## Demonstration of modulatable optical near-field interactions between dispersed resonant quantum dots |

Optics Express, Vol. 19, Issue 19, pp. 18260-18271 (2011)

http://dx.doi.org/10.1364/OE.19.018260

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### Abstract

We experimentally demonstrated the basic concept of modulatable optical near-field interactions by utilizing energy transfer between closely positioned resonant CdSe/ZnS quantum dot (QD) pairs dispersed on a flexible substrate. Modulation by physical flexion of the substrate changes the distances between quantum dots to control the magnitude of the coupling strength. The modulation capability was qualitatively confirmed as a change of the emission spectrum. We defined two kinds of modulatability for quantitative evaluation of the capability, and an evident difference was revealed between resonant and non-resonant QDs.

© 2011 OSA

## 1. Introduction

3. K. Kobayashi, S. Sangu, T. Kawazoe, and M. Ohtsu, “Exciton dynamics and logic operations in a near-field optically coupled quantum-dot system,” J. Lumin. **112**(1-4), 117–121 (2005). [CrossRef]

5. T. Kawazoe, M. Ohtsu, S. Aso, Y. Sawado, Y. Hosoda, K. Yoshizawa, K. Akahane, N. Yamamoto, and M. Naruse, “Two-dimensional array of room-temperature nanophotonic logic gates using InAs quantum dots in mesa structures,” Appl. Phys. B **103**(3), 537–546 (2011). [CrossRef]

6. C. R. Kagan, C. B. Murray, and M. G. Bawendi, “Long-range resonance transfer of electronic excitations in close-packed CdSe quantum-dot solids,” Phys. Rev. B Condens. Matter **54**(12), 8633–8643 (1996). [CrossRef] [PubMed]

10. T. Franzl, T. A. Klar, S. Schietinger, A. L. Rogach, and J. Feldmann, “Exciton recycling in graded gap nanocrystal structures,” Nano Lett. **4**(9), 1599–1603 (2004). [CrossRef]

*one-to-one*correspondence with respect to input signals, because the physical properties, size, shape, and alignment of the components for the characteristic optical near-field interactions are built into the substrate and spatially fixed. In order to realize a

*one-to-many*correspondence with a single nanophotonic device, it is necessary to implement

*modulatable*optical near-field interactions and associated

*modulatable*optical functions. Here, we propose a novel concept of

*Modulatable Nanophotonics*to realize such a system. It is realized by providing appropriate external controls to modulate the parameters of the components. In our concept, optical far-field retrieval of induced optical near-field interactions is achieved via modulation of the intensity, polarization, and spectrum of the subsequent irradiation. This is an important step toward further exploiting the possibilities of light–matter interactions on the nanometer scale [11

11. N. Tate, W. Nomura, T. Yatsui, T. Kawazoe, M. Naruse, and M. Ohtsu, “Parallel retrieval of nanometer-scale light-matter interactions for nanophotonic systems,” Nat. Comput. **2**, 298–307 (2010). [CrossRef]

## 2. Modulation of emission spectra of resonant quantum dot pairs

*resonant*conditions between appropriate QD pairs on a physically flexible substrate. A conceptual diagram is shown in Fig. 1 . Closely positioned resonant QD pairs exhibit high-quantum-efficiency and selective energy transfer via induced optical near-fields between QDs. As a typical case of local energy transfer, here we consider the optical near-field interaction between the exciton of the lowest excited state

*E*

_{1S}in a smaller QD and that of the second-lowest excited state

*E*

_{2L}in a larger QD. These two states are electric dipole allowed and forbidden energy levels, respectively [12

12. N. Sakakura and Y. Masumoto, “Persistent spectral-hole-burning spectroscopy of CuCl quantum cubes,” Phys. Rev. B **56**(7), 4051–4055 (1997). [CrossRef]

13. Z. K. Tang, A. Yanase, T. Yasui, Y. Segawa, and K. Cho, “Optical selection rule and oscillator strength of confined exciton system in CuCl thin films,” Phys. Rev. Lett. **71**(9), 1431–1434 (1993). [CrossRef] [PubMed]

