Abstract

We report unidirectional radiation of a circularly polarized dipole above planar metal surface, the radiation direction can be manipulated via changing the distance between the dipole and the surface. This phenomenon is unique for the combination of circularly polarized dipole and metal surface and does not happen for linearly polarized dipole on metal surface or circularly polarized dipole on dielectric surface. The underlying physics is analytically disclosed by the interference of two orthogonally-oriented dipole component with π/2 phase lag. A substantially different mechanism of introducing the vectorial nature of the dipole itself to control light emission distinguishes the present scheme from nanoantenna and provides a new degree of freedom in light emission engineering.

© 2013 Optical Society of America

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  1. W. Barnes, “Fluorescence near interfaces: the role of photonic mode density,” J. Mod. Opt. 45, 661–699 (1998).
    [Crossref]
  2. H. Gersen, M. Garcia-Parajo, L. Novotny, J. Veerman, L. Kuipers, and N. Van Hulst, “Influencing the angular emission of a single molecule,” Phys. Rev. Lett. 85, 5312–5315 (2000).
    [Crossref]
  3. J. Enderlein, “Single-molecule fluorescence near a metal layer,” Chem. Phys. 247, 1–9 (1999).
    [Crossref]
  4. A. Sommerfeld, “über die ausbreitung der wellen in der drahtlosen telegraphie,” Ann. Phys. 333, 665–736 (1909).
    [Crossref]
  5. K. Drexhage, H. Kuhn, and F. Schäfer, “Variation of the fluorescence decay time of a molecule in front of a mirror,” Ber. Bunsengesellschaft Phys. Chem. 72, 329 (1968).
  6. R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys. 37, 1–65 (1978).
  7. S. Brueck, V. Smagley, and P. Eliseev, “Radiation from a dipole embedded in a multilayer slab,” Phys. Rev. E 68, 036608 (2003).
    [Crossref]
  8. R. Kunz and W. Lukosz, “Changes in fluorescence lifetimes induced by variable optical environments,” Phys. Rev. B 21, 4814–4828 (1980).
    [Crossref]
  9. M. Yeung and T. Gustafson, “Spontaneous emission near an absorbing dielectric surface,” Phys. Rev. A 54, 5227–5242 (1996).
    [Crossref] [PubMed]
  10. L. Luan, P. Sievert, W. Mu, Z. Hong, and J. Ketterson, “Highly directional fluorescence emission from dye molecules embedded in a dielectric layer adjacent to a silver film,” New J. Phys. 10, 073012 (2008).
    [Crossref]
  11. L. Luan, P. Sievert, and J. Ketterson, “Near-field and far-field electric dipole radiation in the vicinity of a planar dielectric half space,” New J. Phys. 8, 264 (2006).
    [Crossref]
  12. F. A. Inam, T. Gaebel, C. Bradac, L. Stewart, M. J. Withford, J. M. Dawes, J. R. Rabeau, and M. J. Steel, “Modification of spontaneous emission from nanodiamond colour centres on a structured surface,” New J. Phys. 13, 073012 (2011).
    [Crossref]
  13. L. Penninck, S. Mladenowski, and K. Neyts, “The effects of planar metallic interfaces on the radiation of nearby electrical dipoles,” J. Opt. 12, 075001 (2010).
    [Crossref]
  14. R. Börner, D. Kowerko, S. Krause, C. von Borczyskowski, and C. G. Hübner, “Efficient simultaneous fluorescence orientation, spectrum, and lifetime detection for single molecule dynamics,” J. Chem. Phys. 137, 164202 (2012).
    [Crossref] [PubMed]
  15. W. Lukosz, “Light emission by magnetic and electric dipoles close to a plane dielectric interface. III. Radiation patterns of dipoles with arbitrary orientation,” J. Opt. Soc. Am. 69, 1495–1503 (1979).
    [Crossref]
  16. W. Lukosz and R. E. Kunz, “Light emission by magnetic and electric dipoles close to a plane dielectric interface. II. radiation patterns of perpendicular oriented dipoles,” J. Opt. Soc. Am. 67, 1615–1619 (1977).
    [Crossref]
  17. W. Lukosz and R. E. Kunz, “Light emission by magnetic and electric dipoles close to a plane interface. I. Total radiated power,” J. Opt. Soc. Am. 67, 1607–1615 (1977).
    [Crossref]
  18. J. B. Mueller and F. Capasso, “Asymmetric surface plasmon polariton emission by a dipole emitter near a metal surface,” Phys. Rev. B 88, 121410 (2013).
    [Crossref]
  19. F. J. Rodríguez-Fortun̂o, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340, 328–330 (2013).
    [Crossref]
  20. J. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998).
  21. L. Novotny and B. Hecht, Principles of Nano-optics (Cambridge University, 2006).
  22. M. Paulus, P. Gay-Balmaz, and O. J. Martin, “Accurate and efficient computation of the Green’s tensor for stratified media,” Phys. Rev. E 62, 5797–5807 (2000).
    [Crossref]
  23. E. Palik, Handbook of Optical Constants of Solids (Academic, 1998).
  24. A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329, 930–933 (2010).
    [Crossref] [PubMed]
  25. T. H. Taminiau, F. D. Stefani, F. B. Segerink, and N. F. van Hulst, “Optical antennas direct single-molecule emission,” Nat. Photonics 2, 234–237 (2008).
    [Crossref]
  26. T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical Yagi-Uda antenna,” Nat. Photonics 4, 312–315 (2010).
    [Crossref]
  27. P. W. Atkins and R. S. Friedman, Molecular Quantum Mechanics (Oxford University, 1997).
  28. S. Petoud, G. Muller, E. G. Moore, J. Xu, J. Sokolnicki, J. P. Riehl, U. N. Le, S. M. Cohen, and K. N. Raymond, “Brilliant Sm, Eu, Tb, and Dy chiral lanthanide complexes with strong circularly polarized luminescence,” J. Am. Chem. Soc. 129, 77–83 (2007).
    [Crossref] [PubMed]
  29. Y. C. Jun, K. C. Huang, and M. L. Brongersma, “Plasmonic beaming and active control over fluorescent emission,” Nat. Commun. 2, 283 (2011).
    [Crossref] [PubMed]
  30. H. Aouani, O. Mahboub, E. Devaux, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Plasmonic antennas for directional sorting of fluorescence emission,” Nano Lett. 11, 2400–2406 (2011).
    [Crossref] [PubMed]
  31. G. Rui, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Demonstration of beam steering via dipole-coupled plasmonic spiral antenna,” Sci. Rep. 3, 2237 (2013).
    [Crossref] [PubMed]
  32. J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493, 195–199 (2013).
    [Crossref] [PubMed]
  33. A. Krasnok, D. Filonov, A. Slobozhanyuk, C. Simovski, P. Belov, and Y. Kivshar, “Superdirective dielectric nanoantennas with effect of light steering,” arXiv:1307.4601 (2013).

