## Tunable slow and fast light device based on a carbon nanotube resonator |

Optics Express, Vol. 20, Issue 6, pp. 5840-5848 (2012)

http://dx.doi.org/10.1364/OE.20.005840

Acrobat PDF (1568 KB)

### Abstract

We report a tunable slow and fast light device based on a carbon nanotube resonator, in the presence of a strong pump laser and a weak signal laser. Detailed analysis shows that the signal laser displays the superluminal and ultraslow light characteristics via passing through a suspended carbon nanotube resonator, while the incident pump laser is on- and off-resonant with the exciton frequency, respectively. In particular, the fast and slow light correspond to the negative and positive dispersion, respectively, associating with the vanished absorption. The bandwidth of the signal spectrum is determined by the vibration decay rate of carbon nanotube.

© 2012 OSA

## 1. Introduction

1. R. W. Boyd and D. J. Gauthier, “Controlling the velocity of light pulses,” Science **326**, 1074 (2009). [CrossRef] [PubMed]

2. B. Gu, N. H. Kwong, R. Binder, and A. L. Smirl, “Slow and fast light associated with polariton interference,” Phys. Rev. B **82**, 035313 (2010). [CrossRef]

3. R. W. Boyd, D. J. Gauthier, and A. L. Gaeta, “Applications of slow light in telecommunications,” Opt. Photon. News **19**, 18 (2006). [CrossRef]

4. A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature **472**, 69 (2011). [CrossRef] [PubMed]

5. V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as a mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett. **107**, 133601 (2011). [CrossRef] [PubMed]

6. 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(1999). [CrossRef]

7. M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. **90**, 113903 (2003). [CrossRef] [PubMed]

8. V. I. Kovalev, N. E. Kotova, and R. G. Harrison, “Slow light in stimulated Brillouin scattering: on the influence of the spectral width of pump radiation on the group index: reply,” Opt. Express **18**, 8055 (2010). [CrossRef] [PubMed]

9. V. P. Kalosha, L. Chen, and X. Bao, “Slow and fast light via SBS in optical fibers for short pulses and broadband pump,” Opt. Express **14**, 12693 (2006). [CrossRef] [PubMed]

10. B. Wu, J. F. Hulbert, E. J. Lunt, K. Hurd, A. R. Hawkins, and H. Schmidt, “Slow light on a chip via atomic quantum state control,” Nat. Photonics **4**, 776 (2010). [CrossRef]

11. S. Stepanov and M. P. Sánchez, “Slow and fast light via two-wave mixing in erbium-doped fibers with saturable absorption,” Phys. Rev. A **80**, 053830 (2009). [CrossRef]

4. A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature **472**, 69 (2011). [CrossRef] [PubMed]

12. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today **50**, 36 (1997). [CrossRef]

*et al.*[4

4. A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature **472**, 69 (2011). [CrossRef] [PubMed]

14. P. Avouris, M. Freitag, and V. Perebeinos, “Carbon-nanotube photonics and optoelectronics,” Nat. Photonics **2**, 341 (2008). [CrossRef]

15. M. Muoth, T. Helbling, L. Durrer, S.-W. Lee, C. Roman, and C. Hierold, “Hysteresis-free operation of suspended carbon nanotube transistors,” Nat. Nanotechnol. **5**, 589 (2010). [CrossRef] [PubMed]

16. R. Singhal, Z. Orynbayeva, R. V. K. Sundaram, J. J. Niu, S. Bhattacharyya, E. A. Vitol, M. G. Schrlau, E. S. Papazoglou, G. Friedman, and Y. Gogotsi, “Multifunctional carbon-nanotube cellular endoscopes,” Nat. Nanotechnol. **6**, 57 (2010) [CrossRef] [PubMed]

20. H. Farhat, S. Berciaud, M. Kalbac, R. Saito, T. F. Heinz, M. S. Dresselhaus, and J. Kong, “Observation of electronic Raman scattering in metallic carbon nanotubes,” Phys. Rev. Lett. **107**, 157401 (2011). [CrossRef] [PubMed]