*E*

_{1S}=

*E*

_{2L}because of the steep gradient field due to the localized nature of the optical near-field. Thus, the excitation energy in the smaller QD is transferred to the larger QD via this optical near-field interaction. The important point is that energy can be successfully transferred from the smaller QD to the larger QD only if

*E*

_{1S}and

*E*

_{2L}are in a resonant condition. Transferred energy is immediately dissipated from

*E*

_{2L}to the lowest excited state

*E*

_{1L}of the larger QD, and a photon is then emitted. Experimental and theoretical results showing good agreement with each other have been discussed in detail in previous papers [6

6. C. R. Kagan, C. B. Murray, and M. G. Bawendi, “Long-range resonance transfer of electronic excitations in close-packed CdSe quantum-dot solids,” Phys. Rev. B Condens. Matter **54**(12), 8633–8643 (1996). [CrossRef] [PubMed]

9. T. Franzl, D. S. Koktysh, T. A. Klar, A. L. Rogach, J. Feldmann, and N. Gaponik, “Fast energy transfer in layer-by-layer aAssembled CdTe nanocrystal bilayers,” Appl. Phys. Lett. **84**(15), 2904–2906 (2004). [CrossRef]

14. T. Kawazoe, K. Kobayashi, J. Lim, Y. Narita, and M. Ohtsu, “Direct observation of optically forbidden energy transfer between CuCl quantum cubes via near-field optical spectroscopy,” Phys. Rev. Lett. **88**(6), 067404 (2002). [CrossRef] [PubMed]

_{S-R}and QD

_{L-R}in Fig. 2(a), energy transfers occur when the QDs are sufficiently close, because the magnitude of the optical near-field interaction, i.e., the coupling strength between QD

_{S-R}and QD

_{L-R}, depends on the distance

*r*between them, as represented by the Yukawa function:where

*μ*and

*A*represent distribution of optical near-fields which determined by exciton energy and amount proportional to the dipole moment, respectively [2]. Thus, emission is preferentially obtained from

*E*

_{1L}of QD

_{L-R}. In contrast, if the separation between QD

_{S-R}and QD

_{L-R}is increased by flexion of the substrate in order to significantly decrease the coupling strength, both QD

_{S-R}and QD

_{L-R}emit independently. This means that the spectral intensities of QD

_{S-R}and QD

_{L-R,}as well as the relative spectral intensity ratio from them, can be modulated by the flexion, i.e., by modulating the coupling strength. Thus, the spectral intensity ratios from QD

_{S-R}and QD

_{L-R}with and without the flexion are evidently different, as shown in Fig. 2(b). On the other hand, in the case of non-resonant QDs, denoted QD

_{S-NR}and QD

_{L-NR}in Fig. 3(a) , energy transfer never occurs between the two. Each QD emits individually regardless of whether the substrate is flexed. In this case, only a change in spectral intensity that depends on the areal density of the QDs is obtained. Therefore, the spectral intensity ratios from QD

_{S-NR}and QD

_{L-NR}with and without flexion are equal, as shown in Fig. 3(b).

*modulatability*

*I*and

_{S}and QD

_{L}are represented as

*E*

_{1S}and

*E*

_{1L}, respectively. In the case of the resonant QDs, as shown in Fig. 2(b), the value of

## 3. Numerical demonstration

_{S-A}and QD

_{S-C}) and two large QDs (QD

_{L-B}and QD

_{L-D}), representing many QDs dispersed on the substrate, as shown in Fig. 4 . We simulated the temporal evolution of exciton populations of the relevant excited states in these QDs by quantum master equations [15]. The exciton populations correspond to the intensity of radiation from each QD, and their evolutions are modulated by modulating the magnitude of the optical near-field coupling strength between QDs, by flexion of the substrate. As previously reported in [16

16. M. Naruse, H. Hori, K. Kobayashi, P. Holmström, L. Thylén, and M. Ohtsu, “Lower bound of energy dissipation in optical excitation transfer via optical near-field interactions,” Opt. Express **18**(Suppl 4), A544–A553 (2010). [CrossRef] [PubMed]

