Abstract

We develop the coupled-mode theory for nanoscale resonant apertures. We show that the maximum transmission and absorption cross sections for subwavelength resonant apertures are only related to the wavelength of the incident light and the directivity of the aperture’s radiation pattern. A general relation between the transmission cross section and the directivity is proven from the coupled-mode theory. As a specific example, we apply the theory to a nanoslit aperture in a metallic film and obtain excellent agreement with direct numerical simulations.

© 2010 Optical Society of America

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  1. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  2. K. L. Kelly, E. Coronado, L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: The influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
    [CrossRef]
  3. A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett. 93, 127401 (2004).
    [CrossRef] [PubMed]
  4. O. Muskens, N. Del Fatti, F. Vallee, J. R. Huntzinger, P. Billaud, and M. Boyer, “Single metal nanoparticle absorption spectroscopy and optical characterization,” Appl. Phys. Lett. 88, 063109 (2006).
    [CrossRef]
  5. M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute extinction cross-section of individual magnetic split-ring resonators,” Nat. Photonics 2, 614–617 (2008).
    [CrossRef]
  6. J. A. Schuller and M. L. Brongersma, “General properties of dielectric optical antennas,” Opt. Express 17, 24084–24095 (2009).
    [CrossRef]
  7. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
    [CrossRef]
  8. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007).
    [CrossRef] [PubMed]
  9. S. Blair and A. Nahata, “Focus issue: Extraordinary light transmission through subwavelength structured surfaces—Introduction,” Opt. Express 12, 3618 (2004).
    [CrossRef] [PubMed]
  10. P. B. Catrysse and S. Fan, “Propagating plasmonic mode in nanoscale apertures and its implications for extraordinary transmission,” J. Nanophotonics 2, 021790 (2008).
    [CrossRef]
  11. F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, “Multiple paths to enhance optical transmission through a single subwavelength slit,” Phys. Rev. Lett. 90, 213901 (2003).
    [CrossRef] [PubMed]
  12. F. J. García de Abajo, “Light transmission through a single cylindrical hole in a metallic film,” Opt. Express 10, 1475–1484 (2002).
    [PubMed]
  13. X. Shi, L. Hesselink, and L. R. Thornton, “Ultrahigh light transmission through a C-shaped nanoaperture,” Opt. Lett. 28, 1320–1322 (2003).
    [CrossRef] [PubMed]
  14. F. J. García-Vidal, E. Moreno, J. A. Porto, and L. Martín-Moreno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett. 95, 103901 (2005).
    [CrossRef] [PubMed]
  15. F. J. García-Vidal, L. Martín-Moreno, E. Moreno, L. K. S. Kumar, and R. Gordon, “Transmission of light through a single rectangular hole in a real metal,” Phys. Rev. B 74, 153411 (2006).
    [CrossRef]
  16. T. Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, “Enhanced light transmission through a single subwavelength aperture,” Opt. Lett. 26, 1972–1974 (2001).
    [CrossRef]
  17. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).
  18. R. E. Hamam, A. Karalis, J. D. Joannopoulos, and M. Soljacic, “Coupled-mode theory for general free-space resonant scattering of waves,” Phys. Rev. A 75, 053801 (2007).
    [CrossRef]
  19. Z. Ruan and S. Fan, “Temporal coupled-mode theory for Fano resonance in light scattering by a single obstacle,” J. Phys. Chem. C 114, 7324–7329 (2010).
    [CrossRef]
  20. J. Bravo-Abad, L. Martín-Moreno, and F. J. García-Vidal, “Transmission properties of a single metallic slit: From the subwavelength regime to the geometrical-optics limit,” Phys. Rev. E 69, 026601 (2004).
    [CrossRef]
  21. O. Mata-Mendez and J. Avendaño, “Some properties of the optical resonances in a single subwavelength slit,” J. Opt. Soc. Am. A 24, 1687–1694 (2007).
    [CrossRef]
  22. F. Yang and J. R. Sambles, “Resonant transmission of microwaves through a narrow metallic slit,” Phys. Rev. Lett. 89, 063901 (2002).
    [CrossRef] [PubMed]
  23. Y. Takakura, “Optical resonance in a narrow slit in a thick metallic screen,” Phys. Rev. Lett. 86, 5601–5603 (2001).
    [CrossRef] [PubMed]
  24. J. R. Suckling, A. P. Hibbins, M. J. Lockyear, T. W. Preist, J. R. Sambles, and C. R. Lawrence, “Finite conductance governs the resonance transmission of thin metal slits at microwave frequencies,” Phys. Rev. Lett. 92, 147401 (2004).
    [CrossRef] [PubMed]
