Abstract

We investigate variable optical delay of a microwave modulated optical beam in semiconductor optical amplifier/absorber waveguides with population oscillation (PO) and nearly degenerate four-wave-mixing (NDFWM) effects. An optical delay variable between 0 and 160 ps with a 1.0 GHz bandwidth is achieved in an InGaAsP/InP semiconductor optical amplifier (SOA) and shown to be electrically and optically controllable. An analytical model of optical delay is developed and found to agree well with the experimental data. Based on this model, we obtain design criteria to optimize the delay-bandwidth product of the optical delay in semiconductor optical amplifiers and absorbers.

© 2006 Optical Society of America

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  1. 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]
  2. J. Marangos, "Slow light in cool atoms," Nature 397, 559-560 (1999).
    [CrossRef]
  3. M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, "Superluminal and slow light propagation in a room-temperature solid," Science 301, 200-202 (2003).
    [CrossRef] [PubMed]
  4. S. W. Chang, S. L. Chuang, P. C. Ku, C. J. Chang-Hasnian, P. Palinginis, and H. L. Wang, "Slow light using excitonic population oscillation," Phys. Rev. B 70, 235333 (2004).
    [CrossRef]
  5. P. C. Ku, F. Sedgwick, C. J. Chang-Hasnain, P. Palinginis, T. Li, H. L. Wang, S. W. Chang, and S. L. Chuang, "Slow light in semiconductor quantum wells," Opt. Lett. 29, 2291-2293 (2004).
    [CrossRef] [PubMed]
  6. S. Minin, M. R. Fisher, and S. L. Chuang, "Current-controlled group delay using a semiconductor Fabry-Perot amplifier," Appl. Phys. Lett. 84, 3238-3240 (2004).
    [CrossRef]
  7. Y. A. Vlasov, M. O'Boyle, H. F. Hamann, and S. J. Mcnab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
    [CrossRef] [PubMed]
  8. H. Su and S. L. Chuang, "Room temperature slow light in quantum-dot devices," Opt. Lett. 31, 271-273 (2006).
    [CrossRef] [PubMed]
  9. H. Su and S. L. Chuang, "Room temperature fast light in a quantum-dot semiconductor amplifier," Appl. Phys. Lett. 88, 061102 (2006).
    [CrossRef]
  10. G. P. Agrawal, "Population Pulsations and Nondegenerate 4-Wave Mixing in Semiconductor-Lasers and Amplifiers," J. Opt. Soc. Am. B 5, 147-159 (1988).
    [CrossRef]
  11. T. Mukai and T. Saitoh, "Detuning Characteristics and Conversion Efficiency of Nearly Degenerate 4-Wave-Mixing in A 1.5-Mu-M Traveling-Wave Semiconductor-Laser Amplifier," IEEE J. Quantum Electron. 26, 865-875 (1990).
    [CrossRef]
  12. G. Eisenstein, N. Tessler, U. Koren, J. M. Wiesenfeld, G. Raybon, and C. A. Burrus, "Length Dependence of the Saturation Characteristics in 1.5-Mu-M Multiple Quantum-Well Optical Amplifiers," IEEE Photon. Technol. Lett. 2, 790-791 (1990).
    [CrossRef]

2006 (2)

H. Su and S. L. Chuang, "Room temperature slow light in quantum-dot devices," Opt. Lett. 31, 271-273 (2006).
[CrossRef] [PubMed]

H. Su and S. L. Chuang, "Room temperature fast light in a quantum-dot semiconductor amplifier," Appl. Phys. Lett. 88, 061102 (2006).
[CrossRef]

2005 (1)

Y. A. Vlasov, M. O'Boyle, H. F. Hamann, and S. J. Mcnab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

2004 (3)

S. W. Chang, S. L. Chuang, P. C. Ku, C. J. Chang-Hasnian, P. Palinginis, and H. L. Wang, "Slow light using excitonic population oscillation," Phys. Rev. B 70, 235333 (2004).
[CrossRef]