2013 (4)

J. B. Mueller and F. Capasso, “Asymmetric surface plasmon polariton emission by a dipole emitter near a metal surface,” Phys. Rev. B 88, 121410 (2013).
[Crossref]

F. J. Rodríguez-Fortun̂o, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340, 328–330 (2013).
[Crossref]

G. Rui, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Demonstration of beam steering via dipole-coupled plasmonic spiral antenna,” Sci. Rep. 3, 2237 (2013).
[Crossref] [PubMed]

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493, 195–199 (2013).
[Crossref] [PubMed]

2012 (1)

R. Börner, D. Kowerko, S. Krause, C. von Borczyskowski, and C. G. Hübner, “Efficient simultaneous fluorescence orientation, spectrum, and lifetime detection for single molecule dynamics,” J. Chem. Phys. 137, 164202 (2012).
[Crossref] [PubMed]

2011 (3)

Y. C. Jun, K. C. Huang, and M. L. Brongersma, “Plasmonic beaming and active control over fluorescent emission,” Nat. Commun. 2, 283 (2011).
[Crossref] [PubMed]

H. Aouani, O. Mahboub, E. Devaux, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Plasmonic antennas for directional sorting of fluorescence emission,” Nano Lett. 11, 2400–2406 (2011).
[Crossref] [PubMed]

F. A. Inam, T. Gaebel, C. Bradac, L. Stewart, M. J. Withford, J. M. Dawes, J. R. Rabeau, and M. J. Steel, “Modification of spontaneous emission from nanodiamond colour centres on a structured surface,” New J. Phys. 13, 073012 (2011).
[Crossref]

2010 (3)

L. Penninck, S. Mladenowski, and K. Neyts, “The effects of planar metallic interfaces on the radiation of nearby electrical dipoles,” J. Opt. 12, 075001 (2010).
[Crossref]

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329, 930–933 (2010).
[Crossref] [PubMed]

T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical Yagi-Uda antenna,” Nat. Photonics 4, 312–315 (2010).
[Crossref]

2008 (2)

T. H. Taminiau, F. D. Stefani, F. B. Segerink, and N. F. van Hulst, “Optical antennas direct single-molecule emission,” Nat. Photonics 2, 234–237 (2008).
[Crossref]

L. Luan, P. Sievert, W. Mu, Z. Hong, and J. Ketterson, “Highly directional fluorescence emission from dye molecules embedded in a dielectric layer adjacent to a silver film,” New J. Phys. 10, 073012 (2008).
[Crossref]

2007 (1)

S. Petoud, G. Muller, E. G. Moore, J. Xu, J. Sokolnicki, J. P. Riehl, U. N. Le, S. M. Cohen, and K. N. Raymond, “Brilliant Sm, Eu, Tb, and Dy chiral lanthanide complexes with strong circularly polarized luminescence,” J. Am. Chem. Soc. 129, 77–83 (2007).
[Crossref] [PubMed]

2006 (1)

L. Luan, P. Sievert, and J. Ketterson, “Near-field and far-field electric dipole radiation in the vicinity of a planar dielectric half space,” New J. Phys. 8, 264 (2006).
[Crossref]

2003 (1)

S. Brueck, V. Smagley, and P. Eliseev, “Radiation from a dipole embedded in a multilayer slab,” Phys. Rev. E 68, 036608 (2003).
[Crossref]

2000 (2)

H. Gersen, M. Garcia-Parajo, L. Novotny, J. Veerman, L. Kuipers, and N. Van Hulst, “Influencing the angular emission of a single molecule,” Phys. Rev. Lett. 85, 5312–5315 (2000).
[Crossref]

M. Paulus, P. Gay-Balmaz, and O. J. Martin, “Accurate and efficient computation of the Green’s tensor for stratified media,” Phys. Rev. E 62, 5797–5807 (2000).
[Crossref]

1999 (1)

J. Enderlein, “Single-molecule fluorescence near a metal layer,” Chem. Phys. 247, 1–9 (1999).
[Crossref]

1998 (1)

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

1996 (1)

M. Yeung and T. Gustafson, “Spontaneous emission near an absorbing dielectric surface,” Phys. Rev. A 54, 5227–5242 (1996).
[Crossref] [PubMed]

1980 (1)

R. Kunz and W. Lukosz, “Changes in fluorescence lifetimes induced by variable optical environments,” Phys. Rev. B 21, 4814–4828 (1980).
[Crossref]

1979 (1)

1978 (1)

R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys. 37, 1–65 (1978).