## 2. Theory

*ω*

*) and a weak signal laser (with frequency*

_{p}*ω*

*). Recently, such two-laser technique has been experimentally investigated by several groups to study the cavity optomechanical system and demonstrate the achievement of slow light and on-chip storage of light pulses [4*

_{s}**472**, 69 (2011). [CrossRef] [PubMed]

5. V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as a mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett. **107**, 133601 (2011). [CrossRef] [PubMed]

21. S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science **330**, 1520 (2010). [CrossRef] [PubMed]

22. J. D. Teufel, D. Li, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, and R. W. Simmonds, “Circuit cavity electromechanics in the strong-coupling regime,” Nature **471**, 204 (2011). [CrossRef] [PubMed]

*E*

_{//}. In turn the normal component

*E*

_{⊥}can be used to induce a tunable parametric coupling between the exciton and the flexural motion of the CNT [23]. This localized exciton is formed in the segment of nanotube between the doubly clamped suspensions, leading to a quantized energy spectrum in the longitudinal direction. The inset of Fig. 1 shows the energy levels of localized exciton in suspended nanotube resonator when dressing with the vibration modes of CNT, which can be modeled as a two-level structure consisting of the ground state |

*g*〉 and the first excited state (single exciton) |

*ex*〉. Such an exciton can be characterized by the pseudospin −1/2 operators

*S*

^{±}and

*S*

*. Then the Hamiltonian of this localized two-level exciton can be described as*

^{z}*H*

*=*

_{ex}*h̄ω*

_{ex}*S*, where

^{z}*ω*

*is the frequency of exciton. Besides, here we consider the flexural branch which is expected to present resonance with a free spectral range larger than the optical linewidth of the zero phonon line of the excitonic transition and focus on laser excitations near resonant with the lowest-frequency flexural phonon mode [23, 24*

_{ex}24. I. Wilson-Rae, “Intrinsic dissipation in nanomechanical resonators due to phonon tunneling,” Phys. Rev. B **77**, 245418 (2008). [CrossRef]

*ω*

*and the resonator is assumed to be characterized by sufficiently high quality factors. The eigenmode of CNT can be described by a quantum harmonic oscillator with*

_{n}*b*and

*b*

^{+}(the bosonic annihilation and creation operators with a quantum energy

*h̄ω*

*). The vibration Hamiltonian of nanotube resonator is given by*

_{n}*H*

*=*

_{n}*h̄ω*

_{n}*b*

^{+}

*b*, where the vibration modes of CNT can be treated as phonon modes.

26. J. J. Li and K. D. Zhu, “All-optical Kerr modulator based on a carbon nanotube resonator,” Phys. Rev. B **83**, 115445 (2011). [CrossRef]

*H*

_{ex}_{–}

*=*

_{n}*h̄ω*

_{n}*ηS*

*(*

^{z}*b*

^{+}+

*b*) represents the interaction between the nanotube resonator and the exciton [23, 27], and

*η*is the coupling strength.

*E*

*and*

_{p}*E*

*are slowly varying envelopes of the pump field and signal field, respectively, and*

_{s}*μ*is the electric dipole moment of the exciton. In a frame rotating at the pump field frequency

*ω*

*, the total Hamiltonian of the coupled system reads as follows where Δ*

_{p}*=*

_{p}*ω*

*–*

_{ex}*ω*

*is the pump field-exciton detuning,*

_{p}*δ*=

*ω*

*–*

_{s}*ω*

*is the signal-pump field detuning, and Ω =*

_{p}*μE*

*/*

_{p}*h̄*is the Rabi frequency of the pump laser.

31. V. Giovannetti and D. Vitali, “Phase-noise measurement in a cavity with a movable mirror undergoing quantum Brownian motion,” Phys. Rev. A **63**, 023812 (2001). [CrossRef]

*Q*=

*ω*

*/*

_{n}*γ*

*≫ 1. The Brownian noise operator can be modeled as Markovian with the decay rate*

_{n}*γ*

*(*

_{n}*γ*

*= 1/*

_{n}*τ*

*) of the resonator mode. Therefore, the Brownian stochastic force has zero mean value 〈*

