulational instability in fiber systems with periodic loss compensation and dispersion management," Opt. Commun. 219, 221-239 (2003).
[CrossRef]

Opt. Express (3)

Opt. Lett. (6)

Phys. Lett. A (1)

F. K. Abdullaev, S. A. Darmanyan, A. Kobyakov, and F. Lederer, "Modulational instability in optical fibers with variable dispersion," Phys. Lett. A 220, 213-218 (1996).
[CrossRef]

Other (1)

D. Derickson, Fiber Optic Test and Measurement, 1st ed. (Prentice Hall, Upper Saddle River, NJ, 1998).

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Figures (7)

Fig. 1.
Fig. 1.

Theoretical phase-matching curve for the high group-index mode (solid line). Superimposed as circles are the experimentally measured sideband wavelengths. Inset is the calculated dispersion.

Fig. 2.
Fig. 2.

Optical spectrum of light exiting the fiber with pump polarized parallel to the high-group index mode for four different pump wavelengths. The pump wavelengths are (a) 672.2 nm, (b) 671.3 nm, (c) 670.0 nm and (d) 667.6 nm. The pump power was 3.2 W.

Fig. 3.
Fig. 3.

Experimental relative conversion efficiencies of the sidebands, superimposed with the theoretical relative conversion efficiencies for stepwise periodic fluctuations with da·dL=±0.011%·m (dashed line), da·dL=±0.22%·m (solid line), and da·dL=±0.44%·m (dotted line).”

Fig. 4.
Fig. 4.

Ω3dB bandwidth as a function of the product da·dL for periodic dispersion fluctuations.

Fig. 5.
Fig. 5.

Example of fiber core diameter fluctuations for Lc =1 m.

Fig. 6.
Fig. 6.

Experimental relative conversion efficiencies of the sidebands, superimposed with theoretical relative conversion efficiencies for a random fluctuation with fluctuation parameters σ a =0.0031% and Lc =1 m.

Fig. 7.
Fig. 7.

Random fluctuation parameter space for constant relative conversion efficiency.

Equations (15)

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

d A p d z = 2 γ A a A s A p sin [ ϕ ( z ) ] α A p 2 ,
d A a d z = γ A s A p 2 sin [ ϕ ( z ) ] α A a 2 ,
d A s d z = γ A a A p 2 sin [ ϕ ( z ) ] α A s 2 ,
d ϕ d z = Δ β L ( z ) + γ ( 2 A p 2 A a 2 A s 2 ) + γ [ A p 2 ( A a A s + A s A a ) 4 A a A s ] cos [ ϕ ( z ) ] ,
ϕ ( z ) = 0 z Δ β L ( Ω , ξ ) d ξ + ϕ a + ϕ s 2 ϕ p ,
Δ β L ( Ω , z ) = β ( ω p + Ω , z ) + β ( ω p Ω , z ) 2 β ( ω p , z ) .
Δ β L ( Ω , z ) = n = 1 β 2 n ( ω p , z ) Ω 2 n ( 2 n ) ! .
d A d z = γ P exp ( α z ) A sin [ ϕ ( z ) ] α A 2 ,
d ϕ d z = Δ β L ( z ) + 2 γ P exp ( α z ) { 1 + cos [ ϕ ( z ) ] } ,
G ( Ω ) = α + 2 γ P L 0 L exp ( α z ) sin [ ϕ ( z ) ] d z .
RCE ( Ω ) = exp [ G ( Ω ) G ( 0 ) ] L .
ϕ ( z ) = ϕ ( 0 ) + 0 z Δ β L ( Ω , ξ ) d ξ ,
g ( Ω ) = 2 γ P L 0 L sin [ ϕ ( z ) ] d z .
L = L c ln ( U ) ,
C ( z ) exp ( z L c ) .

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