Abstract

We theoretically study parametric amplification in highly birefringent optical fibers and show that large tunable optical delay or advancement can be achieved via slow and fast light propagation. We provide a clear derivation of the formula for the optical delay that originates from the imaginary part of the parametric gain. We also perform numerical simulations in both normal and anomalous dispersion regimes. In the latter case, results show that large nanosecond optical delay could, in principle, be obtained at 1550nm in a 1-km-long polarization-maintaining fiber. We further demonstrate that the optical delay and advancement rely on a group-velocity locking between the two cross-polarized signal and idler pulses.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J.B.Khurgin and R.S.Tucker eds., Slow Light: Science and Applications (CRC Press, 2009).
  2. R. Boyd, “Slow and fast light: fundamentals and applications,” J. Mod. Opt. 56, 1908-1915 (2009).
    [Crossref]
  3. L. Thévenaz, “Slow and fast light in optical fibres,” Nat. Photon. 2, 474-481 (2008).
    [Crossref]
  4. D. Dahan and G. Eisenstein, “Tunable all optical delay via slow and fast light propagation in a Raman assisted fiber optical parametric amplifier: a route to all optical buffering,” Opt. Express 13, 6234-6249 (2005).
    [Crossref] [PubMed]
  5. E. Shumakher, A. Willinger, R. Blit, D. Dahan, and G. Eisenstein, “Large tunable delay with low distortion of 10 Gbit/s data in a slow light system based on narrow band fiber parametric amplification,” Opt. Express 14, 8540-8545 (2006).
    [Crossref] [PubMed]
  6. L. Schenato, M. Santagiustina, and C. G. Someda, “Fundamental and random birefringence limitations to delay in slow light fiber parametric amplification,” J. Lightwave Technol. 26, 3721-3726(2008).
    [Crossref]
  7. Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
    [Crossref] [PubMed]
  8. K. Y. Song, M. G. Herráez, and L. Thévenaz, “Observation of pulse delaying and advancement in optical fibers using stimulated Brillouin scattering,” Opt. Express 13, 82-88 (2005).
    [Crossref] [PubMed]
  9. J. E. Sharping, Y. Okawachi, and A. L. Gaeta, “Wide bandwidth slow light using a Raman fiber amplifier,” Opt. Express 13, 6092-6098 (2005).
    [Crossref] [PubMed]
  10. E. Seve, G. Millot, S. Wabnitz, T. Sylvestre, and H. Maillotte, “Generation of vector dark-soliton trains by induced modulational instability in a highly birefringent fiber,” J. Opt. Soc. Am. B 16, 1642-1650 (1999).
    [Crossref]
  11. R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18, 1062-1072 (1982).
    [Crossref]
  12. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).
  13. A. T. Nguyen, K. P. Huy, E. Brainis, P. Mergo, J. Wojcik, T. Nasilowski, J. Van Erps, H. Thienpont, and S. Massar, “Enhanced cross phase modulation instability in birefringent photonic crystal fibers in the anomalous dispersion regime,” Opt. Express 14, 8290-8297 (2006).
    [Crossref] [PubMed]
  14. A. Ortigosa-Blanch, J. C. Knight, W. J. Wadsworth, J. Arriaga, B. J. Mangan, T. A. Birks, and P. St. J. Russell, “Highly birefringent photonic crystal fibers,” Opt. Lett. 25, 1325-1327 (2000).
    [Crossref]
  15. A. Willinger, E. Shumakher, and G. Eisenstein, “On the roles of polarization and Raman-assisted phase matching in narrowband fiber parametric amplifiers,” J. Lightwave Technol. 26, 2260-2268 (2008).
    [Crossref]
  16. T. Torounidis, P. A. Andrekson, and B.-E. Olsson, “Fiber-optical parametric amplifier with 70 dB gain,” IEEE Photon. Technol. Lett. 18, 1194-1196 (2006).
    [Crossref]
  17. R. W. Boyd, D. J. Gauthier, A. L. Gaeta, and A. E. Willner, “Maximum time delay achievable on propagation through a slow-light medium,” Phys. Rev. A 71, 023801 (2005).
    [Crossref]
  18. S. G. Murdoch, R. Leonhardt, and J. D. Harvey, “Polarization modulation instability in weakly birefringent fibers,” Opt. Lett. 20, 866-868 (1995).
    [Crossref] [PubMed]

2009 (1)

R. Boyd, “Slow and fast light: fundamentals and applications,” J. Mod. Opt. 56, 1908-1915 (2009).
[Crossref]

2008 (3)

2006 (3)

2005 (5)

2000 (1)

1999 (1)

1995 (1)

1982 (1)

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

Agrawal, G. P.

