## Lower bound of energy dissipation in optical excitation transfer via optical near-field interactions |

Optics Express, Vol. 18, Issue S4, pp. A544-A553 (2010)

http://dx.doi.org/10.1364/OE.18.00A544

Acrobat PDF (1038 KB)

### Abstract

We theoretically analyzed the lower bound of energy dissipation required for optical excitation transfer from smaller quantum dots to larger ones via optical near-field interactions. The coherent interaction between two quantum dots via optical near-fields results in unidirectional excitation transfer by an energy dissipation process occurring in the larger dot. We investigated the lower bound of this energy dissipation, or the intersublevel energy difference at the larger dot, when the excitation appearing in the larger dot originated from the excitation transfer via optical near-field interactions. We demonstrate that the energy dissipation could be as low as 25 μeV. Compared with the bit flip energy of an electrically wired device, this is about 10^{4} times more energy efficient. The achievable integration density of nanophotonic devices is also analyzed based on the energy dissipation and the error ratio while assuming a Yukawa-type potential for the optical near-field interactions.

© 2010 OSA

## 1. Introduction

_{2}production [1

1. ITU-T Focus Group on ICTs and Climate Change, http://www.itu.int/ITU-T/focusgroups/climate/index.html.

2. L. B. Kish, “Moore's law and the energy requirement of computing versus performance,” IEE Proc., Circ. Devices Syst. **151**(2), 190–194 (2004). [CrossRef]

3. J. Gea-Banacloche, “Minimum energy requirements for quantum computation,” Phys. Rev. Lett. **89**(21), 217901 (2002). [CrossRef] [PubMed]

4. The Green Grid, http://www.thegreengrid.org/.

5. R. S. Tucker, R. Parthiban, J. Baliga, K. Hinton, R. W. A. Ayre, and W. V. Sorin, “Evolution of WDM Optical IP Networks: A Cost and Energy Perspective,” J. Lightwave Technol. **27**(3), 243–252 (2009). [CrossRef]

6. K. Sato and H. Hasegawa, “Prospects and Challenges of Multi-Layer Optical Networks,” IEICE Trans. Commun, E **90-B**, 1890–1902 (2007). [CrossRef]

9. 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]

10. 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**(12), 125325 (2009). [CrossRef]

11. 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]

12. J. H. Lee, Zh. M. Wang, B. L. Liang, K. A. Sablon, N. W. Strom, and G. J. Salamo, “Size and density control of InAs quantum dot ensembles on self-assembled nanostructured templates,” Semicond. Sci. Technol. **21**(12), 1547–1551 (2006). [CrossRef]

13. K. Akahane, N. Yamamoto, and M. Tsuchiya, “Highly stacked quantum-dot laser fabricated using a strain compensation technique,” Appl. Phys. Lett. **93**(4), 041121 (2008). [CrossRef]

14. T. Mano and N. Koguchi, “Nanometer-scale GaAs ring structure grown by droplet epitaxy,” J. Cryst. Growth **278**(1-4), 108–112 (2005). [CrossRef]

15. W. I. Park, G.-C. Yi, M. Y. Kim, and S. J. Pennycook, “Quantum Confinement Observed in ZnO/ZnMgO Nanorod Heterostructures,” Adv. Mater. **15**(6), 526–529 (2003). [CrossRef]

16. T. Kawazoe, K. Kobayashi, S. Sangu, and M. Ohtsu, “Demonstration of a nanophotonic switching operation by optical near-field energy transfer,” Appl. Phys. Lett. **82**(18), 2957–2959 (2003). [CrossRef]

17. T. Yatsui, S. Sangu, T. Kawazoe, M. Ohtsu, S. J. An, J. Yoo, and G.-C. Yi, “Nanophotonic switch using ZnO nanorod double-quantum-well structures,” Appl. Phys. Lett. **90**(22), 223110 (2007). [CrossRef]

18. M. Naruse, T. Kawazoe, S. Sangu, K. Kobayashi, and M. Ohtsu, “Optical interconnects based on optical far- and near-field interactions for high-density data broadcasting,” Opt. Express **14**(1), 306–313 (2006). [CrossRef] [PubMed]

11. 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]

19. M. Naruse, T. Miyazaki, F. Kubota, T. Kawazoe, K. Kobayashi, S. Sangu, and M. Ohtsu, “Nanometric summation architecture based on optical near-field interaction between quantum dots,” Opt. Lett. **30**(2), 201–203 (2005). [CrossRef] [PubMed]