  25. R. Gordon, “Light in a subwavelength slit in a metal: Propagation and reflection,” Phys. Rev. B 73, 153405 (2006).
    [CrossRef]
  26. P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett. 95, 263902 (2005).
    [CrossRef]
  27. L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90, 167401 (2003).
    [CrossRef] [PubMed]
  28. Q. Min and R. Gordon, “Surface plasmon microcavity for resonant transmission through a slit in a gold film,” Opt. Express 16, 9708–9713 (2008).
    [CrossRef] [PubMed]
  29. Z. C. Ruan and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: The role of localized waveguide resonances,” Phys. Rev. Lett. 96, 233901 (2006).
    [CrossRef] [PubMed]
  30. F. J. García-Vidal, L. Martín-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83, 4500–4502 (2003).
    [CrossRef]
  31. Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett. 85, 642–644 (2004).
    [CrossRef]
  32. H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, “Beam manipulating by metallic nano-slits with variant widths,” Opt. Express 13, 6815–6820 (2005).
    [CrossRef] [PubMed]
  33. L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nano-scale slit arrays in a metallic film,” Nano Lett. 9, 235–238 (2009).
    [CrossRef]
  34. L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Planar metallic nanoscale slit lenses for angle compensation,” Appl. Phys. Lett. 95, 071112 (2009).
    [CrossRef]
  35. L. Verslegers, P. B. Catrysse, Z. Yu, W. Shin, Z. C. Ruan, and S. Fan, “Phase front design with metallic pillar arrays,” Opt. Lett. 35, 844–846 (2010).
    [CrossRef] [PubMed]
  36. L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103, 033902 (2009).
    [CrossRef] [PubMed]
  37. Z. Yu, G. Veronis, S. Fan, and M. L. Brongersma, “Design of midinfrared photodetectors enhanced by surface plasmons on grating structures,” Appl. Phys. Lett. 89, 151116 (2006).
    [CrossRef]
  38. J. S. White, G. Veronis, Z. Yu, E. S. Barnard, A. Chandran, S. Fan, and M. L. Brongersma, “Extraordinary optical absorption through sub-wavelength slits,” Opt. Lett. 34, 686–688 (2009).
    [CrossRef] [PubMed]
  39. W. L. Stutzman and G. A. Thiele, Antenna Theory and Design, 2nd ed. (Wiley, 1998).
  40. S. Drabowitch, A. Papiernik, H. Griffiths, J. Encinas, and B. L. Smith, Modern Antennas (Chapman & Hall, 1998).
  41. A. Alu and N. Engheta, “Tuning the scattering response of optical nanoantennas with nanocircuit loads,” Nat. Photonics 2, 307–310 (2008).
    [CrossRef]
  42. Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping for solar cells,” for Proc. Natl. Acad. Sci. (to be published).
  43. S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled mode theory for Fano resonances in optical resonators,” J. Opt. Soc. Am. A 20, 569–573 (2003).
    [CrossRef]
  44. J. B. Keller, “Geometrical theory of diffraction,” J. Opt. Soc. Am. 52, 116–130 (1962).
    [CrossRef] [PubMed]
  45. G. Veronis and S. Fan, in Surface Plasmon Nanophotonics, M.L.Brongersma and P.G.Kik, eds. (Springer, 2007), p. 169.
    [CrossRef]
  46. The directivity, as we defined it, is analogous to the directivity in antenna theory, defined as the ratio of U(θ), the radiation intensity in a certain direction, to Uave, the average radiation intensity: D(θ)=U(θ)/Uave (two-dimensional case).
  47. The factor G is called the (power) gain in antenna theory . We do not adopt this name since in the optics literature gain is commonly related to amplification, which is not the case here.
  48. D.R.Lide, ed., CRC Handbook of Chemistry and Physics, 88th ed. (CRC, 2007).
  49. L. Tang, D. A. B. Miller, A. K. Okyay, J. A. Matteo, Y. Yuen, K. C. Saraswat, and L. Hesselink, “C-shaped nanoaperture-enhanced germanium photodetector,” Opt. Lett. 31, 1519–1521 (2006).
    [CrossRef] [PubMed]
  50. L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D.-S. Ly-Gagnon, K. C. Saraswat, and D. A. B. Miller, “Nanometer-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat. Photonics 2, 226–229 (2008).
    [CrossRef]
  51. P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical antennas,” Adv. Opt. Photon. 1, 438–483 (2009).
    [CrossRef]
  52. K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: Resonators for local field enhancement,” J. Appl. Phys. 94, 4632–4642 (2003).
    [CrossRef]
  53. P. Muhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
    [CrossRef] [PubMed]
  54. A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, “Single-molecule fluorescence enhancements produced by a Bowtie nanoantenna,” Nat. Photonics 3, 654–657 (2009).
    [CrossRef]