1977 (2)

1968 (1)

K. Drexhage, H. Kuhn, and F. Schäfer, “Variation of the fluorescence decay time of a molecule in front of a mirror,” Ber. Bunsengesellschaft Phys. Chem. 72, 329 (1968).

1909 (1)

A. Sommerfeld, “über die ausbreitung der wellen in der drahtlosen telegraphie,” Ann. Phys. 333, 665–736 (1909).
[Crossref]

Abeysinghe, D. C.

G. Rui, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Demonstration of beam steering via dipole-coupled plasmonic spiral antenna,” Sci. Rep. 3, 2237 (2013).
[Crossref] [PubMed]

Aouani, H.

H. Aouani, O. Mahboub, E. Devaux, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Plasmonic antennas for directional sorting of fluorescence emission,” Nano Lett. 11, 2400–2406 (2011).
[Crossref] [PubMed]

Atkins, P. W.

P. W. Atkins and R. S. Friedman, Molecular Quantum Mechanics (Oxford University, 1997).

Barnes, W.

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

Belov, P.

A. Krasnok, D. Filonov, A. Slobozhanyuk, C. Simovski, P. Belov, and Y. Kivshar, “Superdirective dielectric nanoantennas with effect of light steering,” arXiv:1307.4601 (2013).

Börner, R.

R. Börner, D. Kowerko, S. Krause, C. von Borczyskowski, and C. G. Hübner, “Efficient simultaneous fluorescence orientation, spectrum, and lifetime detection for single molecule dynamics,” J. Chem. Phys. 137, 164202 (2012).
[Crossref] [PubMed]

Bradac, C.

F. A. Inam, T. Gaebel, C. Bradac, L. Stewart, M. J. Withford, J. M. Dawes, J. R. Rabeau, and M. J. Steel, “Modification of spontaneous emission from nanodiamond colour centres on a structured surface,” New J. Phys. 13, 073012 (2011).
[Crossref]

Brongersma, M. L.

Y. C. Jun, K. C. Huang, and M. L. Brongersma, “Plasmonic beaming and active control over fluorescent emission,” Nat. Commun. 2, 283 (2011).
[Crossref] [PubMed]

Brueck, S.

S. Brueck, V. Smagley, and P. Eliseev, “Radiation from a dipole embedded in a multilayer slab,” Phys. Rev. E 68, 036608 (2003).
[Crossref]

Capasso, F.

J. B. Mueller and F. Capasso, “Asymmetric surface plasmon polariton emission by a dipole emitter near a metal surface,” Phys. Rev. B 88, 121410 (2013).
[Crossref]

Chance, R.

R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys. 37, 1–65 (1978).

Cohen, S. M.

S. Petoud, G. Muller, E. G. Moore, J. Xu, J. Sokolnicki, J. P. Riehl, U. N. Le, S. M. Cohen, and K. N. Raymond, “Brilliant Sm, Eu, Tb, and Dy chiral lanthanide complexes with strong circularly polarized luminescence,” J. Am. Chem. Soc. 129, 77–83 (2007).
[Crossref] [PubMed]

Curto, A. G.

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329, 930–933 (2010).
[Crossref] [PubMed]

Dawes, J. M.

F. A. Inam, T. Gaebel, C. Bradac, L. Stewart, M. J. Withford, J. M. Dawes, J. R. Rabeau, and M. J. Steel, “Modification of spontaneous emission from nanodiamond colour centres on a structured surface,” New J. Phys. 13, 073012 (2011).
[Crossref]

Devaux, E.

H. Aouani, O. Mahboub, E. Devaux, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Plasmonic antennas for directional sorting of fluorescence emission,” Nano Lett. 11, 2400–2406 (2011).
[Crossref] [PubMed]

Drexhage, K.

K. Drexhage, H. Kuhn, and F. Schäfer, “Variation of the fluorescence decay time of a molecule in front of a mirror,” Ber. Bunsengesellschaft Phys. Chem. 72, 329 (1968).

Ebbesen, T. W.

H. Aouani, O. Mahboub, E. Devaux, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Plasmonic antennas for directional sorting of fluorescence emission,” Nano Lett. 11, 2400–2406 (2011).
[Crossref] [PubMed]

Eliseev, P.

S. Brueck, V. Smagley, and P. Eliseev, “Radiation from a dipole embedded in a multilayer slab,” Phys. Rev. E 68, 036608 (2003).
[Crossref]

Enderlein, J.

J. Enderlein, “Single-molecule fluorescence near a metal layer,” Chem. Phys. 247, 1–9 (1999).
[Crossref]

Filonov, D.

A. Krasnok, D. Filonov, A. Slobozhanyuk, C. Simovski, P. Belov, and Y. Kivshar, “Superdirective dielectric nanoantennas with effect of light steering,” arXiv:1307.4601 (2013).

Friedman, R. S.

P. W. Atkins and R. S. Friedman, Molecular Quantum Mechanics (Oxford University, 1997).

Gaebel, T.

F. A. Inam, T. Gaebel, C. Bradac, L. Stewart, M. J. Withford, J. M. Dawes, J. R. Rabeau, and M. J. Steel, “Modification of spontaneous emission from nanodiamond colour centres on a structured surface,” New J. Phys. 13, 073012 (2011).
[Crossref]

Garcia-Parajo, M.

