Abstract

Based on cascading nonlinear interactions of second harmonic generation (SHG) and difference frequency generation (DFG), we present a novel scheme to control the group velocity of femtosecond pulse in MgO doped periodically poled lithium niobate crystal. Group velocity of tunable signal pulse can be controlled by another pump beam within a wide bandwidth of 180nm. Fractional advancement of 2.4 and fractional delay of 4 are obtained in our simulations.

© 2008 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
  5. M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, "The speed of information in a ’fast-light’ optical medium," Nature 425, 695-698 (2003).
    [CrossRef] [PubMed]
  6. M. O. Scully, "Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas," Phys. Rev. Lett. 82, 5229-5232 (1999).
    [CrossRef]
  7. L. J. Wang, A. Kuzmich, A. Dogariu, "Gain-assisted superluminal light propagation," Nature 406, 277-279 (2000).
    [CrossRef] [PubMed]
  8. YuriiA. Vlasov1, Martin O’Boyle1, Hendrik F. Hamann1 & Sharee J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
    [CrossRef]
  9. Pei-Cheng Ku, Forrest Sedgwick, Connie J. Chang-Hasnain, Phedon Palinginis, Tao Li, Hailin Wang, Shu-Wei Chang and Shun-Lien Chuang, "Slow light in semiconductor quantum wells," Opt. Lett. 29, 2291-2293 (2004).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  14. Y. Okawachi, M.S. Bigelow, J.E. Sharping, Z. Zhu, A. Schweinsberg, D.J. Gautheir, 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]
  15. Z. Zhu, D. J. Gauthier, Y. Okawachi, J. E. Sharping, A. L. Gaeta, R. W. Boyd, and A. E. Willner, "Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber," J.Opt. Soc. Am. B 22, 2378-2384 (2005).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2007 (1)

Daniel J. Gauthier. "Optical communications: Solitons go slow," Nature Photonics. 192-93 (2007)
[CrossRef]

2006 (4)

2005 (6)

Y. Okawachi, M.S. Bigelow, J.E. Sharping, Z. Zhu, A. Schweinsberg, D.J. Gautheir, 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]

Z. Zhu, D. J. Gauthier, Y. Okawachi, J. E. Sharping, A. L. Gaeta, R. W. Boyd, and A. E. Willner, "Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber," J.Opt. Soc. Am. B 22, 2378-2384 (2005).
[CrossRef]

K. Y. Song, M. G. Herr’aez, L. Th’evenaz, "Observation of pulse delaying and advancement in optical fibers using stimulated Brillouin scattering," Opt. Express 13, 82-88 (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]

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]

YuriiA. Vlasov1, Martin O’Boyle1, Hendrik F. Hamann1 & Sharee J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef]

2004 (2)

S. Ashihara, T. Shimura, K. Kuroda, Nan Ei Yu, S. Kurimura, K. Kitamura, Myoungsik Cha, and Takunori Taira, "Optical pulse compression using cascaded quadratic nonlinearities in periodically poled lithium niobate," Appl. Phys. Lett. 84, 1055-1057 (2004).
[CrossRef]

Pei-Cheng Ku, Forrest Sedgwick, Connie J. Chang-Hasnain, Phedon Palinginis, Tao Li, Hailin Wang, Shu-Wei Chang and Shun-Lien Chuang, "Slow light in semiconductor quantum wells," Opt. Lett. 29, 2291-2293 (2004).
[CrossRef] [PubMed]

2003 (3)

M. S. Bigelow MS, N. N. Lepeshkin, R. W. Boyd, "Superluminal and slow light propagation in a room temperature solid," Science 301, 200-202 (2003).
[CrossRef] [PubMed]

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, "The speed of information in a ’fast-light’ optical medium," Nature 425, 695-698 (2003).
[CrossRef] [PubMed]

M. S. Bigelow, N. N. Lepeshkin, R. W. Boyd, "Observation of Ultraslow Light Propagation in a Ruby Crystal at Room Temperature," Phys. Rev. Lett. 90, 113903 (2003).
[CrossRef] [PubMed]

2000 (1)

L. J. Wang, A. Kuzmich, A. Dogariu, "Gain-assisted superluminal light propagation," Nature 406, 277-279 (2000).
[CrossRef] [PubMed]

1999 (2)

M. O. Scully, "Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas," Phys. Rev. Lett. 82, 5229-5232 (1999).
[CrossRef]

L. V. Hau, S. E. Harris, Z. Dutton,and C. H. Behroozi, "Light speed reduction to 17 metres per second in an ultracold atomic gas," Nature 397, 594-598 (1999).
[CrossRef]

1997 (1)

Appl. Opt. (1)

Appl. Phys. Lett. (1)

S. Ashihara, T. Shimura, K. Kuroda, Nan Ei Yu, S. Kurimura, K. Kitamura, Myoungsik Cha, and Takunori Taira, "Optical pulse compression using cascaded quadratic nonlinearities in periodically poled lithium niobate," Appl. Phys. Lett. 84, 1055-1057 (2004).
[CrossRef]

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

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

Z. Zhu, D. J. Gauthier, Y. Okawachi, J. E. Sharping, A. L. Gaeta, R. W. Boyd, and A. E. Willner, "Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber," J.Opt. Soc. Am. B 22, 2378-2384 (2005).
[CrossRef]

Nature (4)

L. V. Hau, S. E. Harris, Z. Dutton,and C. H. Behroozi, "Light speed reduction to 17 metres per second in an ultracold atomic gas," Nature 397, 594-598 (1999).
[CrossRef]