_{n}*ξ̂*〉 = 0 that can be characterized as [31

31. V. Giovannetti and D. Vitali, “Phase-noise measurement in a cavity with a movable mirror undergoing quantum Brownian motion,” Phys. Rev. A **63**, 023812 (2001). [CrossRef]

*δQδS*

^{−}. Since the optical drives are weak, but classical coherent fields, we will identify all operators with their expectation values, and drop the quantum and thermal noise terms [21

21. S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science **330**, 1520 (2010). [CrossRef] [PubMed]

21. S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science **330**, 1520 (2010). [CrossRef] [PubMed]

*δS*

^{−}〉 = S

_{+}e

*+*

^{−iδt}*S*

_{−}

*e*

*,*

^{iδt}*δQ*〉 =

*Q*

_{+}

*e*

*+*

^{−iδt}*Q*

_{−}

*e*

*. Upon substituting the approximation to Eqs. (9)–(11) and working to the lowest order in*

^{iδt}*E*

*, but to all orders in*

_{s}*E*

*, we finally obtain the linear optical susceptibility*

_{p}*S*

^{+}in the steady state as the following solution where Σ

_{1}=

*ρμ*

^{2}/

*ε*

_{0}

*h̄*Γ

_{2},

*ρ*is the number density of CNT, which during the measurement the identical resonator arrays are needed because of the weak measurable signal and weak interaction with light produced by a single nanotube resonator. For a better experimental observation,

*ρ*should be about 10

^{9}

*m*

^{−3}[32

32. S. Yasukochi, T. Murai, S. Moritsubo, T. Shimada, S. Chiashi, S. Maruyama, and Y. K. Kato, “Gate-induced blueshift and quenching of photoluminescence in suspended single-walled carbon nanotubes,” Phys. Rev. B **84**, 121409 (2011). [CrossRef]

*ε*

_{0}is the dielectric constant of vacuum. In Eq. (12), the imaginary part and real part of

*χ*

^{(1)}(

*ω*

*) correspond to the absorption and dispersion of the signal field, respectively [25]. In this case, all the interacting elements are considered during the physical treatment, except for the light-phonons coupling which is induced indirectly through the light-exciton interaction via deformation potential coupling. The dimensionless linear optical susceptibility is given by where*

_{s}*e*

_{1}= Δ

_{p}_{0}–

*ω*

_{n}_{0}

*η*

^{2}

*w*

_{0}+

*i*,

*e*

_{2}= Δ

_{p}_{0}–

*ω*

_{n}_{0}

*η*

^{2}

*w*

_{0}–

*i*, and

_{1}= 2Γ

_{2},

*ω*

_{n}_{0}=

*ω*

*/Γ*

_{n}_{2},

*γ*

_{n}_{0}=

*γ*

*/Γ*

_{n}_{2}, Ω

*= Ω/Γ*

_{R}_{2},

*δ*

_{0}=

*δ*/Γ

_{2}, and Δ

_{p}_{0}= Δ

*/Γ*

_{p}_{2}.

*ζ*(

*δ*

_{0}) and function

*f*(

*δ*

_{0}) are given by The population inversion

*w*

_{0}of the exciton is determined by the following equation

33. R. S. Bennink, R. W. Boyd, C. R. Stroud, and V. Wong, “Enhanced self-action effects by electromagnetically induced transparency in the two-level atom,” Phys. Rev. A **63**, 033804 (2001). [CrossRef]

34. S. E. Harris, J. E. Field, and A. Kasapi, “Dispersive properties of electromagnetically induced transparency,” Phys. Rev. A **46**, R29 (1992). [CrossRef] [PubMed]

*v*

*that when*

_{g}*Reχ*(

*ω*

*)*

_{s}_{ωs=ωex}is zero and the dispersion is steeply positive or negative, the group velocity is significantly reduced or increased, and then we define the group velocity index

*n*

*as where*

_{g}*n*> 0, and the superluminal light when

_{g}*n*< 0 [35

_{g}35. R. W. Boyd and D. J. Gauthier, “Controlling the velocity of light pulses,” Science **326**, 1074 (2009). [CrossRef] [PubMed]

## 3. Numerical results and discussion

*ω*

*/2*

_{n}*π*,Γ

_{2},

*γ*

*,*

_{n}*η*) = (725

*MHz*,310

*MHz*,0.8

*MHz*,0.17) [23, 26

26. J. J. Li and K. D. Zhu, “All-optical Kerr modulator based on a carbon nanotube resonator,” Phys. Rev. B **83**, 115445 (2011). [CrossRef]

*Q*= 900.