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

Andrekson, P. A.

T. Torounidis, P. A. Andrekson, and B.-E. Olsson, “Fiber-optical parametric amplifier with 70 dB gain,” IEEE Photon. Technol. Lett. 18, 1194-1196 (2006).
[Crossref]

Arriaga, J.

Bigelow, M. S.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[Crossref] [PubMed]

Birks, T. A.

Bjorkholm, J. E.

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

Blit, R.

Boyd, R.

R. Boyd, “Slow and fast light: fundamentals and applications,” J. Mod. Opt. 56, 1908-1915 (2009).
[Crossref]

Boyd, R. W.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[Crossref] [PubMed]

R. W. Boyd, D. J. Gauthier, A. L. Gaeta, and A. E. Willner, “Maximum time delay achievable on propagation through a slow-light medium,” Phys. Rev. A 71, 023801 (2005).
[Crossref]

Brainis, E.

Dahan, D.

Eisenstein, G.

Gaeta, A. L.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[Crossref] [PubMed]

J. E. Sharping, Y. Okawachi, and A. L. Gaeta, “Wide bandwidth slow light using a Raman fiber amplifier,” Opt. Express 13, 6092-6098 (2005).
[Crossref] [PubMed]

R. W. Boyd, D. J. Gauthier, A. L. Gaeta, and A. E. Willner, “Maximum time delay achievable on propagation through a slow-light medium,” Phys. Rev. A 71, 023801 (2005).
[Crossref]

Gauthier, D. J.

R. W. Boyd, D. J. Gauthier, A. L. Gaeta, and A. E. Willner, “Maximum time delay achievable on propagation through a slow-light medium,” Phys. Rev. A 71, 023801 (2005).
[Crossref]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[Crossref] [PubMed]

Harvey, J. D.

Herráez, M. G.

Huy, K. P.

Knight, J. C.

Leonhardt, R.

Maillotte, H.

Mangan, B. J.

Massar, S.

Mergo, P.

Millot, G.

Murdoch, S. G.

Nasilowski, T.

Nguyen, A. T.

Okawachi, Y.

J. E. Sharping, Y. Okawachi, and A. L. Gaeta, “Wide bandwidth slow light using a Raman fiber amplifier,” Opt. Express 13, 6092-6098 (2005).
[Crossref] [PubMed]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[Crossref] [PubMed]

Olsson, B.-E.

T. Torounidis, P. A. Andrekson, and B.-E. Olsson, “Fiber-optical parametric amplifier with 70 dB gain,” IEEE Photon. Technol. Lett. 18, 1194-1196 (2006).
[Crossref]

Ortigosa-Blanch, A.

Russell, P. St. J.

Santagiustina, M.

Schenato, L.

Schweinsberg, A.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[Crossref] [PubMed]

Seve, E.

Sharping, J. E.

J. E. Sharping, Y. Okawachi, and A. L. Gaeta, “Wide bandwidth slow light using a Raman fiber amplifier,” Opt. Express 13, 6092-6098 (2005).
[Crossref] [PubMed]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[Crossref] [PubMed]

Shumakher, E.

Someda, C. G.

Song, K. Y.

Stolen, R. H.

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

Sylvestre, T.

Thévenaz, L.

Thienpont, H.

Torounidis, T.

T. Torounidis, P. A. Andrekson, and B.-E. Olsson, “Fiber-optical parametric amplifier with 70 dB gain,” IEEE Photon. Technol. Lett. 18, 1194-1196 (2006).
[Crossref]

Van Erps, J.

Wabnitz, S.

Wadsworth, W. J.

Willinger, A.

Willner, A. E.

R. W. Boyd, D. J. Gauthier, A. L. Gaeta, and A. E. Willner, “Maximum time delay achievable on propagation through a slow-light medium,” Phys. Rev. A 71, 023801 (2005).
[Crossref]

Wojcik, J.

