Abstract

We show that fractional decay may be observable in experiments using quantum dots and photonic crystals with parameters that are currently achievable. We focus on the case of inverse opal photonic crystals and locate the position in the crystal where the effect is most pronounced. Furthermore, we quantify the influence of absorptive loss and show that it is a limiting but not prohibitive effect.

© 2008 Optical Society of America

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  1. R. F. Nabiev, P. Yeh, and J. J. Sanchez-Mondragon, Phys. Rev. A 47, 3380 (1993).
    [CrossRef] [PubMed]
  2. S. John and T. Quang, Phys. Rev. A 50, 1764 (1994).
    [CrossRef] [PubMed]
  3. R. Sprik, B. A. Van Tiggelen, and A. Lagendijk, Europhys. Lett. 35, 265 (1996).
    [CrossRef]
  4. P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, Nature 432, 197 (2004).
    [CrossRef]
  5. N. Vats, S. John, and K. Busch, Phys. Rev. A 65, 043808 (2002).
    [CrossRef]
  6. P. Yu, M. C. Beard, R. J. Ellingson, S. Ferrere, C. Curtis, J. Drexler, F. Luiszer, and A. J. Nozik, J. Phys. Chem. B 109, 7084 (2005).
    [CrossRef]
  7. I. Moreels, K. Lambert, D. De Muynck, F. Vanhaecke, D. Poelman, J. C. Martins, G. Allan, and Z. Hens, Chem. Mater. 19, 6101 (2007).
    [CrossRef]
  8. L. C. Andreani, G. Panzarini, and J. Gérard, Phys. Rev. B 60, 13276 (1999).
    [CrossRef]
  9. S. John and K. Busch, Phys. Rev. E 58, 3896 (1998).
    [CrossRef]
  10. R. Wang, X.-H. Wang, B.-Y. Gu, and G.-Z. Yang, Phys. Rev. B 67, 155114 (2003).
    [CrossRef]
  11. A. A. Krokhin and P. Halevi, Phys. Rev. B 53, 1205 (1996).
    [CrossRef]
  12. Values along the Γ-H route showed poor convergence and have been left out, since they are irrelevant to the conclusions in this Letter.
  13. N. A. Mortensen, S. Ejsing, and S. Xiao, JEOS RP 1, 06032 (2006).
    [CrossRef]
  14. T. Gruner and D.-G. Welsch, Phys. Rev. A 53, 1818 (1996).
    [CrossRef] [PubMed]
  15. M. J. Keevers and M. A. Green, Sol. Energy Mater. Sol. Cells 41, 195 (1996).
    [CrossRef]

2007 (1)

I. Moreels, K. Lambert, D. De Muynck, F. Vanhaecke, D. Poelman, J. C. Martins, G. Allan, and Z. Hens, Chem. Mater. 19, 6101 (2007).
[CrossRef]

2006 (1)

N. A. Mortensen, S. Ejsing, and S. Xiao, JEOS RP 1, 06032 (2006).
[CrossRef]

2005 (1)

P. Yu, M. C. Beard, R. J. Ellingson, S. Ferrere, C. Curtis, J. Drexler, F. Luiszer, and A. J. Nozik, J. Phys. Chem. B 109, 7084 (2005).
[CrossRef]

2004 (1)

P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, Nature 432, 197 (2004).
[CrossRef]

2003 (1)

R. Wang, X.-H. Wang, B.-Y. Gu, and G.-Z. Yang, Phys. Rev. B 67, 155114 (2003).
[CrossRef]

2002 (1)

N. Vats, S. John, and K. Busch, Phys. Rev. A 65, 043808 (2002).
[CrossRef]

1999 (1)

L. C. Andreani, G. Panzarini, and J. Gérard, Phys. Rev. B 60, 13276 (1999).
[CrossRef]

1998 (1)

S. John and K. Busch, Phys. Rev. E 58, 3896 (1998).
[CrossRef]

1996 (4)

R. Sprik, B. A. Van Tiggelen, and A. Lagendijk, Europhys. Lett. 35, 265 (1996).
[CrossRef]

A. A. Krokhin and P. Halevi, Phys. Rev. B 53, 1205 (1996).
[CrossRef]

T. Gruner and D.-G. Welsch, Phys. Rev. A 53, 1818 (1996).
[CrossRef] [PubMed]

M. J. Keevers and M. A. Green, Sol. Energy Mater. Sol. Cells 41, 195 (1996).
[CrossRef]

1994 (1)

S. John and T. Quang, Phys. Rev. A 50, 1764 (1994).
[CrossRef] [PubMed]

1993 (1)

R. F. Nabiev, P. Yeh, and J. J. Sanchez-Mondragon, Phys. Rev. A 47, 3380 (1993).
[CrossRef] [PubMed]

Allan, G.