H. Gersen, M. Garcia-Parajo, L. Novotny, J. Veerman, L. Kuipers, and N. Van Hulst, “Influencing the angular emission of a single molecule,” Phys. Rev. Lett. 85, 5312–5315 (2000).
[Crossref]

Gay-Balmaz, P.

M. Paulus, P. Gay-Balmaz, and O. J. Martin, “Accurate and efficient computation of the Green’s tensor for stratified media,” Phys. Rev. E 62, 5797–5807 (2000).
[Crossref]

Gersen, H.

H. Gersen, M. Garcia-Parajo, L. Novotny, J. Veerman, L. Kuipers, and N. Van Hulst, “Influencing the angular emission of a single molecule,” Phys. Rev. Lett. 85, 5312–5315 (2000).
[Crossref]

Ginzburg, P.

F. J. Rodríguez-Fortun̂o, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340, 328–330 (2013).
[Crossref]

Gustafson, T.

M. Yeung and T. Gustafson, “Spontaneous emission near an absorbing dielectric surface,” Phys. Rev. A 54, 5227–5242 (1996).
[Crossref] [PubMed]

Hecht, B.

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

Hofmann, H. F.

T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical Yagi-Uda antenna,” Nat. Photonics 4, 312–315 (2010).
[Crossref]

Hong, Z.

L. Luan, P. Sievert, W. Mu, Z. Hong, and J. Ketterson, “Highly directional fluorescence emission from dye molecules embedded in a dielectric layer adjacent to a silver film,” New J. Phys. 10, 073012 (2008).
[Crossref]

Hosseini, E. S.

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493, 195–199 (2013).
[Crossref] [PubMed]

Huang, K. C.

Y. C. Jun, K. C. Huang, and M. L. Brongersma, “Plasmonic beaming and active control over fluorescent emission,” Nat. Commun. 2, 283 (2011).
[Crossref] [PubMed]

Hübner, C. G.

R. Börner, D. Kowerko, S. Krause, C. von Borczyskowski, and C. G. Hübner, “Efficient simultaneous fluorescence orientation, spectrum, and lifetime detection for single molecule dynamics,” J. Chem. Phys. 137, 164202 (2012).
[Crossref] [PubMed]

Inam, F. A.

F. A. Inam, T. Gaebel, C. Bradac, L. Stewart, M. J. Withford, J. M. Dawes, J. R. Rabeau, and M. J. Steel, “Modification of spontaneous emission from nanodiamond colour centres on a structured surface,” New J. Phys. 13, 073012 (2011).
[Crossref]

Jackson, J.

J. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998).

Jun, Y. C.

Y. C. Jun, K. C. Huang, and M. L. Brongersma, “Plasmonic beaming and active control over fluorescent emission,” Nat. Commun. 2, 283 (2011).
[Crossref] [PubMed]

Kadoya, Y.

T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical Yagi-Uda antenna,” Nat. Photonics 4, 312–315 (2010).
[Crossref]

Ketterson, J.

L. Luan, P. Sievert, W. Mu, Z. Hong, and J. Ketterson, “Highly directional fluorescence emission from dye molecules embedded in a dielectric layer adjacent to a silver film,” New J. Phys. 10, 073012 (2008).
[Crossref]

L. Luan, P. Sievert, and J. Ketterson, “Near-field and far-field electric dipole radiation in the vicinity of a planar dielectric half space,” New J. Phys. 8, 264 (2006).
[Crossref]

Kivshar, Y.

A. Krasnok, D. Filonov, A. Slobozhanyuk, C. Simovski, P. Belov, and Y. Kivshar, “Superdirective dielectric nanoantennas with effect of light steering,” arXiv:1307.4601 (2013).

Kosako, T.

T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical Yagi-Uda antenna,” Nat. Photonics 4, 312–315 (2010).
[Crossref]

Kowerko, D.

R. Börner, D. Kowerko, S. Krause, C. von Borczyskowski, and C. G. Hübner, “Efficient simultaneous fluorescence orientation, spectrum, and lifetime detection for single molecule dynamics,” J. Chem. Phys. 137, 164202 (2012).
[Crossref] [PubMed]

Krasnok, A.

A. Krasnok, D. Filonov, A. Slobozhanyuk, C. Simovski, P. Belov, and Y. Kivshar, “Superdirective dielectric nanoantennas with effect of light steering,” arXiv:1307.4601 (2013).

Krause, S.

R. Börner, D. Kowerko, S. Krause, C. von Borczyskowski, and C. G. Hübner, “Efficient simultaneous fluorescence orientation, spectrum, and lifetime detection for single molecule dynamics,” J. Chem. Phys. 137, 164202 (2012).
[Crossref] [PubMed]

Kreuzer, M. P.

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329, 930–933 (2010).
[Crossref] [PubMed]

Kuhn, H.

K. Drexhage, H. Kuhn, and F. Schäfer, “Variation of the fluorescence decay time of a molecule in front of a mirror,” Ber. Bunsengesellschaft Phys. Chem. 72, 329 (1968).

Kuipers, L.

H. Gersen, M. Garcia-Parajo, L. Novotny, J. Veerman, L. Kuipers, and N. Van Hulst, “Influencing the angular emission of a single molecule,” Phys. Rev. Lett. 85, 5312–5315 (2000).
[Crossref]

Kunz, R.

R. Kunz and W. Lukosz, “Changes in fluorescence lifetimes induced by variable optical environments,” Phys. Rev. B 21, 4814–4828 (1980).
[Crossref]

Kunz, R. E.

