Abstract

We present a general study of pulse amplification in silicon Raman amplifiers, with special emphasis on the effects of spectral compression and group delay due to the Raman gain dispersion. We use the undepleted-pump approxi mation to analytically calculate the dynamics of an arbitrary pulse spectra and find the temporal profile of the pulse at the amplifier’s output. We show that cw-pumped silicon waveguides are extremely inefficient in amplification of subpicosecond optical pulses but provide large net gains and controllable group delays for pulses with widths of 10ps.

© 2010 Optical Society of America

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References

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  1. B. Jalali, V. Raghunathan, D. Dimitropoulos, and O. Boyraz, IEEE J. Sel. Top. Quantum Electron. 12, 412 (2006).
    [CrossRef]
  2. G. T. Reed and A. P. Knights, Silicon Photonics: an Introduction (Wiley, 2004).
    [CrossRef]
  3. O. Boyraz and B. Jalali, Opt. Express 12, 5269 (2004).
    [CrossRef] [PubMed]
  4. R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali, Opt. Express 11, 1731 (2003).
    [CrossRef] [PubMed]
  5. I. D. Rukhlenko, C. Dissanayake, M. Premaratne, and G. P. Agrawal, Opt. Express 17, 5807 (2009).
    [CrossRef] [PubMed]
  6. R. Claps, V. Raghunathan, D. Dimitropoulos, and B. Jalali, Opt. Express 12, 2774 (2004).
    [CrossRef] [PubMed]
  7. T. K. Liang and H. K. Tsang, Appl. Phys. Lett. 84, 2745 (2004).
    [CrossRef]
  8. I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, IEEE J. Sel. Top. Quantum Electron. 16, 200 (2010).
    [CrossRef]
  9. Q. Lin, O. J. Painter, and G. P. Agrawal, Opt. Express 15, 16604 (2007).
    [CrossRef] [PubMed]
  10. S. Roy, S. K. Bhadra, and G. P. Agrawal, J. Opt. Soc. Am. B 26, 17 (2009).
    [CrossRef]
  11. I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, Opt. Lett. 35, 55 (2010).
    [CrossRef] [PubMed]
  12. Y. Okawachi, M. A. Foster, J. E. Sharping, A. L. Gaeta, Q. Xu, and M. Lipson, Opt. Express 14, 2317 (2006).
    [CrossRef] [PubMed]

2010 (2)

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, IEEE J. Sel. Top. Quantum Electron. 16, 200 (2010).
[CrossRef]

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, Opt. Lett. 35, 55 (2010).
[CrossRef] [PubMed]

2009 (2)

2007 (1)

2006 (2)

Y. Okawachi, M. A. Foster, J. E. Sharping, A. L. Gaeta, Q. Xu, and M. Lipson, Opt. Express 14, 2317 (2006).
[CrossRef] [PubMed]

B. Jalali, V. Raghunathan, D. Dimitropoulos, and O. Boyraz, IEEE J. Sel. Top. Quantum Electron. 12, 412 (2006).
[CrossRef]

2004 (4)

G. T. Reed and A. P. Knights, Silicon Photonics: an Introduction (Wiley, 2004).
[CrossRef]

T. K. Liang and H. K. Tsang, Appl. Phys. Lett. 84, 2745 (2004).
[CrossRef]

R. Claps, V. Raghunathan, D. Dimitropoulos, and B. Jalali, Opt. Express 12, 2774 (2004).
[CrossRef] [PubMed]

O. Boyraz and B. Jalali, Opt. Express 12, 5269 (2004).
[CrossRef] [PubMed]

2003 (1)

Agrawal, G. P.

Bhadra, S. K.

Boyraz, O.

B. Jalali, V. Raghunathan, D. Dimitropoulos, and O. Boyraz, IEEE J. Sel. Top. Quantum Electron. 12, 412 (2006).
[CrossRef]

O. Boyraz and B. Jalali, Opt. Express 12, 5269 (2004).
[CrossRef] [PubMed]

Claps, R.

Dimitropoulos, D.

Dissanayake, C.

Foster, M. A.

Gaeta, A. L.

Han, Y.

Jalali, B.

Knights, A. P.

G. T. Reed and A. P. Knights, Silicon Photonics: an Introduction (Wiley, 2004).
[CrossRef]

Liang, T. K.

T. K. Liang and H. K. Tsang, Appl. Phys. Lett. 84, 2745 (2004).
[CrossRef]

Lin, Q.

Lipson, M.

Okawachi, Y.

Painter, O. J.

Premaratne, M.

Raghunathan, V.

Reed, G. T.

G. T. Reed and A. P. Knights, Silicon Photonics: an Introduction (Wiley, 2004).
[CrossRef]

Roy, S.

Rukhlenko, I. D.

Sharping, J. E.

Tsang, H. K.

T. K. Liang and H. K. Tsang, Appl. Phys. Lett. 84, 2745 (2004).
[CrossRef]

Xu, Q.

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Figures (2)

Fig. 1
Fig. 1

(a), (b) Compression factor and signal gain for Gaussian pulses with FWHM ranging from 0.1 to 100 ps and (c) Raman delay time for different values of free-carrier lifetime, τ c . Dashed curve in (c) shows the maximum delay in the absence of FCA. For simulation parameters refer to text.

Fig. 2
Fig. 2

Dynamics of Gaussian pulses with different FWHM, τ 0 . The numbers in the left panels show signal gains; in the right panels, the gains for the pulses can be found in Fig. 1b. The legend refers to all panels; W 0 = 10 fJ and τ c = 1 ns . The other parameters are the same as in Fig. 1.

Equations (12)

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A ˜ s ( ω ) z = [ i β ( ω ) + g ^ R 2 Γ ( ω ) I p ( z ) f ( z ) 2 ] A ˜ s ( ω ) ,
f ( z ) = α s + ( β s + 2 i γ s ) I p ( z ) + ( ξ r + 2 i ξ i ) I p 2 ( z )
A ˜ s ( ω ) = a ˜ ( ω ) G exp [ i β ( ω ) L + i ω δ R Γ ( ω ) ] ,
ψ = α s L + ( g ^ R β s 2 i γ s ) I 0 L eff ( 1 + 2 i ξ i / ξ r ) Q , L eff = 1 I 0 0 L I p ( z ) d z , Q = ξ r 0 L I p 2 ( z ) d z .
d I p d z = α p I p β p I p 2 ξ p I p 3 ,
L eff = μ β p I 0 ln ( μ K L + 1 μ K L 1 μ K 0 1 μ K 0 + 1 ) , α p + β p I L + ξ p I L 2 α p + β p I 0 + ξ p I 0 2 = ( I L I 0 ) 2 exp ( 2 α p L + β p I 0 L eff ) ,
Q = ω p 2 ω s 2 ( ln I 0 I L β p I 0 L eff α p L ) .
| A ˜ s ( ω ) a ˜ ( ω ) | 2 = exp [ α s L + ( g ^ R | Γ ( ω ) | 2 β s ) I 0 L eff Q ] .
| ω γ R | < ( g ^ R I 0 L eff ln | G | 1 ) 1 / 2
η = W 0 A eff ( + | a ˜ ( ω ) | 2 exp ( ω 2 | Γ ( ω ) | 2 Δ ) d ω ) 1 ,
A s ( τ ) = G + a ˜ ( ω ) exp { i ω [ τ δ R Γ ( ω ) ] } d ω ,
A G ( τ ) = ( W 0 G 2 π 3 / 2 τ G A eff ) 1 / 2 × + exp { q 2 2 i q [ τ τ G δ R τ G Γ ( q τ G ) ] } d q ,

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