*r*, which corresponds to different degrees of coupling, controlled by flexion, as shown by Fig. 4(a). Initial distances between each QD are set on a 2D

*xy*-surface as

_{S}and QD

_{L}, denoted as

17. W. Nomura, T. Yatsui, T. Kawazoe, and M. Ohtsu, “The observation of dissipated optical energy transfer between CdSe quantum dots,” J. Nanophotonics **1**, 011591 (2007). [CrossRef]

18. K. Kobayashi, S. Sangu, H. Ito, and M. Ohtsu, “Near-field optical potential for a neutral atom,” Phys. Rev. A **63**, 013806 (2000). [CrossRef]

*L*, is assumed to be approximately 50 nm, and that of the larger QDs,

*stretching*of the substrate in the

*x*and

*y*directions, as shown in Fig. 5(a) , and calculated the exciton populations with various stretch lengths

*x*-directional stretching,

*y*-directional stretching,

*x*-directional stretching, because the excitons always preferentially transfer from smaller QDs to larger QDs (from QD

_{S-A}to QD

_{L-D}). This result indicates that the coupling strength between the smaller QDs and the larger QDs is decreased by the

*x*-directional stretching, and they emit independently.

*x*-directional stretching, as shown in Fig. 5(a),

*y*-directional stretching gives

*modulatable nanophotonic system*.

*x*-directional shift of QD

_{S-C}and QD

_{L-D}. Its schematic diagram is shown in Fig. 5(c). In the case of the model,

_{S-C}and QD

_{L-D}, only the exciton population at QD

_{L-B}increases, because the magnitude of energy transfer toward QD

_{L-B}increases not only from QD

_{S-A}but also from QD

_{S-C}. In contrast, that to QD

_{L-D}decreases. This is also because of the increase in the energy transferred from QD

_{S-C}not only to QD

_{L-D}but also to QD

_{L-B}. As a result, the population at QD

_{S-C}is decreased, whereas that at QD

_{S-A}remains unchanged, because the main route of energy transfer is from QD

_{S-A}to QD

_{L-B}, regardless of the stretching. Here, by these contributions of the exciton populations at the smaller QDs (QD

_{S-A}and QD

_{S-C}) and the larger QDs (QD

_{L-B}and QD

_{L-D}), the calculated

*M*in the shear model shows a non-zero value (

## 4. Experimental demonstration

*Evident Technologies*) as a test specimen. QDs are uniformly dispersed in toluene solvents with 10 mg/mL of concentration. Their exciton energy transfer has already been studied [7

7. S. A. Crooker, J. A. Hollingsworth, S. Tretiak, and V. I. Klimov, “Spectrally resolved dynamics of energy transfer in quantum-dot assemblies: towards engineered energy flows in artificial materials,” Phys. Rev. Lett. **89**(18), 186802 (2002). [CrossRef] [PubMed]

19. M. Han, X. Gao, J. Z. Su, and S. Nie, “Quantum-dot-tagged microbeads for multiplexed optical coding of biomolecules,” Nat. Biotechnol. **19**(7), 631–635 (2001). [CrossRef] [PubMed]

20. M. Strassburg, M. Dworzak, H. Born, R. Heitz, A. Hoffmann, M. Bartels, K. Lischka, D. Schikora, and J. Christen, “Lateral redistribution of excitons in CdSe/ZnSe quantum dots,” Appl. Phys. Lett. **80**(3), 473–475 (2002). [CrossRef]

*resonant*and

*non-resonant*conditions via optical near-field interactions have been experimentally verified [17

17. W. Nomura, T. Yatsui, T. Kawazoe, and M. Ohtsu, “The observation of dissipated optical energy transfer between CdSe quantum dots,” J. Nanophotonics **1**, 011591 (2007). [CrossRef]

_{L-R}and QD

_{L-NR}. Their peak absorption wavelength

*E*

_{1L}in Fig. 1. The respective diameters

*D*of the resonant pair, QD

_{S-R}and QD

_{L-R}, were assumed to be 8.2 nm and 8.7 nm, and those of the non-resonant pair, QD

_{S-NR}and QD

_{L-NR}, were assumed to be 7.7 nm and 8.7 nm. The QDs adopted as QD

_{S-R}have

_{S-NR}have

*E*

_{1L}. As the flexible substrate, we used polydimethylsiloxane (PDMS), which is particularly known for its obvious rhelogical properties. We mixed 5 mL of each QD solution as resonant and non-resonant QD pairs. The mixed QD solutions were dispersed on a 2 cm × 2 cm square of PDMS substrate and allowed to dry naturally. In our experiments, although evident heterogeneity of the distributions was observed, the average

*r*was assumed to be approximately 5–10 nm from the thickness of the ZnS shell and the length of the modified ligand to each QD.