I. Moreels, K. Lambert, D. De Muynck, F. Vanhaecke, D. Poelman, J. C. Martins, G. Allan, and Z. Hens, Chem. Mater. 19, 6101 (2007).
[CrossRef]

Andreani, L. C.

L. C. Andreani, G. Panzarini, and J. Gérard, Phys. Rev. B 60, 13276 (1999).
[CrossRef]

Beard, M. C.

P. Yu, M. C. Beard, R. J. Ellingson, S. Ferrere, C. Curtis, J. Drexler, F. Luiszer, and A. J. Nozik, J. Phys. Chem. B 109, 7084 (2005).
[CrossRef]

Busch, K.

N. Vats, S. John, and K. Busch, Phys. Rev. A 65, 043808 (2002).
[CrossRef]

S. John and K. Busch, Phys. Rev. E 58, 3896 (1998).
[CrossRef]

Curtis, C.

P. Yu, M. C. Beard, R. J. Ellingson, S. Ferrere, C. Curtis, J. Drexler, F. Luiszer, and A. J. Nozik, J. Phys. Chem. B 109, 7084 (2005).
[CrossRef]

De Muynck, D.

I. Moreels, K. Lambert, D. De Muynck, F. Vanhaecke, D. Poelman, J. C. Martins, G. Allan, and Z. Hens, Chem. Mater. 19, 6101 (2007).
[CrossRef]

Drexler, J.

P. Yu, M. C. Beard, R. J. Ellingson, S. Ferrere, C. Curtis, J. Drexler, F. Luiszer, and A. J. Nozik, J. Phys. Chem. B 109, 7084 (2005).
[CrossRef]

Ejsing, S.

N. A. Mortensen, S. Ejsing, and S. Xiao, JEOS RP 1, 06032 (2006).
[CrossRef]

Ellingson, R. J.

P. Yu, M. C. Beard, R. J. Ellingson, S. Ferrere, C. Curtis, J. Drexler, F. Luiszer, and A. J. Nozik, J. Phys. Chem. B 109, 7084 (2005).
[CrossRef]

Ferrere, S.

P. Yu, M. C. Beard, R. J. Ellingson, S. Ferrere, C. Curtis, J. Drexler, F. Luiszer, and A. J. Nozik, J. Phys. Chem. B 109, 7084 (2005).
[CrossRef]

Gérard, J.

L. C. Andreani, G. Panzarini, and J. Gérard, Phys. Rev. B 60, 13276 (1999).
[CrossRef]

Green, M. A.

M. J. Keevers and M. A. Green, Sol. Energy Mater. Sol. Cells 41, 195 (1996).
[CrossRef]

Gruner, T.

T. Gruner and D.-G. Welsch, Phys. Rev. A 53, 1818 (1996).
[CrossRef] [PubMed]

Gu, B.-Y.

R. Wang, X.-H. Wang, B.-Y. Gu, and G.-Z. Yang, Phys. Rev. B 67, 155114 (2003).
[CrossRef]

Halevi, P.

A. A. Krokhin and P. Halevi, Phys. Rev. B 53, 1205 (1996).
[CrossRef]

Hens, Z.

I. Moreels, K. Lambert, D. De Muynck, F. Vanhaecke, D. Poelman, J. C. Martins, G. Allan, and Z. Hens, Chem. Mater. 19, 6101 (2007).
[CrossRef]

Irman, A.

P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, Nature 432, 197 (2004).
[CrossRef]

John, S.

N. Vats, S. John, and K. Busch, Phys. Rev. A 65, 043808 (2002).
[CrossRef]

S. John and K. Busch, Phys. Rev. E 58, 3896 (1998).
[CrossRef]

S. John and T. Quang, Phys. Rev. A 50, 1764 (1994).
[CrossRef] [PubMed]

Keevers, M. J.

M. J. Keevers and M. A. Green, Sol. Energy Mater. Sol. Cells 41, 195 (1996).
[CrossRef]

Krokhin, A. A.

A. A. Krokhin and P. Halevi, Phys. Rev. B 53, 1205 (1996).
[CrossRef]

Lagendijk, A.

R. Sprik, B. A. Van Tiggelen, and A. Lagendijk, Europhys. Lett. 35, 265 (1996).
[CrossRef]

Lambert, K.

I. Moreels, K. Lambert, D. De Muynck, F. Vanhaecke, D. Poelman, J. C. Martins, G. Allan, and Z. Hens, Chem. Mater. 19, 6101 (2007).
[CrossRef]

Lodahl, P.