16. T. Kawazoe, K. Kobayashi, S. Sangu, and M. Ohtsu, “Demonstration of a nanophotonic switching operation by optical near-field energy transfer,” Appl. Phys. Lett. **82**(18), 2957–2959 (2003). [CrossRef]

18. M. Naruse, T. Kawazoe, S. Sangu, K. Kobayashi, and M. Ohtsu, “Optical interconnects based on optical far- and near-field interactions for high-density data broadcasting,” Opt. Express **14**(1), 306–313 (2006). [CrossRef] [PubMed]

21. P. Kocher, J. Jaffe, and B. Jun, “Introduction to Differential Power Analysis and Related Attacks,” http://www.cryptography.com/resources/whitepapers/DPATechInfo.pdf.

22. M. Naruse, H. Hori, K. Kobayashi, and M. Ohtsu, “Tamper resistance in optical excitation transfer based on optical near-field interactions,” Opt. Lett. **32**(12), 1761–1763 (2007). [CrossRef] [PubMed]

## 2. Modeling

*e*represents a charge,

*i*,

*j*=

*e*) or a hole (

*i*,

*j*=

*h*) at

**, and**

*r***(**

*E***) is the electric field [23]. In usual light–matter interactions,**

*r***(**

*E***) is a constant since the electric field of diffraction-limited propagating light is homogeneous on the nanometer scale. Therefore, as is well known, we can derive optical selection rules by calculating the dipole transition matrix elements. As a consequence, in the case of cubic quantum dots for instance, transitions to states containing an even quantum number are prohibited. In the case of optical near-field interactions, on the other hand, due to the steep electric field of optical near-fields in the vicinity of nano-scale material, an optical transition that violates conventional optical selection rules is allowed. A detailed physical discussion is found in Ref [7].**

*r**a*and

*and QD*

_{S}*, respectively, as shown in Fig. 1(a) . Suppose that the energy eigenvalues for the quantized exciton energy level specified by quantum numbers (*

_{L}*n*,

_{x}*n*,

_{y}*n*) in a QD with side length

_{z}*L*are given bywhere

*E*is the transition energy of the bulk exciton, and

_{B}*M*is the effective mass of the exciton. According to Eq. (2), there exists a resonance between the level of quantum number (1,1,1) for QD

*and that of quantum number (2,1,1) for QD*

_{S}*. Hereafter, the (1,1,1)-level of QD*

_{L}*is denoted by*

_{S}*E*, and the (2,1,1)-level of QD

_{S}*is called*

_{L}*. Therefore, excitons in*

_{S}*S*can move to

*L*

_{2}in QD

*. Note that such a transfer is prohibited in propagating light since the (2,1,1)-level in QD*

_{L}*contains an even number. In QD*

_{L}*, the exciton undergoes intersublevel energy relaxation due to exciton–phonon coupling, denoted by*

_{L}*Γ*, which is faster than the near-field interaction [9

9. 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]

24. S. Sangu, K. Kobayashi, A. Shojiguchi, T. Kawazoe, and M. Ohtsu, “Excitation energy transfer and population dynamics in a quantum dot system induced by optical near-field interaction,” J. Appl. Phys. **93**(5), 2937–2945 (2003). [CrossRef]

*, which is called*

_{L}*to QD*

_{S}*. Also, we assume far-field input light irradiation at the optical frequency*

_{L}*ω*.

_{ext}*S*,

*L*

_{1}, and

*L*

_{2}in the system, as schematically summarized in the diagram shown in Fig. 1(a). Here, the interactions between QD

*and QD*

_{S}*are denoted by*

_{L}*i*=1,2), and the radiative relaxation rates from

*E*and

_{S}*i*,

*i*) element of the density matrix correspond to the state denoted by

*i*in Fig. 1(b), the quantum master equation of the total system is given by [25]

*H*is given by

_{int}*S*,

*L*

_{1}, and

*L*

_{2}in Eq. (4) are respectively annihilation operators given by the transposes of the matrices of Eq. (5).

