Abstract

We experimentally demonstrate slow-down of light by a factor of three in a 100 μm long semiconductor waveguide at room temperature and at a record-high frequency of 16.7 GHz. It is shown that the group velocity can be controlled all-optically as well as through an applied bias voltage. A semi-analytical model based on the effect of coherent population oscillations and taking into account propagation effects is derived and is shown to well account for the experimental results. It is shown that the carrier lifetime limits the maximum achievable delay. Based on the general model we analyze fundamental limitations in the application of light slowdown due to coherent population oscillations.

© 2005 Optical Society of America

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References

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  1. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meters per second in an ultracold atomic gas,” Nature 397, 594—598 (1999).
    [Crossref]
  2. C. J. Chang-Hasnain, P. -C. Ku, J. Kim, and S. -L. Chuang, “Variable optical buffer using slow light in semiconductor nanostructures,” Proc. IEEE 91, 1884–1897 (2003).
    [Crossref]
  3. M. S. Bigelow, N. N. Lepeshkin, and R. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90, 113903-1–4 (2003).
    [Crossref] [PubMed]
  4. P. Palinginis, M. Moewe, E. Kim, F. G. Sedgwick, S. Crankshaw, C. J. Chang-Hasnain, H. Wang, and S. L. Chuang, “Ultra-slow light (<200 m/s) in a semiconductor nanostructure,” Proc. CLEO, Post deadline paper CPDB6, Baltimore, USA, May 2005.
  5. J. Shim, B. Liu, and J. E. Bowers, “Dependence of transmission curves on input optical power in an electroabsorption modulator,” IEEE J. Quantum Electron. 40, 1622–1628 (2004).
    [Crossref]
  6. A. Uskov, J. Mørk, and J. Mark, “Wave mixing in semiconductor laser amplifiers due to carrier heating and spectral-hole burning,” IEEE J. Quantum Electron. 30, 1769– 1781 (1994).
    [Crossref]
  7. S. Højfeldt and J. Mørk, “Modeling of carrier dynamics in quantum-well electroabsorption modulators,” IEEE J. Select. Topics Quantum Electron.,  8, 1265–1276 (2002).
    [Crossref]
  8. J. Mørk and A. Mecozzi, “Theory of the ultrafast optical response of active semiconductor waveguides,” J. Opt. Soc. Am. B 13, 1803–1816 (1996).
    [Crossref]
  9. G. P. Agrawal and N. A. Olsson, “Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers,” IEEE J. Quantum Electron. 25, 2297–2306 (1989).
    [Crossref]
  10. 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, 61–62 (2005).
    [Crossref]
  11. R. W. Boyd, D. J. Gauthier, A. L. Gaeta, and A. E. Willner, “Maximum time delay achievable on propagation through a slow-time medium,” Phys. Rev. A 71, 023801-1 – 023801-4 (2005).
    [Crossref]
  12. D. Marcenac and A. Mecozzi, “Switches and frequency converters based on cross-gain modulation in semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 9, 749–751 (1997).
    [Crossref]
  13. M. v.d. Poel, J. Mørk, and J. M. Hvam, “Controllable delay of ultrashort optical pulses in a semiconductor quantum dot amplifier,” accepted for publication in Optics Express.

2005 (2)

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, 61–62 (2005).
[Crossref]

R. W. Boyd, D. J. Gauthier, A. L. Gaeta, and A. E. Willner, “Maximum time delay achievable on propagation through a slow-time medium,” Phys. Rev. A 71, 023801-1 – 023801-4 (2005).
[Crossref]

2004 (1)

J. Shim, B. Liu, and J. E. Bowers, “Dependence of transmission curves on input optical power in an electroabsorption modulator,” IEEE J. Quantum Electron. 40, 1622–1628 (2004).
[Crossref]

2003 (2)

C. J. Chang-Hasnain, P. -C. Ku, J. Kim, and S. -L. Chuang, “Variable optical buffer using slow light in semiconductor nanostructures,” Proc. IEEE 91, 1884–1897 (2003).
[Crossref]

M. S. Bigelow, N. N. Lepeshkin, and R. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90, 113903-1–4 (2003).
[Crossref] [PubMed]

2002 (1)

