Abstract

We study a nanoemitter in the vicinity of an impedance plane. We provide analytical expressions for the spontaneous emission rate γ and the angular emission pattern of the emitter in terms of the impedance, distance to the plane z0, and radiation wavelength λ0. We find that near a resistive plane, γ diverges as λ02/z02 in the limit z0λ0. In the opposite limit z0λ0, γ is an undulating function of z0/λ0 whose amplitude depends on the impedance. Both resistive and reactive components of the impedance can be harnessed to modify the angular emission pattern.

© 2013 Optical Society of America

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  1. S. Ramakrishna and T. M. Grzegorczyk, Physics and Applications of Negative Refractive Index Materials (CRC Press and SPIE, 2009).
  2. W. Cai and V. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, 2010).
  3. M. Silveirinha and N. Engheta, “Tunnelling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett. 97, 157403 (2006).
    [CrossRef]
  4. E. J. R. Vesseur, T. Coenen, H. Caglayan, N. Engheta, and A. Polman, “Experimental verification of n=0 structures for visible light,” Phys. Rev. Lett. 110, 013902 (2013).
    [CrossRef]
  5. J. Elser, R. Wangberg, V. A. Podolskiy, and E. E. Narimanov, “Nanowire metamaterials with extreme optical anisotropy,” Appl. Phys. Lett. 89, 261102 (2006).
    [CrossRef]
  6. M. G. Silveirinha, C. A. Fernandes, and J. R. Costa, “Additional boundary condition for a wire medium connected to a metallic surface,” New J. Phys. 10, 053011 (2008).
    [CrossRef]
  7. P. A. Belov, Y. Zhao, Y. Hao, and C. Parini, “Enhancement of evanescent spatial harmonics inside media with extreme optical anisotropy,” Opt. Lett. 34, 527–529 (2009).
    [CrossRef]
  8. A. S. Schwanecke, V. A. Fedotov, V. V. Khardikov, S. L. Prosvirnin, Y. Chen, and N. I. Zheludev, “Optical magnetic mirrors,” J. Opt. A 9, L1–L2 (2007).
    [CrossRef]
  9. H. Rostami, Y. Abdi, and E. Arzi, “Fabrication of optical magnetic mirrors using bent and mushroom-like carbon nanotubes,” Carbon 48, 3659–3666 (2010).
    [CrossRef]
  10. D. Sievenpiper, L. Zhang, R. Broas, N. G. Alexopolous, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microwave Theory Tech. 47, 2059–2074 (1999).
    [CrossRef]
  11. Y. Zhang, J. von Hagen, M. Younis, C. Fischer, and W. Wiesbeck, “Planar artificial magnetic conductors and patch antennas,” IEEE Trans. Antennas Propag. 51, 2704–2712 (2003).
    [CrossRef]
  12. K.-P. Ma, K. Hirose, F.-R. Yang, Y. Qian, and T. Itoh, “Realization of magnetic conducting surface using novel photonic bandgap structure,” Electron. Lett. 34, 2041–2042 (1998).
  13. S. V. Yuferev and N. Ida, Surface Impedance Boundary Conditions (CRC Press, 2010).
  14. H. Mosallaei and K. Sarabandi, “Antenna miniaturization and bandwidth enhancement using a reactive impedance substrate,” IEEE Trans. Antennas Propag. 52, 2403–2414 (2004).
    [CrossRef]
  15. K. Sarabandi, M. D. Casciato, and I. Koh, “Efficient calculation of the fields of a dipole radiating above an impedance surface,” IEEE Trans. Antennas Propag. 50, 1222–1235 (2002).
    [CrossRef]
  16. K. Matsugatani, M. Tanaka, and T. Saito, “Radiation characteristics of antenna with external high-impedance-plane shield,” IEICE Trans. Electron. E86-C, 1542–1549 (2003).
  17. P. M. Morse and K. U. Ingard, Theoretical Acoustics (McGraw-Hill, 1968), Chaps. 6, 7, and 9.
  18. M. Ochmanna, “Exact solutions for sound radiation from a moving monopole above an impedance plane,” J. Acoust. Soc. Am. 133, 1911–1921 (2013) and references therein.
    [CrossRef]
  19. M. Ochmanna, “Closed form solutions for the acoustical impulse response over a masslike or an absorbing plane,” J. Acoust. Soc. Am. 129, 3502–3512 (2011).
    [CrossRef]
  20. M. Ochmanna, “The complex equivalent source method for sound propagation over an impedance plane,” J. Acoust. Soc. Am. 116, 3304–3311 (2004).
    [CrossRef]
  21. I. V. Lindell and A. H. Sihvola, “Realization of impedance boundary,” IEEE Trans. Antennas Propag. 54, 3669–3676 (2006).
    [CrossRef]
  22. S. M. Hashemi, S. A. Tretyakov, M. Soleimani, and C. R. Simovski, “Dual-polarized angularly stable high-impedance surface,” IEEE Trans. Antennas Propag. 61, 4101–4108 (2013).
    [CrossRef]
  23. E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681–686 (1946).
  24. K. H. Drexhage, “Interaction of light with monomolecular dye layers,” Prog. Opt. 12, 163–232 (1974).
    [CrossRef]
  25. E. Fort and S. Grésillon, “Surface enhanced fluorescence,” J. Phys. D 41, 013001 (2008) and references therein.
    [CrossRef]
  26. W. L. Barnes, “Fluorescence near interfaces: the role of photonic mode density,” J. Mod. Opt. 45, 661–699 (1998) and references therein.
    [CrossRef]
  27. C. Gell, D. Brockwell, and A. Smith, Handbook of Single Molecule Fluorescence Spectroscopy (Oxford University, 2008).
  28. C. Wang and C. Bai, Single Molecule Chemistry and Physics (Springer, 2006).
  29. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).
  30. A. Lakhtakia, “Green’s functions and Brewster condition for a half space bounded by an anisotropic impedance plane,” Int. J. Infrared Millim. Waves 13, 161–170 (1992).
    [CrossRef]
  31. J. M. Wylie and J. E. Sipe, “Quantum electrodynamics near an interface,” Phys. Rev. A 30, 1185–1193 (1984).
    [CrossRef]
  32. Let us denote by R− (R+) the radial distance of the observation point and the dipole (image dipole). R∓≈∓z0 cos θ+r−x0 cos ϕ sin θ−y0 sin ϕ sin θ. The electric field of the dipole and the image dipole are proportional to eik0R−/R− and eik0R+/R+, respectively. One can write eik0R∓/R∓≈e∓ik0z0 cos θ×eik0re−ik0(x0 cos ϕ sin θ+y0 sin ϕ sin θ)/r. This explains the different exponential factors of the first and the second terms of Φ1−Φ3 [29].
  33. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).
  34. S. Ohshima and Y. Ishibashi, “Spectra and angular distributions of fluorescence emitted from anthracene on a silver surface,” J. Phys. Chem. 96, 6361–6367 (1992).
    [CrossRef]
  35. Y. Ishibashi, S. Ohshima, and T. Kajiwara, “Angular distributions of fluorescence emitted from tetraphenylporphine (H2TPP) near metal surfaces,” Surf. Sci. 201, 311–320 (1988).
    [CrossRef]
  36. M. Böhmer and J. Enderlein, “Orientation imaging of single molecules by wide-field epifluorescence microscopy,” J. Opt. Soc. Am. B 20, 554–559 (2003).
    [CrossRef]
  37. M. A. Lieb, J. M. Zavislan, and L. Novotny, “Single-molecule orientations determined by direct emission pattern imaging,” J. Opt. Soc. Am. B 21, 1210–1215 (2004).
    [CrossRef]
  38. A. S. Backer, M. P. Backlund, M. D. Lew, and W. E. Moerner, “Single-molecule orientation measurements with a quadrated pupil,” Opt. Lett. 38, 1521–1523 (2013).
    [CrossRef]
  39. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995), Chap. 3.
  40. G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists (Academic, 1995), p. 392.

