## Photoinduced diffraction grating in hybrid artificial molecule |

Optics Express, Vol. 20, Issue 2, pp. 1219-1229 (2012)

http://dx.doi.org/10.1364/OE.20.001219

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### Abstract

Photoinduced diffraction grating is theoretically investigated in a three-level ladder-type hybrid artificial molecule comprised of a semiconductor quantum dot (SQD) and a metal nanoparticle (MNP). The SQD and the MNP are coupled via the Coulomb interaction. The probe absorption vanishes under the action of a strong coupling field, indicating an effect of electromagnetically induced transparency (EIT). Based on this EIT effect, diffraction grating is achievable when a standing-wave coupling field is applied. It turns out that the efficiency of diffraction grating is greatly improved due to the existence of the MNP. Furthermore, the diffraction efficiency can be controlled by tuning the interaction strength between the SQD and the MNP. Nearly pure phase grating is obtained, showing high transmissivity and high diffraction efficiency up to 33%.

© 2012 OSA

## 1. Introduction

1. W. Zhang, A. O. Govorov, and G. W. Bryant, “Semiconductor-metal nanoparticle molecules: hybrid excitons and the nonlinear fano effect,” Phys. Rev. Lett. **97**(14), 146804 (2006). [CrossRef] [PubMed]

9. S. M. Sadeghi, “The inhibition of optical excitations and enhancement of Rabi flopping in hybrid quantum dot-metallic nanoparticle systems,” Nanotechnology **20**(22), 225401 (2009). [CrossRef] [PubMed]

1. W. Zhang, A. O. Govorov, and G. W. Bryant, “Semiconductor-metal nanoparticle molecules: hybrid excitons and the nonlinear fano effect,” Phys. Rev. Lett. **97**(14), 146804 (2006). [CrossRef] [PubMed]

2. R. D. Artuso and G. W. Bryant, “Optical response of strongly coupled quantum dot-metal nanoparticle systems: double peaked Fano structure and bistability,” Nano Lett. **8**(7), 2106–2111 (2008). [CrossRef] [PubMed]

5. R. D. Artuso and G. W. Bryant, “Strongly coupled quantum dot-metal nanoparticle systems: Exciton-induced transparency, discontinuous response, and suppression as driven quantum oscillator effects,” Phys. Rev. B **82**(19), 195419 (2010). [CrossRef]

8. S. M. Sadeghi, L. Deng, X. Li, and W.-P. Huang, “Plasmonic (thermal) electromagnetically induced transparency in metallic nanoparticle-quantum dot hybrid systems,” Nanotechnology **20**(36), 365401 (2009). [CrossRef] [PubMed]

9. S. M. Sadeghi, “The inhibition of optical excitations and enhancement of Rabi flopping in hybrid quantum dot-metallic nanoparticle systems,” Nanotechnology **20**(22), 225401 (2009). [CrossRef] [PubMed]

## 2. Hybrid molecule

10. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B **6**(12), 4370–4379 (1972). [CrossRef]

11. P. K. Nielsen, H. Thyrrestrup, J. Mørk, and B. Tromborg, “Numerical investigation of electromagnetically induced transparency in a quantum dot structure,” Opt. Express **15**(10), 6396–6408 (2007). [CrossRef] [PubMed]

*eV*is taken from

*Ref.*

*10*

10. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B **6**(12), 4370–4379 (1972). [CrossRef]

7. R. D. Artuso, G. W. Bryant, A. Garcia-Etxarri, and J. Aizpurua, “Using local fields to tailor hybrid quantum-dot/metal nanoparticle systems,” Phys. Rev. B **83**(23), 235406 (2011). [CrossRef]

## 3. Photoinduced diffraction grating

*x-*direction. Therefore, the dynamic response of the probe field exhibits periodical modulation, and leads to form the absorption or phase grating.

