Abstract

We have obtained a simple numerical model that explains the temperature behavior of multi-quantum-dot (QD) nanophotonic devices whose operations are based on optical near-field (ONF) interactions between any two resonant QDs that are in thermal equilibrium. This model involves a set of coupled rate equations that govern the temporal behavior of the QDs’ energy level occupancies. Under a certain operating condition, this simple model can substitute for the more complex density matrix (DM) approach in modeling the temperature dependence of the ONF energy transfer rate (RONF) between any two resonant QDs in thermal equilibrium. The same applies for modeling the system state-filling time (τS). Applying our simple model to a two-QD system, we have derived analytical formulas for the interdot and the intradot transfer rates at finite temperatures (T0). Furthermore, by assuming a unidirectional energy transport operating condition, we have also derived an analytic formula for calculating τS for a two-QD system. To the best of our knowledge, this work is the first instance of reporting such analytic equations. Approximated values of τS obtained from our simple analytic equation are in reasonable agreements with those calculated by the DM approach.

© 2010 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2009 (1)

2008 (2)

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, 1404-1417 (2008).
[CrossRef]

M. Naruse, T. Yatsui, T. Kawazoe, Y. Akao, and M. Ohtsu, “Design and simulation of a nanophotonic traceable memory using localized energy dissipation and hierarchy of optical near-field interactions,” IEEE Trans. Nanotechnol. 7, 14-19 (2008).
[CrossRef]

2006 (1)

2005 (2)

M. Naruse, T. Miyazaki, T. Kawazoe, S. Sangu, K. Kobayashi, F. Kubota, and M. Ohtsu, “Nanophotonic computing based on optical near-field interactions between quantum dots,” IEICE Trans. E88-C (2005).
[CrossRef]

S. Sangu, K. Kobayashi, and M. Ohtsu, “Nanophotonic devices and fundamental functional operations,” IEICE Trans. E88-C (2005).
[CrossRef]

2002 (1)

M. Ohtsu, K. Kobayashi, T. Kawazoe, S. Sangu, and T. Yatsui, “Nanophotonics: design, fabrication, and operation of nanometric devices using optical near fields,” IEEE J. Sel. Top. Quantum Electron. 8, 839-862 (2002).
[CrossRef]

2001 (1)

1972 (1)

T. C. Hissa, “On the simplification of linear system,” IEEE Trans. Autom. Control 17, 372-374 (1972).
[CrossRef]

Akao, Y.

M. Naruse, T. Yatsui, T. Kawazoe, Y. Akao, and M. Ohtsu, “Design and simulation of a nanophotonic traceable memory using localized energy dissipation and hierarchy of optical near-field interactions,” IEEE Trans. Nanotechnol. 7, 14-19 (2008).
[CrossRef]

Ebbesen, T. W.

Hissa, T. C.

T. C. Hissa, “On the simplification of linear system,” IEEE Trans. Autom. Control 17, 372-374 (1972).
[CrossRef]

Karimkhani, A.

Kawazoe, T.

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, 1404-1417 (2008).
[CrossRef]

M. Naruse, T. Yatsui, T. Kawazoe, Y. Akao, and M. Ohtsu, “Design and simulation of a nanophotonic traceable memory using localized energy dissipation and hierarchy of optical near-field interactions,” IEEE Trans. Nanotechnol. 7, 14-19 (2008).
[CrossRef]

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

M. Naruse, T. Miyazaki, T. Kawazoe, S. Sangu, K. Kobayashi, F. Kubota, and M. Ohtsu, “Nanophotonic computing based on optical near-field interactions between quantum dots,” IEICE Trans. E88-C (2005).
[CrossRef]

M. Ohtsu, K. Kobayashi, T. Kawazoe, S. Sangu, and T. Yatsui, “Nanophotonics: design, fabrication, and operation of nanometric devices using optical near fields,” IEEE J. Sel. Top. Quantum Electron. 8, 839-862 (2002).
[CrossRef]

M. Ohtsu, K. Kobayashi, T. Kawazoe, T. Yatsui, and M. Naruse, Principles of Nanophotonics (CRC, 2008).
[CrossRef]

Kobayashi, K.