Le, U. N.

S. Petoud, G. Muller, E. G. Moore, J. Xu, J. Sokolnicki, J. P. Riehl, U. N. Le, S. M. Cohen, and K. N. Raymond, “Brilliant Sm, Eu, Tb, and Dy chiral lanthanide complexes with strong circularly polarized luminescence,” J. Am. Chem. Soc. 129, 77–83 (2007).
[Crossref] [PubMed]

Luan, L.

L. Luan, P. Sievert, W. Mu, Z. Hong, and J. Ketterson, “Highly directional fluorescence emission from dye molecules embedded in a dielectric layer adjacent to a silver film,” New J. Phys. 10, 073012 (2008).
[Crossref]

L. Luan, P. Sievert, and J. Ketterson, “Near-field and far-field electric dipole radiation in the vicinity of a planar dielectric half space,” New J. Phys. 8, 264 (2006).
[Crossref]

Lukosz, W.

Mahboub, O.

H. Aouani, O. Mahboub, E. Devaux, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Plasmonic antennas for directional sorting of fluorescence emission,” Nano Lett. 11, 2400–2406 (2011).
[Crossref] [PubMed]

Marino, G.

F. J. Rodríguez-Fortun̂o, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340, 328–330 (2013).
[Crossref]

Martin, O. J.

M. Paulus, P. Gay-Balmaz, and O. J. Martin, “Accurate and efficient computation of the Green’s tensor for stratified media,” Phys. Rev. E 62, 5797–5807 (2000).
[Crossref]

Martínez, A.

F. J. Rodríguez-Fortun̂o, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340, 328–330 (2013).
[Crossref]

Mladenowski, S.

L. Penninck, S. Mladenowski, and K. Neyts, “The effects of planar metallic interfaces on the radiation of nearby electrical dipoles,” J. Opt. 12, 075001 (2010).
[Crossref]

Moore, E. G.

S. Petoud, G. Muller, E. G. Moore, J. Xu, J. Sokolnicki, J. P. Riehl, U. N. Le, S. M. Cohen, and K. N. Raymond, “Brilliant Sm, Eu, Tb, and Dy chiral lanthanide complexes with strong circularly polarized luminescence,” J. Am. Chem. Soc. 129, 77–83 (2007).
[Crossref] [PubMed]

Mu, W.

L. Luan, P. Sievert, W. Mu, Z. Hong, and J. Ketterson, “Highly directional fluorescence emission from dye molecules embedded in a dielectric layer adjacent to a silver film,” New J. Phys. 10, 073012 (2008).
[Crossref]

Mueller, J. B.

J. B. Mueller and F. Capasso, “Asymmetric surface plasmon polariton emission by a dipole emitter near a metal surface,” Phys. Rev. B 88, 121410 (2013).
[Crossref]

Muller, G.

S. Petoud, G. Muller, E. G. Moore, J. Xu, J. Sokolnicki, J. P. Riehl, U. N. Le, S. M. Cohen, and K. N. Raymond, “Brilliant Sm, Eu, Tb, and Dy chiral lanthanide complexes with strong circularly polarized luminescence,” J. Am. Chem. Soc. 129, 77–83 (2007).
[Crossref] [PubMed]

Nelson, R. L.

G. Rui, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Demonstration of beam steering via dipole-coupled plasmonic spiral antenna,” Sci. Rep. 3, 2237 (2013).
[Crossref] [PubMed]

Neyts, K.

L. Penninck, S. Mladenowski, and K. Neyts, “The effects of planar metallic interfaces on the radiation of nearby electrical dipoles,” J. Opt. 12, 075001 (2010).
[Crossref]

Novotny, L.

H. Gersen, M. Garcia-Parajo, L. Novotny, J. Veerman, L. Kuipers, and N. Van Hulst, “Influencing the angular emission of a single molecule,” Phys. Rev. Lett. 85, 5312–5315 (2000).
[Crossref]

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

O’Connor, D.

F. J. Rodríguez-Fortun̂o, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340, 328–330 (2013).
[Crossref]

Palik, E.

E. Palik, Handbook of Optical Constants of Solids (Academic, 1998).

Paulus, M.

M. Paulus, P. Gay-Balmaz, and O. J. Martin, “Accurate and efficient computation of the Green’s tensor for stratified media,” Phys. Rev. E 62, 5797–5807 (2000).
[Crossref]

Penninck, L.

L. Penninck, S. Mladenowski, and K. Neyts, “The effects of planar metallic interfaces on the radiation of nearby electrical dipoles,” J. Opt. 12, 075001 (2010).
[Crossref]

Petoud, S.

S. Petoud, G. Muller, E. G. Moore, J. Xu, J. Sokolnicki, J. P. Riehl, U. N. Le, S. M. Cohen, and K. N. Raymond, “Brilliant Sm, Eu, Tb, and Dy chiral lanthanide complexes with strong circularly polarized luminescence,” J. Am. Chem. Soc. 129, 77–83 (2007).
[Crossref] [PubMed]

Prock, A.

R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys. 37, 1–65 (1978).

Quidant, R.

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329, 930–933 (2010).
[Crossref] [PubMed]

Rabeau, J. R.

F. A. Inam, T. Gaebel, C. Bradac, L. Stewart, M. J. Withford, J. M. Dawes, J. R. Rabeau, and M. J. Steel, “Modification of spontaneous emission from nanodiamond colour centres on a structured surface,” New J. Phys. 13, 073012 (2011).
[Crossref]

Raymond, K. N.