^{2}power density. In our experiment, as shown in Fig. 6 , the PDMS substrate was set on an aperture formed at the side of a vacuum desiccator and was flexed by evacuation. The flexion brings dispersed QDs close to each other, as represented by

_{S-R}was suppressed. This is because the average distance between QD

_{S-R}to QD

_{L-R}is shorten by the flexion, which induces energy transfer from QD

_{S-R}to QD

_{L-R}. Similar behavior was predicted by our numerical demonstrations described above. For quantitative evaluation of this behavior, we evaluated the intensities at the spectral peak from the fitted curves and calculated the values of

21. M. Naruse, T. Kawazoe, R. Ohta, W. Nomura, and M. Ohtsu, “Optimal mixture of randomly dispersed quantum dots for optical excitation transfer via optical near-field interactions,” Phys. Rev. B **80**, 125325 (2009). [CrossRef]

## 5. Summary

*modulatabilities*of the emission spectrum based on nanophotonics. By developing the concept further and experimentally examining various implementations, our idea can be applied to a

*modulatable multi-spectrum emitting element*whose emission spectrum can be freely switched by applying external modulation.

## Acknowledgments

## References and links

1. | M. Ohtsu, K. Kobayashi, T. Kawazoe, T. Yatsui, and M. Naruse, eds., |

2. | M. Ohtsu and K. Kobayashi, |

3. | K. Kobayashi, S. Sangu, T. Kawazoe, and M. Ohtsu, “Exciton dynamics and logic operations in a near-field optically coupled quantum-dot system,” J. Lumin. |

4. | M. Ohtsu, T. Kawazoe, T. Yatsui, and M. Naruse, “Nanophotonics: application of dressed photons to novel photonic devices and systems,” IEEE J. Sel. Top. Quantum Electron. |

5. | T. Kawazoe, M. Ohtsu, S. Aso, Y. Sawado, Y. Hosoda, K. Yoshizawa, K. Akahane, N. Yamamoto, and M. Naruse, “Two-dimensional array of room-temperature nanophotonic logic gates using InAs quantum dots in mesa structures,” Appl. Phys. B |

6. | C. R. Kagan, C. B. Murray, and M. G. Bawendi, “Long-range resonance transfer of electronic excitations in close-packed CdSe quantum-dot solids,” Phys. Rev. B Condens. Matter |

7. | S. A. Crooker, J. A. Hollingsworth, S. Tretiak, and V. I. Klimov, “Spectrally resolved dynamics of energy transfer in quantum-dot assemblies: towards engineered energy flows in artificial materials,” Phys. Rev. Lett. |

8. | M. Achermann, M. A. Petruska, S. A. Crooker, and V. I. Klimov, “Picosecond energy transfer in quantum dot Langmuir-Blodgett nanoassemblies,” J. Phys. Chem. B |

9. | T. Franzl, D. S. Koktysh, T. A. Klar, A. L. Rogach, J. Feldmann, and N. Gaponik, “Fast energy transfer in layer-by-layer aAssembled CdTe nanocrystal bilayers,” Appl. Phys. Lett. |

10. | T. Franzl, T. A. Klar, S. Schietinger, A. L. Rogach, and J. Feldmann, “Exciton recycling in graded gap nanocrystal structures,” Nano Lett. |

11. | N. Tate, W. Nomura, T. Yatsui, T. Kawazoe, M. Naruse, and M. Ohtsu, “Parallel retrieval of nanometer-scale light-matter interactions for nanophotonic systems,” Nat. Comput. |