2010

Z. Ruan and S. Fan, “Temporal coupled-mode theory for Fano resonance in light scattering by a single obstacle,” J. Phys. Chem. C 114, 7324–7329 (2010).
[CrossRef]

L. Verslegers, P. B. Catrysse, Z. Yu, W. Shin, Z. C. Ruan, and S. Fan, “Phase front design with metallic pillar arrays,” Opt. Lett. 35, 844–846 (2010).
[CrossRef] [PubMed]

2009

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef] [PubMed]

P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical antennas,” Adv. Opt. Photon. 1, 438–483 (2009).
[CrossRef]

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, “Single-molecule fluorescence enhancements produced by a Bowtie nanoantenna,” Nat. Photonics 3, 654–657 (2009).
[CrossRef]

J. A. Schuller and M. L. Brongersma, “General properties of dielectric optical antennas,” Opt. Express 17, 24084–24095 (2009).
[CrossRef]

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nano-scale slit arrays in a metallic film,” Nano Lett. 9, 235–238 (2009).
[CrossRef]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Planar metallic nanoscale slit lenses for angle compensation,” Appl. Phys. Lett. 95, 071112 (2009).
[CrossRef]

J. S. White, G. Veronis, Z. Yu, E. S. Barnard, A. Chandran, S. Fan, and M. L. Brongersma, “Extraordinary optical absorption through sub-wavelength slits,” Opt. Lett. 34, 686–688 (2009).
[CrossRef] [PubMed]

2008

A. Alu and N. Engheta, “Tuning the scattering response of optical nanoantennas with nanocircuit loads,” Nat. Photonics 2, 307–310 (2008).
[CrossRef]

Q. Min and R. Gordon, “Surface plasmon microcavity for resonant transmission through a slit in a gold film,” Opt. Express 16, 9708–9713 (2008).
[CrossRef] [PubMed]

M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute extinction cross-section of individual magnetic split-ring resonators,” Nat. Photonics 2, 614–617 (2008).
[CrossRef]

P. B. Catrysse and S. Fan, “Propagating plasmonic mode in nanoscale apertures and its implications for extraordinary transmission,” J. Nanophotonics 2, 021790 (2008).
[CrossRef]

L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D.-S. Ly-Gagnon, K. C. Saraswat, and D. A. B. Miller, “Nanometer-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat. Photonics 2, 226–229 (2008).
[CrossRef]

2007

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007).
[CrossRef] [PubMed]

O. Mata-Mendez and J. Avendaño, “Some properties of the optical resonances in a single subwavelength slit,” J. Opt. Soc. Am. A 24, 1687–1694 (2007).
[CrossRef]

R. E. Hamam, A. Karalis, J. D. Joannopoulos, and M. Soljacic, “Coupled-mode theory for general free-space resonant scattering of waves,” Phys. Rev. A 75, 053801 (2007).
[CrossRef]

2006

Z. C. Ruan and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: The role of localized waveguide resonances,” Phys. Rev. Lett. 96, 233901 (2006).
[CrossRef] [PubMed]

R. Gordon, “Light in a subwavelength slit in a metal: Propagation and reflection,” Phys. Rev. B 73, 153405 (2006).
[CrossRef]

O. Muskens, N. Del Fatti, F. Vallee, J. R. Huntzinger, P. Billaud, and M. Boyer, “Single metal nanoparticle absorption spectroscopy and optical characterization,” Appl. Phys. Lett. 88, 063109 (2006).
[CrossRef]

F. J. García-Vidal, L. Martín-Moreno, E. Moreno, L. K. S. Kumar, and R. Gordon, “Transmission of light through a single rectangular hole in a real metal,” Phys. Rev. B 74, 153411 (2006).
[CrossRef]

L. Tang, D. A. B. Miller, A. K. Okyay, J. A. Matteo, Y. Yuen, K. C. Saraswat, and L. Hesselink, “C-shaped nanoaperture-enhanced germanium photodetector,” Opt. Lett. 31, 1519–1521 (2006).
[CrossRef] [PubMed]

Z. Yu, G. Veronis, S. Fan, and M. L. Brongersma, “Design of midinfrared photodetectors enhanced by surface plasmons on grating structures,” Appl. Phys. Lett. 89, 151116 (2006).
[CrossRef]

2005

P. Muhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[CrossRef] [PubMed]

F. J. García-Vidal, E. Moreno, J. A. Porto, and L. Martín-Moreno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett. 95, 103901 (2005).
[CrossRef] [PubMed]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett. 95, 263902 (2005).
[CrossRef]

H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, “Beam manipulating by metallic nano-slits with variant widths,” Opt. Express 13, 6815–6820 (2005).
[CrossRef] [PubMed]

2004

Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett. 85, 642–644 (2004).
[CrossRef]

J. R. Suckling, A. P. Hibbins, M. J. Lockyear, T. W. Preist, J. R. Sambles, and C. R. Lawrence, “Finite conductance governs the resonance transmission of thin metal slits at microwave frequencies,” Phys. Rev. Lett. 92, 147401 (2004).
[CrossRef] [PubMed]

J. Bravo-Abad, L. Martín-Moreno, and F. J. García-Vidal, “Transmission properties of a single metallic slit: From the subwavelength regime to the geometrical-optics limit,” Phys. Rev. E 69, 026601 (2004).
[CrossRef]

A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett. 93, 127401 (2004).
[CrossRef] [PubMed]

S. Blair and A. Nahata, “Focus issue: Extraordinary light transmission through subwavelength structured surfaces—Introduction,” Opt. Express 12, 3618 (2004).
[CrossRef] [PubMed]

2003

K. L. Kelly, E. Coronado, L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: The influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[CrossRef]

X. Shi, L. Hesselink, and L. R. Thornton, “Ultrahigh light transmission through a C-shaped nanoaperture,” Opt. Lett. 28, 1320–1322 (2003).
[CrossRef] [PubMed]