2013 (4)

E. J. R. Vesseur, T. Coenen, H. Caglayan, N. Engheta, and A. Polman, “Experimental verification of n=0 structures for visible light,” Phys. Rev. Lett. 110, 013902 (2013).
[CrossRef]

M. Ochmanna, “Exact solutions for sound radiation from a moving monopole above an impedance plane,” J. Acoust. Soc. Am. 133, 1911–1921 (2013) and references therein.
[CrossRef]

S. M. Hashemi, S. A. Tretyakov, M. Soleimani, and C. R. Simovski, “Dual-polarized angularly stable high-impedance surface,” IEEE Trans. Antennas Propag. 61, 4101–4108 (2013).
[CrossRef]

A. S. Backer, M. P. Backlund, M. D. Lew, and W. E. Moerner, “Single-molecule orientation measurements with a quadrated pupil,” Opt. Lett. 38, 1521–1523 (2013).
[CrossRef]

2011 (1)

M. Ochmanna, “Closed form solutions for the acoustical impulse response over a masslike or an absorbing plane,” J. Acoust. Soc. Am. 129, 3502–3512 (2011).
[CrossRef]

2010 (1)

H. Rostami, Y. Abdi, and E. Arzi, “Fabrication of optical magnetic mirrors using bent and mushroom-like carbon nanotubes,” Carbon 48, 3659–3666 (2010).
[CrossRef]

2009 (1)