*H*indicates the Hamiltonian representing the interaction between the external input light at frequency

_{ext}*ω*and the quantum dot system, given by

_{ext}*gate*(

*t*) specifies the duration and the amplitude of the external input light. Also, note that the input light could couple to the (1,1,1)-level

*E*in QD

_{S}*, and to the (1,1,1)-level*

_{S}*, because those levels are electric dipole-allowed energy levels. Setting the initial condition as an empty state, and giving the external input light in Eq. (6), the time evolution of the population is obtained by solving the master equation given by Eq. (3).*

_{L}## 3. Lower bound of energy dissipation in the optical excitation transfer

*to QD*

_{S}*occurs. We assume*

_{L}16. T. Kawazoe, K. Kobayashi, S. Sangu, and M. Ohtsu, “Demonstration of a nanophotonic switching operation by optical near-field energy transfer,” Appl. Phys. Lett. **82**(18), 2957–2959 (2003). [CrossRef]

17. T. Yatsui, S. Sangu, T. Kawazoe, M. Ohtsu, S. J. An, J. Yoo, and G.-C. Yi, “Nanophotonic switch using ZnO nanorod double-quantum-well structures,” Appl. Phys. Lett. **90**(22), 223110 (2007). [CrossRef]

26. T. Yatsui, H. Jeong, and M. Ohtsu, “Controlling the energy transfer between near-field optically coupled ZnO quantum dots,” Appl. Phys. B **93**(1), 199–202 (2008). [CrossRef]

27. W. Nomura, T. Yatsui, T. Kawazoe, and M. Ohtsu, “The observation of dissipated optical energy transfer between CdSe quantum dots,” J. Nanophoton. **1**(1), 1–8 (2007). [CrossRef]

9. 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]

24. S. Sangu, K. Kobayashi, A. Shojiguchi, T. Kawazoe, and M. Ohtsu, “Excitation energy transfer and population dynamics in a quantum dot system induced by optical near-field interaction,” J. Appl. Phys. **93**(5), 2937–2945 (2003). [CrossRef]

28. W. Nomura, T. Yatsui, T. Kawazoe, M. Naruse, and M. Ohtsu, “Structural dependency of optical excitation transfer via optical near-field interactions between semiconductor quantum dots,” Appl. Phys. B **100**(1), 181–187 (2010). [CrossRef]

*and QD*

_{S}*are negligible, and thus the optical excitation transfer from QD*

_{L}*to QD*

_{S}*does not occur, and the radiation from QD*

_{L}*should normally be zero. We assume*

_{L}*to QD*

_{S}*is the intersublevel relaxation in QD*

_{L}*given by*

_{L}*Δ*. When this energy difference is too small, the input light may directly couple to

*L*

_{1}, resulting in output radiation from QD

*, even in System B. In other words, we would not be able to recognize the origin of the output radiation from QD*

_{L}*if it involves the optical excitation transfer from QD*

_{L}*to QD*

_{S}*in System A, or it directly couples to*

_{L}*L*

_{1}in System B. Therefore, the

*intended*proper system behavior is to observe higher populations from

*L*

_{2}in System A while at the same time observing lower populations from

*L*

_{2}in System B.

*is observed with its radiation decay rate (*

_{S}*t*= 150 ps), whereas the population involving

*E*at

_{S}*t*= 150 ps is 0.81. Therefore, the increased population from

*t*= 150 ps is due to the optical excitation transfer from QD

*to QD*

_{S}*. In the case of (iii), due to the small energy difference, the input light directly couples with*

_{L}*L*

_{1}; therefore, both System A and System B yield higher populations from

*L*

_{1}in System B is not as large as in case (iii), but it exhibits a non-zero value compared with case (i), indicating that the energy difference Δ = 17 μeV may be around the middle of the intended and unintended system operations involving optical excitation transfer between QD

*and QD*

_{S}*.*

_{L}*t*= 10 ns as a function of the energy dissipation. The intended system behavior, that is, higher output population in System A and lower one in System B, is obtained in the region where energy dissipation is larger than around 25 μeV.

