Abstract

We present a theoretical study of fluorescence enhancement in the vicinity of a superlens slab, the other side of which is connected to a prism. The fluorescent molecule is regarded as an electric dipole. The dipole excitation rate follows Fermi’s golden rule, while its relaxation process has several pathways that can be analyzed within the range of classical electromagnetic theory. The calculated results are explained by surface modes and reveal a great potential of the proposed configuration in enhancing and detecting fluorescence.

© 2009 Optical Society of America

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  1. R. W. Gruhlke, W. R. Holland, and D. G. Hall, “Surface-plasmon cross coupling in molecular fluorescence near a corrugated thin film,” Phys. Rev. Lett. 562838-2841 (1986).
    [CrossRef] [PubMed]
  2. H. Knobloch, H. Brunner, A. Leitner, F. Aussenegg, and W. J. Knoll, “Probing the evanescent field of propagating plasmon surface polaritons by fluorescence and Raman spectroscopies,” J. Chem. Phys. 98, 10093-10095 (1993).
    [CrossRef]
  3. J. Enderlein, “A theoretical investigation of single molecule fluorescence detection on thin metallic layers,” Biophys. J. 78, 2151-2158 (2000).
    [CrossRef] [PubMed]
  4. K. Vasilev, W. Knoll, and M. Kreiter, “Fluorescence intensities of chromophores in front of a thin metal film,” J. Chem. Phys. 120, 3439-3445 (2004).
    [CrossRef] [PubMed]
  5. J. R. Lakowicz, “Radiative decay engineering 3. Surface plasmon-coupled directional emission,” Anal. Biochem. 324, 153-169 (2004).
    [CrossRef]
  6. F. D. Stefani, K. Vasilev, N. Bocchio, N. Stoyanova, and M. Kreiter, “Surface-plasmon-mediated single-molecule fluorescence through a thin metallic film,” Phys. Rev. Lett. 94, 023005 (2005).
    [CrossRef] [PubMed]
  7. Y. J. Hung, I. I. Smolyaninov, C. C. Davis, and H. C. Wu, “Fluorescence enhancement by surface gratings,” Opt. Express 14, 10825-10830 (2006).
    [CrossRef] [PubMed]
  8. J. Gómez Rivas, G. Vecchi, and V. Giannini, “Surface plasmon-polariton mediated enhancement of the emission of dye molecules on metallic gratings,” New J. Phys. 10, 105007 (2008).
    [CrossRef]
  9. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ɛ and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  10. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187 (2000).
    [CrossRef] [PubMed]
  11. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  12. R. Ruppin, “Surface polaritons of a left-handed medium,” Phys. Lett. A 277, 61-64 (2000).
    [CrossRef]
  13. R. Ruppin, “Surface polaritons of a left-handed material slab,” J. Phys.: Condens. Matter 13, 1811-1819 (2001).
    [CrossRef]
  14. I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Guided modes in negative-refractive-index waveguides,” Phys. Rev. E 67, 057602 (2003).
    [CrossRef]
  15. K. Park, B. J. Lee, C. Fu, and Z. M. Zhang, “Study of the surface and bulk polaritons with a negative index metamaterial,” J. Opt. Soc. Am. B 22, 1016-1023 (2005).
    [CrossRef]
  16. J. Kastel and M. Fleischhauer, “Suppression of spontaneous emission and superradiance over macroscopic distances in media with negative refraction,” Phys. Rev. A 71, 011804(R) (2005).
    [CrossRef]
  17. J. P. Xu, Y. P. Yang, H. Chen, and S. Y. Zhu, “Spontaneous decay process of a two-level atom embedded in a one-dimensional structure containing left-handed material,” Phys. Rev. A 76, 063813 (2007).
    [CrossRef]
  18. L. S. Froufe-Pérez and R. Carminati, “Controlling the fluorescence lifetime of a single emitter on the nanoscale using a plasmonic superlens,” Phys. Rev. B 78, 125403 (2008).
    [CrossRef]
  19. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge Univ. Press, 1999).
  20. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge Univ. Press, 2006).