*z*. Thus we may derive the transmission function for an interaction length

*L*of mediumwhere the first and second terms correspond to the absorption and phase modulation, respectively. For a standing-wave coupling field with Rabi frequency

*x-*direction as gratings. By performing the Fourier transformation on the transmission function, we obtain the Fraunhofer distribution (i.e. far-field distribution) of a single space period in the formwith

*z*-direction, and

*n-*order diffraction intensity is determined by Eq. (8), with

### 3.1 Absorption grating

*R*between the SQD and the MNP on the amplitude and phase of the transmission function, respectively. At large

*R,*the amplitude modulation is small [blue dotted line in Fig. 4a] which limits the diffraction efficiency of grating [blue solid line in Fig. 5a ]; while the amplitude modulation becomes large at small

*R*[red dashed (green solid) line in Fig. 4a] leading to the increment of the diffraction efficiency [red (green) solid line in Fig. 5a]. According to Eq. (7), it is seen that both amplitude and phase of the transmission function depend on the inter-particle distance

*R*, i.e., are influenced by the interaction strength between the SQD and the MNP. At the resonant case, the amplitude modulation is very sensitive to the value of

*R.*This effect can be understood as that the dipole-dipole interaction between the SQD and the MNP becomes weak when increasing the value of

*R*. The

*R*-dependent destructive or constructive interference causes the change of the probe absorption at the nodes or antinodes of standing wave.

*L*and the coupling intensity of standing-wave field

*R*. The first-order diffraction efficiency at different inter-particle distance

*R*is plotted as a function of the interaction length

*L*and the coupling intensity of standing-wave field

*R*and large

*L*or at large

*R*but small

*L*. Figure 7 indicates that the first-order diffraction efficiency for a fixed interaction length

*L*can be also slightly improved by properly increasing both the coupling intensity of standing-wave field and the inter-particle distance. Figure 6 and Fig. 7 illustrate that the absorption modulation depth and correspondingly the efficiency of the grating can be optimized by choosing the above physical parameters properly.

### 3.2 Phase grating

*R*between the SQD and the MNP can affect the diffraction efficiency of phase grating. The interaction strength between the SQD and the MNP varies as

*R*changes. The diffraction efficiency is low at small

*R*while increases at larger

*R*. For instance, the diffraction efficiency is approximate 33% at

*R*not only enhances the refractive index for the probe field, but also restrains the Columbic coupling strength between the SQD and the MNP. Therefore, in order to obtain a phase grating with the best performance in such a hybrid artificial molecule,

*R*has to be properly chosen.

## 4. Conclusions

## Acknowledgments

## References and links

1. | W. Zhang, A. O. Govorov, and G. W. Bryant, “Semiconductor-metal nanoparticle molecules: hybrid excitons and the nonlinear fano effect,” Phys. Rev. Lett. |

2. | R. D. Artuso and G. W. Bryant, “Optical response of strongly coupled quantum dot-metal nanoparticle systems: double peaked Fano structure and bistability,” Nano Lett. |

3. | J.-Y. Yan, W. Zhang, S. Duan, X.-G. Zhao, and A. Govorov, “Optical Properties of coupled metal-semiconductor and metal-molecule nanocrystal complexes: role of multipole effects,” Phys. Rev. B |

4. | A. O. Govorov, “Semiconductor-metal nanoparticle molecules in a magnetic field: Spin-plasmon and exciton-plasmon interactions,” Phys. Rev. B |

5. | R. D. Artuso and G. W. Bryant, “Strongly coupled quantum dot-metal nanoparticle systems: Exciton-induced transparency, discontinuous response, and suppression as driven quantum oscillator effects,” Phys. Rev. B |

6. | A. Ridolfo, O. Di Stefano, N. Fina, R. Saija, and S. Savasta, “Quantum plasmonics with quantum dot-metal nanoparticle molecules: influence of the Fano effect on photon statistics,” Phys. Rev. Lett. |

7. | R. D. Artuso, G. W. Bryant, A. Garcia-Etxarri, and J. Aizpurua, “Using local fields to tailor hybrid quantum-dot/metal nanoparticle systems,” Phys. Rev. B |