2008 (2)

M. G. Silveirinha, C. A. Fernandes, and J. R. Costa, “Additional boundary condition for a wire medium connected to a metallic surface,” New J. Phys. 10, 053011 (2008).
[CrossRef]

E. Fort and S. Grésillon, “Surface enhanced fluorescence,” J. Phys. D 41, 013001 (2008) and references therein.
[CrossRef]

2007 (1)

A. S. Schwanecke, V. A. Fedotov, V. V. Khardikov, S. L. Prosvirnin, Y. Chen, and N. I. Zheludev, “Optical magnetic mirrors,” J. Opt. A 9, L1–L2 (2007).
[CrossRef]

2006 (3)

M. Silveirinha and N. Engheta, “Tunnelling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett. 97, 157403 (2006).
[CrossRef]

J. Elser, R. Wangberg, V. A. Podolskiy, and E. E. Narimanov, “Nanowire metamaterials with extreme optical anisotropy,” Appl. Phys. Lett. 89, 261102 (2006).
[CrossRef]

I. V. Lindell and A. H. Sihvola, “Realization of impedance boundary,” IEEE Trans. Antennas Propag. 54, 3669–3676 (2006).
[CrossRef]

2004 (3)

M. Ochmanna, “The complex equivalent source method for sound propagation over an impedance plane,” J. Acoust. Soc. Am. 116, 3304–3311 (2004).
[CrossRef]

H. Mosallaei and K. Sarabandi, “Antenna miniaturization and bandwidth enhancement using a reactive impedance substrate,” IEEE Trans. Antennas Propag. 52, 2403–2414 (2004).
[CrossRef]

M. A. Lieb, J. M. Zavislan, and L. Novotny, “Single-molecule orientations determined by direct emission pattern imaging,” J. Opt. Soc. Am. B 21, 1210–1215 (2004).
[CrossRef]

2003 (3)

M. Böhmer and J. Enderlein, “Orientation imaging of single molecules by wide-field epifluorescence microscopy,” J. Opt. Soc. Am. B 20, 554–559 (2003).
[CrossRef]

Y. Zhang, J. von Hagen, M. Younis, C. Fischer, and W. Wiesbeck, “Planar artificial magnetic conductors and patch antennas,” IEEE Trans. Antennas Propag. 51, 2704–2712 (2003).
[CrossRef]

K. Matsugatani, M. Tanaka, and T. Saito, “Radiation characteristics of antenna with external high-impedance-plane shield,” IEICE Trans. Electron. E86-C, 1542–1549 (2003).

2002 (1)

K. Sarabandi, M. D. Casciato, and I. Koh, “Efficient calculation of the fields of a dipole radiating above an impedance surface,” IEEE Trans. Antennas Propag. 50, 1222–1235 (2002).
[CrossRef]

1999 (1)

D. Sievenpiper, L. Zhang, R. Broas, N. G. Alexopolous, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microwave Theory Tech. 47, 2059–2074 (1999).
[CrossRef]

1998 (2)

K.-P. Ma, K. Hirose, F.-R. Yang, Y. Qian, and T. Itoh, “Realization of magnetic conducting surface using novel photonic bandgap structure,” Electron. Lett. 34, 2041–2042 (1998).

W. L. Barnes, “Fluorescence near interfaces: the role of photonic mode density,” J. Mod. Opt. 45, 661–699 (1998) and references therein.
[CrossRef]

1992 (2)

A. Lakhtakia, “Green’s functions and Brewster condition for a half space bounded by an anisotropic impedance plane,” Int. J. Infrared Millim. Waves 13, 161–170 (1992).
[CrossRef]

S. Ohshima and Y. Ishibashi, “Spectra and angular distributions of fluorescence emitted from anthracene on a silver surface,” J. Phys. Chem. 96, 6361–6367 (1992).
[CrossRef]

1988 (1)

Y. Ishibashi, S. Ohshima, and T. Kajiwara, “Angular distributions of fluorescence emitted from tetraphenylporphine (H2TPP) near metal surfaces,” Surf. Sci. 201, 311–320 (1988).
[CrossRef]

1984 (1)

J. M. Wylie and J. E. Sipe, “Quantum electrodynamics near an interface,” Phys. Rev. A 30, 1185–1193 (1984).
[CrossRef]

1974 (1)

K. H. Drexhage, “Interaction of light with monomolecular dye layers,” Prog. Opt. 12, 163–232 (1974).
[CrossRef]

1946 (1)

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681–686 (1946).

Abdi, Y.

H. Rostami, Y. Abdi, and E. Arzi, “Fabrication of optical magnetic mirrors using bent and mushroom-like carbon nanotubes,” Carbon 48, 3659–3666 (2010).
[CrossRef]

Alexopolous, N. G.