*), the signal should come from QD*

_{L}*in its proximity (as in the case of System A), not from QD*

_{S}*far from QD*

_{S}*(as in the case of System B); such a picture will aid in understanding the physical meaning of the SNR defined here. Also, here we suppose that the input data are coded in an external system, and the input light at frequency*

_{L}*ω*irradiates QD

_{ext}*. With SNR, the error ratio (*

_{S}*P*), or equivalently Bit Error Rate (BER), is derived by the formula

_{E}2. L. B. Kish, “Moore's law and the energy requirement of computing versus performance,” IEE Proc., Circ. Devices Syst. **151**(2), 190–194 (2004). [CrossRef]

*E*) in classical electrically wired devices (specifically, energy dissipation required for a single bit flip in a CMOS logic gate) is given bywhich is indicated by the squares in Fig. 4(b). For example, when the error ratio is 10

_{d}^{−6}, the minimum

*Δ*in the optical excitation transfer is about 0.024 meV, whereas that of the classical electrical device is about 303 meV; the former is about 10

^{4}times more energy efficient than the latter.

*L*

_{1}is as indicated by the triangular marks in Fig. 4(a); the population stays higher even with increasing energy dissipation compared with the former case of

^{−4}, even with increasing energy dissipation. The lower bound of the BER decreases as the interaction time

*U*

_{B}so that no interference occurs between adjacent circuits; this gives the integration density of nanophotonic circuits in a unit area. When the energy cost paid (namely, the energy dissipation) is 3.4 meV, the BER of the system is evaluated as the square marks in Fig. 4(c) as a function of the number of independent functional blocks within an area of 1 μm

^{2}; we can observe that the system likely sacrifices more errors as the integration density increases.

## 4. Summary

^{4}times more energy efficient than the bit flip energy in a conventional electrically wired device. We also discussed the integration density of nanophotonic devices by taking account of energy dissipation, bit error rate, and the optical near-field interactions whose spatial nature is characterized by a Yukawa-type potential.

34. H. Imahori, “Giant Multiporphyrin Arrays as Artificial Light-Harvesting Antennas,” J. Phys. Chem. B **108**(20), 6130–6143 (2004). [CrossRef]

35. H. Tamura, J.-M. Mallet, M. Oheim, and I. Burghardt, “Ab Initio Study of Excitation Energy Transfer between Quantum Dots and Dye Molecules,” J. Phys. Chem. C **113**(18), 7548–7552 (2009). [CrossRef]

^{4}times superior to today’s electrical computers [36

36. V. P. Carey and A. J. Shah, “The Exergy Cost of Information Processing: A Comparison of Computer-Based Technologies and Biological Systems,” J. Electron. Packag. **128**(4), 346–352 (2006). [CrossRef]

## References and links

1. | ITU-T Focus Group on ICTs and Climate Change, http://www.itu.int/ITU-T/focusgroups/climate/index.html. |

2. | L. B. Kish, “Moore's law and the energy requirement of computing versus performance,” IEE Proc., Circ. Devices Syst. |

3. | J. Gea-Banacloche, “Minimum energy requirements for quantum computation,” Phys. Rev. Lett. |

4. | The Green Grid, http://www.thegreengrid.org/. |

5. | R. S. Tucker, R. Parthiban, J. Baliga, K. Hinton, R. W. A. Ayre, and W. V. Sorin, “Evolution of WDM Optical IP Networks: A Cost and Energy Perspective,” J. Lightwave Technol. |

6. | K. Sato and H. Hasegawa, “Prospects and Challenges of Multi-Layer Optical Networks,” IEICE Trans. Commun, E |

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

8. | L. Thylén, P. Holmström, A. Bratkovsky, J. Li, and S.-Y. Wang, “Limits on Integration as Determined by Power Dissipation and Signal-to-Noise Ratio in Loss-Compensated Photonic Integrated Circuits Based on Metal/Quantum-Dot Materials,” IEEE J. Quantum Electron. |

9. | 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. |

10. | 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 |

11. | T. Franzl, T. A. Klar, S. Schietinger, A. L. Rogach, and J. Feldmann, “Exciton Recycling in Graded Gap Nanocrystal Structures,” Nano Lett. |

12. | J. H. Lee, Zh. M. Wang, B. L. Liang, K. A. Sablon, N. W. Strom, and G. J. Salamo, “Size and density control of InAs quantum dot ensembles on self-assembled nanostructured templates,” Semicond. Sci. Technol. |

13. | K. Akahane, N. Yamamoto, and M. Tsuchiya, “Highly stacked quantum-dot laser fabricated using a strain compensation technique,” Appl. Phys. Lett. |

14. | T. Mano and N. Koguchi, “Nanometer-scale GaAs ring structure grown by droplet epitaxy,” J. Cryst. Growth |

