Abstract

We present an efficient optical model to study spontaneous emission in a cylindrically layered nanostructure. The total emission power of an emitter in the nanostructure is efficiently calculated. A formula is derived to calculate the lateral-surface emission power. As examples of practical interest, spontaneous emission properties, including radiative transition rate of the emitter, the assignment of the emission to lateralsurface emission and waveguided emission, are comprehensively studied at the first time for an isolated ZnO nanowire and a ZnO/SiO2 nanocable.

© 2007 Optical Society of America

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References

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  1. C. J. Barrelet, A. B. Greytak and C. M. Lieber, "Nanowire photonic circuit elements," Nano Lett. 4, 1981-1985 (2004).
    [CrossRef]
  2. J. M. Bao, M. A. Zimmler, F. Capasso, X. W. Wang and Z.F. Ren, "Broadband ZnO single-nanowire light-emitting diode," Nano Lett. 6, 1719-1722 (2006).
    [CrossRef] [PubMed]
  3. L Dai, X. L. Chen, X. Zhang, T. Zhou and H. Hu "Coaxial ZnO/SiO2 nanocables fabricated by thermal evaporation/oxidation," Appl. Phys. A 78, 557-559 (2004).
    [CrossRef]
  4. Y. Wang, Z. Tang, X. Liang, L. M. Liz-Marzan and N. A. Kotov, "SiO2-Coated CdTe Nanowires: Bristled Nano Centipedes, "Nano Lett. 4, 225-231 (2004).
    [CrossRef]
  5. O. Hayden, A. B. Greytak and D. C. Bell, "Core-shell nanowire light-emitting diodes,"Adv. Mater. 17, 701- 704 (2005).
    [CrossRef]
  6. J. Goldberger, R. R. He, Y. F. Zhang, S. K. Lee, H. Q. Yan, H. J. Choi, and P. D. Yang, "Single-crystal gallium nitride nanotubes," Nature 422, 599-602 (2003).
    [CrossRef] [PubMed]
  7. E. M. Purcell, "Spontaneous emission probabilities at radio frequencies," Phys. Rev. 69,681-681 (1946).
  8. W. Lukosz, ‘‘Theory of optical-environment-dependent spontaneous emission rates for emitters in thin layers,’’Phys. Rev. B 22, 3030-3038 (1980).
    [CrossRef]
  9. X. W. Chen, W. C. H. Choy, S. L. He and P. C. Chui, "Comprehensive Analysis and Optimal Design of Top-Emitting Organic Light Emitting Devices," J. Appl. Phys. 101, 113107 (2007).
    [CrossRef]
  10. J. R. Lovell and W. C. Chew, "Response of a point source in a multicylindrically layered medium," IEEE Trans. Geosci. Remote Sensing,  GE-25, 850-858 (1987).
    [CrossRef]
  11. I. Vurgaftman and J. Singh, "Spatial and spectral characteristics of spontaneous emission from semiconductor quantum wells in microscopic cylindrical cavities," Appl. Phys. Lett. 67, 3865-3867 (1995).
    [CrossRef]
  12. K. Oshiro K and K. Kakazu, "Spontaneous emission in coaxial cylindrical cavities," Prog. Theor. Phys 98, 533-550 (1997).
    [CrossRef]
  13. C. C. Wang and Z. Ye, "Spontaneous emission in cylindrical periodically-layered structures," Phys. Stat. Solid I A- Applied Research 174, 527-540 (1999).
    [CrossRef]
  14. W. Zakowicz and M. Janowicz, "Spontaneous emission in the presence of a dielectric cylinder," Phys. Rev. A,  62, 013820 (2000).
    [CrossRef]
  15. D. P. Fussell, R. C. McPhedran and C. M. de Sterke, "Decay rate and level shift in a circular dielectric waveguide," Phys. Rev. A 71, 013815 (2005).
    [CrossRef]
  16. P. Bermel, J. D. Joannopoulos and Y. Fink, "Properties of radiating pointlike sources in cylindrically omnidirectionally reflecting waveguides," Phys. Rev. B 69, 035316 (2004).
    [CrossRef]
  17. S. Wakelin and C. R. Bagshaw, "A prism combination for near isotropic fluorescence excitation by total internal reflection," J. Microsc 209, 143-148 (2003).
    [CrossRef] [PubMed]
  18. J. Enderlein, "Theoretical study of single molecule fluorescence in a metallic nanocavity," Appl. Phys. Lett. 80, 315-317 (2002).
    [CrossRef]
  19. W. C. Chew, Waves and Fields in Inhomogeneous Media, Chap. 3 (IEEE Press, New York, 1995).
  20. P. Gay-Balmaz and J. R. Mosig, "Three-Dimensional planar radiating structures in stratified media," Int.J. Microwave Millimeter Wave Computer-Aided Eng. 37, 330 -343(1997).
    [CrossRef]
  21. Y. Zhang and R. E. Russo,"Quantum efficiency of ZnO nanowire nanolasers,"Appl. Phys. Lett. 87, 043106 (2005).
    [CrossRef]