P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, Nature 432, 197 (2004).
[CrossRef]

Luiszer, F.

P. Yu, M. C. Beard, R. J. Ellingson, S. Ferrere, C. Curtis, J. Drexler, F. Luiszer, and A. J. Nozik, J. Phys. Chem. B 109, 7084 (2005).
[CrossRef]

Martins, J. C.

I. Moreels, K. Lambert, D. De Muynck, F. Vanhaecke, D. Poelman, J. C. Martins, G. Allan, and Z. Hens, Chem. Mater. 19, 6101 (2007).
[CrossRef]

Moreels, I.

I. Moreels, K. Lambert, D. De Muynck, F. Vanhaecke, D. Poelman, J. C. Martins, G. Allan, and Z. Hens, Chem. Mater. 19, 6101 (2007).
[CrossRef]

Mortensen, N. A.

N. A. Mortensen, S. Ejsing, and S. Xiao, JEOS RP 1, 06032 (2006).
[CrossRef]

Nabiev, R. F.

R. F. Nabiev, P. Yeh, and J. J. Sanchez-Mondragon, Phys. Rev. A 47, 3380 (1993).
[CrossRef] [PubMed]

Nikolaev, I. S.

P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, Nature 432, 197 (2004).
[CrossRef]

Nozik, A. J.

P. Yu, M. C. Beard, R. J. Ellingson, S. Ferrere, C. Curtis, J. Drexler, F. Luiszer, and A. J. Nozik, J. Phys. Chem. B 109, 7084 (2005).
[CrossRef]

Overgaag, K.

P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, Nature 432, 197 (2004).
[CrossRef]

Panzarini, G.

L. C. Andreani, G. Panzarini, and J. Gérard, Phys. Rev. B 60, 13276 (1999).
[CrossRef]

Poelman, D.

I. Moreels, K. Lambert, D. De Muynck, F. Vanhaecke, D. Poelman, J. C. Martins, G. Allan, and Z. Hens, Chem. Mater. 19, 6101 (2007).
[CrossRef]

Quang, T.

S. John and T. Quang, Phys. Rev. A 50, 1764 (1994).
[CrossRef] [PubMed]

Sanchez-Mondragon, J. J.

R. F. Nabiev, P. Yeh, and J. J. Sanchez-Mondragon, Phys. Rev. A 47, 3380 (1993).
[CrossRef] [PubMed]

Sprik, R.

R. Sprik, B. A. Van Tiggelen, and A. Lagendijk, Europhys. Lett. 35, 265 (1996).
[CrossRef]

van Driel, A. F.

P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, Nature 432, 197 (2004).
[CrossRef]

Van Tiggelen, B. A.

R. Sprik, B. A. Van Tiggelen, and A. Lagendijk, Europhys. Lett. 35, 265 (1996).
[CrossRef]

Vanhaecke, F.

I. Moreels, K. Lambert, D. De Muynck, F. Vanhaecke, D. Poelman, J. C. Martins, G. Allan, and Z. Hens, Chem. Mater. 19, 6101 (2007).
[CrossRef]

Vanmaekelbergh, D.

P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, Nature 432, 197 (2004).
[CrossRef]

Vats, N.

N. Vats, S. John, and K. Busch, Phys. Rev. A 65, 043808 (2002).
[CrossRef]

Vos, W. L.

P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, Nature 432, 197 (2004).
[CrossRef]

Wang, R.

R. Wang, X.-H. Wang, B.-Y. Gu, and G.-Z. Yang, Phys. Rev. B 67, 155114 (2003).
[CrossRef]

Wang, X.-H.

R. Wang, X.-H. Wang, B.-Y. Gu, and G.-Z. Yang, Phys. Rev. B 67, 155114 (2003).
[CrossRef]

Welsch, D.-G.

T. Gruner and D.-G. Welsch, Phys. Rev. A 53, 1818 (1996).
[CrossRef] [PubMed]

Xiao, S.

N. A. Mortensen, S. Ejsing, and S. Xiao, JEOS RP 1, 06032 (2006).
[CrossRef]

Yang, G.-Z.

R. Wang, X.-H. Wang, B.-Y. Gu, and G.-Z. Yang, Phys. Rev. B 67, 155114 (2003).
[CrossRef]

Yeh, P.

R. F. Nabiev, P. Yeh, and J. J. Sanchez-Mondragon, Phys. Rev. A 47, 3380 (1993).
[CrossRef] [PubMed]

Yu, P.