2008

J. Gómez Rivas, G. Vecchi, and V. Giannini, “Surface plasmon-polariton mediated enhancement of the emission of dye molecules on metallic gratings,” New J. Phys. 10, 105007 (2008).
[CrossRef]

L. S. Froufe-Pérez and R. Carminati, “Controlling the fluorescence lifetime of a single emitter on the nanoscale using a plasmonic superlens,” Phys. Rev. B 78, 125403 (2008).
[CrossRef]

2007

J. P. Xu, Y. P. Yang, H. Chen, and S. Y. Zhu, “Spontaneous decay process of a two-level atom embedded in a one-dimensional structure containing left-handed material,” Phys. Rev. A 76, 063813 (2007).
[CrossRef]

2006

2005

K. Park, B. J. Lee, C. Fu, and Z. M. Zhang, “Study of the surface and bulk polaritons with a negative index metamaterial,” J. Opt. Soc. Am. B 22, 1016-1023 (2005).
[CrossRef]

F. D. Stefani, K. Vasilev, N. Bocchio, N. Stoyanova, and M. Kreiter, “Surface-plasmon-mediated single-molecule fluorescence through a thin metallic film,” Phys. Rev. Lett. 94, 023005 (2005).
[CrossRef] [PubMed]

J. Kastel and M. Fleischhauer, “Suppression of spontaneous emission and superradiance over macroscopic distances in media with negative refraction,” Phys. Rev. A 71, 011804(R) (2005).
[CrossRef]

2004

K. Vasilev, W. Knoll, and M. Kreiter, “Fluorescence intensities of chromophores in front of a thin metal film,” J. Chem. Phys. 120, 3439-3445 (2004).
[CrossRef] [PubMed]

J. R. Lakowicz, “Radiative decay engineering 3. Surface plasmon-coupled directional emission,” Anal. Biochem. 324, 153-169 (2004).
[CrossRef]

2003

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Guided modes in negative-refractive-index waveguides,” Phys. Rev. E 67, 057602 (2003).
[CrossRef]

2001

R. Ruppin, “Surface polaritons of a left-handed material slab,” J. Phys.: Condens. Matter 13, 1811-1819 (2001).
[CrossRef]

2000

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

R. Ruppin, “Surface polaritons of a left-handed medium,” Phys. Lett. A 277, 61-64 (2000).
[CrossRef]

J. Enderlein, “A theoretical investigation of single molecule fluorescence detection on thin metallic layers,” Biophys. J. 78, 2151-2158 (2000).
[CrossRef] [PubMed]

1993

H. Knobloch, H. Brunner, A. Leitner, F. Aussenegg, and W. J. Knoll, “Probing the evanescent field of propagating plasmon surface polaritons by fluorescence and Raman spectroscopies,” J. Chem. Phys. 98, 10093-10095 (1993).
[CrossRef]

1986

R. W. Gruhlke, W. R. Holland, and D. G. Hall, “Surface-plasmon cross coupling in molecular fluorescence near a corrugated thin film,” Phys. Rev. Lett. 562838-2841 (1986).
[CrossRef] [PubMed]

1968

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ɛ and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Aussenegg, F.

H. Knobloch, H. Brunner, A. Leitner, F. Aussenegg, and W. J. Knoll, “Probing the evanescent field of propagating plasmon surface polaritons by fluorescence and Raman spectroscopies,” J. Chem. Phys. 98, 10093-10095 (1993).
[CrossRef]

Bocchio, N.

F. D. Stefani, K. Vasilev, N. Bocchio, N. Stoyanova, and M. Kreiter, “Surface-plasmon-mediated single-molecule fluorescence through a thin metallic film,” Phys. Rev. Lett. 94, 023005 (2005).
[CrossRef] [PubMed]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge Univ. Press, 1999).

Brunner, H.

H. Knobloch, H. Brunner, A. Leitner, F. Aussenegg, and W. J. Knoll, “Probing the evanescent field of propagating plasmon surface polaritons by fluorescence and Raman spectroscopies,” J. Chem. Phys. 98, 10093-10095 (1993).
[CrossRef]

Carminati, R.

L. S. Froufe-Pérez and R. Carminati, “Controlling the fluorescence lifetime of a single emitter on the nanoscale using a plasmonic superlens,” Phys. Rev. B 78, 125403 (2008).
[CrossRef]

Chen, H.

J. P. Xu, Y. P. Yang, H. Chen, and S. Y. Zhu, “Spontaneous decay process of a two-level atom embedded in a one-dimensional structure containing left-handed material,” Phys. Rev. A 76, 063813 (2007).
[CrossRef]

Davis, C. C.

Enderlein, J.