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

S. Sangu, K. Kobayashi, and M. Ohtsu, “Nanophotonic devices and fundamental functional operations,” IEICE Trans. E88-C (2005).
[CrossRef]

M. Naruse, T. Miyazaki, T. Kawazoe, S. Sangu, K. Kobayashi, F. Kubota, and M. Ohtsu, “Nanophotonic computing based on optical near-field interactions between quantum dots,” IEICE Trans. E88-C (2005).
[CrossRef]

M. Ohtsu, K. Kobayashi, T. Kawazoe, S. Sangu, and T. Yatsui, “Nanophotonics: design, fabrication, and operation of nanometric devices using optical near fields,” IEEE J. Sel. Top. Quantum Electron. 8, 839-862 (2002).
[CrossRef]

M. Ohtsu, K. Kobayashi, T. Kawazoe, T. Yatsui, and M. Naruse, Principles of Nanophotonics (CRC, 2008).
[CrossRef]

M. Ohtsu and K. Kobayashi, Optical Near Fields (Springer-Verlag, 2004).

Kubota, F.

M. Naruse, T. Miyazaki, T. Kawazoe, S. Sangu, K. Kobayashi, F. Kubota, and M. Ohtsu, “Nanophotonic computing based on optical near-field interactions between quantum dots,” IEICE Trans. E88-C (2005).
[CrossRef]

Kühn, O.

V. May and O. Kühn, Charge and Energy Transfer Dynamics in Molecular Systems (Wiley-VCH, 2004).

Lezec, H. J.

Linke, R. A.

May, V.

V. May and O. Kühn, Charge and Energy Transfer Dynamics in Molecular Systems (Wiley-VCH, 2004).

Miyazaki, T.

M. Naruse, T. Miyazaki, T. Kawazoe, S. Sangu, K. Kobayashi, F. Kubota, and M. Ohtsu, “Nanophotonic computing based on optical near-field interactions between quantum dots,” IEICE Trans. E88-C (2005).
[CrossRef]

Moravvej-Farshi, M. K.

Naruse, M.

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, 1404-1417 (2008).
[CrossRef]

M. Naruse, T. Yatsui, T. Kawazoe, Y. Akao, and M. Ohtsu, “Design and simulation of a nanophotonic traceable memory using localized energy dissipation and hierarchy of optical near-field interactions,” IEEE Trans. Nanotechnol. 7, 14-19 (2008).
[CrossRef]

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

M. Naruse, T. Miyazaki, T. Kawazoe, S. Sangu, K. Kobayashi, F. Kubota, and M. Ohtsu, “Nanophotonic computing based on optical near-field interactions between quantum dots,” IEICE Trans. E88-C (2005).
[CrossRef]

M. Ohtsu, K. Kobayashi, T. Kawazoe, T. Yatsui, and M. Naruse, Principles of Nanophotonics (CRC, 2008).
[CrossRef]

Ohtsu, M.

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, 1404-1417 (2008).
[CrossRef]

M. Naruse, T. Yatsui, T. Kawazoe, Y. Akao, and M. Ohtsu, “Design and simulation of a nanophotonic traceable memory using localized energy dissipation and hierarchy of optical near-field interactions,” IEEE Trans. Nanotechnol. 7, 14-19 (2008).
[CrossRef]

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

M. Naruse, T. Miyazaki, T. Kawazoe, S. Sangu, K. Kobayashi, F. Kubota, and M. Ohtsu, “Nanophotonic computing based on optical near-field interactions between quantum dots,” IEICE Trans. E88-C (2005).
[CrossRef]

S. Sangu, K. Kobayashi, and M. Ohtsu, “Nanophotonic devices and fundamental functional operations,” IEICE Trans. E88-C (2005).
[CrossRef]

M. Ohtsu, K. Kobayashi, T. Kawazoe, S. Sangu, and T. Yatsui, “Nanophotonics: design, fabrication, and operation of nanometric devices using optical near fields,” IEEE J. Sel. Top. Quantum Electron. 8, 839-862 (2002).
[CrossRef]

M. Ohtsu, K. Kobayashi, T. Kawazoe, T. Yatsui, and M. Naruse, Principles of Nanophotonics (CRC, 2008).
[CrossRef]

M. Ohtsu and K. Kobayashi, Optical Near Fields (Springer-Verlag, 2004).

Pellerin, K. M.