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, “Multiple paths to enhance optical transmission through a single subwavelength slit,” Phys. Rev. Lett. 90, 213901 (2003).
[CrossRef] [PubMed]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef] [PubMed]

F. J. García-Vidal, L. Martín-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83, 4500–4502 (2003).
[CrossRef]

S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled mode theory for Fano resonances in optical resonators,” J. Opt. Soc. Am. A 20, 569–573 (2003).
[CrossRef]

K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: Resonators for local field enhancement,” J. Appl. Phys. 94, 4632–4642 (2003).
[CrossRef]

2002

F. Yang and J. R. Sambles, “Resonant transmission of microwaves through a narrow metallic slit,” Phys. Rev. Lett. 89, 063901 (2002).
[CrossRef] [PubMed]

F. J. García de Abajo, “Light transmission through a single cylindrical hole in a metallic film,” Opt. Express 10, 1475–1484 (2002).
[PubMed]

2001

1998

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

1962

Alu, A.

A. Alu and N. Engheta, “Tuning the scattering response of optical nanoantennas with nanocircuit loads,” Nat. Photonics 2, 307–310 (2008).
[CrossRef]

Arbouet, A.

A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett. 93, 127401 (2004).
[CrossRef] [PubMed]

Arnaud, L.

A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett. 93, 127401 (2004).
[CrossRef] [PubMed]

Avendaño, J.

Avlasevich, Y.

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, “Single-molecule fluorescence enhancements produced by a Bowtie nanoantenna,” Nat. Photonics 3, 654–657 (2009).
[CrossRef]

Barnard, E.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nano-scale slit arrays in a metallic film,” Nano Lett. 9, 235–238 (2009).
[CrossRef]

Barnard, E. S.

Bharadwaj, P.

Billaud, P.

O. Muskens, N. Del Fatti, F. Vallee, J. R. Huntzinger, P. Billaud, and M. Boyer, “Single metal nanoparticle absorption spectroscopy and optical characterization,” Appl. Phys. Lett. 88, 063109 (2006).
[CrossRef]

A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett. 93, 127401 (2004).
[CrossRef] [PubMed]

Blair, S.

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Boyer, M.

O. Muskens, N. Del Fatti, F. Vallee, J. R. Huntzinger, P. Billaud, and M. Boyer, “Single metal nanoparticle absorption spectroscopy and optical characterization,” Appl. Phys. Lett. 88, 063109 (2006).
[CrossRef]

Bravo-Abad, J.

J. Bravo-Abad, L. Martín-Moreno, and F. J. García-Vidal, “Transmission properties of a single metallic slit: From the subwavelength regime to the geometrical-optics limit,” Phys. Rev. E 69, 026601 (2004).
[CrossRef]

Brongersma, M. L.

J. A. Schuller and M. L. Brongersma, “General properties of dielectric optical antennas,” Opt. Express 17, 24084–24095 (2009).
[CrossRef]

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nano-scale slit arrays in a metallic film,” Nano Lett. 9, 235–238 (2009).
[CrossRef]

J. S. White, G. Veronis, Z. Yu, E. S. Barnard, A. Chandran, S. Fan, and M. L. Brongersma, “Extraordinary optical absorption through sub-wavelength slits,” Opt. Lett. 34, 686–688 (2009).
[CrossRef] [PubMed]

Z. Yu, G. Veronis, S. Fan, and M. L. Brongersma, “Design of midinfrared photodetectors enhanced by surface plasmons on grating structures,” Appl. Phys. Lett. 89, 151116 (2006).
[CrossRef]

Broyer, M.

A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett. 93, 127401 (2004).
[CrossRef] [PubMed]

Busch, K.

M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute extinction cross-section of individual magnetic split-ring resonators,” Nat. Photonics 2, 614–617 (2008).
[CrossRef]

Catrysse, P. B.

L. Verslegers, P. B. Catrysse, Z. Yu, W. Shin, Z. C. Ruan, and S. Fan, “Phase front design with metallic pillar arrays,” Opt. Lett. 35, 844–846 (2010).
[CrossRef] [PubMed]

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nano-scale slit arrays in a metallic film,” Nano Lett. 9, 235–238 (2009).
[CrossRef]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Planar metallic nanoscale slit lenses for angle compensation,” Appl. Phys. Lett. 95, 071112 (2009).
[CrossRef]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef] [PubMed]

P. B. Catrysse and S. Fan, “Propagating plasmonic mode in nanoscale apertures and its implications for extraordinary transmission,” J. Nanophotonics 2, 021790 (2008).
[CrossRef]

Chandran, A.

Christofilos, D.

A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett. 93, 127401 (2004).
[CrossRef] [PubMed]

Coronado, E.

K. L. Kelly, E. Coronado, L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: The influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[CrossRef]

Crozier, K. B.

K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: Resonators for local field enhancement,” J. Appl. Phys. 94, 4632–4642 (2003).
[CrossRef]

Degiron, A.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef] [PubMed]

Del Fatti, N.

