## Variable optical delay using population oscillation and four-wave-mixing in semiconductor optical amplifiers

Optics Express, Vol. 14, Issue 11, pp. 4800-4807 (2006)

http://dx.doi.org/10.1364/OE.14.004800

Acrobat PDF (301 KB)

### 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

## 1. Introduction

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]

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]

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]

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]

## 2. Theory and Experiment

*E*is the DC component,

_{0}*E*and

_{-1}*E*are the amplitudes of the two side bands, and Ω is the beat frequency. For simplicity, the optical intensities are normalized to the saturation intensity of the SOA, which is defined as

_{1}*P*=

_{sat}*hν/(g’τ)*, where

*hν*is the photon energy,

*g*’ is the differential gain, and

*τ*is the carrier lifetime. Therefore, Eq. (1) becomes,

*N*is the carrier density,

*I*is the injection current,

*q*is the unit electron charge,

*V*is the volume of the active region,

*hω*the photon energy,

_{0}*Γ*is the modal gain, N

_{g}_{0}is the DC carrier density, N

_{tr}is the transparency carrier density. Conversely, the population oscillation, functioning as a temporal grating, causes dispersive gain and index modifications on the two sidebands and effectively induces wave-mixings between the three optical fields as described by the following equations:

*a*is the unsaturable loss of the semiconductor waveguide. Detailed derivation of Eq. (7–9) can be found in Ref. 10. As shown in Eq. (8) and Eq. (9), the effective gain and refractive index of the two sidebands are modified by the DC optical pump

*p*

_{0}(

*χ*

^{(1)}effect), and the sidebands are coupled to each other through the FWM term which is proportional to the square of

*E*

_{0}(

*χ*

^{(3)}effect) [10

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]

*p*

_{1}or its conjugate), instead of the E-fields. From Eq. (8) and (9), we derive the following equations describing the propagation of DC (

*p*

_{0}) and AC (

*p*

_{1}) optical signals along the waveguide:

*p*

_{1}and

*p*

_{0}. This is not surprising since slow light was realized in solid state crystals where atomic energy systems of active ions provide a zero linewidth enhancement factor. Therefore, we would like to point out that the small linewidth enhancement factor of quantum dots is not a disadvantage in term of the variable optical delay discussed in this paper.

*p*

_{1}, however, it is unfeasible to integrate Eq. (11) directly over the spatial variation. Fortunately, if we divide Eq. (11) by Eq. (10) and integrate over the variable of

*p*

_{0}, we obtain the expressions for the gain and optical delay of the optical signal

*p*

_{1}:

*p*and

_{out}*p*are the output and input power of

_{in}*p*

_{0}, respectively.

## 3. Experimental Results and Comparison with Theory

*p*to 240

_{s}*p*, which is reasonable for typical SOAs [11

_{s}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]

*a/Γg*, is found to 0.1, and the normalized output power,

*p*, about 2.0. In the case of low current injection, these two parameters become more intervened with each other and, thus, have large uncertainties. However, the loss-gain ratio and output power are still within a reasonable range.

_{out}## 4. Generalization of the theory and discussion

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]

*p*)

_{out}^{0.5}as described by Eq. (13), while the mean-field theory gives a dependence of (1+

*p*) [10

_{ave}**5**, 147–159 (1988). [CrossRef]

*p*is the normalized average optical power of the DC component.

_{ave}*p*will saturate and the only term scaled with the cavity length is

_{out}*(Γg-a)L*. Therefore, from Eq. (13), the optical delay of a long device can be simplified into:

*Γg*~50-100 cm

_{max}^{-1}) of QW semiconductors, we need to increase the loss (typically 10–20 cm

^{-1}) either by ion implantation in the materials or by roughening the sidewalls of the waveguide. As predicted by Eq. (15), a maximum delay can be achieved when the unsaturable loss equals to the value of 2

*Γg*/3. In this case, the maximum delay, with a bandwidth of 3/(2

_{max}*τ*), is given as:

*ΓgL*/4, the loss of the waveguide needs to be designed to be half of the maximum gain. For a length of 1 cm and a typical modal gain of 80 cm

^{-1}, the delay-bandwidth product of 20 can be achievable with the unsaturable loss designed to be 40 cm

^{-1}. To the best of our knowledge, it is for the first time that these criteria are established to optimize the variable delay in SOAs. Physically, for a long device, the optical power will be saturated at the value of

*Γg/a*-1 as predicted by Eq. (10). Thus, under this situation, the solution of Eq. (11) under mean-field approximation is exactly the same as Eq. (15).

*p*can be ignored under the circumstance of either strong absorption or long devices.

_{out}*p*is also a small value in real communication systems considering the few mW output from distributed feedback lasers (as light source) and the loss (typically 6–10 dB) in the coupling between fibers and SOAs. Under these approximations, the delay described by Eq.(13) can be simplified into:

_{in}*p*, a linear dependence on the pump power and independent of the device length. To achieve maximum delay-bandwidth product in a semiconductor optical absorber, the loss of the waveguide needs to be minimized.

_{in}## 5. Summary

## Acknowledgments

## References and Links

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 |

2. | J. Marangos, “Slow light in cool atoms,” Nature |

3. | M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science |

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 |

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. |

6. | S. Minin, M. R. Fisher, and S. L. Chuang, “Current-controlled group delay using a semiconductor Fabry-Perot amplifier,” Appl. Phys. Lett. |

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 |

8. | H. Su and S. L. Chuang, “Room temperature slow light in quantum-dot devices,” Opt. Lett. |

9. | H. Su and S. L. Chuang, “Room temperature fast light in a quantum-dot semiconductor amplifier,” Appl. Phys. Lett. |

10. | G. P. Agrawal, “Population Pulsations and Nondegenerate 4-Wave Mixing in Semiconductor-Lasers and Amplifiers,” J. Opt. Soc. Am. B |

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. |

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. |

**OCIS Codes**

(140.4480) Lasers and laser optics : Optical amplifiers

(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing

(230.1150) Optical devices : All-optical devices

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: March 9, 2006

Revised Manuscript: May 9, 2006

Manuscript Accepted: May 11, 2006

Published: May 29, 2006

**Citation**

Hui Su, Piotr Kondratko, and Shun L. Chuang, "Variable optical delay using population oscillation and four-wave-mixing in semiconductor optical amplifiers," Opt. Express **14**, 4800-4807 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-11-4800

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### References

- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]

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