D. Sievenpiper, L. Zhang, R. Broas, N. G. Alexopolous, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microwave Theory Tech. 47, 2059–2074 (1999).
[CrossRef]

Arfken, G. B.

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists (Academic, 1995), p. 392.

Arzi, E.

H. Rostami, Y. Abdi, and E. Arzi, “Fabrication of optical magnetic mirrors using bent and mushroom-like carbon nanotubes,” Carbon 48, 3659–3666 (2010).
[CrossRef]

Backer, A. S.

Backlund, M. P.

Bai, C.

C. Wang and C. Bai, Single Molecule Chemistry and Physics (Springer, 2006).

Barnes, W. L.

W. L. Barnes, “Fluorescence near interfaces: the role of photonic mode density,” J. Mod. Opt. 45, 661–699 (1998) and references therein.
[CrossRef]

Belov, P. A.

Böhmer, M.

Broas, R.

D. Sievenpiper, L. Zhang, R. Broas, N. G. Alexopolous, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microwave Theory Tech. 47, 2059–2074 (1999).
[CrossRef]

Brockwell, D.

C. Gell, D. Brockwell, and A. Smith, Handbook of Single Molecule Fluorescence Spectroscopy (Oxford University, 2008).

Caglayan, H.

E. J. R. Vesseur, T. Coenen, H. Caglayan, N. Engheta, and A. Polman, “Experimental verification of n=0 structures for visible light,” Phys. Rev. Lett. 110, 013902 (2013).
[CrossRef]

Cai, W.

W. Cai and V. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, 2010).

Casciato, M. D.

K. Sarabandi, M. D. Casciato, and I. Koh, “Efficient calculation of the fields of a dipole radiating above an impedance surface,” IEEE Trans. Antennas Propag. 50, 1222–1235 (2002).
[CrossRef]

Chen, Y.

A. S. Schwanecke, V. A. Fedotov, V. V. Khardikov, S. L. Prosvirnin, Y. Chen, and N. I. Zheludev, “Optical magnetic mirrors,” J. Opt. A 9, L1–L2 (2007).
[CrossRef]

Coenen, T.

E. J. R. Vesseur, T. Coenen, H. Caglayan, N. Engheta, and A. Polman, “Experimental verification of n=0 structures for visible light,” Phys. Rev. Lett. 110, 013902 (2013).
[CrossRef]

Costa, J. R.

M. G. Silveirinha, C. A. Fernandes, and J. R. Costa, “Additional boundary condition for a wire medium connected to a metallic surface,” New J. Phys. 10, 053011 (2008).
[CrossRef]

Drexhage, K. H.

K. H. Drexhage, “Interaction of light with monomolecular dye layers,” Prog. Opt. 12, 163–232 (1974).
[CrossRef]

Elser, J.

J. Elser, R. Wangberg, V. A. Podolskiy, and E. E. Narimanov, “Nanowire metamaterials with extreme optical anisotropy,” Appl. Phys. Lett. 89, 261102 (2006).
[CrossRef]

Enderlein, J.

Engheta, N.

E. J. R. Vesseur, T. Coenen, H. Caglayan, N. Engheta, and A. Polman, “Experimental verification of n=0 structures for visible light,” Phys. Rev. Lett. 110, 013902 (2013).
[CrossRef]

M. Silveirinha and N. Engheta, “Tunnelling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett. 97, 157403 (2006).
[CrossRef]

Fedotov, V. A.

A. S. Schwanecke, V. A. Fedotov, V. V. Khardikov, S. L. Prosvirnin, Y. Chen, and N. I. Zheludev, “Optical magnetic mirrors,” J. Opt. A 9, L1–L2 (2007).
[CrossRef]

Fernandes, C. A.

M. G. Silveirinha, C. A. Fernandes, and J. R. Costa, “Additional boundary condition for a wire medium connected to a metallic surface,” New J. Phys. 10, 053011 (2008).
[CrossRef]

Fischer, C.

Y. Zhang, J. von Hagen, M. Younis, C. Fischer, and W. Wiesbeck, “Planar artificial magnetic conductors and patch antennas,” IEEE Trans. Antennas Propag. 51, 2704–2712 (2003).
[CrossRef]

Fort, E.

E. Fort and S. Grésillon, “Surface enhanced fluorescence,” J. Phys. D 41, 013001 (2008) and references therein.
[CrossRef]

Gell, C.

C. Gell, D. Brockwell, and A. Smith, Handbook of Single Molecule Fluorescence Spectroscopy (Oxford University, 2008).

Grésillon, S.

E. Fort and S. Grésillon, “Surface enhanced fluorescence,” J. Phys. D 41, 013001 (2008) and references therein.
[CrossRef]

Grzegorczyk, T. M.