8. | S. M. Sadeghi, L. Deng, X. Li, and W.-P. Huang, “Plasmonic (thermal) electromagnetically induced transparency in metallic nanoparticle-quantum dot hybrid systems,” Nanotechnology |

9. | S. M. Sadeghi, “The inhibition of optical excitations and enhancement of Rabi flopping in hybrid quantum dot-metallic nanoparticle systems,” Nanotechnology |

10. | P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B |

11. | P. K. Nielsen, H. Thyrrestrup, J. Mørk, and B. Tromborg, “Numerical investigation of electromagnetically induced transparency in a quantum dot structure,” Opt. Express |

**OCIS Codes**

(050.1950) Diffraction and gratings : Diffraction gratings

(270.1670) Quantum optics : Coherent optical effects

(160.1245) Materials : Artificially engineered materials

(160.4236) Materials : Nanomaterials

**ToC Category:**

Diffraction and Gratings

**History**

Original Manuscript: October 3, 2011

Revised Manuscript: November 21, 2011

Manuscript Accepted: November 30, 2011

Published: January 5, 2012

**Citation**

Zhi-Hong Xiao, Li Zheng, and HongZhen Lin, "Photoinduced diffraction grating in hybrid artificial molecule," Opt. Express **20**, 1219-1229 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-2-1219

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### References

- W. Zhang, A. O. Govorov, and G. W. Bryant, “Semiconductor-metal nanoparticle molecules: hybrid excitons and the nonlinear fano effect,” Phys. Rev. Lett.97(14), 146804 (2006). [CrossRef] [PubMed]
- R. D. Artuso and G. W. Bryant, “Optical response of strongly coupled quantum dot-metal nanoparticle systems: double peaked Fano structure and bistability,” Nano Lett.8(7), 2106–2111 (2008). [CrossRef] [PubMed]
- J.-Y. Yan, W. Zhang, S. Duan, X.-G. Zhao, and A. Govorov, “Optical Properties of coupled metal-semiconductor and metal-molecule nanocrystal complexes: role of multipole effects,” Phys. Rev. B77(16), 165301 (2008). [CrossRef]
- A. O. Govorov, “Semiconductor-metal nanoparticle molecules in a magnetic field: Spin-plasmon and exciton-plasmon interactions,” Phys. Rev. B82(15), 155322 (2010). [CrossRef]
- R. D. Artuso and G. W. Bryant, “Strongly coupled quantum dot-metal nanoparticle systems: Exciton-induced transparency, discontinuous response, and suppression as driven quantum oscillator effects,” Phys. Rev. B82(19), 195419 (2010). [CrossRef]
- A. Ridolfo, O. Di Stefano, N. Fina, R. Saija, and S. Savasta, “Quantum plasmonics with quantum dot-metal nanoparticle molecules: influence of the Fano effect on photon statistics,” Phys. Rev. Lett.105(26), 263601 (2010). [CrossRef] [PubMed]
- R. D. Artuso, G. W. Bryant, A. Garcia-Etxarri, and J. Aizpurua, “Using local fields to tailor hybrid quantum-dot/metal nanoparticle systems,” Phys. Rev. B83(23), 235406 (2011). [CrossRef]
- S. M. Sadeghi, L. Deng, X. Li, and W.-P. Huang, “Plasmonic (thermal) electromagnetically induced transparency in metallic nanoparticle-quantum dot hybrid systems,” Nanotechnology20(36), 365401 (2009). [CrossRef] [PubMed]
- S. M. Sadeghi, “The inhibition of optical excitations and enhancement of Rabi flopping in hybrid quantum dot-metallic nanoparticle systems,” Nanotechnology20(22), 225401 (2009). [CrossRef] [PubMed]
- P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972). [CrossRef]
- P. K. Nielsen, H. Thyrrestrup, J. Mørk, and B. Tromborg, “Numerical investigation of electromagnetically induced transparency in a quantum dot structure,” Opt. Express15(10), 6396–6408 (2007). [CrossRef] [PubMed]

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