O. Muskens, N. Del Fatti, F. Vallee, J. R. Huntzinger, P. Billaud, and M. Boyer, “Single metal nanoparticle absorption spectroscopy and optical characterization,” Appl. Phys. Lett. 88, 063109 (2006).
[CrossRef]

A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett. 93, 127401 (2004).
[CrossRef] [PubMed]

Deutsch, B.

Dong, X.

Drabowitch, S.

S. Drabowitch, A. Papiernik, H. Griffiths, J. Encinas, and B. L. Smith, Modern Antennas (Chapman & Hall, 1998).

Du, C.

Ebbesen, T. W.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007).
[CrossRef] [PubMed]

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, “Multiple paths to enhance optical transmission through a single subwavelength slit,” Phys. Rev. Lett. 90, 213901 (2003).
[CrossRef] [PubMed]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef] [PubMed]

F. J. García-Vidal, L. Martín-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83, 4500–4502 (2003).
[CrossRef]

T. Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, “Enhanced light transmission through a single subwavelength aperture,” Opt. Lett. 26, 1972–1974 (2001).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Eisler, H. J.

P. Muhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[CrossRef] [PubMed]

Encinas, J.

S. Drabowitch, A. Papiernik, H. Griffiths, J. Encinas, and B. L. Smith, Modern Antennas (Chapman & Hall, 1998).

Engheta, N.

A. Alu and N. Engheta, “Tuning the scattering response of optical nanoantennas with nanocircuit loads,” Nat. Photonics 2, 307–310 (2008).
[CrossRef]

Fan, S.

Z. Ruan and S. Fan, “Temporal coupled-mode theory for Fano resonance in light scattering by a single obstacle,” J. Phys. Chem. C 114, 7324–7329 (2010).
[CrossRef]

L. Verslegers, P. B. Catrysse, Z. Yu, W. Shin, Z. C. Ruan, and S. Fan, “Phase front design with metallic pillar arrays,” Opt. Lett. 35, 844–846 (2010).
[CrossRef] [PubMed]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef] [PubMed]

J. S. White, G. Veronis, Z. Yu, E. S. Barnard, A. Chandran, S. Fan, and M. L. Brongersma, “Extraordinary optical absorption through sub-wavelength slits,” Opt. Lett. 34, 686–688 (2009).
[CrossRef] [PubMed]

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nano-scale slit arrays in a metallic film,” Nano Lett. 9, 235–238 (2009).
[CrossRef]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Planar metallic nanoscale slit lenses for angle compensation,” Appl. Phys. Lett. 95, 071112 (2009).
[CrossRef]

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, “Single-molecule fluorescence enhancements produced by a Bowtie nanoantenna,” Nat. Photonics 3, 654–657 (2009).
[CrossRef]

P. B. Catrysse and S. Fan, “Propagating plasmonic mode in nanoscale apertures and its implications for extraordinary transmission,” J. Nanophotonics 2, 021790 (2008).
[CrossRef]

Z. Yu, G. Veronis, S. Fan, and M. L. Brongersma, “Design of midinfrared photodetectors enhanced by surface plasmons on grating structures,” Appl. Phys. Lett. 89, 151116 (2006).
[CrossRef]

S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled mode theory for Fano resonances in optical resonators,” J. Opt. Soc. Am. A 20, 569–573 (2003).
[CrossRef]

Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping for solar cells,” for Proc. Natl. Acad. Sci. (to be published).

G. Veronis and S. Fan, in Surface Plasmon Nanophotonics, M.L.Brongersma and P.G.Kik, eds. (Springer, 2007), p. 169.
[CrossRef]

Feth, N.

M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute extinction cross-section of individual magnetic split-ring resonators,” Nat. Photonics 2, 614–617 (2008).
[CrossRef]

Gao, H.

García de Abajo, F. J.

García-Vidal, F. J.

F. J. García-Vidal, L. Martín-Moreno, E. Moreno, L. K. S. Kumar, and R. Gordon, “Transmission of light through a single rectangular hole in a real metal,” Phys. Rev. B 74, 153411 (2006).
[CrossRef]

F. J. García-Vidal, E. Moreno, J. A. Porto, and L. Martín-Moreno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett. 95, 103901 (2005).
[CrossRef] [PubMed]

J. Bravo-Abad, L. Martín-Moreno, and F. J. García-Vidal, “Transmission properties of a single metallic slit: From the subwavelength regime to the geometrical-optics limit,” Phys. Rev. E 69, 026601 (2004).
[CrossRef]

F. J. García-Vidal, L. Martín-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83, 4500–4502 (2003).
[CrossRef]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef] [PubMed]

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, “Multiple paths to enhance optical transmission through a single subwavelength slit,” Phys. Rev. Lett. 90, 213901 (2003).
[CrossRef] [PubMed]

Genet, C.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007).
[CrossRef] [PubMed]

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Gordon, R.

Q. Min and R. Gordon, “Surface plasmon microcavity for resonant transmission through a slit in a gold film,” Opt. Express 16, 9708–9713 (2008).
[CrossRef] [PubMed]

R. Gordon, “Light in a subwavelength slit in a metal: Propagation and reflection,” Phys. Rev. B 73, 153405 (2006).
[CrossRef]

F. J. García-Vidal, L. Martín-Moreno, E. Moreno, L. K. S. Kumar, and R. Gordon, “Transmission of light through a single rectangular hole in a real metal,” Phys. Rev. B 74, 153411 (2006).
[CrossRef]

Griffiths, H.

