Abstract

Continuous-wave and quasi-cw operation of tunable optical parametric generation has been demonstrated in a photonic-crystal fiber. The frequency shift of the generated sidebands, which arise from modulation instability, depends strongly on the detuning of the pump from the fiber’s zero-dispersion wavelength. Over 30nm of sideband tunability has been demonstrated using a 300mW cw pump, and over 185nm of tunability using a 1.6W quasi-cw pump. Continuous wave and quasi-cw pumps eliminate the detrimental effects of pump–sideband walk-off. In the absence of walk-off it is the fluctuations in the index profile of the photonic-crystal fiber along its length that limit the tunable sideband range.

© 2005 Optical Society of America

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References

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  1. R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron.  QE-18, 1062–1072 (1982).
    [CrossRef]
  2. T. V. Andersen, K. M. Hilligsøe, C. K. Nielsen, J. Thøgersen, K. P. Hansen, S. R. Keiding, and J. J. Larsen, “Continuous-wave wavelength conversion in a photonic crystal fiber with two zero-dispersion wavelengths,” Opt. Express  12, 4113–4122 (2004).
    [CrossRef] [PubMed]
  3. C. J. S. de Matos, J. R. Taylor, and K. P. Hansen, “Continuous-wave, totally fiber integrated optical parametric oscillator using holey fiber,” Opt. Lett.  29, 983–985 (2004).
    [CrossRef] [PubMed]
  4. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed., Optics and Photonics Series (Academic, 2001).
  5. 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]
  6. J. E. Sharping, M. Fiorention, A. Coker, P. Kumar, and R. S. Windeler, “Four-wave mixing in a microstructure fiber,” Opt. Lett.  26, 1048–1050 (2001).
    [CrossRef]
  7. A. Yariv, Optical Electronics in Modern Communications, 5th ed., The Oxford Series in Electrical and Computer Engineering (Oxford U. Press, 1997).
  8. 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]
  9. S. Trillo and S. Wabnitz, “Dynamics of the nonlinear modulational instability in optical fibers,” Opt. Lett.  16, 986–988 (1991).
    [CrossRef] [PubMed]
  10. F. Matera, A. Mecozzi, M. Romagnoli, and M. Settembre, “Sideband instability induced by periodic power variation in long-distance fiber links,” Opt. Lett.  18, 1499–1501 (1993).
    [CrossRef] [PubMed]
  11. N. J. Smith and N. J. Doran, “Modulational instabilities in fibers with periodic dispersion management,” Opt. Lett.  21, 570–572 (1996).
    [CrossRef] [PubMed]
  12. J. C. Bronski and J. N. Kutz, “Modulational stability of plane waves in nonreturn-to-zero communications systems with dispersion management,” Opt. Lett.  21, 937–939 (1996).
    [CrossRef] [PubMed]
  13. S. G. Murdoch, M. D. Thomson, R. Leonhardt, and J. D. Harvey, “Quasi-phase-matched modulation instability in birefringent fibers,” Opt. Lett.  22, 682–684 (1997).
    [CrossRef] [PubMed]
  14. 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]
  15. M. Karlsson, “Four-wave mixing in fibers with randomly varying zero-dispersion wavelength,” J. Opt. Soc. Am. B  15, 2269–2275 (1998).
    [CrossRef]
  16. M. Farahmand and M. de Sterke, “Parametric amplification in presence of dispersion fluctuations,” Opt. Express  12, 136–142 (2004).
    [CrossRef] [PubMed]
  17. J. D. Harvey, R. Leonhardt, G. K. L. Wong, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “An optical parametric oscillator in the visible using PCF,” in Conference on Lasers and Electro-Optics, Vol. 89 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2003), paper CMR3.
  18. J. E. Sharping, M. Fiorentino, P. Kumar, and R. S. Windeler, “Optical parametric oscillator based on four-wave mixing in microstructure fiber,” Opt. Lett.  27, 1675–1677 (2002).
    [CrossRef]
  19. 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]

2005 (1)

2004 (4)

2002 (1)

2001 (1)

1998 (1)

1997 (2)

1996 (2)

1993 (1)

1991 (2)

1982 (1)

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron.  QE-18, 1062–1072 (1982).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed., Optics and Photonics Series (Academic, 2001).

Andersen, T. V.

Bjorkholm, J. E.

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron.  QE-18, 1062–1072 (1982).
[CrossRef]

Bronski, J. C.

Cappellini, G.

Chen, A. Y. H.