15. | W. I. Park, G.-C. Yi, M. Y. Kim, and S. J. Pennycook, “Quantum Confinement Observed in ZnO/ZnMgO Nanorod Heterostructures,” Adv. Mater. |

16. | T. Kawazoe, K. Kobayashi, S. Sangu, and M. Ohtsu, “Demonstration of a nanophotonic switching operation by optical near-field energy transfer,” Appl. Phys. Lett. |

17. | T. Yatsui, S. Sangu, T. Kawazoe, M. Ohtsu, S. J. An, J. Yoo, and G.-C. Yi, “Nanophotonic switch using ZnO nanorod double-quantum-well structures,” Appl. Phys. Lett. |

18. | M. Naruse, T. Kawazoe, S. Sangu, K. Kobayashi, and M. Ohtsu, “Optical interconnects based on optical far- and near-field interactions for high-density data broadcasting,” Opt. Express |

19. | M. Naruse, T. Miyazaki, F. Kubota, T. Kawazoe, K. Kobayashi, S. Sangu, and M. Ohtsu, “Nanometric summation architecture based on optical near-field interaction between quantum dots,” Opt. Lett. |

20. | H. Hori, “Electronic and Electromagnetic Properties in Nanometer Scales,” in |

21. | P. Kocher, J. Jaffe, and B. Jun, “Introduction to Differential Power Analysis and Related Attacks,” http://www.cryptography.com/resources/whitepapers/DPATechInfo.pdf. |

22. | M. Naruse, H. Hori, K. Kobayashi, and M. Ohtsu, “Tamper resistance in optical excitation transfer based on optical near-field interactions,” Opt. Lett. |

23. | H. Haug, and S. W. Koch, |

24. | S. Sangu, K. Kobayashi, A. Shojiguchi, T. Kawazoe, and M. Ohtsu, “Excitation energy transfer and population dynamics in a quantum dot system induced by optical near-field interaction,” J. Appl. Phys. |

25. | H. J. Carmichael, |

26. | T. Yatsui, H. Jeong, and M. Ohtsu, “Controlling the energy transfer between near-field optically coupled ZnO quantum dots,” Appl. Phys. B |

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

28. | W. Nomura, T. Yatsui, T. Kawazoe, M. Naruse, and M. Ohtsu, “Structural dependency of optical excitation transfer via optical near-field interactions between semiconductor quantum dots,” Appl. Phys. B |

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

30. | S. Haykin, |

31. | M. Naruse, T. Inoue, and H. Hori, “Analysis and Synthesis of Hierarchy in Optical Near-Field Interactions at the Nanoscale Based on Angular Spectrum,” Jpn. J. Appl. Phys. |

32. | K. Ohmori, K. Kodama, T. Muranaka, Y. Nabetani, and T. Matsumoto, “Tunneling of spin polarized excitons in ZnCdSe and ZnCdMnSe coupled double quantum wells,” Phys. Status Solidi |

33. | J. Seufert, G. Bacher, H. Schömig, A. Forchel, L. Hansen, G. Schmidt, and L. W. Molenkamp, “Spin injection into a single self-assembled quantum dot,” Phys. Rev. B |

34. | H. Imahori, “Giant Multiporphyrin Arrays as Artificial Light-Harvesting Antennas,” J. Phys. Chem. B |

35. | H. Tamura, J.-M. Mallet, M. Oheim, and I. Burghardt, “Ab Initio Study of Excitation Energy Transfer between Quantum Dots and Dye Molecules,” J. Phys. Chem. C |

36. | V. P. Carey and A. J. Shah, “The Exergy Cost of Information Processing: A Comparison of Computer-Based Technologies and Biological Systems,” J. Electron. Packag. |

**OCIS Codes**

(200.3050) Optics in computing : Information processing

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

(260.2160) Physical optics : Energy transfer

(180.4243) Microscopy : Near-field microscopy

**ToC Category:**

Energy Transfer

**History**

Original Manuscript: August 2, 2010

Revised Manuscript: August 31, 2010

Manuscript Accepted: September 23, 2010

Published: October 5, 2010

**Citation**

Makoto Naruse, Hirokazu Hori, Kiyoshi Kobayashi, Petter Holmström, Lars Thylén, and Motoichi Ohtsu, "Lower bound of energy dissipation in optical excitation transfer via optical near-field interactions," Opt. Express **18**, A544-A553 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-S4-A544

