Abstract

We propose and demonstrate the use of narrow band optical parametric amplification for tunable slow and fast light propagation in optical fibers. The parametric gain is coupled to the Raman process which changes the gain value moderately but modifies the gain spectral shape. Consequently, the delay is enhanced at short wavelengths while it is moderated at long wavelengths. The maximum delay and tuning range can be optimized with respect to each other considering saturation effects in long fibers. The proposed scheme offers tunable delay in the presence of gain and with a bandwidth which is sufficiently wide to process digital data streams at tens of Gbit/s rates as well as picoseconds pulses.

© 2005 Optical Society of America

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References

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CLEO 2005

J. Mork, R. Kjaer, M. van der Poerl,L. Oxwenloewe and K. Yvind, "Experimental demonstration and theoretical analysis of slow light in a semiconductor waveguide at GHz frequencies,�?? in Proceedings of CLEO 2005 Paper number CMCC5 (2005).

CLEO'05

J.E. Sharping, Y. Okawachi, J. van Howe, C. Xu and A. Gaeta, " All-optical tunable, nanosecond delay using wavelength conversion and fiber dispersion,�?? in proceedings of CLEO'05, paper CTuT1 (2005).

Electron. Lett.

R.S. Tucker, P.C. Ku and C.J. Chang-Hasnain, "Delay �??bandwidth product and storage density in slow-light optical buffers,�?? Electron. Lett. 41, 208-209 (2005).
[CrossRef]

IEEE 91

C.J. Chang-Hasnian, P.C. Ku, J. Kim, and S.L. Chuang, "Variable optical buffer using slow light in semiconductor nanostructures,�?? in Proceedings of IEEE 91 11, 1884-1897 (2003).
[CrossRef]

IEEE Photonics Technol. Lett.

H Kidorf, K. Rottwitt, M. Nissov, M. Ma and E.Rabarijaona, " Pump interactions in a 100-nm bandwidth Raman amplifier,�?? IEEE Photonics Technol. Lett. 11, 530-532 (1999).
[CrossRef]

IEEE. J. Sel. Top. Quantum Electron.

J. Hansryd, P. A. Andrekson, M. Westlund, L. Lie and P.O. Hedekvist, "Fiber-based optical parametric amplifiers and their applications ,�?? IEEE. J. Sel. Top. Quantum Electron. 8, 506-520 (2002).
[CrossRef]

M. Xiao, "Novel linear and nonlinear optical properties of electromagnetically induced transparency systems,�?? IEEE. J. Sel. Top. Quantum Electron. 9, 86-92 (2003).
[CrossRef]

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. Lightwave Technol.

J. Ligthwave Technol.

M.C. Ho, K. Uesaka, M. E. Marhic, Y. Akasaka, L. G. Kazovsky, " 200 nm bandwidth fiber optical amplifier combining parametric and Raman gain" J. Ligthwave Technol. 19, 977-999 (2001).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys.

J. Kim, S.L. Chuang, P.C. Ku and C.J. Chang-Hasnian, "Slow light using semiconductor quantum dots,�?? J. Phys. 16, S3727-S3735 (2004).

Nature

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]

Opt. Commun.

D. Dahan and G. Eisenstein, "The properties of amplified spontaneous emission noise in saturated fiber Raman amplifiers operating with CW signals," Opt. Commun. 236, 279-288 (2004).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

Y. Okawachi, M.S. Bigelow, J.E. Sharping ,Z.M.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 Art. No. 153902 (2005).
[CrossRef] [PubMed]

Other

R.W. Boyd and D. J. Gauthier., "'Slow' and 'Fast' light ,�?? Ch 6 in Progress in Optics 43, E. Wolf, Ed. (Elsevier , Amsterdam, 2002), 497-530.
[CrossRef]

G. P. Agrawal, �??Nonlinear Fiber Optics�?? 2nd Ed., (Academic Press, San Diego CA, 1995).

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Figures (15)

Fig. 1.
Fig. 1.

system set up : MZ (Mach Zendher), IM (Intensity modulation), EDFAs (Erbium Doped Fiber Amplifiers), OBPF (Optical Band Pass Filter), OSA (Optical Spectrum Analyzer)

Fig. 2.
Fig. 2.

Phase mismatching as a function of detuning for β 2=8.73 10-28 s2/m and β 4=-5.6 10-55 s4/m at λp =1530 nm

Fig. 3.
Fig. 3.

Calculated OPA gain and induced time delay spectra at (a) the short and (b) long wavelength region using a 200 m long DSF for β 2=8.73 10-28 s2/m and β 4=-5.6 10-55 s4/m at λp =1530 nm

Fig. 4.
Fig. 4.

Calculated Raman assisted OPA gain and induced time delay spectra at the (a) short and (b) long wavelength region using a 200 m long DSF for β 2=3.95 10-28 s2/m and β 4=-5.7 10-55 s4/m at λp =1535 nm

Fig. 5.
Fig. 5.