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, "The speed of information in a ’fast-light’ optical medium," Nature 425, 695-698 (2003).
[CrossRef] [PubMed]

L. J. Wang, A. Kuzmich, A. Dogariu, "Gain-assisted superluminal light propagation," Nature 406, 277-279 (2000).
[CrossRef] [PubMed]

YuriiA. Vlasov1, Martin O’Boyle1, Hendrik F. Hamann1 & Sharee J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef]

Nature Photonics. (1)

Daniel J. Gauthier. "Optical communications: Solitons go slow," Nature Photonics. 192-93 (2007)
[CrossRef]

Opt. Express (4)

Opt. Lett. (2)

Phys. Rev. Lett. (3)

M. S. Bigelow, N. N. Lepeshkin, R. W. Boyd, "Observation of Ultraslow Light Propagation in a Ruby Crystal at Room Temperature," Phys. Rev. Lett. 90, 113903 (2003).
[CrossRef] [PubMed]

Y. Okawachi, M.S. Bigelow, J.E. Sharping, Z. Zhu, A. Schweinsberg, D.J. Gautheir, 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]

M. O. Scully, "Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas," Phys. Rev. Lett. 82, 5229-5232 (1999).
[CrossRef]

Science (2)

M. S. Bigelow MS, N. N. Lepeshkin, R. W. Boyd, "Superluminal and slow light propagation in a room temperature solid," Science 301, 200-202 (2003).
[CrossRef] [PubMed]

George M. Gehring, Aaron Schweinsberg, Christopher Barsi, Natalie Kostinski and Robert W. Boyd, "Observation of Backwards Pulse Propagation Through a Medium with a Negative Group Velocity," Science 312, 895-897 (2006).
[CrossRef] [PubMed]

Other (5)

M. S. Bigelow, Ultra-Slow and Superluminal Light Propagation in Solids at Room Temperature (PHD thesis, 2004), Chap. 6.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, 1995).

L. Brillouin, Wave propagation and group velocity (Academic Press, New York, 1960).

R.W. Boyd and D. J. Gauthier, "Slow and fast light," Progress in Optics 43, edited by E.Wolf, 497-529, (Elsevier, Amsterdam, 2002).

Yuping Chen, Zhimin Shi, Petros Zerom and Robert W. Boyd, "Slow Light with Gain Induced by Three Photon Effect in Strongly Driven Two-Level Atoms," in Slow and Fast Light 2006, Technical Digest (CD) (Optical Society of America, 2006), paper ME1.

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Figures (5)

Fig. 1
Fig. 1

Schematic of the SHG-DFG cascading process in periodically poled MgO doped lithium niobate crystal

Fig. 2.
Fig. 2.

Normalized pulse intensity of the interaction pulses. Dotted line (solid line) represents the input (output) pulse intensity. The central wavelength of the input pump (signal) pulse is 1550nm (1600nm) with the intensity of 50GW/cm2 (1GW/cm2). The group velocity mismatching between SH and the signal is 9.7227fs/mm, and the corresponding phase mismatching are Δ kpL=101.5π and Δ kcL=100π. Both widths of two pulses durations (FWHM) are 80fs. It can be seen that output signal pulse has been delayed for 120fs with the pulse of 38fs.

Fig. 3
Fig. 3

Demonstration of the group velocity control by changing pump intensity. The black curve is the input pulse and the green (blue and red) curve is the output intensity with input pump intensity at 0.1 GW/cm2 (100 GW/cm2). The red line refers to the advancement case due to negative GVM. The width (FWHM) of red, blue and green pulses is 18fs, 18fs and 150fs and the corresponding delay is -194fs, 326fs and 0fs respectively.

Fig. 4.
Fig. 4.

Time delay of the output signal as a function of the pump input peak intensity. The red and black lines represent the small (9.7227 fs/mm) and large (11.064 fs/mm) positive GVM, and the blue and green lines show the negative GVM of -22.188fs/mm and -11.364fs/mm. Fractional time delay (advancement) over unit (i.e. time delay more than 80fs) can be achieved when input pump intensity is larger than 10 GW/cm2 (20GW/cm2). The phase matching conditions above are Δ kpL=101.31π and Δ kcL=100π

Fig 5.
Fig 5.

Time delay and output signal intensity as a function of input signal wavelength. Solid line is time delay with different input signal wavelength and dashed line is the corresponding output intensity.

Equations (8)

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A p z = δ p A p t j 2 β 2 p 2 A p t 2 j ω p κ pp A p * A SH exp ( j Δ k p z ) α p 2 A p
A SH ∂z = δ SH A SH t j 2 β 2 SH 2 A SH t 2 j ω p κ pp A p A p exp ( j Δ k p z )
2 j ω p κ sc A s A c exp ( j Δ k c z ) α SH 2 A SH
A s z = j 2 β 2 s 2 A s t 2 j ω s κ sc A c * A SH exp ( j Δ k c z ) α s 2 A s
A c z = δ c A c t j 2 β 2 c 2 A c t 2 j ω c κ sc A s * A SH exp ( j Δ k c z ) α c 2 A c
Δ k p = β ( ω SH ) 2 β ( ω p ) 2 π Λ
Δ k c = β ( ω SH ) β ( ω s ) β ( ω c ) 2 π Λ
κ pp = 2 μ 0 cd eff n ( λ SH ) n ( λ p ) 2 A eff , κ sc = 2 μ 0 c d eff n ( λ SH ) n ( λ s ) n ( λ c ) A eff , d eff = 2 π d 31

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