S. Ramakrishna and T. M. Grzegorczyk, Physics and Applications of Negative Refractive Index Materials (CRC Press and SPIE, 2009).

Hao, Y.

Hashemi, S. M.

S. M. Hashemi, S. A. Tretyakov, M. Soleimani, and C. R. Simovski, “Dual-polarized angularly stable high-impedance surface,” IEEE Trans. Antennas Propag. 61, 4101–4108 (2013).
[CrossRef]

Hecht, B.

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

Hirose, K.

K.-P. Ma, K. Hirose, F.-R. Yang, Y. Qian, and T. Itoh, “Realization of magnetic conducting surface using novel photonic bandgap structure,” Electron. Lett. 34, 2041–2042 (1998).

Ida, N.

S. V. Yuferev and N. Ida, Surface Impedance Boundary Conditions (CRC Press, 2010).

Ingard, K. U.

P. M. Morse and K. U. Ingard, Theoretical Acoustics (McGraw-Hill, 1968), Chaps. 6, 7, and 9.

Ishibashi, Y.

S. Ohshima and Y. Ishibashi, “Spectra and angular distributions of fluorescence emitted from anthracene on a silver surface,” J. Phys. Chem. 96, 6361–6367 (1992).
[CrossRef]

Y. Ishibashi, S. Ohshima, and T. Kajiwara, “Angular distributions of fluorescence emitted from tetraphenylporphine (H2TPP) near metal surfaces,” Surf. Sci. 201, 311–320 (1988).
[CrossRef]

Itoh, T.

K.-P. Ma, K. Hirose, F.-R. Yang, Y. Qian, and T. Itoh, “Realization of magnetic conducting surface using novel photonic bandgap structure,” Electron. Lett. 34, 2041–2042 (1998).

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).

Kajiwara, T.

Y. Ishibashi, S. Ohshima, and T. Kajiwara, “Angular distributions of fluorescence emitted from tetraphenylporphine (H2TPP) near metal surfaces,” Surf. Sci. 201, 311–320 (1988).
[CrossRef]

Khardikov, V. V.

A. S. Schwanecke, V. A. Fedotov, V. V. Khardikov, S. L. Prosvirnin, Y. Chen, and N. I. Zheludev, “Optical magnetic mirrors,” J. Opt. A 9, L1–L2 (2007).
[CrossRef]

Koh, I.

K. Sarabandi, M. D. Casciato, and I. Koh, “Efficient calculation of the fields of a dipole radiating above an impedance surface,” IEEE Trans. Antennas Propag. 50, 1222–1235 (2002).
[CrossRef]

Lakhtakia, A.

A. Lakhtakia, “Green’s functions and Brewster condition for a half space bounded by an anisotropic impedance plane,” Int. J. Infrared Millim. Waves 13, 161–170 (1992).
[CrossRef]

Lew, M. D.

Lieb, M. A.

Lindell, I. V.

I. V. Lindell and A. H. Sihvola, “Realization of impedance boundary,” IEEE Trans. Antennas Propag. 54, 3669–3676 (2006).
[CrossRef]

Ma, K.-P.

K.-P. Ma, K. Hirose, F.-R. Yang, Y. Qian, and T. Itoh, “Realization of magnetic conducting surface using novel photonic bandgap structure,” Electron. Lett. 34, 2041–2042 (1998).

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995), Chap. 3.

Matsugatani, K.

K. Matsugatani, M. Tanaka, and T. Saito, “Radiation characteristics of antenna with external high-impedance-plane shield,” IEICE Trans. Electron. E86-C, 1542–1549 (2003).

Moerner, W. E.

Morse, P. M.

P. M. Morse and K. U. Ingard, Theoretical Acoustics (McGraw-Hill, 1968), Chaps. 6, 7, and 9.

Mosallaei, H.

H. Mosallaei and K. Sarabandi, “Antenna miniaturization and bandwidth enhancement using a reactive impedance substrate,” IEEE Trans. Antennas Propag. 52, 2403–2414 (2004).
[CrossRef]

Narimanov, E. E.

J. Elser, R. Wangberg, V. A. Podolskiy, and E. E. Narimanov, “Nanowire metamaterials with extreme optical anisotropy,” Appl. Phys. Lett. 89, 261102 (2006).
[CrossRef]

Novotny, L.

Ochmanna, M.

M. Ochmanna, “Exact solutions for sound radiation from a moving monopole above an impedance plane,” J. Acoust. Soc. Am. 133, 1911–1921 (2013) and references therein.
[CrossRef]

M. Ochmanna, “Closed form solutions for the acoustical impulse response over a masslike or an absorbing plane,” J. Acoust. Soc. Am. 129, 3502–3512 (2011).
[CrossRef]

M. Ochmanna, “The complex equivalent source method for sound propagation over an impedance plane,” J. Acoust. Soc. Am. 116, 3304–3311 (2004).
[CrossRef]

Ohshima, S.