S. Højfeldt and J. Mørk, “Modeling of carrier dynamics in quantum-well electroabsorption modulators,” IEEE J. Select. Topics Quantum Electron.,  8, 1265–1276 (2002).
[Crossref]

1999 (1)

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meters per second in an ultracold atomic gas,” Nature 397, 594—598 (1999).
[Crossref]

1997 (1)

D. Marcenac and A. Mecozzi, “Switches and frequency converters based on cross-gain modulation in semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 9, 749–751 (1997).
[Crossref]

1996 (1)

1994 (1)

A. Uskov, J. Mørk, and J. Mark, “Wave mixing in semiconductor laser amplifiers due to carrier heating and spectral-hole burning,” IEEE J. Quantum Electron. 30, 1769– 1781 (1994).
[Crossref]

1989 (1)

G. P. Agrawal and N. A. Olsson, “Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers,” IEEE J. Quantum Electron. 25, 2297–2306 (1989).
[Crossref]

Agrawal, G. P.

G. P. Agrawal and N. A. Olsson, “Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers,” IEEE J. Quantum Electron. 25, 2297–2306 (1989).
[Crossref]

Behroozi, C. H.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meters per second in an ultracold atomic gas,” Nature 397, 594—598 (1999).
[Crossref]

Bigelow, M. S.

M. S. Bigelow, N. N. Lepeshkin, and R. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90, 113903-1–4 (2003).
[Crossref] [PubMed]

Bowers, J. E.

J. Shim, B. Liu, and J. E. Bowers, “Dependence of transmission curves on input optical power in an electroabsorption modulator,” IEEE J. Quantum Electron. 40, 1622–1628 (2004).
[Crossref]

Boyd, R.

M. S. Bigelow, N. N. Lepeshkin, and R. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90, 113903-1–4 (2003).
[Crossref] [PubMed]

Boyd, R. W.

R. W. Boyd, D. J. Gauthier, A. L. Gaeta, and A. E. Willner, “Maximum time delay achievable on propagation through a slow-time medium,” Phys. Rev. A 71, 023801-1 – 023801-4 (2005).
[Crossref]

Chang-Hasnain, C. J.

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, 61–62 (2005).
[Crossref]

C. J. Chang-Hasnain, P. -C. Ku, J. Kim, and S. -L. Chuang, “Variable optical buffer using slow light in semiconductor nanostructures,” Proc. IEEE 91, 1884–1897 (2003).
[Crossref]

P. Palinginis, M. Moewe, E. Kim, F. G. Sedgwick, S. Crankshaw, C. J. Chang-Hasnain, H. Wang, and S. L. Chuang, “Ultra-slow light (<200 m/s) in a semiconductor nanostructure,” Proc. CLEO, Post deadline paper CPDB6, Baltimore, USA, May 2005.

Chuang, S. L.

P. Palinginis, M. Moewe, E. Kim, F. G. Sedgwick, S. Crankshaw, C. J. Chang-Hasnain, H. Wang, and S. L. Chuang, “Ultra-slow light (<200 m/s) in a semiconductor nanostructure,” Proc. CLEO, Post deadline paper CPDB6, Baltimore, USA, May 2005.

Chuang, S. -L.

C. J. Chang-Hasnain, P. -C. Ku, J. Kim, and S. -L. Chuang, “Variable optical buffer using slow light in semiconductor nanostructures,” Proc. IEEE 91, 1884–1897 (2003).
[Crossref]

Crankshaw, S.

P. Palinginis, M. Moewe, E. Kim, F. G. Sedgwick, S. Crankshaw, C. J. Chang-Hasnain, H. Wang, and S. L. Chuang, “Ultra-slow light (<200 m/s) in a semiconductor nanostructure,” Proc. CLEO, Post deadline paper CPDB6, Baltimore, USA, May 2005.

Dutton, Z.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meters per second in an ultracold atomic gas,” Nature 397, 594—598 (1999).
[Crossref]

Gaeta, A. L.

R. W. Boyd, D. J. Gauthier, A. L. Gaeta, and A. E. Willner, “Maximum time delay achievable on propagation through a slow-time medium,” Phys. Rev. A 71, 023801-1 – 023801-4 (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-time medium,” Phys. Rev. A 71, 023801-1 – 023801-4 (2005).
[Crossref]

Harris, S. E.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meters per second in an ultracold atomic gas,” Nature 397, 594—598 (1999).
[Crossref]

Hau, L. V.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meters per second in an ultracold atomic gas,” Nature 397, 594—598 (1999).
[Crossref]

Højfeldt, S.