S. Drabowitch, A. Papiernik, H. Griffiths, J. Encinas, and B. L. Smith, Modern Antennas (Chapman & Hall, 1998).

Hamam, R. E.

R. E. Hamam, A. Karalis, J. D. Joannopoulos, and M. Soljacic, “Coupled-mode theory for general free-space resonant scattering of waves,” Phys. Rev. A 75, 053801 (2007).
[CrossRef]

Haus, H. A.

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

Hecht, B.

P. Muhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[CrossRef] [PubMed]

Hesselink, L.

Hibbins, A. P.

J. R. Suckling, A. P. Hibbins, M. J. Lockyear, T. W. Preist, J. R. Sambles, and C. R. Lawrence, “Finite conductance governs the resonance transmission of thin metal slits at microwave frequencies,” Phys. Rev. Lett. 92, 147401 (2004).
[CrossRef] [PubMed]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Hugonin, J. P.

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett. 95, 263902 (2005).
[CrossRef]

Huntzinger, J. R.

O. Muskens, N. Del Fatti, F. Vallee, J. R. Huntzinger, P. Billaud, and M. Boyer, “Single metal nanoparticle absorption spectroscopy and optical characterization,” Appl. Phys. Lett. 88, 063109 (2006).
[CrossRef]

A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett. 93, 127401 (2004).
[CrossRef] [PubMed]

Husnik, M.

M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute extinction cross-section of individual magnetic split-ring resonators,” Nat. Photonics 2, 614–617 (2008).
[CrossRef]

Joannopoulos, J. D.

R. E. Hamam, A. Karalis, J. D. Joannopoulos, and M. Soljacic, “Coupled-mode theory for general free-space resonant scattering of waves,” Phys. Rev. A 75, 053801 (2007).
[CrossRef]

S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled mode theory for Fano resonances in optical resonators,” J. Opt. Soc. Am. A 20, 569–573 (2003).
[CrossRef]

Karalis, A.

R. E. Hamam, A. Karalis, J. D. Joannopoulos, and M. Soljacic, “Coupled-mode theory for general free-space resonant scattering of waves,” Phys. Rev. A 75, 053801 (2007).
[CrossRef]

Keller, J. B.

Kelly, K. L.

K. L. Kelly, E. Coronado, L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: The influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[CrossRef]

Kim, H. K.

Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett. 85, 642–644 (2004).
[CrossRef]

Kinkhabwala, A.

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, “Single-molecule fluorescence enhancements produced by a Bowtie nanoantenna,” Nat. Photonics 3, 654–657 (2009).
[CrossRef]

Kino, G. S.

K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: Resonators for local field enhancement,” J. Appl. Phys. 94, 4632–4642 (2003).
[CrossRef]

Klein, M. W.

M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute extinction cross-section of individual magnetic split-ring resonators,” Nat. Photonics 2, 614–617 (2008).
[CrossRef]

Kocabas, S. E.

L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D.-S. Ly-Gagnon, K. C. Saraswat, and D. A. B. Miller, “Nanometer-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat. Photonics 2, 226–229 (2008).
[CrossRef]

König, M.

M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute extinction cross-section of individual magnetic split-ring resonators,” Nat. Photonics 2, 614–617 (2008).
[CrossRef]

Kumar, L. K. S.

F. J. García-Vidal, L. Martín-Moreno, E. Moreno, L. K. S. Kumar, and R. Gordon, “Transmission of light through a single rectangular hole in a real metal,” Phys. Rev. B 74, 153411 (2006).
[CrossRef]

Lalanne, P.

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett. 95, 263902 (2005).
[CrossRef]

Latif, S.

L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D.-S. Ly-Gagnon, K. C. Saraswat, and D. A. B. Miller, “Nanometer-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat. Photonics 2, 226–229 (2008).
[CrossRef]

Lawrence, C. R.

J. R. Suckling, A. P. Hibbins, M. J. Lockyear, T. W. Preist, J. R. Sambles, and C. R. Lawrence, “Finite conductance governs the resonance transmission of thin metal slits at microwave frequencies,” Phys. Rev. Lett. 92, 147401 (2004).
[CrossRef] [PubMed]

Lezec, H. J.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef] [PubMed]

F. J. García-Vidal, L. Martín-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83, 4500–4502 (2003).
[CrossRef]

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, “Multiple paths to enhance optical transmission through a single subwavelength slit,” Phys. Rev. Lett. 90, 213901 (2003).
[CrossRef] [PubMed]

T. Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, “Enhanced light transmission through a single subwavelength aperture,” Opt. Lett. 26, 1972–1974 (2001).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Linden, S.

M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute extinction cross-section of individual magnetic split-ring resonators,” Nat. Photonics 2, 614–617 (2008).
[CrossRef]

Linke, R. A.

Lockyear, M. J.