S. Ohshima and Y. Ishibashi, “Spectra and angular distributions of fluorescence emitted from anthracene on a silver surface,” J. Phys. Chem. 96, 6361–6367 (1992).
[CrossRef]

Y. Ishibashi, S. Ohshima, and T. Kajiwara, “Angular distributions of fluorescence emitted from tetraphenylporphine (H2TPP) near metal surfaces,” Surf. Sci. 201, 311–320 (1988).
[CrossRef]

Parini, C.

Podolskiy, V. A.

J. Elser, R. Wangberg, V. A. Podolskiy, and E. E. Narimanov, “Nanowire metamaterials with extreme optical anisotropy,” Appl. Phys. Lett. 89, 261102 (2006).
[CrossRef]

Polman, A.

E. J. R. Vesseur, T. Coenen, H. Caglayan, N. Engheta, and A. Polman, “Experimental verification of n=0 structures for visible light,” Phys. Rev. Lett. 110, 013902 (2013).
[CrossRef]

Prosvirnin, S. L.

A. S. Schwanecke, V. A. Fedotov, V. V. Khardikov, S. L. Prosvirnin, Y. Chen, and N. I. Zheludev, “Optical magnetic mirrors,” J. Opt. A 9, L1–L2 (2007).
[CrossRef]

Purcell, E. M.

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681–686 (1946).

Qian, Y.

K.-P. Ma, K. Hirose, F.-R. Yang, Y. Qian, and T. Itoh, “Realization of magnetic conducting surface using novel photonic bandgap structure,” Electron. Lett. 34, 2041–2042 (1998).

Ramakrishna, S.

S. Ramakrishna and T. M. Grzegorczyk, Physics and Applications of Negative Refractive Index Materials (CRC Press and SPIE, 2009).

Rostami, H.

H. Rostami, Y. Abdi, and E. Arzi, “Fabrication of optical magnetic mirrors using bent and mushroom-like carbon nanotubes,” Carbon 48, 3659–3666 (2010).
[CrossRef]

Saito, T.

K. Matsugatani, M. Tanaka, and T. Saito, “Radiation characteristics of antenna with external high-impedance-plane shield,” IEICE Trans. Electron. E86-C, 1542–1549 (2003).

Sarabandi, K.

H. Mosallaei and K. Sarabandi, “Antenna miniaturization and bandwidth enhancement using a reactive impedance substrate,” IEEE Trans. Antennas Propag. 52, 2403–2414 (2004).
[CrossRef]

K. Sarabandi, M. D. Casciato, and I. Koh, “Efficient calculation of the fields of a dipole radiating above an impedance surface,” IEEE Trans. Antennas Propag. 50, 1222–1235 (2002).
[CrossRef]

Schwanecke, A. S.

A. S. Schwanecke, V. A. Fedotov, V. V. Khardikov, S. L. Prosvirnin, Y. Chen, and N. I. Zheludev, “Optical magnetic mirrors,” J. Opt. A 9, L1–L2 (2007).
[CrossRef]

Shalaev, V.

W. Cai and V. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, 2010).

Sievenpiper, D.

D. Sievenpiper, L. Zhang, R. Broas, N. G. Alexopolous, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microwave Theory Tech. 47, 2059–2074 (1999).
[CrossRef]

Sihvola, A. H.

I. V. Lindell and A. H. Sihvola, “Realization of impedance boundary,” IEEE Trans. Antennas Propag. 54, 3669–3676 (2006).
[CrossRef]

Silveirinha, M.

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Other (11)

Let us denote by R− (R+) the radial distance of the observation point and the dipole (image dipole). R∓≈∓z0 cos θ+r−x0 cos ϕ sin θ−y0 sin ϕ sin θ. The electric field of the dipole and the image dipole are proportional to eik0R−/R− and eik0R+/R+, respectively. One can write eik0R∓/R∓≈e∓ik0z0 cos θ×eik0re−ik0(x0 cos ϕ sin θ+y0 sin ϕ sin θ)/r. This explains the different exponential factors of the first and the second terms of Φ1−Φ3 [29].

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P. M. Morse and K. U. Ingard, Theoretical Acoustics (McGraw-Hill, 1968), Chaps. 6, 7, and 9.

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Figures (4)

Fig. 1.
Fig. 1.

(a) γ/γ0 of a nanoemitter as a function of ζr for various k0z0. (b) γ/γ0 as a function of k0z0 for various ζr. Here ζi=0 is assumed.

Fig. 2.
Fig. 2.