S. Højfeldt and J. Mørk, “Modeling of carrier dynamics in quantum-well electroabsorption modulators,” IEEE J. Select. Topics Quantum Electron.,  8, 1265–1276 (2002).
[Crossref]

Hvam, J. M.

M. v.d. Poel, J. Mørk, and J. M. Hvam, “Controllable delay of ultrashort optical pulses in a semiconductor quantum dot amplifier,” accepted for publication in Optics Express.

Kim, E.

P. Palinginis, M. Moewe, E. Kim, F. G. Sedgwick, S. Crankshaw, C. J. Chang-Hasnain, H. Wang, and S. L. Chuang, “Ultra-slow light (<200 m/s) in a semiconductor nanostructure,” Proc. CLEO, Post deadline paper CPDB6, Baltimore, USA, May 2005.

Kim, J.

C. J. Chang-Hasnain, P. -C. Ku, J. Kim, and S. -L. Chuang, “Variable optical buffer using slow light in semiconductor nanostructures,” Proc. IEEE 91, 1884–1897 (2003).
[Crossref]

Ku, P. -C.

C. J. Chang-Hasnain, P. -C. Ku, J. Kim, and S. -L. Chuang, “Variable optical buffer using slow light in semiconductor nanostructures,” Proc. IEEE 91, 1884–1897 (2003).
[Crossref]

Ku, P.C.

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, 61–62 (2005).
[Crossref]

Lepeshkin, N. N.

M. S. Bigelow, N. N. Lepeshkin, and R. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90, 113903-1–4 (2003).
[Crossref] [PubMed]

Liu, B.

J. Shim, B. Liu, and J. E. Bowers, “Dependence of transmission curves on input optical power in an electroabsorption modulator,” IEEE J. Quantum Electron. 40, 1622–1628 (2004).
[Crossref]

Marcenac, D.

D. Marcenac and A. Mecozzi, “Switches and frequency converters based on cross-gain modulation in semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 9, 749–751 (1997).
[Crossref]

Mark, J.

A. Uskov, J. Mørk, and J. Mark, “Wave mixing in semiconductor laser amplifiers due to carrier heating and spectral-hole burning,” IEEE J. Quantum Electron. 30, 1769– 1781 (1994).
[Crossref]

Mecozzi, A.

D. Marcenac and A. Mecozzi, “Switches and frequency converters based on cross-gain modulation in semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 9, 749–751 (1997).
[Crossref]

J. Mørk and A. Mecozzi, “Theory of the ultrafast optical response of active semiconductor waveguides,” J. Opt. Soc. Am. B 13, 1803–1816 (1996).
[Crossref]

Moewe, M.

P. Palinginis, M. Moewe, E. Kim, F. G. Sedgwick, S. Crankshaw, C. J. Chang-Hasnain, H. Wang, and S. L. Chuang, “Ultra-slow light (<200 m/s) in a semiconductor nanostructure,” Proc. CLEO, Post deadline paper CPDB6, Baltimore, USA, May 2005.

Mørk, J.

S. Højfeldt and J. Mørk, “Modeling of carrier dynamics in quantum-well electroabsorption modulators,” IEEE J. Select. Topics Quantum Electron.,  8, 1265–1276 (2002).
[Crossref]

J. Mørk and A. Mecozzi, “Theory of the ultrafast optical response of active semiconductor waveguides,” J. Opt. Soc. Am. B 13, 1803–1816 (1996).
[Crossref]

A. Uskov, J. Mørk, and J. Mark, “Wave mixing in semiconductor laser amplifiers due to carrier heating and spectral-hole burning,” IEEE J. Quantum Electron. 30, 1769– 1781 (1994).
[Crossref]

M. v.d. Poel, J. Mørk, and J. M. Hvam, “Controllable delay of ultrashort optical pulses in a semiconductor quantum dot amplifier,” accepted for publication in Optics Express.

Olsson, N. A.

G. P. Agrawal and N. A. Olsson, “Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers,” IEEE J. Quantum Electron. 25, 2297–2306 (1989).
[Crossref]

Palinginis, P.