S. Petoud, G. Muller, E. G. Moore, J. Xu, J. Sokolnicki, J. P. Riehl, U. N. Le, S. M. Cohen, and K. N. Raymond, “Brilliant Sm, Eu, Tb, and Dy chiral lanthanide complexes with strong circularly polarized luminescence,” J. Am. Chem. Soc. 129, 77–83 (2007).
[Crossref] [PubMed]

Riehl, J. P.

S. Petoud, G. Muller, E. G. Moore, J. Xu, J. Sokolnicki, J. P. Riehl, U. N. Le, S. M. Cohen, and K. N. Raymond, “Brilliant Sm, Eu, Tb, and Dy chiral lanthanide complexes with strong circularly polarized luminescence,” J. Am. Chem. Soc. 129, 77–83 (2007).
[Crossref] [PubMed]

Rigneault, H.

H. Aouani, O. Mahboub, E. Devaux, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Plasmonic antennas for directional sorting of fluorescence emission,” Nano Lett. 11, 2400–2406 (2011).
[Crossref] [PubMed]

Rodríguez-Fortun^o, F. J.

F. J. Rodríguez-Fortun̂o, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340, 328–330 (2013).
[Crossref]

Rui, G.

G. Rui, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Demonstration of beam steering via dipole-coupled plasmonic spiral antenna,” Sci. Rep. 3, 2237 (2013).
[Crossref] [PubMed]

Schäfer, F.

K. Drexhage, H. Kuhn, and F. Schäfer, “Variation of the fluorescence decay time of a molecule in front of a mirror,” Ber. Bunsengesellschaft Phys. Chem. 72, 329 (1968).

Segerink, F. B.

T. H. Taminiau, F. D. Stefani, F. B. Segerink, and N. F. van Hulst, “Optical antennas direct single-molecule emission,” Nat. Photonics 2, 234–237 (2008).
[Crossref]

Sievert, P.

L. Luan, P. Sievert, W. Mu, Z. Hong, and J. Ketterson, “Highly directional fluorescence emission from dye molecules embedded in a dielectric layer adjacent to a silver film,” New J. Phys. 10, 073012 (2008).
[Crossref]

L. Luan, P. Sievert, and J. Ketterson, “Near-field and far-field electric dipole radiation in the vicinity of a planar dielectric half space,” New J. Phys. 8, 264 (2006).
[Crossref]

Silbey, R.

R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys. 37, 1–65 (1978).

Simovski, C.

A. Krasnok, D. Filonov, A. Slobozhanyuk, C. Simovski, P. Belov, and Y. Kivshar, “Superdirective dielectric nanoantennas with effect of light steering,” arXiv:1307.4601 (2013).

Slobozhanyuk, A.

A. Krasnok, D. Filonov, A. Slobozhanyuk, C. Simovski, P. Belov, and Y. Kivshar, “Superdirective dielectric nanoantennas with effect of light steering,” arXiv:1307.4601 (2013).

Smagley, V.

S. Brueck, V. Smagley, and P. Eliseev, “Radiation from a dipole embedded in a multilayer slab,” Phys. Rev. E 68, 036608 (2003).
[Crossref]

Sokolnicki, J.

S. Petoud, G. Muller, E. G. Moore, J. Xu, J. Sokolnicki, J. P. Riehl, U. N. Le, S. M. Cohen, and K. N. Raymond, “Brilliant Sm, Eu, Tb, and Dy chiral lanthanide complexes with strong circularly polarized luminescence,” J. Am. Chem. Soc. 129, 77–83 (2007).
[Crossref] [PubMed]

Sommerfeld, A.

A. Sommerfeld, “über die ausbreitung der wellen in der drahtlosen telegraphie,” Ann. Phys. 333, 665–736 (1909).
[Crossref]

Steel, M. J.

F. A. Inam, T. Gaebel, C. Bradac, L. Stewart, M. J. Withford, J. M. Dawes, J. R. Rabeau, and M. J. Steel, “Modification of spontaneous emission from nanodiamond colour centres on a structured surface,” New J. Phys. 13, 073012 (2011).
[Crossref]

Stefani, F. D.

T. H. Taminiau, F. D. Stefani, F. B. Segerink, and N. F. van Hulst, “Optical antennas direct single-molecule emission,” Nat. Photonics 2, 234–237 (2008).
[Crossref]

Stewart, L.

F. A. Inam, T. Gaebel, C. Bradac, L. Stewart, M. J. Withford, J. M. Dawes, J. R. Rabeau, and M. J. Steel, “Modification of spontaneous emission from nanodiamond colour centres on a structured surface,” New J. Phys. 13, 073012 (2011).
[Crossref]

Sun, J.

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493, 195–199 (2013).
[Crossref] [PubMed]

Taminiau, T. H.

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329, 930–933 (2010).
[Crossref] [PubMed]

T. H. Taminiau, F. D. Stefani, F. B. Segerink, and N. F. van Hulst, “Optical antennas direct single-molecule emission,” Nat. Photonics 2, 234–237 (2008).
[Crossref]

Timurdogan, E.

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493, 195–199 (2013).
[Crossref] [PubMed]

Van Hulst, N.

H. Gersen, M. Garcia-Parajo, L. Novotny, J. Veerman, L. Kuipers, and N. Van Hulst, “Influencing the angular emission of a single molecule,” Phys. Rev. Lett. 85, 5312–5315 (2000).
[Crossref]

van Hulst, N. F.

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329, 930–933 (2010).
[Crossref] [PubMed]

T. H. Taminiau, F. D. Stefani, F. B. Segerink, and N. F. van Hulst, “Optical antennas direct single-molecule emission,” Nat. Photonics 2, 234–237 (2008).
[Crossref]

Veerman, J.