(a) γ/γ0 of a nanoemitter as a function of ζi for various k0z0. (b) γ/γ0 as a function of k0z0 for various ζi. Here ζr=0 is assumed.

Fig. 3.
Fig. 3.

(a) Polar plot of p(θ,ϕ)/P0 as a function of θ (in units of radians) for various ζ. Here d=(0,0,1) and k0z0=0.42. (b) p(θ,ϕ)/P0 as a function of θ and ϕ (in units of radians). Here d=(1,0,0), ζ=0.1+5i, and k0z0=0.42.

Fig. 4.
Fig. 4.

Green surface: γ/γ0 of a nanoemitter as a function of ζr and ζi. Here k0z0=0.42. Violet surface: γ/γ0=1 for an emitter in free space.

Equations (52)

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E(r)uzuz·E(r)=η0ζ¯¯·[uz×H(r)],z=0.
γ=2ω02c2ε0|d|2n·Im(G(r0,r0))·n,
γ=2ω023c2ε0|d|2Im{Trace(G(r0,r0))}.
G0(r,r0)=(I+1k02)eik0|rr0|4π|rr0|,=i8π2dκxdκy1k0zeik0±·(rr0)×[t0t0+p0±p0±],
k0+(κx,κy)=κxux+κyuy+k0zuz,k0(κx,κy)=κxux+κyuyk0zuz,t0(κx,κy)=1κ(κyuxκxuy),p0+(κx,κy)=k0zκk0(κxux+κyuy)+κk0uz,p0(κx,κy)=+k0zκk0(κxux+κyuy)+κk0uz,κ(κx,κy)=κx2+κy2,k0z(κx,κy)=k02κ2.
Gref(r,r0)=i8π2dκxdκy1k0zeik0+·reik0·r0×[rttt0t0+rppp0+p0].
rtt=12k0k0zζ+k0,rpp=2k0zk0z+k0ζ1,
GrefI(r,r0)=i8π2dκxdκy1k0zeik0+·reik0·r0×[t0t0p0+p0]
GrefII(r,r0)=i8π2dκxdκy1k0zeik0+·reik0·r0×[2k0k0zζ+k0t0t0+2k0zk0z+k0ζp0+p0].
F1(z)dκxdκye2ik0zzk0z,F2(z,k0,ζ)dκxdκyζe2ik0zzk0k0zζ+k02,
Trace(GrefI(r,r))=i4π2dκxdκyk0zk02e2ik0zz,=i16π2k022F1(z)z2,
Trace(GrefII(r,r))=id2κ4π2(ζk0zζ+k01k0z+12ζ2k0z+k0ζ2k0zk02+2ζk0)e2ik0zz=i4π2(k0F2(z,k0,ζ)F1(z)+(12ζ2)k0F2(z,k0,1ζ)+12k022F1(z)z2iζk0F1(z)z).
F1(z)=iπze2ik0z,
F2(z,k0,ζ)=2πζ01duue2ik0zu1+ζu+2πζ0dvve2k0zv1+iζv.
Im{Trace(G(r0,r0))}=k02π+Re[k0F2(z0,k0,ζ)4π2]+Re[(12ζ2)k0F2(z0,k0,1ζ)4π2]+Im[e2ik0z0(ζ12πz0+iζi4πk0z02+18πk02z03)].
γ0=2ω023c2ε0|d|2Im{Trace(G0(r0,r0))},=ω033πc3ε0|d|2.
γγ0=Im{Trace(G(r0,r0))Im{Trace(G0(r0,r0)),=1+Re[F2(z0,k0,ζ)2π]+Re[(12ζ2)F2(z0,k0,1ζ)2π]+Im[e2ik0z0(ζ1k0z0+iζi2k02z02+14k03z03)].
γPECγ0=1+(14k03z0312k0z0)sin(2k0z0)cos(2k0z0)2k02z02.
γPMCγ0=1(14k03z0312k0z0)sin(2k0z0)+cos(2k0z0)2k02z02.
γγ0ζr2k02z02(1ζr+ζr2ζr3)ln(2k0z0(ζr+1))+(12ζr2)(1γEulerζr)+23γEulerζr+ζr+lnζrζr,
γγ01+ζr1ζr+1sin(2k0z0)2k0z0.
z0λ04π|ζr1|ζr+1.
γγ0231ζiarctanζi+(1+2ζi2)(1+ζiarctan(1ζi)),