J. R. Suckling, A. P. Hibbins, M. J. Lockyear, T. W. Preist, J. R. Sambles, and C. R. Lawrence, “Finite conductance governs the resonance transmission of thin metal slits at microwave frequencies,” Phys. Rev. Lett. 92, 147401 (2004).
[CrossRef] [PubMed]

Luo, X.

Ly-Gagnon, D. -S.

L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D.-S. Ly-Gagnon, K. C. Saraswat, and D. A. B. Miller, “Nanometer-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat. Photonics 2, 226–229 (2008).
[CrossRef]

Martin, O. J. F.

P. Muhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[CrossRef] [PubMed]

Martín-Moreno, L.

F. J. García-Vidal, L. Martín-Moreno, E. Moreno, L. K. S. Kumar, and R. Gordon, “Transmission of light through a single rectangular hole in a real metal,” Phys. Rev. B 74, 153411 (2006).
[CrossRef]

F. J. García-Vidal, E. Moreno, J. A. Porto, and L. Martín-Moreno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett. 95, 103901 (2005).
[CrossRef] [PubMed]

J. Bravo-Abad, L. Martín-Moreno, and F. J. García-Vidal, “Transmission properties of a single metallic slit: From the subwavelength regime to the geometrical-optics limit,” Phys. Rev. E 69, 026601 (2004).
[CrossRef]

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, “Multiple paths to enhance optical transmission through a single subwavelength slit,” Phys. Rev. Lett. 90, 213901 (2003).
[CrossRef] [PubMed]

F. J. García-Vidal, L. Martín-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83, 4500–4502 (2003).
[CrossRef]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef] [PubMed]

Mata-Mendez, O.

Matteo, J. A.

Miller, D. A. B.

L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D.-S. Ly-Gagnon, K. C. Saraswat, and D. A. B. Miller, “Nanometer-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat. Photonics 2, 226–229 (2008).
[CrossRef]

L. Tang, D. A. B. Miller, A. K. Okyay, J. A. Matteo, Y. Yuen, K. C. Saraswat, and L. Hesselink, “C-shaped nanoaperture-enhanced germanium photodetector,” Opt. Lett. 31, 1519–1521 (2006).
[CrossRef] [PubMed]

Min, Q.

Moerner, W. E.

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, “Single-molecule fluorescence enhancements produced by a Bowtie nanoantenna,” Nat. Photonics 3, 654–657 (2009).
[CrossRef]

Moreno, E.

F. J. García-Vidal, L. Martín-Moreno, E. Moreno, L. K. S. Kumar, and R. Gordon, “Transmission of light through a single rectangular hole in a real metal,” Phys. Rev. B 74, 153411 (2006).
[CrossRef]

F. J. García-Vidal, E. Moreno, J. A. Porto, and L. Martín-Moreno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett. 95, 103901 (2005).
[CrossRef] [PubMed]

Muhlschlegel, P.

P. Muhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[CrossRef] [PubMed]

Mullen, K.

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, “Single-molecule fluorescence enhancements produced by a Bowtie nanoantenna,” Nat. Photonics 3, 654–657 (2009).
[CrossRef]

Muskens, O.

O. Muskens, N. Del Fatti, F. Vallee, J. R. Huntzinger, P. Billaud, and M. Boyer, “Single metal nanoparticle absorption spectroscopy and optical characterization,” Appl. Phys. Lett. 88, 063109 (2006).
[CrossRef]

Nahata, A.

Niegemann, J.

M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute extinction cross-section of individual magnetic split-ring resonators,” Nat. Photonics 2, 614–617 (2008).
[CrossRef]

Novotny, L.

Okyay, A. K.

L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D.-S. Ly-Gagnon, K. C. Saraswat, and D. A. B. Miller, “Nanometer-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat. Photonics 2, 226–229 (2008).
[CrossRef]

L. Tang, D. A. B. Miller, A. K. Okyay, J. A. Matteo, Y. Yuen, K. C. Saraswat, and L. Hesselink, “C-shaped nanoaperture-enhanced germanium photodetector,” Opt. Lett. 31, 1519–1521 (2006).
[CrossRef] [PubMed]

Papiernik, A.

S. Drabowitch, A. Papiernik, H. Griffiths, J. Encinas, and B. L. Smith, Modern Antennas (Chapman & Hall, 1998).

Pellerin, K. M.

Pohl, D. W.

P. Muhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[CrossRef] [PubMed]

Porto, J. A.

F. J. García-Vidal, E. Moreno, J. A. Porto, and L. Martín-Moreno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett. 95, 103901 (2005).
[CrossRef] [PubMed]

Preist, T. W.

J. R. Suckling, A. P. Hibbins, M. J. Lockyear, T. W. Preist, J. R. Sambles, and C. R. Lawrence, “Finite conductance governs the resonance transmission of thin metal slits at microwave frequencies,” Phys. Rev. Lett. 92, 147401 (2004).
[CrossRef] [PubMed]

Qiu, M.

Z. C. Ruan and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: The role of localized waveguide resonances,” Phys. Rev. Lett. 96, 233901 (2006).
[CrossRef] [PubMed]

Quate, C. F.