12. | N. Sakakura and Y. Masumoto, “Persistent spectral-hole-burning spectroscopy of CuCl quantum cubes,” Phys. Rev. B |

13. | Z. K. Tang, A. Yanase, T. Yasui, Y. Segawa, and K. Cho, “Optical selection rule and oscillator strength of confined exciton system in CuCl thin films,” Phys. Rev. Lett. |

14. | T. Kawazoe, K. Kobayashi, J. Lim, Y. Narita, and M. Ohtsu, “Direct observation of optically forbidden energy transfer between CuCl quantum cubes via near-field optical spectroscopy,” Phys. Rev. Lett. |

15. | H. J. Calmichael, |

16. | M. Naruse, H. Hori, K. Kobayashi, P. Holmström, L. Thylén, and M. Ohtsu, “Lower bound of energy dissipation in optical excitation transfer via optical near-field interactions,” Opt. Express |

17. | W. Nomura, T. Yatsui, T. Kawazoe, and M. Ohtsu, “The observation of dissipated optical energy transfer between CdSe quantum dots,” J. Nanophotonics |

18. | K. Kobayashi, S. Sangu, H. Ito, and M. Ohtsu, “Near-field optical potential for a neutral atom,” Phys. Rev. A |

19. | M. Han, X. Gao, J. Z. Su, and S. Nie, “Quantum-dot-tagged microbeads for multiplexed optical coding of biomolecules,” Nat. Biotechnol. |

20. | M. Strassburg, M. Dworzak, H. Born, R. Heitz, A. Hoffmann, M. Bartels, K. Lischka, D. Schikora, and J. Christen, “Lateral redistribution of excitons in CdSe/ZnSe quantum dots,” Appl. Phys. Lett. |

21. | M. Naruse, T. Kawazoe, R. Ohta, W. Nomura, and M. Ohtsu, “Optimal mixture of randomly dispersed quantum dots for optical excitation transfer via optical near-field interactions,” Phys. Rev. B |

**OCIS Codes**

(200.3050) Optics in computing : Information processing

(200.4740) Optics in computing : Optical processing

(230.5590) Optical devices : Quantum-well, -wire and -dot devices

(350.4238) Other areas of optics : Nanophotonics and photonic crystals

**ToC Category:**

Optics in Computing

**History**

Original Manuscript: June 7, 2011

Revised Manuscript: July 31, 2011

Manuscript Accepted: August 25, 2011

Published: September 2, 2011

**Citation**

Naoya Tate, Makoto Naruse, Wataru Nomura, Tadashi Kawazoe, Takashi Yatsui, Morihisa Hoga, Yasuyuki Ohyagi, Yoko Sekine, Hiroshi Fujita, and Motoichi Ohtsu, "Demonstration of modulatable optical near-field interactions between dispersed resonant quantum dots," Opt. Express **19**, 18260-18271 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-19-18260