γγ01+ζi21ζi2+1sin(2k0z0)2k0z0+2ζiζi2+1cos(2k0z0)2k0z0,
z0λ04πmax{|ζi21|ζi2+1,2|ζi|ζi2+1}.
γγ0ζr2k02z022ζrζik0z0+(ζrζr2+ζi2ζr+2ζr36ζrζi2)×(ln(2k0z0)+γEuler+12ln((ζr+1)2+ζi2ζr2+ζi2))+532ζr2+2ζi2+ζrπ2(ζi6ζr2+2ζi3)+(ζiζr2+ζi2+ζi6ζr2+2ζi3)arctan(ζiζr+1)+(ζiζr2+ζi2+6ζiζr26ζr2)arctan(ζrζi)12(ζr2ζr3+6ζrζi2)ln(ζr2+ζi2)
γγ01+ζr2+ζi21(ζr+1)2+ζi2sin(2k0z0)2k0z0+2ζi(ζr+1)2+ζi2cos(2k0z0)2k0z04ζrζi2k0z0.
E(r)=ω02ε0c2[G0(r,r0)+Gref(r,r0)]·d,
G0(r,r0)=eik0r4πreik0(x0x+y0y+z0z)/r×(1x2/r2xy/r2xz/r2xy/r21y2/r2yz/r2xz/r2yz/r21z2/r2),
Gref(r,r0)=eik0r4πreik0(x0x+y0yz0z)/r×[zζ/r1zζ/r+1(y2x2+y2xyx2+y20xyx2+y2x2x2+y20000)+z/rζz/r+ζ(x2x2+y2z2r2xyx2+y2z2r2xzr2xyx2+y2z2r2y2x2+y2z2r2yzr2xzr2yzr21z2r2)].
[ErEθEϕ]=eik0r4πr[0Φ2(dxcosϕ+dysinϕ)cosθΦ1dzsinθΦ3(dxsinϕdycosϕ)]×ω02ε0c2eik0(x0cosϕsinθ+y0sinϕsinθ),
Φ1=eik0z0cosθ+cosθζcosθ+ζeik0z0cosθ,Φ2=eik0z0cosθcosθζcosθ+ζeik0z0cosθ,Φ3=eik0z0cosθ+ζcosθ1ζcosθ+1eik0z0cosθ,
p(θ,ϕ)P0=(|Φ2|2(dxcosϕ+dysinϕ)2cos2θ+|Φ1|2dz2sin2θ2Re[Φ1*Φ2](dxcosϕ+dysinϕ)dzcosθsinθ+|Φ3|2(dxsinϕdycosϕ)2)38π(dx2+dy2+dz2),
pfree(θ,ϕ)P0=38π(dx2+dy2+dz2)(dx2+dy2+dz2(dxsinθcosϕ+dysinθsinϕ+dzcosθ)2),=38π(1cos2ϑ),
Re[Φ1*Φ2]cosθsinθ=4ζrcos2θsinθ(cosθ+ζr)2+ζi2
η0ζ=iη0cosαwεwtan(k0Twεwsecαw).
dκxdκye2ik0zz=i2F1(z)z,dκxdκyk0ze2ik0zz=142F1(z)z2,dκxdκye2ik0zzk0k0z+k02ζ=F2(z,k0,1ζ).
eik0rr=ik02πdpdq1m(p,q)eik0(px+qy+m|z|),
m(p,q)=+1p2q2whenp2+q2<1,=+ip2+q21whenp2+q2>1.
F1(z)=iπze2ik0z.
F2(z,k0,ζ)=dκxdκyζe2ik0zzk0k0zζ+k02=0π2dα02πdβζsinαcosαζcosα+1e2ik0zcosα+0idα02πdβ[ζsin(π2+iα)cos(π2+iα)ζcos(π2+iα)+1×e2ik0zcos(π2+iα)].
F2(z,k0,ζ)=2πζ01duue2ik0zu1+ζu+2πζ0dvve2k0zv1+iζv=2πζ01duue2ik0zu1+ζuiπk0z+2πi0dve2k0zv1+iζv,
Re[F2(z,k0,ζr)]2πζr01duu1+ζru+ζr0dvve2k0zv1+ζr2v2.
0dvvexv1+v2=Ci(x)cosxsi(x)sinx,
Ci(x)=xdtcostt,si(x)=xdtsintt,
Re[F2(z,k0,ζr)]2π11ζrln(2k0zζr)γEulerζrln(1+ζr)ζr
Re[F2(z,k0,ζr)]2πRe[01duζru1+ζrue2ik0zu].
Re[F2(z,k0,ζr)]2πζrζr+1sin(2k0z)2k0z
abf(u)eiτg(u)du1iτ(f(b)g(b)eiτg(b)f(a)g(a)eiτg(a))
Re[F2(z,k0,iζi)]2π=Re[01duiζiu+ζi2u21+ζi2u2e2ik0zu].
Re[F2(z,k0,iζi)]2π11ζiarctanζi
Re[F2(z,k0,iζi)]2πζiζi2+1cos(2k0z)2k0z+ζi2ζi2+1sin(2k0z)2k0z

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