2007 (1)

X. W. Chen, W. C. H. Choy, S. L. He and P. C. Chui, "Comprehensive Analysis and Optimal Design of Top-Emitting Organic Light Emitting Devices," J. Appl. Phys. 101, 113107 (2007).
[CrossRef]

2006 (1)

J. M. Bao, M. A. Zimmler, F. Capasso, X. W. Wang and Z.F. Ren, "Broadband ZnO single-nanowire light-emitting diode," Nano Lett. 6, 1719-1722 (2006).
[CrossRef] [PubMed]

2005 (3)

O. Hayden, A. B. Greytak and D. C. Bell, "Core-shell nanowire light-emitting diodes,"Adv. Mater. 17, 701- 704 (2005).
[CrossRef]

D. P. Fussell, R. C. McPhedran and C. M. de Sterke, "Decay rate and level shift in a circular dielectric waveguide," Phys. Rev. A 71, 013815 (2005).
[CrossRef]

Y. Zhang and R. E. Russo,"Quantum efficiency of ZnO nanowire nanolasers,"Appl. Phys. Lett. 87, 043106 (2005).
[CrossRef]

2004 (4)

P. Bermel, J. D. Joannopoulos and Y. Fink, "Properties of radiating pointlike sources in cylindrically omnidirectionally reflecting waveguides," Phys. Rev. B 69, 035316 (2004).
[CrossRef]

L Dai, X. L. Chen, X. Zhang, T. Zhou and H. Hu "Coaxial ZnO/SiO2 nanocables fabricated by thermal evaporation/oxidation," Appl. Phys. A 78, 557-559 (2004).
[CrossRef]

Y. Wang, Z. Tang, X. Liang, L. M. Liz-Marzan and N. A. Kotov, "SiO2-Coated CdTe Nanowires: Bristled Nano Centipedes, "Nano Lett. 4, 225-231 (2004).
[CrossRef]

C. J. Barrelet, A. B. Greytak and C. M. Lieber, "Nanowire photonic circuit elements," Nano Lett. 4, 1981-1985 (2004).
[CrossRef]

2003 (2)

J. Goldberger, R. R. He, Y. F. Zhang, S. K. Lee, H. Q. Yan, H. J. Choi, and P. D. Yang, "Single-crystal gallium nitride nanotubes," Nature 422, 599-602 (2003).
[CrossRef] [PubMed]

S. Wakelin and C. R. Bagshaw, "A prism combination for near isotropic fluorescence excitation by total internal reflection," J. Microsc 209, 143-148 (2003).
[CrossRef] [PubMed]

2002 (1)

J. Enderlein, "Theoretical study of single molecule fluorescence in a metallic nanocavity," Appl. Phys. Lett. 80, 315-317 (2002).
[CrossRef]

2000 (1)

W. Zakowicz and M. Janowicz, "Spontaneous emission in the presence of a dielectric cylinder," Phys. Rev. A,  62, 013820 (2000).
[CrossRef]

1997 (2)

K. Oshiro K and K. Kakazu, "Spontaneous emission in coaxial cylindrical cavities," Prog. Theor. Phys 98, 533-550 (1997).
[CrossRef]

P. Gay-Balmaz and J. R. Mosig, "Three-Dimensional planar radiating structures in stratified media," Int.J. Microwave Millimeter Wave Computer-Aided Eng. 37, 330 -343(1997).
[CrossRef]

1995 (1)

I. Vurgaftman and J. Singh, "Spatial and spectral characteristics of spontaneous emission from semiconductor quantum wells in microscopic cylindrical cavities," Appl. Phys. Lett. 67, 3865-3867 (1995).
[CrossRef]

1987 (1)