P. Yu, M. C. Beard, R. J. Ellingson, S. Ferrere, C. Curtis, J. Drexler, F. Luiszer, and A. J. Nozik, J. Phys. Chem. B 109, 7084 (2005).
[CrossRef]

Chem. Mater. (1)

I. Moreels, K. Lambert, D. De Muynck, F. Vanhaecke, D. Poelman, J. C. Martins, G. Allan, and Z. Hens, Chem. Mater. 19, 6101 (2007).
[CrossRef]

Europhys. Lett. (1)

R. Sprik, B. A. Van Tiggelen, and A. Lagendijk, Europhys. Lett. 35, 265 (1996).
[CrossRef]

J. Phys. Chem. B (1)

P. Yu, M. C. Beard, R. J. Ellingson, S. Ferrere, C. Curtis, J. Drexler, F. Luiszer, and A. J. Nozik, J. Phys. Chem. B 109, 7084 (2005).
[CrossRef]

JEOS RP (1)

N. A. Mortensen, S. Ejsing, and S. Xiao, JEOS RP 1, 06032 (2006).
[CrossRef]

Nature (1)

P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, Nature 432, 197 (2004).
[CrossRef]

Phys. Rev. A (4)

N. Vats, S. John, and K. Busch, Phys. Rev. A 65, 043808 (2002).
[CrossRef]

R. F. Nabiev, P. Yeh, and J. J. Sanchez-Mondragon, Phys. Rev. A 47, 3380 (1993).
[CrossRef] [PubMed]

S. John and T. Quang, Phys. Rev. A 50, 1764 (1994).
[CrossRef] [PubMed]

T. Gruner and D.-G. Welsch, Phys. Rev. A 53, 1818 (1996).
[CrossRef] [PubMed]

Phys. Rev. B (3)

L. C. Andreani, G. Panzarini, and J. Gérard, Phys. Rev. B 60, 13276 (1999).
[CrossRef]

R. Wang, X.-H. Wang, B.-Y. Gu, and G.-Z. Yang, Phys. Rev. B 67, 155114 (2003).
[CrossRef]

A. A. Krokhin and P. Halevi, Phys. Rev. B 53, 1205 (1996).
[CrossRef]

Phys. Rev. E (1)

S. John and K. Busch, Phys. Rev. E 58, 3896 (1998).
[CrossRef]

Sol. Energy Mater. Sol. Cells (1)

M. J. Keevers and M. A. Green, Sol. Energy Mater. Sol. Cells 41, 195 (1996).
[CrossRef]

Other (1)

Values along the Γ-H route showed poor convergence and have been left out, since they are irrelevant to the conclusions in this Letter.

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Figures (4)

Fig. 1
Fig. 1

Projected LDOS of a closed packed Si inverse opal close to the band edge at the H and Γ points as indicated. Solid curves are analytical approximations to the plane-wave calculations (histograms), and the dashed curve shows the influence of loss. Inset shows the unit cell of an inverse opal and high symmetry points.

Fig. 2
Fig. 2

The parameter K BE (in units of ρ 0 ( ω e g ) ω e g 1 2 ) as a function of position in the Wigner–Seitz cell (shown in the inset) for the three principal emitter orientations. The gray dashed-dotted line shows values of K BE at the H point for different R a .

Fig. 3
Fig. 3

Decay from PbSe QDs at the H point in an Si inverse opal ( β K BE = 5.5 × 10 7 ) at detuning ω BE ω Pb Se = 1 8.309 × 10 7 and different losses. Dashed curves show exponential parts only.

Fig. 4
Fig. 4

Degree of fractional decay obtainable versus light-matter coupling strength, β K BE , at different absorption.

Equations (6)

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c ̃ e ( r , ω ̃ ) = 1 β G ( r , ω ̃ ) i ( ω ̃ 1 ) = a 1 ω ̃ ω ̃ 0 + c ̃ ( ω ̃ ) ,
G ( r , ω ̃ ) = i ω ̃ 0 ω ̃ C ρ ̃ p ( r , x ) x 2 ( ω ̃ x ) d x ,
ρ p ( r , ω ) = μ e p E μ ( r ) 2 δ ( ω ω μ ) ,
ρ p ( r , ω ) = i V ( 2 π ) 3 S ( ω ) e p E k , i ( r ) 2 ω ( k ) d k ,
δ = ω ( 0 ) 2 E μ i ϵ I E μ C E μ i ϵ R E μ V = ω ( 0 ) ϵ I 2 ϵ R f ,
ρ BE ( r , ω ) = K BE ( r ) ω BE x ω BE δ π ( ω x ) 2 + δ 2 d x ,

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