P. C. Ku, F. Sedgwick, C. J. Chang-Hasnain, P. Palinginis, T. Li, H. L. Wang, S. W. Chang, and S. L. Chuang, "Slow light in semiconductor quantum wells," Opt. Lett. 29, 2291-2293 (2004).
[CrossRef] [PubMed]

S. Minin, M. R. Fisher, and S. L. Chuang, "Current-controlled group delay using a semiconductor Fabry-Perot amplifier," Appl. Phys. Lett. 84, 3238-3240 (2004).
[CrossRef]

2003 (1)

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

1999 (2)

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]

J. Marangos, "Slow light in cool atoms," Nature 397, 559-560 (1999).
[CrossRef]

1990 (2)

T. Mukai and T. Saitoh, "Detuning Characteristics and Conversion Efficiency of Nearly Degenerate 4-Wave-Mixing in A 1.5-Mu-M Traveling-Wave Semiconductor-Laser Amplifier," IEEE J. Quantum Electron. 26, 865-875 (1990).
[CrossRef]

G. Eisenstein, N. Tessler, U. Koren, J. M. Wiesenfeld, G. Raybon, and C. A. Burrus, "Length Dependence of the Saturation Characteristics in 1.5-Mu-M Multiple Quantum-Well Optical Amplifiers," IEEE Photon. Technol. Lett. 2, 790-791 (1990).
[CrossRef]

1988 (1)

Agrawal, G. P.

Behroozi, C. H.

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]

Bigelow, M. S.

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

Boyd, R. W.

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

Burrus, C. A.

G. Eisenstein, N. Tessler, U. Koren, J. M. Wiesenfeld, G. Raybon, and C. A. Burrus, "Length Dependence of the Saturation Characteristics in 1.5-Mu-M Multiple Quantum-Well Optical Amplifiers," IEEE Photon. Technol. Lett. 2, 790-791 (1990).
[CrossRef]

Chang, S. W.

S. W. Chang, S. L. Chuang, P. C. Ku, C. J. Chang-Hasnian, P. Palinginis, and H. L. Wang, "Slow light using excitonic population oscillation," Phys. Rev. B 70, 235333 (2004).
[CrossRef]

P. C. Ku, F. Sedgwick, C. J. Chang-Hasnain, P. Palinginis, T. Li, H. L. Wang, S. W. Chang, and S. L. Chuang, "Slow light in semiconductor quantum wells," Opt. Lett. 29, 2291-2293 (2004).
[CrossRef] [PubMed]

Chang-Hasnain, C. J.

Chang-Hasnian, C. J.

S. W. Chang, S. L. Chuang, P. C. Ku, C. J. Chang-Hasnian, P. Palinginis, and H. L. Wang, "Slow light using excitonic population oscillation," Phys. Rev. B 70, 235333 (2004).
[CrossRef]

Chuang, S. L.

H. Su and S. L. Chuang, "Room temperature fast light in a quantum-dot semiconductor amplifier," Appl. Phys. Lett. 88, 061102 (2006).
[CrossRef]

H. Su and S. L. Chuang, "Room temperature slow light in quantum-dot devices," Opt. Lett. 31, 271-273 (2006).
[CrossRef] [PubMed]

P. C. Ku, F. Sedgwick, C. J. Chang-Hasnain, P. Palinginis, T. Li, H. L. Wang, S. W. Chang, and S. L. Chuang, "Slow light in semiconductor quantum wells," Opt. Lett. 29, 2291-2293 (2004).
[CrossRef] [PubMed]

S. Minin, M. R. Fisher, and S. L. Chuang, "Current-controlled group delay using a semiconductor Fabry-Perot amplifier," Appl. Phys. Lett. 84, 3238-3240 (2004).
[CrossRef]

S. W. Chang, S. L. Chuang, P. C. Ku, C. J. Chang-Hasnian, P. Palinginis, and H. L. Wang, "Slow light using excitonic population oscillation," Phys. Rev. B 70, 235333 (2004).
[CrossRef]

Dutton, Z.

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]

Eisenstein, G.