J. R. Lovell and W. C. Chew, "Response of a point source in a multicylindrically layered medium," IEEE Trans. Geosci. Remote Sensing,  GE-25, 850-858 (1987).
[CrossRef]

1980 (1)

W. Lukosz, ‘‘Theory of optical-environment-dependent spontaneous emission rates for emitters in thin layers,’’Phys. Rev. B 22, 3030-3038 (1980).
[CrossRef]

1946 (1)

E. M. Purcell, "Spontaneous emission probabilities at radio frequencies," Phys. Rev. 69,681-681 (1946).

Adv. Mater. (1)

O. Hayden, A. B. Greytak and D. C. Bell, "Core-shell nanowire light-emitting diodes,"Adv. Mater. 17, 701- 704 (2005).
[CrossRef]

Appl. Phys. A (1)

L Dai, X. L. Chen, X. Zhang, T. Zhou and H. Hu "Coaxial ZnO/SiO2 nanocables fabricated by thermal evaporation/oxidation," Appl. Phys. A 78, 557-559 (2004).
[CrossRef]

Appl. Phys. Lett. (3)

I. Vurgaftman and J. Singh, "Spatial and spectral characteristics of spontaneous emission from semiconductor quantum wells in microscopic cylindrical cavities," Appl. Phys. Lett. 67, 3865-3867 (1995).
[CrossRef]

J. Enderlein, "Theoretical study of single molecule fluorescence in a metallic nanocavity," Appl. Phys. Lett. 80, 315-317 (2002).
[CrossRef]

Y. Zhang and R. E. Russo,"Quantum efficiency of ZnO nanowire nanolasers,"Appl. Phys. Lett. 87, 043106 (2005).
[CrossRef]

IEEE Trans. Geosci. Remote Sensing (1)

J. R. Lovell and W. C. Chew, "Response of a point source in a multicylindrically layered medium," IEEE Trans. Geosci. Remote Sensing,  GE-25, 850-858 (1987).
[CrossRef]

J. Appl. Phys. (1)

X. W. Chen, W. C. H. Choy, S. L. He and P. C. Chui, "Comprehensive Analysis and Optimal Design of Top-Emitting Organic Light Emitting Devices," J. Appl. Phys. 101, 113107 (2007).
[CrossRef]

J. Microsc (1)

S. Wakelin and C. R. Bagshaw, "A prism combination for near isotropic fluorescence excitation by total internal reflection," J. Microsc 209, 143-148 (2003).
[CrossRef] [PubMed]

J. Microwave Millimeter Wave Computer-Aided Eng. (1)

P. Gay-Balmaz and J. R. Mosig, "Three-Dimensional planar radiating structures in stratified media," Int.J. Microwave Millimeter Wave Computer-Aided Eng. 37, 330 -343(1997).
[CrossRef]

Nano Lett. (3)

Y. Wang, Z. Tang, X. Liang, L. M. Liz-Marzan and N. A. Kotov, "SiO2-Coated CdTe Nanowires: Bristled Nano Centipedes, "Nano Lett. 4, 225-231 (2004).
[CrossRef]

C. J. Barrelet, A. B. Greytak and C. M. Lieber, "Nanowire photonic circuit elements," Nano Lett. 4, 1981-1985 (2004).
[CrossRef]

J. M. Bao, M. A. Zimmler, F. Capasso, X. W. Wang and Z.F. Ren, "Broadband ZnO single-nanowire light-emitting diode," Nano Lett. 6, 1719-1722 (2006).
[CrossRef] [PubMed]

Nature (1)

J. Goldberger, R. R. He, Y. F. Zhang, S. K. Lee, H. Q. Yan, H. J. Choi, and P. D. Yang, "Single-crystal gallium nitride nanotubes," Nature 422, 599-602 (2003).
[CrossRef] [PubMed]

Phys. Rev. (1)

E. M. Purcell, "Spontaneous emission probabilities at radio frequencies," Phys. Rev. 69,681-681 (1946).

Phys. Rev. A (2)

W. Zakowicz and M. Janowicz, "Spontaneous emission in the presence of a dielectric cylinder," Phys. Rev. A,  62, 013820 (2000).
[CrossRef]

D. P. Fussell, R. C. McPhedran and C. M. de Sterke, "Decay rate and level shift in a circular dielectric waveguide," Phys. Rev. A 71, 013815 (2005).
[CrossRef]