H. Gersen, M. Garcia-Parajo, L. Novotny, J. Veerman, L. Kuipers, and N. Van Hulst, “Influencing the angular emission of a single molecule,” Phys. Rev. Lett. 85, 5312–5315 (2000).
[Crossref]

Volpe, G.

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329, 930–933 (2010).
[Crossref] [PubMed]

von Borczyskowski, C.

R. Börner, D. Kowerko, S. Krause, C. von Borczyskowski, and C. G. Hübner, “Efficient simultaneous fluorescence orientation, spectrum, and lifetime detection for single molecule dynamics,” J. Chem. Phys. 137, 164202 (2012).
[Crossref] [PubMed]

Watts, M. R.

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493, 195–199 (2013).
[Crossref] [PubMed]

Wenger, J.

H. Aouani, O. Mahboub, E. Devaux, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Plasmonic antennas for directional sorting of fluorescence emission,” Nano Lett. 11, 2400–2406 (2011).
[Crossref] [PubMed]

Withford, M. J.

F. A. Inam, T. Gaebel, C. Bradac, L. Stewart, M. J. Withford, J. M. Dawes, J. R. Rabeau, and M. J. Steel, “Modification of spontaneous emission from nanodiamond colour centres on a structured surface,” New J. Phys. 13, 073012 (2011).
[Crossref]

Wurtz, G. A.

F. J. Rodríguez-Fortun̂o, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340, 328–330 (2013).
[Crossref]

Xu, J.

S. Petoud, G. Muller, E. G. Moore, J. Xu, J. Sokolnicki, J. P. Riehl, U. N. Le, S. M. Cohen, and K. N. Raymond, “Brilliant Sm, Eu, Tb, and Dy chiral lanthanide complexes with strong circularly polarized luminescence,” J. Am. Chem. Soc. 129, 77–83 (2007).
[Crossref] [PubMed]

Yaacobi, A.

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493, 195–199 (2013).
[Crossref] [PubMed]

Yeung, M.

M. Yeung and T. Gustafson, “Spontaneous emission near an absorbing dielectric surface,” Phys. Rev. A 54, 5227–5242 (1996).
[Crossref] [PubMed]

Zayats, A. V.

F. J. Rodríguez-Fortun̂o, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340, 328–330 (2013).
[Crossref]

Zhan, Q.

G. Rui, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Demonstration of beam steering via dipole-coupled plasmonic spiral antenna,” Sci. Rep. 3, 2237 (2013).
[Crossref] [PubMed]

Adv. Chem. Phys. (1)

R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys. 37, 1–65 (1978).

Ann. Phys. (1)

A. Sommerfeld, “über die ausbreitung der wellen in der drahtlosen telegraphie,” Ann. Phys. 333, 665–736 (1909).
[Crossref]

Ber. Bunsengesellschaft Phys. Chem. (1)

K. Drexhage, H. Kuhn, and F. Schäfer, “Variation of the fluorescence decay time of a molecule in front of a mirror,” Ber. Bunsengesellschaft Phys. Chem. 72, 329 (1968).

Chem. Phys. (1)

J. Enderlein, “Single-molecule fluorescence near a metal layer,” Chem. Phys. 247, 1–9 (1999).
[Crossref]

J. Am. Chem. Soc. (1)

S. Petoud, G. Muller, E. G. Moore, J. Xu, J. Sokolnicki, J. P. Riehl, U. N. Le, S. M. Cohen, and K. N. Raymond, “Brilliant Sm, Eu, Tb, and Dy chiral lanthanide complexes with strong circularly polarized luminescence,” J. Am. Chem. Soc. 129, 77–83 (2007).
[Crossref] [PubMed]

J. Chem. Phys. (1)

R. Börner, D. Kowerko, S. Krause, C. von Borczyskowski, and C. G. Hübner, “Efficient simultaneous fluorescence orientation, spectrum, and lifetime detection for single molecule dynamics,” J. Chem. Phys. 137, 164202 (2012).
[Crossref] [PubMed]

J. Mod. Opt. (1)

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

J. Opt. (1)

L. Penninck, S. Mladenowski, and K. Neyts, “The effects of planar metallic interfaces on the radiation of nearby electrical dipoles,” J. Opt. 12, 075001 (2010).
[Crossref]

J. Opt. Soc. Am. (3)

Nano Lett. (1)

H. Aouani, O. Mahboub, E. Devaux, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Plasmonic antennas for directional sorting of fluorescence emission,” Nano Lett. 11, 2400–2406 (2011).
[Crossref] [PubMed]

Nat. Commun. (1)

Y. C. Jun, K. C. Huang, and M. L. Brongersma, “Plasmonic beaming and active control over fluorescent emission,” Nat. Commun. 2, 283 (2011).
[Crossref] [PubMed]

Nat. Photonics (2)

T. H. Taminiau, F. D. Stefani, F. B. Segerink, and N. F. van Hulst, “Optical antennas direct single-molecule emission,” Nat. Photonics 2, 234–237 (2008).
[Crossref]

T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical Yagi-Uda antenna,” Nat. Photonics 4, 312–315 (2010).
[Crossref]

Nature (1)

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493, 195–199 (2013).
[Crossref] [PubMed]

New J. Phys. (3)

L. Luan, P. Sievert, W. Mu, Z. Hong, and J. Ketterson, “Highly directional fluorescence emission from dye molecules embedded in a dielectric layer adjacent to a silver film,” New J. Phys. 10, 073012 (2008).
[Crossref]