G. Eisenstein, N. Tessler, U. Koren, J. M. Wiesenfeld, G. Raybon, and C. A. Burrus, "Length Dependence of the Saturation Characteristics in 1.5-Mu-M Multiple Quantum-Well Optical Amplifiers," IEEE Photon. Technol. Lett. 2, 790-791 (1990).
[CrossRef]

Fisher, M. R.

S. Minin, M. R. Fisher, and S. L. Chuang, "Current-controlled group delay using a semiconductor Fabry-Perot amplifier," Appl. Phys. Lett. 84, 3238-3240 (2004).
[CrossRef]

Hamann, H. F.

Y. A. Vlasov, M. O'Boyle, H. F. Hamann, and S. J. Mcnab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

Harris, S. E.

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]

Hau, L. V.

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]

Koren, U.

G. Eisenstein, N. Tessler, U. Koren, J. M. Wiesenfeld, G. Raybon, and C. A. Burrus, "Length Dependence of the Saturation Characteristics in 1.5-Mu-M Multiple Quantum-Well Optical Amplifiers," IEEE Photon. Technol. Lett. 2, 790-791 (1990).
[CrossRef]

Ku, P. C.

P. C. Ku, F. Sedgwick, C. J. Chang-Hasnain, P. Palinginis, T. Li, H. L. Wang, S. W. Chang, and S. L. Chuang, "Slow light in semiconductor quantum wells," Opt. Lett. 29, 2291-2293 (2004).
[CrossRef] [PubMed]

S. W. Chang, S. L. Chuang, P. C. Ku, C. J. Chang-Hasnian, P. Palinginis, and H. L. Wang, "Slow light using excitonic population oscillation," Phys. Rev. B 70, 235333 (2004).
[CrossRef]

Lepeshkin, N. N.

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

Li, T.

Marangos, J.

J. Marangos, "Slow light in cool atoms," Nature 397, 559-560 (1999).
[CrossRef]

Mcnab, S. J.

Y. A. Vlasov, M. O'Boyle, H. F. Hamann, and S. J. Mcnab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

Minin, S.

S. Minin, M. R. Fisher, and S. L. Chuang, "Current-controlled group delay using a semiconductor Fabry-Perot amplifier," Appl. Phys. Lett. 84, 3238-3240 (2004).
[CrossRef]

Mukai, T.

T. Mukai and T. Saitoh, "Detuning Characteristics and Conversion Efficiency of Nearly Degenerate 4-Wave-Mixing in A 1.5-Mu-M Traveling-Wave Semiconductor-Laser Amplifier," IEEE J. Quantum Electron. 26, 865-875 (1990).
[CrossRef]

O'Boyle, M.

Y. A. Vlasov, M. O'Boyle, H. F. Hamann, and S. J. Mcnab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

Palinginis, P.

S. W. Chang, S. L. Chuang, P. C. Ku, C. J. Chang-Hasnian, P. Palinginis, and H. L. Wang, "Slow light using excitonic population oscillation," Phys. Rev. B 70, 235333 (2004).
[CrossRef]

P. C. Ku, F. Sedgwick, C. J. Chang-Hasnain, P. Palinginis, T. Li, H. L. Wang, S. W. Chang, and S. L. Chuang, "Slow light in semiconductor quantum wells," Opt. Lett. 29, 2291-2293 (2004).
[CrossRef] [PubMed]

Raybon, G.

G. Eisenstein, N. Tessler, U. Koren, J. M. Wiesenfeld, G. Raybon, and C. A. Burrus, "Length Dependence of the Saturation Characteristics in 1.5-Mu-M Multiple Quantum-Well Optical Amplifiers," IEEE Photon. Technol. Lett. 2, 790-791 (1990).
[CrossRef]

Saitoh, T.

T. Mukai and T. Saitoh, "Detuning Characteristics and Conversion Efficiency of Nearly Degenerate 4-Wave-Mixing in A 1.5-Mu-M Traveling-Wave Semiconductor-Laser Amplifier," IEEE J. Quantum Electron. 26, 865-875 (1990).
[CrossRef]

Sedgwick, F.

Su, H.