Coker, A.

de Matos, C. J. S.

de Sterke, M.

Doran, N. J.

Farahmand, M.

Fiorentino, M.

Fiorention, M.

Hansen, K. P.

Harvey, J. D.

Hilligsøe, K. M.

Karlsson, M.

Kazovsky, L. G.

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]

Keiding, S. R.

Kennedy, T. A. B.

Knight, J. C.

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]

J. D. Harvey, R. Leonhardt, G. K. L. Wong, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “An optical parametric oscillator in the visible using PCF,” in Conference on Lasers and Electro-Optics, Vol. 89 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2003), paper CMR3.

Kumar, P.

Kutz, J. N.

Larsen, J. J.

Leonhardt, R.

Marhic, M. E.

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]

Matera, F.

Mecozzi, A.

Murdoch, S. G.

Nielsen, C. K.

Romagnoli, M.

Russell, P. St. J.

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]

J. D. Harvey, R. Leonhardt, G. K. L. Wong, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “An optical parametric oscillator in the visible using PCF,” in Conference on Lasers and Electro-Optics, Vol. 89 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2003), paper CMR3.

Settembre, M.

Sharping, J. E.

Smith, N. J.

Stolen, R. H.

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron.  QE-18, 1062–1072 (1982).
[CrossRef]

Taylor, J. R.

Thøgersen, J.

Thomson, M. D.

Trillo, S.

Wabnitz, S.

Wadsworth, W. J.

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]

J. D. Harvey, R. Leonhardt, G. K. L. Wong, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “An optical parametric oscillator in the visible using PCF,” in Conference on Lasers and Electro-Optics, Vol. 89 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2003), paper CMR3.

Windeler, R. S.

Wong, G. K. L.

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]

J. D. Harvey, R. Leonhardt, G. K. L. Wong, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “An optical parametric oscillator in the visible using PCF,” in Conference on Lasers and Electro-Optics, Vol. 89 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2003), paper CMR3.

Wong, K. K. Y.

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]

Yariv, A.

A. Yariv, Optical Electronics in Modern Communications, 5th ed., The Oxford Series in Electrical and Computer Engineering (Oxford U. Press, 1997).

IEEE J. Quantum Electron. (1)

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron.  QE-18, 1062–1072 (1982).
[CrossRef]

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

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]

J. Opt. Soc. Am. B (3)

Opt. Express (2)

Opt. Lett. (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]

C. J. S. de Matos, J. R. Taylor, and K. P. Hansen, “Continuous-wave, totally fiber integrated optical parametric oscillator using holey fiber,” Opt. Lett.  29, 983–985 (2004).
[CrossRef] [PubMed]

S. G. Murdoch, M. D. Thomson, R. Leonhardt, and J. D. Harvey, “Quasi-phase-matched modulation instability in birefringent fibers,” Opt. Lett.  22, 682–684 (1997).
[CrossRef] [PubMed]

N. J. Smith and N. J. Doran, “Modulational instabilities in fibers with periodic dispersion management,” Opt. Lett.  21, 570–572 (1996).
[CrossRef] [PubMed]

J. C. Bronski and J. N. Kutz, “Modulational stability of plane waves in nonreturn-to-zero communications systems with dispersion management,” Opt. Lett.  21, 937–939 (1996).
[CrossRef] [PubMed]

J. E. Sharping, M. Fiorention, A. Coker, P. Kumar, and R. S. Windeler, “Four-wave mixing in a microstructure fiber,” Opt. Lett.  26, 1048–1050 (2001).
[CrossRef]

J. E. Sharping, M. Fiorentino, P. Kumar, and R. S. Windeler, “Optical parametric oscillator based on four-wave mixing in microstructure fiber,” Opt. Lett.  27, 1675–1677 (2002).
[CrossRef]

S. Trillo and S. Wabnitz, “Dynamics of the nonlinear modulational instability in optical fibers,” Opt. Lett.  16, 986–988 (1991).
[CrossRef] [PubMed]

F. Matera, A. Mecozzi, M. Romagnoli, and M. Settembre, “Sideband instability induced by periodic power variation in long-distance fiber links,” Opt. Lett.  18, 1499–1501 (1993).
[CrossRef] [PubMed]

Other (3)

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed., Optics and Photonics Series (Academic, 2001).

A. Yariv, Optical Electronics in Modern Communications, 5th ed., The Oxford Series in Electrical and Computer Engineering (Oxford U. Press, 1997).