P. Palinginis, M. Moewe, E. Kim, F. G. Sedgwick, S. Crankshaw, C. J. Chang-Hasnain, H. Wang, and S. L. Chuang, “Ultra-slow light (<200 m/s) in a semiconductor nanostructure,” Proc. CLEO, Post deadline paper CPDB6, Baltimore, USA, May 2005.

Poel, M. v.d.

M. v.d. Poel, J. Mørk, and J. M. Hvam, “Controllable delay of ultrashort optical pulses in a semiconductor quantum dot amplifier,” accepted for publication in Optics Express.

Sedgwick, F. G.

P. Palinginis, M. Moewe, E. Kim, F. G. Sedgwick, S. Crankshaw, C. J. Chang-Hasnain, H. Wang, and S. L. Chuang, “Ultra-slow light (<200 m/s) in a semiconductor nanostructure,” Proc. CLEO, Post deadline paper CPDB6, Baltimore, USA, May 2005.

Shim, J.

J. Shim, B. Liu, and J. E. Bowers, “Dependence of transmission curves on input optical power in an electroabsorption modulator,” IEEE J. Quantum Electron. 40, 1622–1628 (2004).
[Crossref]

Tucker, R. S.

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, 61–62 (2005).
[Crossref]

Uskov, A.

A. Uskov, J. Mørk, and J. Mark, “Wave mixing in semiconductor laser amplifiers due to carrier heating and spectral-hole burning,” IEEE J. Quantum Electron. 30, 1769– 1781 (1994).
[Crossref]

Wang, H.

P. Palinginis, M. Moewe, E. Kim, F. G. Sedgwick, S. Crankshaw, C. J. Chang-Hasnain, H. Wang, and S. L. Chuang, “Ultra-slow light (<200 m/s) in a semiconductor nanostructure,” Proc. CLEO, Post deadline paper CPDB6, Baltimore, USA, May 2005.

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-time medium,” Phys. Rev. A 71, 023801-1 – 023801-4 (2005).
[Crossref]

Electron. Lett. (1)

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, 61–62 (2005).
[Crossref]

IEEE J. Quantum Electron. (3)

G. P. Agrawal and N. A. Olsson, “Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers,” IEEE J. Quantum Electron. 25, 2297–2306 (1989).
[Crossref]

J. Shim, B. Liu, and J. E. Bowers, “Dependence of transmission curves on input optical power in an electroabsorption modulator,” IEEE J. Quantum Electron. 40, 1622–1628 (2004).
[Crossref]

A. Uskov, J. Mørk, and J. Mark, “Wave mixing in semiconductor laser amplifiers due to carrier heating and spectral-hole burning,” IEEE J. Quantum Electron. 30, 1769– 1781 (1994).
[Crossref]

IEEE J. Select. Topics Quantum Electron. (1)

S. Højfeldt and J. Mørk, “Modeling of carrier dynamics in quantum-well electroabsorption modulators,” IEEE J. Select. Topics Quantum Electron.,  8, 1265–1276 (2002).
[Crossref]

IEEE Photon. Technol. Lett. (1)

D. Marcenac and A. Mecozzi, “Switches and frequency converters based on cross-gain modulation in semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 9, 749–751 (1997).
[Crossref]

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

Nature (1)

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meters per second in an ultracold atomic gas,” Nature 397, 594—598 (1999).
[Crossref]

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-time medium,” Phys. Rev. A 71, 023801-1 – 023801-4 (2005).
[Crossref]

Phys. Rev. Lett. (1)

M. S. Bigelow, N. N. Lepeshkin, and R. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90, 113903-1–4 (2003).
[Crossref] [PubMed]

Proc. IEEE (1)

C. J. Chang-Hasnain, P. -C. Ku, J. Kim, and S. -L. Chuang, “Variable optical buffer using slow light in semiconductor nanostructures,” Proc. IEEE 91, 1884–1897 (2003).
[Crossref]

Other (2)

P. Palinginis, M. Moewe, E. Kim, F. G. Sedgwick, S. Crankshaw, C. J. Chang-Hasnain, H. Wang, and S. L. Chuang, “Ultra-slow light (<200 m/s) in a semiconductor nanostructure,” Proc. CLEO, Post deadline paper CPDB6, Baltimore, USA, May 2005.