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### References

- M. Ohtsu, K. Kobayashi, T. Kawazoe, T. Yatsui, and M. Naruse, eds., Principles of Nanophotonics, (Taylor and Francis, 2008).
- M. Ohtsu and K. Kobayashi, Optical Near Fields (Springer-Verlag, 2003), pp. 109–150.
- K. Kobayashi, S. Sangu, T. Kawazoe, and M. Ohtsu, “Exciton dynamics and logic operations in a near-field optically coupled quantum-dot system,” J. Lumin.112(1-4), 117–121 (2005). [CrossRef]
- M. Ohtsu, T. Kawazoe, T. Yatsui, and M. Naruse, “Nanophotonics: application of dressed photons to novel photonic devices and systems,” IEEE J. Sel. Top. Quantum Electron.14(6), 1404–1417 (2008). [CrossRef]
- T. Kawazoe, M. Ohtsu, S. Aso, Y. Sawado, Y. Hosoda, K. Yoshizawa, K. Akahane, N. Yamamoto, and M. Naruse, “Two-dimensional array of room-temperature nanophotonic logic gates using InAs quantum dots in mesa structures,” Appl. Phys. B103(3), 537–546 (2011). [CrossRef]
- C. R. Kagan, C. B. Murray, and M. G. Bawendi, “Long-range resonance transfer of electronic excitations in close-packed CdSe quantum-dot solids,” Phys. Rev. B Condens. Matter54(12), 8633–8643 (1996). [CrossRef] [PubMed]
- S. A. Crooker, J. A. Hollingsworth, S. Tretiak, and V. I. Klimov, “Spectrally resolved dynamics of energy transfer in quantum-dot assemblies: towards engineered energy flows in artificial materials,” Phys. Rev. Lett.89(18), 186802 (2002). [CrossRef] [PubMed]
- M. Achermann, M. A. Petruska, S. A. Crooker, and V. I. Klimov, “Picosecond energy transfer in quantum dot Langmuir-Blodgett nanoassemblies,” J. Phys. Chem. B107(50), 13782–13787 (2003). [CrossRef]
- T. Franzl, D. S. Koktysh, T. A. Klar, A. L. Rogach, J. Feldmann, and N. Gaponik, “Fast energy transfer in layer-by-layer aAssembled CdTe nanocrystal bilayers,” Appl. Phys. Lett.84(15), 2904–2906 (2004). [CrossRef]
- T. Franzl, T. A. Klar, S. Schietinger, A. L. Rogach, and J. Feldmann, “Exciton recycling in graded gap nanocrystal structures,” Nano Lett.4(9), 1599–1603 (2004). [CrossRef]
- N. Tate, W. Nomura, T. Yatsui, T. Kawazoe, M. Naruse, and M. Ohtsu, “Parallel retrieval of nanometer-scale light-matter interactions for nanophotonic systems,” Nat. Comput.2, 298–307 (2010). [CrossRef]
- N. Sakakura and Y. Masumoto, “Persistent spectral-hole-burning spectroscopy of CuCl quantum cubes,” Phys. Rev. B56(7), 4051–4055 (1997). [CrossRef]
- Z. K. Tang, A. Yanase, T. Yasui, Y. Segawa, and K. Cho, “Optical selection rule and oscillator strength of confined exciton system in CuCl thin films,” Phys. Rev. Lett.71(9), 1431–1434 (1993). [CrossRef] [PubMed]
- T. Kawazoe, K. Kobayashi, J. Lim, Y. Narita, and M. Ohtsu, “Direct observation of optically forbidden energy transfer between CuCl quantum cubes via near-field optical spectroscopy,” Phys. Rev. Lett.88(6), 067404 (2002). [CrossRef] [PubMed]
- H. J. Calmichael, Statistical Methods in Quantum Optics 1. (Springer-Verlag, 1999).
- M. Naruse, H. Hori, K. Kobayashi, P. Holmström, L. Thylén, and M. Ohtsu, “Lower bound of energy dissipation in optical excitation transfer via optical near-field interactions,” Opt. Express18(Suppl 4), A544–A553 (2010). [CrossRef] [PubMed]
- W. Nomura, T. Yatsui, T. Kawazoe, and M. Ohtsu, “The observation of dissipated optical energy transfer between CdSe quantum dots,” J. Nanophotonics1, 011591 (2007). [CrossRef]
- K. Kobayashi, S. Sangu, H. Ito, and M. Ohtsu, “Near-field optical potential for a neutral atom,” Phys. Rev. A63, 013806 (2000). [CrossRef]
- M. Han, X. Gao, J. Z. Su, and S. Nie, “Quantum-dot-tagged microbeads for multiplexed optical coding of biomolecules,” Nat. Biotechnol.19(7), 631–635 (2001). [CrossRef] [PubMed]
- M. Strassburg, M. Dworzak, H. Born, R. Heitz, A. Hoffmann, M. Bartels, K. Lischka, D. Schikora, and J. Christen, “Lateral redistribution of excitons in CdSe/ZnSe quantum dots,” Appl. Phys. Lett.80(3), 473–475 (2002). [CrossRef]
- M. Naruse, T. Kawazoe, R. Ohta, W. Nomura, and M. Ohtsu, “Optimal mixture of randomly dispersed quantum dots for optical excitation transfer via optical near-field interactions,” Phys. Rev. B80, 125325 (2009). [CrossRef]

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