J. D. Harvey, R. Leonhardt, G. K. L. Wong, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “An optical parametric oscillator in the visible using PCF,” in Conference on Lasers and Electro-Optics, Vol. 89 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2003), paper CMR3.

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Figures (11)

Fig. 1
Fig. 1

Scanning electron microscope image of the photonic-crystal fiber used in this paper. The gray regions are fused silica; the black regions are air.

Fig. 2
Fig. 2

Modulation instability phase-matching diagram for a photonic-crystal fiber with a core diameter of 1.540 μ m , an effective air-filling fraction of 70%, and a pump power of 1.6 W . Inset, dispersion of the fiber as a function of wavelength.

Fig. 3
Fig. 3

Sideband wavelength as a function of pump wavelength around the zero-dispersion wavelength of a photonic-crystal fiber, with a core diameter of 1.540 μ m , an effective air-filling fraction of 70%, and a pump power of 1.6 W . Inset, dispersion of the fiber as a function of wavelength.

Fig. 4
Fig. 4

Sideband gain bandwidth as a function of pump wavelength for the same parameters as the phase-matching curve of Fig. 3.

Fig. 5
Fig. 5

Walk-off between the pump and sidebands for the phase-matching curve of Fig. 3.

Fig. 6
Fig. 6

Quasi-matching gain curve and phase evolution for a 50 THz modulation instability sideband in a photonic-crystal fiber with a periodic stepwise fluctuation in its core diameter. (a) fluctuation period 10 cm , fluctuation magnitude 1%; (b) fluctuation period 10 cm , fluctuation magnitude 3%; (c) fluctuation period 30 cm , fluctuation magnitude 1%. The fiber parameters are the same as those of Fig. 3.

Fig. 7
Fig. 7

Core diameter fluctuation required to reduce modulation instability gain by a factor of two as a function of sideband frequency shift. The fiber parameters are the same as those of Fig. 3.

Fig. 8
Fig. 8

Experimental measured sideband wavelengths as a function of pump wavelength for the high group-index mode (circles), and low group-index mode (squares). The pump power used was 1.6 W (quasi-cw). The solid curves are the theoretical sidebands wavelengths predicted by Eq. (7) for an effective core diameter of 1.540 μ m (high group-index mode), and 1.546 μ m (low group-index mode). The effective air filling fraction is 70%.

Fig. 9
Fig. 9

Spectrum of light exiting the fiber for pump wavelengths (i) 681.5, (ii) 682.5, and (iii) 683.25 nm (pump polarized parallel to the high group-index mode). The pump power used was 1.6 W (quasi-cw).

Fig. 10
Fig. 10

Experimental measured sideband wavelengths as a function of pump wavelength for the low group-index mode (circles). The cw power of the pump was 300 mW . The solid curves are the theoretical sidebands wavelengths predicted by Eq. (7) for an effective core diameter of 1.546 μ m (low group-index mode). The effective air-filling fraction is 70%.

Fig. 11
Fig. 11

Spectrum of light exiting the fiber for pump wavelengths of 683.25 nm (pump polarized parallel to the low group-index mode). The cw power of the pump was 300 mW .

Equations (13)

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

γ = n 2 ω 0 c A eff ,
d A p d z = 2 γ A a A s A p sin [ ϕ ( z ) ] ,
d A a d z = γ A s A p 2 sin [ ϕ ( z ) ] ,
d A s d z = γ A a A p 2 sin [ ϕ ( z ) ] ,
d ϕ d z = Δ β L + 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 ) = Δ β L z + ϕ a + ϕ s 2 ϕ p ,
Δ β L = β ( ω p + Ω ) + β ( ω p Ω ) 2 β ( ω p ) ,
d ϕ d z = Δ β L ( Ω ) + 2 γ P + 2 γ P cos ( ϕ ) .
G ( Ω , z ) = 2 γ P 1 z 0 z sin [ ϕ ( ξ ) ] d ξ .
ϕ ( 0 ) = cos 1 [ Δ β L ( Ω ) 2 γ P 2 γ P ] .
Δ β L ( Ω ) + 2 γ P = 0 .
Δ k 1 L 1 + Δ k 2 L 2 = 2 n π ,
( T 1 Γ 1 + T 2 Γ 2 ) tan 2 [ ϕ ( 0 ) 2 ] + ( Γ 1 Γ 2 Γ 2 Γ 1 ) T 1 T 2 tan [ ϕ ( 0 ) 2 ] + ( Γ 1 T 1 + Γ 2 T 2 ) = 0 ,

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