M. v.d. Poel, J. Mørk, and J. M. Hvam, “Controllable delay of ultrashort optical pulses in a semiconductor quantum dot amplifier,” accepted for publication in Optics Express.

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Figures (7)

Fig. 1.
Fig. 1.

Experimental set-up for measuring the propagation speed of a modulated optical signal in a semiconductor waveguide device (electro-absorption modulator – EAM).

Fig. 2.
Fig. 2.

Contour plot of measured absolute change in group refractive index versus input intensity and reverse voltage for a 100 μm long semiconductor waveguide. The measurements were carried out at a modulation frequency f0 = 15 GHz.

Fig. 3.
Fig. 3.

Measured transmission (a) and phase shift (time delay) (b) versus voltage for different input power levels. Modulation frequency (detuning): 16.7 GHz.

Fig. 4.
Fig. 4.

Imaginary (a) and real (b) parts of the third-order probe susceptibility due to coherent population oscillations and corresponding group refractive index (c) calculated for different values of α. Other parameters are: P = 10 mW, Psat , = 10 mW, τ s = 200 ps, and Γg0 = -5∙104 m-1.

Fig. 5.
Fig. 5.

Calculated transmission (a) and phase / time delay (b) versus reverse bias voltage for different input power levels. Frequency detuning: 16.7 GHz.

Fig. 6.
Fig. 6.

Calculated (a) transmission and (b) relative time delay ξ = Δtmod /τ (at zero detuning) versus input power for different levels of small-signal (unsaturated) transmission T0 .

Fig. 7.
Fig. 7.

Calculated variation of (a) delay relative to carrier lifetime and (b) length-averaged modulation refractive index versus waveguide length. The absorption is Γg0 =-5∙104 m-1.

Equations (19)

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

Δ n g = c L Δ t = c L Δ φ Ω
χ r ( ω 0 + Ω ) = c n b ω 0 g sat P P sat α + i i Ω τ s + 1 + P P sat
g sat = Γ g 0 1 + P P sat ,
dP dz = ( g sat α int ) P ,
n 2 = 1 + χ b + χ r ,
n g = n + ω 0 dn n gb + ω 0 2 n b d χ r .
n g ( Ω = 0 ) = n gb 1 2 c τ s Γ g 0 P P sat ( 1 + P P sat ) 3 .
n mod = n + ω 0 n ( ω 0 + Ω ) n ( ω 0 Ω ) 2 Ω n gb + 2 ω 0 2 n b χ r ( ω 0 + Ω ) χ r ( ω 0 Ω ) 2 Ω ,
n mod = n gb c τ s Γ g 0 P P sat 1 + P P sat 1 ( Ω τ s ) 2 + ( 1 + P P sat ) 2 .
t mod = 0 L n mod ( z ) dz n ¯ mod c L
Δ φ mod = ΩΔ t mod = Ω L c ( n ¯ mod n gb ) .
n ¯ mod = n gb c L 1 Ω Arctan { Ω τ s ( T sat 1 ) P ( 0 ) / P sat ( Ω τ s ) 2 + 1 + ( T sat + 1 ) P ( 0 ) / P sat + T sat ( P ( 0 ) / P sat ) 2 }
T sat = P ( L ) P ( 0 ) .
ln ( T sat ) + ( T sat 1 ) P ( 0 ) P sat = Γ g 0 L ,
n ¯ mod = n gb c L τ s ( T sat 1 ) P ( 0 ) / P sat ( Ω τ s ) 2 + 1 + ( T sat + 1 ) P ( 0 ) / P sat + T sat ( P ( 0 ) / P sat ) 2 .
Δ P ( Ω , L ) Δ P ( Ω , 0 ) = G sat ( 1 ( G sat 1 ) P ( 0 ) / P sat i Ω τ s + 1 + G sat P ( 0 ) / P sat ) .
n ¯ g = n gb + 1 2 c τ s 1 L ( 1 1 + T sat P ( 0 ) / P sat 1 1 + P ( 0 ) / P sat ) .
Δ t g = L c Δ n ¯ g = 1 2 τ s ( 1 1 + T sat P ( 0 ) / P sat 1 1 + P ( 0 ) / P sat ) .
g 0 = a V ( V V on ) 2 , τ s = τ s 0 exp ( V V ref ) ,

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