*δ*with Δ

_{p}_{0}= 0 (as shown in Fig. 2). Since the original energy levels of the localized exciton have been dressed by the vibration modes of the nanotube (here the vibration modes is the same as the phonon modes), the uncoupled energy levels (|

*ex*〉 and |

*g*〉) split into dressed states |

*ex*,

*n*〉 and |

*g*,

*n*〉, which is shown in Fig. 2(b) (|

*n*〉 denotes the number state of the resonance mode). The curve shown in the Fig. 2(a) displays three prominent features - the middle part consisting of three weak peaks and two sharp peaks at the both sides. The middle part is analogy with conventional atomic two-level systems [25], which shows the origin of nanotube vibration induced stimulated Rayleigh resonance. Here the electrons make a transition from the lowest dressed level |

*g*,

*n*〉 to the dressed level |

*ex*,

*n*〉, which is signified by the transition 2. Besides, it’s worth notice that the two sharp peaks at the both sides in absorption spectrum are totally different from those in atomic system [25]. These two sharp peaks represent the resonance amplification and absorption of the carbon nanotube, which can be interpreted by the transition 1 and 3. The left peak corresponds to the amplification of the signal laser, where electrons making a transition from the lowest dressed level |

*g*,

*n*〉 to the highest dressed level |

*ex*,

*n*+ 1〉 by the simultaneous absorption of two pump laser photons and emission of a photon at

*ω*

*–*

_{p}*ω*

*. This process can amplify a wave at*

_{n}*δ*= −

*ω*

*. Otherwise, the right peak is an absorption process, which corresponds to the usual absorption resonance as modified by the ac-Stark effect. The underlying physical mechanism for this phenomenon can also be understood as follows. The simultaneous presence of the pump and signal fields generates a beat wave oscillating at the beat frequency*

_{n}*δ*=

*ω*

*–*

_{s}*ω*

*to drive the CNT via the localized exciton. If the beat frequency*

_{p}*δ*is close to the resonance frequency

*ω*

*, the CNT starts to oscillate coherently, which will result in Stokes (*

_{n}*ω*

*=*

_{s}*ω*

*–*

_{p}*ω*

*) and anti-Stokes (*

_{n}*ω*

*=*

_{as}*ω*

*+*

_{p}*ω*

*) scattering of light from the pump field via the localized exciton. For the near-resonant signal laser, the signal field will interfere with the Stokes field and the anti-Stokes field, respectively. As a result the signal spectrum can be modified significantly. In the picture of the dressed states, the system is similar to the conventional three-level system in EIT. Here coupling to phonons seems to provide the exciton with additional energy levels to realize EIT phenomena. Therefore in our structure one can obtain the slow output light without absorption only by simply adjusting the pump-exciton detuning to the vibrational frequency of the nanotube resonator. In this case, we conclude that the coupling between exciton and the vibration of carbon nanotube plays an important role in the implement of these specific features.*

_{n}*= 0, while the right part exhibits the slow light situation with Δ*

_{p}*=*

_{p}*ω*

*. Figure 3(a) shows the imaginary part and real part of linear optical susceptibility while fixing Δ*

_{n}*= 0, which correspond to the absorption and dispersion of the signal light, respectively. From this figure, we find that the the imaginary part has a zero absorption and the real part has a negative steep slope at Δ*

_{p}*= 0, which signifies the potential of superluminal light achievement. We next plot the group velocity index of signal laser*

_{s}*n*

*(in the unit of Σ) as a function of the Rabi frequency Ω*

_{g}^{2}, as shown in Fig. 3(b). Figure 3(b) indicates that the output signal pulse can be about 10 times faster than input signal pulse in vacuum simply via tuning the pump laser on the resonant with exciton frequency in CNT resonator(Δ