J. Enderlein, “A theoretical investigation of single molecule fluorescence detection on thin metallic layers,” Biophys. J. 78, 2151-2158 (2000).
[CrossRef] [PubMed]

Fleischhauer, M.

J. Kastel and M. Fleischhauer, “Suppression of spontaneous emission and superradiance over macroscopic distances in media with negative refraction,” Phys. Rev. A 71, 011804(R) (2005).
[CrossRef]

Froufe-Pérez, L. S.

L. S. Froufe-Pérez and R. Carminati, “Controlling the fluorescence lifetime of a single emitter on the nanoscale using a plasmonic superlens,” Phys. Rev. B 78, 125403 (2008).
[CrossRef]

Fu, C.

Giannini, V.

J. Gómez Rivas, G. Vecchi, and V. Giannini, “Surface plasmon-polariton mediated enhancement of the emission of dye molecules on metallic gratings,” New J. Phys. 10, 105007 (2008).
[CrossRef]

Gómez Rivas, J.

J. Gómez Rivas, G. Vecchi, and V. Giannini, “Surface plasmon-polariton mediated enhancement of the emission of dye molecules on metallic gratings,” New J. Phys. 10, 105007 (2008).
[CrossRef]

Gruhlke, R. W.

R. W. Gruhlke, W. R. Holland, and D. G. Hall, “Surface-plasmon cross coupling in molecular fluorescence near a corrugated thin film,” Phys. Rev. Lett. 562838-2841 (1986).
[CrossRef] [PubMed]

Hall, D. G.

R. W. Gruhlke, W. R. Holland, and D. G. Hall, “Surface-plasmon cross coupling in molecular fluorescence near a corrugated thin film,” Phys. Rev. Lett. 562838-2841 (1986).
[CrossRef] [PubMed]

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge Univ. Press, 2006).

Holland, W. R.

R. W. Gruhlke, W. R. Holland, and D. G. Hall, “Surface-plasmon cross coupling in molecular fluorescence near a corrugated thin film,” Phys. Rev. Lett. 562838-2841 (1986).
[CrossRef] [PubMed]

Hung, Y. J.

Kastel, J.

J. Kastel and M. Fleischhauer, “Suppression of spontaneous emission and superradiance over macroscopic distances in media with negative refraction,” Phys. Rev. A 71, 011804(R) (2005).
[CrossRef]

Kivshar, Y. S.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Guided modes in negative-refractive-index waveguides,” Phys. Rev. E 67, 057602 (2003).
[CrossRef]

Knobloch, H.

H. Knobloch, H. Brunner, A. Leitner, F. Aussenegg, and W. J. Knoll, “Probing the evanescent field of propagating plasmon surface polaritons by fluorescence and Raman spectroscopies,” J. Chem. Phys. 98, 10093-10095 (1993).
[CrossRef]

Knoll, W.

K. Vasilev, W. Knoll, and M. Kreiter, “Fluorescence intensities of chromophores in front of a thin metal film,” J. Chem. Phys. 120, 3439-3445 (2004).
[CrossRef] [PubMed]

Knoll, W. J.

H. Knobloch, H. Brunner, A. Leitner, F. Aussenegg, and W. J. Knoll, “Probing the evanescent field of propagating plasmon surface polaritons by fluorescence and Raman spectroscopies,” J. Chem. Phys. 98, 10093-10095 (1993).
[CrossRef]

Kreiter, M.

F. D. Stefani, K. Vasilev, N. Bocchio, N. Stoyanova, and M. Kreiter, “Surface-plasmon-mediated single-molecule fluorescence through a thin metallic film,” Phys. Rev. Lett. 94, 023005 (2005).
[CrossRef] [PubMed]

K. Vasilev, W. Knoll, and M. Kreiter, “Fluorescence intensities of chromophores in front of a thin metal film,” J. Chem. Phys. 120, 3439-3445 (2004).
[CrossRef] [PubMed]

Lakowicz, J. R.

J. R. Lakowicz, “Radiative decay engineering 3. Surface plasmon-coupled directional emission,” Anal. Biochem. 324, 153-169 (2004).
[CrossRef]

Lee, B. J.

Leitner, A.

H. Knobloch, H. Brunner, A. Leitner, F. Aussenegg, and W. J. Knoll, “Probing the evanescent field of propagating plasmon surface polaritons by fluorescence and Raman spectroscopies,” J. Chem. Phys. 98, 10093-10095 (1993).
[CrossRef]

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Novotny, L.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge Univ. Press, 2006).