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### References

- ITU-T Focus Group on ICTs and Climate Change, http://www.itu.int/ITU-T/focusgroups/climate/index.html .
- L. B. Kish, “Moore's law and the energy requirement of computing versus performance,” IEE Proc., Circ. Devices Syst. 151(2), 190–194 (2004). [CrossRef]
- J. Gea-Banacloche, “Minimum energy requirements for quantum computation,” Phys. Rev. Lett. 89(21), 217901 (2002). [CrossRef] [PubMed]
- The Green Grid, http://www.thegreengrid.org/ .
- R. S. Tucker, R. Parthiban, J. Baliga, K. Hinton, R. W. A. Ayre, and W. V. Sorin, “Evolution of WDM Optical IP Networks: A Cost and Energy Perspective,” J. Lightwave Technol. 27(3), 243–252 (2009). [CrossRef]
- K. Sato and H. Hasegawa, “Prospects and Challenges of Multi-Layer Optical Networks,” IEICE Trans. Commun, E 90-B, 1890–1902 (2007). [CrossRef]
- M. Ohtsu, K. Kobayashi, T. Kawazoe, T. Yatsui, and M. Naruse, Principles of Nanophotonics (Taylor and Francis, Boca Raton, 2008).
- L. Thylén, P. Holmström, A. Bratkovsky, J. Li, and S.-Y. Wang, “Limits on Integration as Determined by Power Dissipation and Signal-to-Noise Ratio in Loss-Compensated Photonic Integrated Circuits Based on Metal/Quantum-Dot Materials,” IEEE J. Quantum Electron. 46(4), 518–524 (2010). [CrossRef]
- 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]
- 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(12), 125325 (2009). [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]
- J. H. Lee, Zh. M. Wang, B. L. Liang, K. A. Sablon, N. W. Strom, and G. J. Salamo, “Size and density control of InAs quantum dot ensembles on self-assembled nanostructured templates,” Semicond. Sci. Technol. 21(12), 1547–1551 (2006). [CrossRef]
- K. Akahane, N. Yamamoto, and M. Tsuchiya, “Highly stacked quantum-dot laser fabricated using a strain compensation technique,” Appl. Phys. Lett. 93(4), 041121 (2008). [CrossRef]
- T. Mano and N. Koguchi, “Nanometer-scale GaAs ring structure grown by droplet epitaxy,” J. Cryst. Growth 278(1-4), 108–112 (2005). [CrossRef]
- W. I. Park, G.-C. Yi, M. Y. Kim, and S. J. Pennycook, “Quantum Confinement Observed in ZnO/ZnMgO Nanorod Heterostructures,” Adv. Mater. 15(6), 526–529 (2003). [CrossRef]
- T. Kawazoe, K. Kobayashi, S. Sangu, and M. Ohtsu, “Demonstration of a nanophotonic switching operation by optical near-field energy transfer,” Appl. Phys. Lett. 82(18), 2957–2959 (2003). [CrossRef]
- T. Yatsui, S. Sangu, T. Kawazoe, M. Ohtsu, S. J. An, J. Yoo, and G.-C. Yi, “Nanophotonic switch using ZnO nanorod double-quantum-well structures,” Appl. Phys. Lett. 90(22), 223110 (2007). [CrossRef]
- M. Naruse, T. Kawazoe, S. Sangu, K. Kobayashi, and M. Ohtsu, “Optical interconnects based on optical far- and near-field interactions for high-density data broadcasting,” Opt. Express 14(1), 306–313 (2006). [CrossRef] [PubMed]
- M. Naruse, T. Miyazaki, F. Kubota, T. Kawazoe, K. Kobayashi, S. Sangu, and M. Ohtsu, “Nanometric summation architecture based on optical near-field interaction between quantum dots,” Opt. Lett. 30(2), 201–203 (2005). [CrossRef] [PubMed]
- H. Hori, “Electronic and Electromagnetic Properties in Nanometer Scales,” in Optical and Electronic Process of Nano-Matters, M. Ohtsu, ed. (Kluwer Academic, 2001), pp. 1–55.
- P. Kocher, J. Jaffe, and B. Jun, “Introduction to Differential Power Analysis and Related Attacks,” http://www.cryptography.com/resources/whitepapers/DPATechInfo.pdf .
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