L. Luan, P. Sievert, and J. Ketterson, “Near-field and far-field electric dipole radiation in the vicinity of a planar dielectric half space,” New J. Phys. 8, 264 (2006).
[Crossref]

F. A. Inam, T. Gaebel, C. Bradac, L. Stewart, M. J. Withford, J. M. Dawes, J. R. Rabeau, and M. J. Steel, “Modification of spontaneous emission from nanodiamond colour centres on a structured surface,” New J. Phys. 13, 073012 (2011).
[Crossref]

Phys. Rev. A (1)

M. Yeung and T. Gustafson, “Spontaneous emission near an absorbing dielectric surface,” Phys. Rev. A 54, 5227–5242 (1996).
[Crossref] [PubMed]

Phys. Rev. B (2)

R. Kunz and W. Lukosz, “Changes in fluorescence lifetimes induced by variable optical environments,” Phys. Rev. B 21, 4814–4828 (1980).
[Crossref]

J. B. Mueller and F. Capasso, “Asymmetric surface plasmon polariton emission by a dipole emitter near a metal surface,” Phys. Rev. B 88, 121410 (2013).
[Crossref]

Phys. Rev. E (2)

M. Paulus, P. Gay-Balmaz, and O. J. Martin, “Accurate and efficient computation of the Green’s tensor for stratified media,” Phys. Rev. E 62, 5797–5807 (2000).
[Crossref]

S. Brueck, V. Smagley, and P. Eliseev, “Radiation from a dipole embedded in a multilayer slab,” Phys. Rev. E 68, 036608 (2003).
[Crossref]

Phys. Rev. Lett. (1)

H. Gersen, M. Garcia-Parajo, L. Novotny, J. Veerman, L. Kuipers, and N. Van Hulst, “Influencing the angular emission of a single molecule,” Phys. Rev. Lett. 85, 5312–5315 (2000).
[Crossref]

Sci. Rep. (1)

G. Rui, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Demonstration of beam steering via dipole-coupled plasmonic spiral antenna,” Sci. Rep. 3, 2237 (2013).
[Crossref] [PubMed]

Science (2)

F. J. Rodríguez-Fortun̂o, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340, 328–330 (2013).
[Crossref]

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329, 930–933 (2010).
[Crossref] [PubMed]

Other (5)

J. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998).

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

E. Palik, Handbook of Optical Constants of Solids (Academic, 1998).

P. W. Atkins and R. S. Friedman, Molecular Quantum Mechanics (Oxford University, 1997).

A. Krasnok, D. Filonov, A. Slobozhanyuk, C. Simovski, P. Belov, and Y. Kivshar, “Superdirective dielectric nanoantennas with effect of light steering,” arXiv:1307.4601 (2013).

Supplementary Material (1)

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Figures (4)

Fig. 1
Fig. 1 Schematic illustration of the considered geometry. A dipole (green dot) is placed at z0 above an underneath material. θ is the polar angle and ϕ is the azimuthal angle.

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Fig. 2
Fig. 2 Electric field |E| distribution of (a) a 45° linearly polarized dipole above a gold surface, (c) a circularly polarized dipole above a gold surface ( Media 1) and (e) a circularly polarized dipole above n = 1.5 dielectric material with different dipole surface distances z0. The far field power patterns in the XZ plane are also plotted in (b,d,f). The emission wavelength of the dipole is taken to be 500nm and the permittivity of gold is taken from Palik [23].

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Fig. 3
Fig. 3 Contributions of different terms for a 45° linearly polarized dipole. (a) The total radiated power in the far field. (b) The cosine term represents a horizontally oriented dipole. (c) The sine term represents a vertically oriented dipole. (d) The interference term between different dipoles, the three overlapping lines are shifted for clarity. The blue, black and red lines correspond to dipole-surface distance of 20nm, 100nm and 200nm respectively.

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Fig. 4
Fig. 4 Radiation of circularly polarized dipole over metal surface. (a) The total radiated power in the far field. (b) The change of radiation direction by changing dipole-surface distance. (c) The cosine term represents a horizontally oriented dipole. (d) The sine term represents a vertically oriented dipole. (e) The interference term between different dipoles. The blue, black and red lines in (a), (c–e) correspond to dipole-surface distance of 20nm, 100nm and 200nm respectively.

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Equations (6)

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

E → ( r → ) up , low = ω 2 μ μ 0 ( G ↔ 0 ( r → , r → 0 ) + G ↔ ref , trans ( r → , r → 0 ) ) p →
E → far , up ( r → ) = k 2 4 π ε 0 ε 1 e i k → ⋅ r → r ( p x cos θ Φ 2 − p z sin θ Φ 1 ) e → θ
P far ( θ ) ∝ | p x | 2 cos 2 θ | Φ 2 | 2 + | p z | 2 sin 2 θ | Φ 1 | 2 − sin θ cos θ ( p x p z * Φ 1 * Φ 2 + p x * p z Φ 1 Φ 2 * )
P 45 , far ( θ ) ∝ cos 2 θ | Φ 2 | 2 + sin 2 θ | Φ 1 | 2 − 2 sin θ cos θ ( 1 − | r p | 2 )
P ( θ ) cir , far ∝ cos 2 θ | Φ 2 | 2 + sin 2 θ | Φ 1 | 2 − 4 sin θ cos θ Im ( r p e i 2 k z 0 cos θ )
P ( θ ) cir , far , die ∝ cos 2 θ | Φ 2 | 2 + sin 2 θ | Φ 1 | 2 − 4 sin θ cos θ r p sin ( 2 k z 0 cos θ )

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