*= 0). Furthermore, in the case of pump-off resonant (Δ*

_{p}*=*

_{p}*ω*

*), the imaginary part and real part of linear optical susceptibility exhibit zero absorption and positive steep slope at Δ*

_{n}*= 0 in Fig. 3(c), which denotes the possibility of ultraslow light realization. Figure 3(d) exhibits the slow light curve, where the most slow-light index can be produced in CNT resonator device as 180 as Ω*

_{s}^{2}= 0.02(

*GHz*)

^{2}. That is, the output signal pulse will be 180 times slower than the input light with a single CNT resonator. The total magnitude of slow light and fast light is determined by the number density of CNT resonator. The physical origin of this result is the coupling between exciton and CNT vibration, which makes quantum interference between the CNT and the two optical fields via the exciton as

*δ*=

*ω*

*. Such nonlinear process is analogy with electromagnetically induced transparency (EIT), which has been discussed in Fig. 2(b).*

_{n}*=*

_{p}*ω*

*just corresponds to that the pump field couples to the optical transition via the Stokes process and the system becomes fully transparent to the signal beam. In this case, the system is similar to the conventional three-level systems in EIT [36*

_{n}36. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. **77**, 633 (2005). [CrossRef]

*χ*

^{(1)}as a function of Δ

*for three different decay rates of*

_{s}*γ*

*. The inset of Fig. 4 shows the amplification of the most remarkable region of transparency. From this figure, we can demonstrate that the width of the signal spectrum increases as the decay rate*

_{n}*γ*

*increases. Therefore the shorter the CNT resonator decay is, the narrower of the signal spectrum width is. When the decay rate of the resonator is 0.1*

_{n}*GHz*, the hole width in the spectrum becomes flat as shown in the inset. As a result, the CNT resonator with small decay rate is beneficial to the transparency window. Due to the hight quality factor and short decay rate of CNT resonator, the slow light and fast light effect performed in CNT is obviously better than that in other quantum systems such as quantum wells and quantum dots.

*=*

_{s}*ω*

*= 725*

_{n}*MHz*). That is, fixing the pump laser on the exciton frequency Δ

*= 0 and scanning the exciton frequency using another signal laser, one can obtain the vibrational frequency of CNT resonator at signal absorption or dispersion spectrum efficiently. This is a precise and easy method to get the vibrational frequency of CNT resonator in all optical domain.*

_{p}## 4. Conclusion

## Acknowledgments

## References and links

1. | R. W. Boyd and D. J. Gauthier, “Controlling the velocity of light pulses,” Science |

2. | B. Gu, N. H. Kwong, R. Binder, and A. L. Smirl, “Slow and fast light associated with polariton interference,” Phys. Rev. B |

3. | R. W. Boyd, D. J. Gauthier, and A. L. Gaeta, “Applications of slow light in telecommunications,” Opt. Photon. News |

4. | A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature |

5. | V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as a mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett. |

6. | 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 |

7. | M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. |

8. | V. I. Kovalev, N. E. Kotova, and R. G. Harrison, “Slow light in stimulated Brillouin scattering: on the influence of the spectral width of pump radiation on the group index: reply,” Opt. Express |

9. | V. P. Kalosha, L. Chen, and X. Bao, “Slow and fast light via SBS in optical fibers for short pulses and broadband pump,” Opt. Express |

10. | B. Wu, J. F. Hulbert, E. J. Lunt, K. Hurd, A. R. Hawkins, and H. Schmidt, “Slow light on a chip via atomic quantum state control,” Nat. Photonics |

11. | S. Stepanov and M. P. Sánchez, “Slow and fast light via two-wave mixing in erbium-doped fibers with saturable absorption,” Phys. Rev. A |

12. | S. E. Harris, “Electromagnetically induced transparency,” Phys. Today |

13. | M. O. Scully and M. S. Zubairy, |

14. | P. Avouris, M. Freitag, and V. Perebeinos, “Carbon-nanotube photonics and optoelectronics,” Nat. Photonics |

15. | M. Muoth, T. Helbling, L. Durrer, S.-W. Lee, C. Roman, and C. Hierold, “Hysteresis-free operation of suspended carbon nanotube transistors,” Nat. Nanotechnol. |