H. Su and S. L. Chuang, "Room temperature fast light in a quantum-dot semiconductor amplifier," Appl. Phys. Lett. 88, 061102 (2006).
[CrossRef]

H. Su and S. L. Chuang, "Room temperature slow light in quantum-dot devices," Opt. Lett. 31, 271-273 (2006).
[CrossRef] [PubMed]

Tessler, N.

G. Eisenstein, N. Tessler, U. Koren, J. M. Wiesenfeld, G. Raybon, and C. A. Burrus, "Length Dependence of the Saturation Characteristics in 1.5-Mu-M Multiple Quantum-Well Optical Amplifiers," IEEE Photon. Technol. Lett. 2, 790-791 (1990).
[CrossRef]

Vlasov, Y. A.

Y. A. Vlasov, M. O'Boyle, H. F. Hamann, and S. J. Mcnab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

Wang, H. L.

S. W. Chang, S. L. Chuang, P. C. Ku, C. J. Chang-Hasnian, P. Palinginis, and H. L. Wang, "Slow light using excitonic population oscillation," Phys. Rev. B 70, 235333 (2004).
[CrossRef]

P. C. Ku, F. Sedgwick, C. J. Chang-Hasnain, P. Palinginis, T. Li, H. L. Wang, S. W. Chang, and S. L. Chuang, "Slow light in semiconductor quantum wells," Opt. Lett. 29, 2291-2293 (2004).
[CrossRef] [PubMed]

Wiesenfeld, J. M.

G. Eisenstein, N. Tessler, U. Koren, J. M. Wiesenfeld, G. Raybon, and C. A. Burrus, "Length Dependence of the Saturation Characteristics in 1.5-Mu-M Multiple Quantum-Well Optical Amplifiers," IEEE Photon. Technol. Lett. 2, 790-791 (1990).
[CrossRef]

Appl. Phys. Lett. (2)

S. Minin, M. R. Fisher, and S. L. Chuang, "Current-controlled group delay using a semiconductor Fabry-Perot amplifier," Appl. Phys. Lett. 84, 3238-3240 (2004).
[CrossRef]

H. Su and S. L. Chuang, "Room temperature fast light in a quantum-dot semiconductor amplifier," Appl. Phys. Lett. 88, 061102 (2006).
[CrossRef]

IEEE J. Quantum Electron. (1)

T. Mukai and T. Saitoh, "Detuning Characteristics and Conversion Efficiency of Nearly Degenerate 4-Wave-Mixing in A 1.5-Mu-M Traveling-Wave Semiconductor-Laser Amplifier," IEEE J. Quantum Electron. 26, 865-875 (1990).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

G. Eisenstein, N. Tessler, U. Koren, J. M. Wiesenfeld, G. Raybon, and C. A. Burrus, "Length Dependence of the Saturation Characteristics in 1.5-Mu-M Multiple Quantum-Well Optical Amplifiers," IEEE Photon. Technol. Lett. 2, 790-791 (1990).
[CrossRef]

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

Nature (3)

Y. A. Vlasov, M. O'Boyle, H. F. Hamann, and S. J. Mcnab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

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]

J. Marangos, "Slow light in cool atoms," Nature 397, 559-560 (1999).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. B (1)

S. W. Chang, S. L. Chuang, P. C. Ku, C. J. Chang-Hasnian, P. Palinginis, and H. L. Wang, "Slow light using excitonic population oscillation," Phys. Rev. B 70, 235333 (2004).
[CrossRef]

Science (1)

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

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Figures (4)

Fig. 1.
Fig. 1.

Experimental setup and schematic physics picture of variable optical delay of a microwave modulated beam in a QW SOA. I1 and I2 are optical isolators. PC1 and PC2 are polarization controllers. VOA is a variable optical attenuator. The network analyzer modulates the pump beam from the DFB laser and generates two side-bands and a dc component on the output spectrum, which induce population oscillation and nearly degenerate FWM in the QW SOA.

Fig. 2.
Fig. 2.