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Park, K.

Pendry, J. B.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Ruppin, R.

R. Ruppin, “Surface polaritons of a left-handed material slab,” J. Phys.: Condens. Matter 13, 1811-1819 (2001).
[CrossRef]

R. Ruppin, “Surface polaritons of a left-handed medium,” Phys. Lett. A 277, 61-64 (2000).
[CrossRef]

Schultz, S.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Shadrivov, I. V.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Guided modes in negative-refractive-index waveguides,” Phys. Rev. E 67, 057602 (2003).
[CrossRef]

Smith, D. R.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Smolyaninov, I. I.

Stefani, F. D.

F. D. Stefani, K. Vasilev, N. Bocchio, N. Stoyanova, and M. Kreiter, “Surface-plasmon-mediated single-molecule fluorescence through a thin metallic film,” Phys. Rev. Lett. 94, 023005 (2005).
[CrossRef] [PubMed]

Stoyanova, N.

F. D. Stefani, K. Vasilev, N. Bocchio, N. Stoyanova, and M. Kreiter, “Surface-plasmon-mediated single-molecule fluorescence through a thin metallic film,” Phys. Rev. Lett. 94, 023005 (2005).
[CrossRef] [PubMed]

Sukhorukov, A. A.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Guided modes in negative-refractive-index waveguides,” Phys. Rev. E 67, 057602 (2003).
[CrossRef]

Vasilev, K.

F. D. Stefani, K. Vasilev, N. Bocchio, N. Stoyanova, and M. Kreiter, “Surface-plasmon-mediated single-molecule fluorescence through a thin metallic film,” Phys. Rev. Lett. 94, 023005 (2005).
[CrossRef] [PubMed]

K. Vasilev, W. Knoll, and M. Kreiter, “Fluorescence intensities of chromophores in front of a thin metal film,” J. Chem. Phys. 120, 3439-3445 (2004).
[CrossRef] [PubMed]

Vecchi, G.

J. Gómez Rivas, G. Vecchi, and V. Giannini, “Surface plasmon-polariton mediated enhancement of the emission of dye molecules on metallic gratings,” New J. Phys. 10, 105007 (2008).
[CrossRef]

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ɛ and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge Univ. Press, 1999).

Wu, H. C.

Xu, J. P.

J. P. Xu, Y. P. Yang, H. Chen, and S. Y. Zhu, “Spontaneous decay process of a two-level atom embedded in a one-dimensional structure containing left-handed material,” Phys. Rev. A 76, 063813 (2007).
[CrossRef]

Yang, Y. P.

J. P. Xu, Y. P. Yang, H. Chen, and S. Y. Zhu, “Spontaneous decay process of a two-level atom embedded in a one-dimensional structure containing left-handed material,” Phys. Rev. A 76, 063813 (2007).
[CrossRef]

Zhang, Z. M.

Zhu, S. Y.

J. P. Xu, Y. P. Yang, H. Chen, and S. Y. Zhu, “Spontaneous decay process of a two-level atom embedded in a one-dimensional structure containing left-handed material,” Phys. Rev. A 76, 063813 (2007).
[CrossRef]

Anal. Biochem.

J. R. Lakowicz, “Radiative decay engineering 3. Surface plasmon-coupled directional emission,” Anal. Biochem. 324, 153-169 (2004).
[CrossRef]

Biophys. J.

J. Enderlein, “A theoretical investigation of single molecule fluorescence detection on thin metallic layers,” Biophys. J. 78, 2151-2158 (2000).
[CrossRef] [PubMed]

J. Chem. Phys.

K. Vasilev, W. Knoll, and M. Kreiter, “Fluorescence intensities of chromophores in front of a thin metal film,” J. Chem. Phys. 120, 3439-3445 (2004).
[CrossRef] [PubMed]

H. Knobloch, H. Brunner, A. Leitner, F. Aussenegg, and W. J. Knoll, “Probing the evanescent field of propagating plasmon surface polaritons by fluorescence and Raman spectroscopies,” J. Chem. Phys. 98, 10093-10095 (1993).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys.: Condens. Matter

R. Ruppin, “Surface polaritons of a left-handed material slab,” J. Phys.: Condens. Matter 13, 1811-1819 (2001).
[CrossRef]

New J. Phys.