Calculated OPA gain and induced time delay spectra with the Raman effect omitted artificially. (a) short and (b) long wavelength region using a 200 m long DSF with for β 2=3.95 10-28 s2/m and β 4=-5.7 10-55 s4/m at λp =1535 nm

Fig. 6.
Fig. 6.

(a) Experimental ASE power spectra and (b) Theoretical gain spectra for 200 m DSF using different pump wavelengths.

Fig 7.
Fig 7.

(a) Experimental ASE power spectra and (b) theoretical gain spectra for 200 m DSF using different pump power levels with λp =1535nm. The gain is evaluated at λs =1428.6 nm

Fig 8.
Fig 8.

Pulse position for different gain values at λs =1448.8 nm using a 200 m long DSF (a) Experimental results (b) Simulated results

Fig 9.
Fig 9.

Experimental traces for different gain values at λs =1428.6 nm using different DSF lengths :(a) 200 m , (b) 500 m, (c) 1000m, (d) 2000 m The curves indexes represent different gain values which are summarized in Fig. 10

Fig. 10.
Fig. 10.

Measured delay as a function of gain for different fiber lengths at λs =1428.6 nm

Fig. 11.
Fig. 11.

Calculated delay as a function of gain for different fiber lengths. (a) λs =1428.6 nm, (b) λs =1377.1 nm

Fig. 12.
Fig. 12.

(a) Theoretical gain spectra using 200 m and 2000 m long DSF, (b) Group index variations along the fiber at λs and λ peak

Fig. 13:
Fig. 13:

(a) ASE power spectra for different pump wavelengths (b) The corresponding signals at λs =1428.6 nm

Fig. 14.
Fig. 14.

Fast light observation at λs =1600 nm using (a) 2000 m long DSF (b) 3000 m long DSF

Fig. 15.
Fig. 15.

Calculated negative delay as a function of gain for different fiber lengths. (a) λs =1658.3 nm, (b) λs =1721.1 nm

Tables (1)

Tables Icon

Table 1. Gain and delay values achieved at λs =1428.6 nm using different lengths of DSF

Equations (17)

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{ A p z = j γ ( A p 2 + 2 A s 2 + 2 A i 2 ) A p + j 2 γ A p * A s A i exp ( j Δ kz ) A s z = j γ ( 2 A p 2 + 2 A s 2 + 2 A i 2 ) A s + j γ A p 2 A p * exp ( j Δ kz ) g R 2 A p 2 A i z = j γ ( 2 A p 2 + 2 A s 2 + 2 A i 2 ) A i + j γ A p 2 A p * exp ( j Δ kz ) g R 2 + A p 2 A i A s
A p ( z ) = P 0 exp ( j γ P 0 z )
{ A s z = j 2 γ P 0 A s + j γ P 0 A i * exp ( j ( 2 γ P 0 Δ k ) z ) g R 2 P 0 A s A i z = j 2 γ P 0 A i + j γ P 0 A s * exp ( j ( 2 γ P 0 Δ k ) z ) g R 2 P 0 A i
{ g s = j γ P 0 A i * A s exp ( j ( 2 γ P 0 Δ k ) z ) g R 2 P 0 g i = j γ P 0 A s * A i exp ( j ( 2 γ P 0 Δ k ) z ) g R 2 P 0
Δ n g = c ( d Im ( g s , i ) d ω )
Δ T = 0 L Δ n g ( z ) c dz
{ A s ( z ) = A s ( 0 ) ( cosh ( gz ) + ( g R 2 P 0 + j ( γ P 0 + Δ k 2 ) ) sinh ( gz ) g ) exp ( j ( Δ k 2 γ P 0 2 ) z ) A i ( z ) = j γ P 0 g A s * ( 0 ) sinh ( gz ) exp ( j ( Δ k 2 γ P 0 2 ) z )
g 2 = { ( γ P 0 ) 2 ( γ P 0 + Δ k 2 ) 2 + g R P 0 ( g R P 0 4 j ( γ P 0 + Δ k 2 ) ) }
g s ( z ) = ( γ P 0 ) 2 g sinh ( gz ) ( cosh ( gz ) + ( g R 2 P 0 + j ( γ P 0 + Δ k 2 ) ) sinh ( gz ) g ) g R 2 P 0
g i ( z ) = g cosh ( gz ) sinh ( gz ) + j ( γ P 0 + Δ k 2 )
g 2 = { ( γ P 0 ) 2 ( γ P 0 + Δ k 2 ) 2 }
g s ( z ) = g s r ( z ) + j g s i ( z )
g s r = ( γ P 0 ) 2 g sinh ( gz ) cosh ( gz ) 1 + ( γ P 0 g sinh ( gz ) ) 2
g s i = ( γ P 0 + Δ k 2 ) ( γ P 0 g sinh ( gz ) ) 2 1 + ( γ P 0 g sinh ( gz ) ) 2
Δ k = β 2 ( ω ω p ) 2 + β 4 ( ω ω p ) 4 / 12
g s i ( γ P 0 + Δ k 2 )
Δ n g c 2 d Δ k = C ( β 2 ( ω ω p ) + β 4 ( ω ω p ) 3 / 6 )

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