Sangu, S.

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

M. Naruse, T. Miyazaki, T. Kawazoe, S. Sangu, K. Kobayashi, F. Kubota, and M. Ohtsu, “Nanophotonic computing based on optical near-field interactions between quantum dots,” IEICE Trans. E88-C (2005).
[CrossRef]

S. Sangu, K. Kobayashi, and M. Ohtsu, “Nanophotonic devices and fundamental functional operations,” IEICE Trans. E88-C (2005).
[CrossRef]

M. Ohtsu, K. Kobayashi, T. Kawazoe, S. Sangu, and T. Yatsui, “Nanophotonics: design, fabrication, and operation of nanometric devices using optical near fields,” IEEE J. Sel. Top. Quantum Electron. 8, 839-862 (2002).
[CrossRef]

Thio, T.

Yatsui, T.

M. Naruse, T. Yatsui, T. Kawazoe, Y. Akao, and M. Ohtsu, “Design and simulation of a nanophotonic traceable memory using localized energy dissipation and hierarchy of optical near-field interactions,” IEEE Trans. Nanotechnol. 7, 14-19 (2008).
[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, 1404-1417 (2008).
[CrossRef]

M. Ohtsu, K. Kobayashi, T. Kawazoe, S. Sangu, and T. Yatsui, “Nanophotonics: design, fabrication, and operation of nanometric devices using optical near fields,” IEEE J. Sel. Top. Quantum Electron. 8, 839-862 (2002).
[CrossRef]

M. Ohtsu, K. Kobayashi, T. Kawazoe, T. Yatsui, and M. Naruse, Principles of Nanophotonics (CRC, 2008).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

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, 1404-1417 (2008).
[CrossRef]

M. Ohtsu, K. Kobayashi, T. Kawazoe, S. Sangu, and T. Yatsui, “Nanophotonics: design, fabrication, and operation of nanometric devices using optical near fields,” IEEE J. Sel. Top. Quantum Electron. 8, 839-862 (2002).
[CrossRef]

IEEE Trans. Autom. Control (1)

T. C. Hissa, “On the simplification of linear system,” IEEE Trans. Autom. Control 17, 372-374 (1972).
[CrossRef]

IEEE Trans. Nanotechnol. (1)

M. Naruse, T. Yatsui, T. Kawazoe, Y. Akao, and M. Ohtsu, “Design and simulation of a nanophotonic traceable memory using localized energy dissipation and hierarchy of optical near-field interactions,” IEEE Trans. Nanotechnol. 7, 14-19 (2008).
[CrossRef]

IEICE Trans. (2)

M. Naruse, T. Miyazaki, T. Kawazoe, S. Sangu, K. Kobayashi, F. Kubota, and M. Ohtsu, “Nanophotonic computing based on optical near-field interactions between quantum dots,” IEICE Trans. E88-C (2005).
[CrossRef]

S. Sangu, K. Kobayashi, and M. Ohtsu, “Nanophotonic devices and fundamental functional operations,” IEICE Trans. E88-C (2005).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Express (1)

Opt. Lett. (1)

Other (4)

M.Ohtsu, ed., Progress in Nano-Electro-Optics VI (Springer-Verlag, 2008).
[CrossRef]

V. May and O. Kühn, Charge and Energy Transfer Dynamics in Molecular Systems (Wiley-VCH, 2004).

M. Ohtsu and K. Kobayashi, Optical Near Fields (Springer-Verlag, 2004).

M. Ohtsu, K. Kobayashi, T. Kawazoe, T. Yatsui, and M. Naruse, Principles of Nanophotonics (CRC, 2008).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Schematic representation of a two-QD nanophotonic system, consisting two QDs and a heat bath with n oscillators.

Fig. 2
Fig. 2

Temperature dependence of the occupation probabilities for the sublevels in the two-QD system of Fig. 1, which consists of CuCl QDs in a NaCl matrix, for steady-state condition.

Fig. 3
Fig. 3

Variation of the maximum operating temperature, T max , versus the minimum QD effective length (a) for the two-QD system of Fig. 1, which consists of CuCl QDs in a NaCl matrix.