Zhu, Z.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[Crossref] [PubMed]

IEEE J. Quantum Electron. (1)

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

IEEE Photon. Technol. Lett. (1)

T. Torounidis, P. A. Andrekson, and B.-E. Olsson, “Fiber-optical parametric amplifier with 70 dB gain,” IEEE Photon. Technol. Lett. 18, 1194-1196 (2006).
[Crossref]

J. Lightwave Technol. (2)

J. Mod. Opt. (1)

R. Boyd, “Slow and fast light: fundamentals and applications,” J. Mod. Opt. 56, 1908-1915 (2009).
[Crossref]

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

Nat. Photon. (1)

L. Thévenaz, “Slow and fast light in optical fibres,” Nat. Photon. 2, 474-481 (2008).
[Crossref]

Opt. Express (5)

Opt. Lett. (2)

Phys. Rev. A (1)

R. W. Boyd, D. J. Gauthier, A. L. Gaeta, and A. E. Willner, “Maximum time delay achievable on propagation through a slow-light medium,” Phys. Rev. A 71, 023801 (2005).
[Crossref]

Phys. Rev. Lett. (1)

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[Crossref] [PubMed]

Other (2)

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

J.B.Khurgin and R.S.Tucker eds., Slow Light: Science and Applications (CRC Press, 2009).

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 (8)

Fig. 1
Fig. 1

(a) Evolution of the complex parameters g s and g i versus the angular frequency detuning Ω: the real part (parametric gain) as solid bell-shaped curves and the imaginary part as dashed curves. (b) Slow-light optical delay Δ t N L (bold solid curve) and linear optical delay Δ t L (dashed curve) due to birefringence and dispersion in the pump mean reference frame, and total delay δ t = Δ t L + Δ t N L (solid curve). Parameters are pump wavelength λ p = 532 nm , β 2 = 65.69 × 10 27 s 2 · m 1 , δ = 2 ps · m 1 , γ = 45 × 10 3 W 1 · m 1 , P = 100 W , and L = 10 m .

Fig. 2
Fig. 2

Numerical simulations. (a) Output intensity pulse profiles in normalized units and (b) optical delay versus the propagation distance, for the signal and for the spontaneously generated idler in the nonlinear regime as solid and dotted curves, respectively. For comparison, the dashed curve indicates the signal position in the linear regime. Parameters are the same as in Fig. 1.

Fig. 3
Fig. 3

(a) Optical delay (left, squares) and pulse duration (right, open circles) versus the pump power and for a fiber length of 10 m . (b) Optical delay versus the propagation distance for four different pump powers. Dashed curves in both frames show comparison with Eq. (4).

Fig. 4
Fig. 4

Parametric optical delay as a function of both the pump power and the fiber length. Comparison of numerical simulations from CNLSEs (color map) with analytical predictions from Eq. (4) (mesh black curves).

Fig. 5
Fig. 5

Optical delay (color bar) generated by vector optical parametric amplification in a polarization-maintaining single-mode fiber versus both the pump power and the fiber length. Param eters are: signal wavelength λ s = 1550 nm , β 2 = 60 × 10 27 s 2 · m 1 , δ = 2 ps · m 1 , and γ = 5 × 10 3 W 1 · m 1 .

Fig. 6
Fig. 6

Comparison between output pulses with and without the Raman scattering for two angular frequency detuning Ω showing the beneficial effect of Raman contribution to the parametric optical delay. (a)  Ω / 2 π = 3.5 THz and (b)  Ω / 2 π = 15 THz . Dashed curves, input signal pulse; dotted curves, output signal in the linear regime; solid red (left) and green (right) curves, output signal in the nonlinear regime without and with Raman contribution, respectively.

Fig. 7
Fig. 7

Analytical prediction for the gain (in decibels) in function of the pump power and the fiber length ( 10 dB per curve).

Fig. 8
Fig. 8

Optical delay (right, solid curves) and broadening coefficient (left, dashed curves) versus the parametric gain in decibels and for propagation distances ranging from 500 m (green curves) to 2 km (red curves). The blue curves correspond to 1 km of propagation. The input signal pulse duration is 1 ns .

Equations (8)

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

A s x z = i γ P 3 A i y * exp ( i κ z ) , A i y z = i γ P 3 A s x * exp ( i κ z ) ,
g s = ( γ P 3 ) 2 1 g sinh ( g z ) cosh ( g z ) + i κ 2 g sinh ( g z ) , g i = g cosh ( g z ) sinh ( g z ) i κ 2 ,
g = ( γ P 3 ) 2 ( κ 2 ) 2
Δ n g s , i = c m ( g s , i ) Ω ,
Δ t N L s , i = 0 L Δ n g s , i ( z ) c d z ,
Δ t N L s = Δ t N L i = ( β 2 Ω + δ 2 ) L .
Δ t N L s = Δ t N L i = L ( δ 2 ) 2 β 2 γ P .
R = T T 0 = 1 + G L ( Δ Ω T 0 ) 2 ,

Metrics