Phys. Rev. B (2)

P. Bermel, J. D. Joannopoulos and Y. Fink, "Properties of radiating pointlike sources in cylindrically omnidirectionally reflecting waveguides," Phys. Rev. B 69, 035316 (2004).
[CrossRef]

W. Lukosz, ‘‘Theory of optical-environment-dependent spontaneous emission rates for emitters in thin layers,’’Phys. Rev. B 22, 3030-3038 (1980).
[CrossRef]

Prog. Theor. Phys (1)

K. Oshiro K and K. Kakazu, "Spontaneous emission in coaxial cylindrical cavities," Prog. Theor. Phys 98, 533-550 (1997).
[CrossRef]

Other (2)

C. C. Wang and Z. Ye, "Spontaneous emission in cylindrical periodically-layered structures," Phys. Stat. Solid I A- Applied Research 174, 527-540 (1999).
[CrossRef]

W. C. Chew, Waves and Fields in Inhomogeneous Media, Chap. 3 (IEEE Press, New York, 1995).

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Figures (3)

Fig. 1.
Fig. 1.

Schematic diagram of a cylindrically multilayered media with M inner layers and N outer layers. The asterisk denotes an emitter.

Fig. 2.
Fig. 2.

The dashed line denotes the new integration path in the complex plane of k z. The crosses are the pole singularities of the cylindrically multilayered media.

Fig. 3.
Fig. 3.

(a) The dependences of F and U on the radius of the ZnO NW for the emitter located at the origin of the NW. Inset of (a) shows dependence of F of ρ-oriented emitter on the refractive index of the NW with extremely small radius. The dependences of ηU and ηW on the radius of the ZnO NW for the emitter (b) located at the origin of the NW and (c) located near the boundary of the NW. (d) The dependences of ηU and ηW on the silica shell thickness of the ZnO/SiO2 NC. The superscripts of the symbols and asterisk denote the orientation and location of the emitter.

Equations (17)

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Γ r = F · Γ r 0
η F Γ r ( Γ r + Γ nr ) = F η 0 [ F η 0 + ( 1 η 0 ) ]
η U η F · U F = U η 0 [ F η 0 + ( 1 η 0 ) ]
η W η F · W F = W η 0 [ F η 0 + ( 1 η 0 ) ]
E = E 0 + E r
F α = 1 α · Im ( i E r ( r , r ) ) ( ω μ k Θ 6 π )
[ E z 0 H z 0 ] = { v = e iv θ d k z a 00 v H v ( 1 ) ( k ρ ρ ) e i k z z ( ρ > ρ ' ) v = e i v θ d k z b 00 v J v ( k ρ ρ ) e i k z z ( ρ < ρ ' )
where a 00 v = Θ 8 πεω [ ( z k 2 + z ) · α i ω ε α · z × ] e i v θ ' i k z z J v ( k ρ ρ )
b 00 v = Θ 8 πεω [ ( z k 2 + z ) · α i ω ε α · z × ] e i v θ ' i k z z H v ( 1 ) ( k ρ ρ )
[ E z r H z r ] = v = e i v θ d k z ( a 0 v H v ( 1 ) ( k ρ ρ ) + b 0 v J v ( k ρ ρ ) ) e i k z z
[ E z t H z t ] = v = e i v θ d k z a N v H v ( 1 ) ( k ρ ρ ) e i k z z
a 0 v = [ I M 0 v N 0 v ] 1 [ M 0 v b 00 v + a 00 v ] a 00 v
b 0 v = [ I N 0 v M 0 v ] 1 [ N 0 v a 00 v + b 00 v ] b 00 v
a N v = T N v ( a 0 v + a 00 v )
[ E z r H z r ] = 2 v = e i v θ ( C R + 2 k r ) ( a 0 v H v ( 1 ) ( k ρ ρ ) + b 0 v J v ( k ρ ρ ) ) e i k z z d k z
U 0 2 π ρ d θ d z 1 2 Re ( E θ × H z * E z × H θ * ) L 0
U = ω ρ L 0 v = 0 k out d k z Re [ i ε out H v ( 1 ) ( k ρ ρ ) H v ( 1 ) * ( k ρ ρ ) a N v ( 1 ) 2 i μ H v ( 1 ) * ( k ρ ρ ) H v ( 1 ) ( k ρ ρ ) a N v ( 2 ) 2 ] k ρ

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