(a) The optical gain and (b) negative optical delay (or optical advance) versus modulation frequency in a 1.3 µm InGaAsP/InP QW SOA under different current injection. The circle curves are experimental data, while the line curves are the theoretical results based on Eq. (12) and (13). The current is increased from 150 mA to 400 mA with a step of 50 mA.

Fig. 3.
Fig. 3.

The dependence of variable delay on optical pump power which is controlled by an optical attenuator. A variable phase change of 25 degree at 1 GHz is achieved.

Fig. 4.
Fig. 4.

Time domain measurement of the optical negative delay (or optical advance) using an Aglient DCA 86100A system as an oscilloscope. An extra loss of about 4 dB is introduced in this measurement due to the splitting of the optical power to trigger the oscilloscope. This result agrees well with the data given in Fig. 3.

Equations (22)

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E ( t ) 2 E 0 2 + [ ( E 1 * E 0 + E 0 * E 1 ) e i Ω t + c . c . ]
p [ E ( t ) ] 2 P sat = p 0 + [ p 1 e i Ω t + c . c . ]
p 0 = E 0 2 P sat
p 1 = ( E 1 * E 0 + E 0 * E 1 ) P sat
dN dt = 1 qV N τ Γ g ( N ) ω 0 E ( t ) 2
N = N 0 [ ( N 0 N tr ) p 1 1 + p 0 i Ω τ e i Ω t + c . c . ]
d E 0 dz = 1 2 ( Γ g ( 1 i α ) 1 + p 0 a ) E 0
d E 1 dz = 1 2 [ Γ g ( 1 i α ) 1 + p 0 ( 1 p 0 1 + p 0 i Ω τ ) a ] E 1 1 2 Γ g ( 1 i α ) 1 + p 0 E 0 2 E 1 * P sat 1 + p 0 i Ω τ
d E 1 dz = 1 2 [ Γ g ( 1 i α ) 1 + p 0 ( 1 p 0 1 + p 0 + i Ω τ ) a ] E 1 1 2 Γ g ( 1 i α ) 1 + p 0 E 0 2 E 1 * P sat 1 + p 0 + i Ω τ
d p 0 dz = [ Γ g 1 + p 0 a ] p 0
d p 1 dz = [ a + Γ g 1 + p 0 ( 1 p 0 1 + p 0 i Ω τ ) ] p 1
G = Γ g a + Γ g aL [ 1 a Γ g ( 1 + p out ) 1 a Γ g ( 1 + p in ) ] 1 2 L 1 1 + ( Ω τ a Γ g ) 2
× { ln [ ( 1 + p out ) 2 + ( Ω τ ) 2 ( 1 + p in ) 2 + ( Ω τ ) 2 ] 2 ln [ 1 a Γ g ( 1 + p out ) 1 a Γ g ( 1 + p in ) ] 2 Ω τ a Γ g tan 1 [ ( p out p in ) Ω τ ( 1 + p out ) ( 1 + p in ) + ( Ω τ ) 2 ] }
Δ t = τ 2 1 1 + ( Ω τ a Γ g ) 2
× { a Γ g ln [ ( 1 + p out ) 2 + ( Ω τ ) 2 ( 1 + p in ) 2 + ( Ω τ ) 2 ] 2 ( a Γ g ) ln [ 1 a Γ g ( 1 + p out ) 1 a Γ g ( 1 + p in ) ] + a Ω τ tan 1 [ ( p out p in ) Ω τ ( 1 + p out ) ( 1 + p in ) + ( Ω τ ) 2 ] }
Γ g a ln ( Γ g a ( 1 + p out ) Γ g a ( 1 + p in ) ) = ln ( p out p in ) ( Γ g a ) L .
Δ t = τ ( a Γ g ) 2 ( Γ g a ) L 1 + ( Ω τ a Γ g ) 2
Δ t max = 4 τ Γ g L 27
Δ t Δ Ω FWHM = a ( Γ g a ) Γ g L
( Δ t Δ Ω FWHM ) max = Γ g L 4 at a = Γ g 2
Δ t = τ p in Γ g a Γ g 1 1 + ( Ω τ ) 2
Δ t Δ Ω FWHM = p in Γ g a Γ g Γ g a p in

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