Fig. 4
Fig. 4

Variation of U τ S versus γ / 2 U for the two-dot system of Fig. 1, which consists of CuCl QDs in a NaCl matrix, at temperature (a)  0 K , (b)  0.1 Δ E / k , (c)  0.4 Δ E / k , and (d)  0.7 Δ E / k . Solid curves, bullets, and diamonds represent the data obtained from the analytic model of Eq. (11), the numerical model of Eq. (4), and the DM method, respectively.

Fig. 5
Fig. 5

Temperature dependence of U τ S for nanophotonic system of Fig. 1, for values of γ / 2 U = 2 , 3, and 5. Solid curve, bullets, and diamonds represent the data obtained from the analytic model of Eq. (11), the numerical model of Eq. (4), and the DM method, respectively.

Fig. 6
Fig. 6

Variation of normalized ONF energy transfer rate R ONF / U versus γ / 2 U for the nanophotonic device of Fig. 1, at three different temperatures T = 0.1 Δ E / k (circles) 0.4 Δ E / k (squares), and 0.7 Δ E / k (diamonds).

Equations (24)

Equations on this page are rendered with MathJax. Learn more.

d P i p ( t ) d t = [ R d i p p + R u i p h p + R ONF i p i q ] P i p ( t ) + R d h p i p P h p ( t ) + R u p i p P p ( t ) + R ONF i p i q P i q ( t ) ,
d P i q ( t ) d t = [ R d i q q + R u i q h q + R ONF i p i q ] P i q ( t ) + R d h q i q P h p ( t ) + R u q i q P p ( t ) + R ONF i p i q P i p ( t ) ,
i p , i q P i p ( q ) = 1.
R ONF i p i q 4 ( U i p i q ) 2 R out i p & i q ,
U i p i q = Y 1 exp ( m eff r p q ) m eff r p q
R out i p & i q p , q R d i p p + R d i q q + h p , h q R u i p h p + R u i q h q .
d P 1 1 d t = R ONF P 1 1 + R ONF P 2 2 ,
d P 2 2 d t = R ONF P 1 1 R ONF P 2 2 R d P 2 2 + R u P 1 2 ,
d P 1 2 d t = R d P 2 2 R u P 1 2 ,
P 1 1 + P 1 2 + P 2 2 = 1 ,
ρ ˙ 11 ( t ) = i U ( r ) [ ρ 12 ( t ) ρ 21 ( t ) ] , ρ ˙ 12 ( t ) ρ ˙ 21 ( t ) = 2 i U [ ρ 11 ( t ) ρ 22 ( t ) ] ( 1 + n ) γ [ ρ 12 ( t ) ρ 21 ( t ) ] , ρ ˙ 22 = i U ( r ) [ ρ 12 ( t ) ρ 21 ( t ) ] 2 ( 1 + n ) γ ρ 22 ( t ) + 2 n γ ρ 33 ( t ) , ρ ˙ 33 = 2 ( 1 + n ) γ ρ 22 ( t ) 2 n γ ρ 33 ( t ) ,
R d 2 ( n + 1 ) γ ,
R u 2 n γ ,
R ONF 4 U 1 1 2 2 R d 2 2 1 2 4 U 2 R d = 2 U 2 ( n + 1 ) γ .
R d 0 R d ( T = 0 K ) 2 γ ,
R u 0 R u ( T = 0 K ) 0 ,
R ONF 0 R ONF ( T = 0 K ) = 2 U 2 / γ .
d P 1 1 ( t ) d t 2 U 2 γ P 1 1 ( t ) ,
P 1 2 1 P 1 1 .
τ S 0 τ S ( T = 0 K ) γ / 2 U 2 R ONF 0 1 .
P 1 2 = ( 1 + n 1 + 3 n ) { 1 exp ( t τ S 1 ) } ,
τ S 1 = 4 R d [ 1 + ( R d + R u ) 2 R ONF 1 + ( R d + R u 2 R ONF ) 2 R u R ONF ] .
τ S = τ S 1 × ln [ 1 + n ( 1 + 3 n ) exp ( 1 ) 2 n ] .
P 1 1 | SS ρ 11 | SS = n 3 n + 1 , P 2 2 | SS ρ 22 | SS = n 3 n + 1 , P 1 2 | SS ρ 33 | SS = n + 1 3 n + 1 .

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