J. Gómez Rivas, G. Vecchi, and V. Giannini, “Surface plasmon-polariton mediated enhancement of the emission of dye molecules on metallic gratings,” New J. Phys. 10, 105007 (2008).
[CrossRef]

Opt. Express

Phys. Lett. A

R. Ruppin, “Surface polaritons of a left-handed medium,” Phys. Lett. A 277, 61-64 (2000).
[CrossRef]

Phys. Rev. A

J. Kastel and M. Fleischhauer, “Suppression of spontaneous emission and superradiance over macroscopic distances in media with negative refraction,” Phys. Rev. A 71, 011804(R) (2005).
[CrossRef]

J. P. Xu, Y. P. Yang, H. Chen, and S. Y. Zhu, “Spontaneous decay process of a two-level atom embedded in a one-dimensional structure containing left-handed material,” Phys. Rev. A 76, 063813 (2007).
[CrossRef]

Phys. Rev. B

L. S. Froufe-Pérez and R. Carminati, “Controlling the fluorescence lifetime of a single emitter on the nanoscale using a plasmonic superlens,” Phys. Rev. B 78, 125403 (2008).
[CrossRef]

Phys. Rev. E

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Guided modes in negative-refractive-index waveguides,” Phys. Rev. E 67, 057602 (2003).
[CrossRef]

Phys. Rev. Lett.

R. W. Gruhlke, W. R. Holland, and D. G. Hall, “Surface-plasmon cross coupling in molecular fluorescence near a corrugated thin film,” Phys. Rev. Lett. 562838-2841 (1986).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

F. D. Stefani, K. Vasilev, N. Bocchio, N. Stoyanova, and M. Kreiter, “Surface-plasmon-mediated single-molecule fluorescence through a thin metallic film,” Phys. Rev. Lett. 94, 023005 (2005).
[CrossRef] [PubMed]

Sov. Phys. Usp.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ɛ and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Other

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge Univ. Press, 1999).

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge Univ. Press, 2006).

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Figures (8)

Fig. 1
Fig. 1

One widely used configuration used to excite SPs in the two vacuum–LHM interfaces. θ i denotes the incident angle of the plane wave.

Fig. 2
Fig. 2

Proposed configuration to excite SP and enhance fluorescence. The fluorescent molecule is regarded as a dipole, the orientation of which has a separation angle of θ d with the z axis.

Fig. 3
Fig. 3

Reflectivity of the superlens. The bottom positions of the dip (from left to right) are 43.8°, 55.5°, and 76.5°, respectively.

Fig. 4
Fig. 4

T 0 versus incident angle. The peak positions in (a), (b), (c), and (d) are 44.7°, 55.2°, 71.8°, and 74.2°, respectively.

Fig. 5
Fig. 5

Field distribution T versus z λ 0 . The incident angles in (a), (b), (c), and (d) are chosen as the peak positions in Fig. 4a, (b), (c), and (d), respectively. For (b), (c), and (d), the field pattern of exponential decay on both sides of the superlens–vacuum interface is observed, clearly indicating the existence of SP modes.

Fig. 6
Fig. 6

(a) Enhancement of various radiated powers versus the distance of the dipole from the lower surface of the superlens. We can see that P f is the dominant part of P r when d < λ 0 . (b) Enhancement of quantum efficiency.

Fig. 7
Fig. 7

Radiation pattern. θ denotes the separation angle of the radiation direction with respect to the z axis.

Fig. 8
Fig. 8

Fluorescence enhancement versus the position of the dipole. The peak position of the upper solid curve is (0.22, 47.90).

Equations (14)

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

β 2 μ 2 ( ω ) + β 3 μ 3 = 0 for s polarization ,
β 2 ε 2 ( ω ) + β 3 ε 3 = 0 for p polarization ,
β j = ( k x 2 ε j μ j ω 2 c 2 ) 1 2 , j = 1 , 2 , 3 .
E = e ̂ y A exp [ β 2 ( z h ) + i k x x ] , 0 < z < h ,
E = e ̂ y B exp [ β 3 ( z h ) + i k x x ] , z > h ,
h ex ( ω 0 ) = | p E d | 2 | p E d | 2 ,
h ex ( ω 0 ) = | E d | 2 | E d | 2 .
P total = P r + P m + P i ,
P r = P + P ,
P = P a + P f .
h q = q q i .
h fluo = h ex h q ,
h fluo = h ex h q ,
h fluo = h ex h q ,

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