16. | R. Singhal, Z. Orynbayeva, R. V. K. Sundaram, J. J. Niu, S. Bhattacharyya, E. A. Vitol, M. G. Schrlau, E. S. Papazoglou, G. Friedman, and Y. Gogotsi, “Multifunctional carbon-nanotube cellular endoscopes,” Nat. Nanotechnol. |

17. | W. Belzig, “Hybrid superconducting devices: bound in a nanotube,” Nat. Phys. |

18. | A. Pályi, P. R. Struck, M. Rudner, K. Flensberg, and G. Burkard, “Spin-orbit induced strong coupling of a single spin to a nanomechanical resonator,” ArXiv:1110.4893v1 (2011). |

19. | C. Ohm, C. Stampfer, J. Splettstoesser, and M. R. Wegewijs, “Readout of carbon nanotube vibrations based on spin-phonon coupling,” ArXiv:1110.5165v1 (2011). |

20. | H. Farhat, S. Berciaud, M. Kalbac, R. Saito, T. F. Heinz, M. S. Dresselhaus, and J. Kong, “Observation of electronic Raman scattering in metallic carbon nanotubes,” Phys. Rev. Lett. |

21. | S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science |

22. | J. D. Teufel, D. Li, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, and R. W. Simmonds, “Circuit cavity electromechanics in the strong-coupling regime,” Nature |

23. | I. Wilson-Rae, C. Galland, W. Zwerger, and A. Imamoğlu, “Nano-optomechanics with localized carbon nanotube excitons,” arXiv:0911.1330 (2009). |

24. | I. Wilson-Rae, “Intrinsic dissipation in nanomechanical resonators due to phonon tunneling,” Phys. Rev. B |

25. | R. W. Boyd, |

26. | J. J. Li and K. D. Zhu, “All-optical Kerr modulator based on a carbon nanotube resonator,” Phys. Rev. B |

27. | K. F. Graff, |

28. | C. W. Gardiner and P. Zoller, |

29. | D. F. Walls and G. J. Milburn, |

30. | K. L. Ekinci and M. L. Roukes, “Nanoelectromechanical systems,” Rev. Sci. Instrum. |

31. | V. Giovannetti and D. Vitali, “Phase-noise measurement in a cavity with a movable mirror undergoing quantum Brownian motion,” Phys. Rev. A |

32. | S. Yasukochi, T. Murai, S. Moritsubo, T. Shimada, S. Chiashi, S. Maruyama, and Y. K. Kato, “Gate-induced blueshift and quenching of photoluminescence in suspended single-walled carbon nanotubes,” Phys. Rev. B |

33. | R. S. Bennink, R. W. Boyd, C. R. Stroud, and V. Wong, “Enhanced self-action effects by electromagnetically induced transparency in the two-level atom,” Phys. Rev. A |

34. | S. E. Harris, J. E. Field, and A. Kasapi, “Dispersive properties of electromagnetically induced transparency,” Phys. Rev. A |

35. | R. W. Boyd and D. J. Gauthier, “Controlling the velocity of light pulses,” Science |

36. | M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. |

**OCIS Codes**

(230.1150) Optical devices : All-optical devices

(270.0270) Quantum optics : Quantum optics

**ToC Category:**

Optical Devices

**History**

Original Manuscript: November 14, 2011

Revised Manuscript: December 24, 2011

Manuscript Accepted: January 20, 2012

Published: February 27, 2012

**Citation**

Jin-Jin Li and Ka-Di Zhu, "Tunable slow and fast light device based on a carbon nanotube resonator," Opt. Express **20**, 5840-5848 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-6-5840

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### References

- R. W. Boyd and D. J. Gauthier, “Controlling the velocity of light pulses,” Science326, 1074 (2009). [CrossRef] [PubMed]
- B. Gu, N. H. Kwong, R. Binder, and A. L. Smirl, “Slow and fast light associated with polariton interference,” Phys. Rev. B82, 035313 (2010). [CrossRef]
- R. W. Boyd, D. J. Gauthier, and A. L. Gaeta, “Applications of slow light in telecommunications,” Opt. Photon. News19, 18 (2006). [CrossRef]
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