K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: Resonators for local field enhancement,” J. Appl. Phys. 94, 4632–4642 (2003).
[CrossRef]

Raman, A.

Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping for solar cells,” for Proc. Natl. Acad. Sci. (to be published).

Rodier, J. C.

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett. 95, 263902 (2005).
[CrossRef]

Ruan, Z.

Z. Ruan and S. Fan, “Temporal coupled-mode theory for Fano resonance in light scattering by a single obstacle,” J. Phys. Chem. C 114, 7324–7329 (2010).
[CrossRef]

Ruan, Z. C.

L. Verslegers, P. B. Catrysse, Z. Yu, W. Shin, Z. C. Ruan, and S. Fan, “Phase front design with metallic pillar arrays,” Opt. Lett. 35, 844–846 (2010).
[CrossRef] [PubMed]

Z. C. Ruan and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: The role of localized waveguide resonances,” Phys. Rev. Lett. 96, 233901 (2006).
[CrossRef] [PubMed]

Sambles, J. R.

J. R. Suckling, A. P. Hibbins, M. J. Lockyear, T. W. Preist, J. R. Sambles, and C. R. Lawrence, “Finite conductance governs the resonance transmission of thin metal slits at microwave frequencies,” Phys. Rev. Lett. 92, 147401 (2004).
[CrossRef] [PubMed]

F. Yang and J. R. Sambles, “Resonant transmission of microwaves through a narrow metallic slit,” Phys. Rev. Lett. 89, 063901 (2002).
[CrossRef] [PubMed]

Saraswat, K. C.

L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D.-S. Ly-Gagnon, K. C. Saraswat, and D. A. B. Miller, “Nanometer-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat. Photonics 2, 226–229 (2008).
[CrossRef]

L. Tang, D. A. B. Miller, A. K. Okyay, J. A. Matteo, Y. Yuen, K. C. Saraswat, and L. Hesselink, “C-shaped nanoaperture-enhanced germanium photodetector,” Opt. Lett. 31, 1519–1521 (2006).
[CrossRef] [PubMed]

Schatz, G. C.

K. L. Kelly, E. Coronado, L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: The influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[CrossRef]

Schuller, J. A.

Shi, H.

Shi, X.

Shin, W.

Smith, B. L.

S. Drabowitch, A. Papiernik, H. Griffiths, J. Encinas, and B. L. Smith, Modern Antennas (Chapman & Hall, 1998).

Soljacic, M.

R. E. Hamam, A. Karalis, J. D. Joannopoulos, and M. Soljacic, “Coupled-mode theory for general free-space resonant scattering of waves,” Phys. Rev. A 75, 053801 (2007).
[CrossRef]

Stutzman, W. L.

W. L. Stutzman and G. A. Thiele, Antenna Theory and Design, 2nd ed. (Wiley, 1998).

Suckling, J. R.

J. R. Suckling, A. P. Hibbins, M. J. Lockyear, T. W. Preist, J. R. Sambles, and C. R. Lawrence, “Finite conductance governs the resonance transmission of thin metal slits at microwave frequencies,” Phys. Rev. Lett. 92, 147401 (2004).
[CrossRef] [PubMed]

Suh, W.

Sun, Z.

Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett. 85, 642–644 (2004).
[CrossRef]

Sundaramurthy, A.

K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: Resonators for local field enhancement,” J. Appl. Phys. 94, 4632–4642 (2003).
[CrossRef]

Takakura, Y.

Y. Takakura, “Optical resonance in a narrow slit in a thick metallic screen,” Phys. Rev. Lett. 86, 5601–5603 (2001).
[CrossRef] [PubMed]

Tang, L.

L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D.-S. Ly-Gagnon, K. C. Saraswat, and D. A. B. Miller, “Nanometer-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat. Photonics 2, 226–229 (2008).
[CrossRef]

L. Tang, D. A. B. Miller, A. K. Okyay, J. A. Matteo, Y. Yuen, K. C. Saraswat, and L. Hesselink, “C-shaped nanoaperture-enhanced germanium photodetector,” Opt. Lett. 31, 1519–1521 (2006).
[CrossRef] [PubMed]

Thiele, G. A.

W. L. Stutzman and G. A. Thiele, Antenna Theory and Design, 2nd ed. (Wiley, 1998).

Thio, T.

T. Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, “Enhanced light transmission through a single subwavelength aperture,” Opt. Lett. 26, 1972–1974 (2001).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Thornton, L. R.

Vallee, F.

O. Muskens, N. Del Fatti, F. Vallee, J. R. Huntzinger, P. Billaud, and M. Boyer, “Single metal nanoparticle absorption spectroscopy and optical characterization,” Appl. Phys. Lett. 88, 063109 (2006).
[CrossRef]

Vallée, F.

A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett. 93, 127401 (2004).
[CrossRef] [PubMed]

Veronis, G.

J. S. White, G. Veronis, Z. Yu, E. S. Barnard, A. Chandran, S. Fan, and M. L. Brongersma, “Extraordinary optical absorption through sub-wavelength slits,” Opt. Lett. 34, 686–688 (2009).
[CrossRef] [PubMed]

Z. Yu, G. Veronis, S. Fan, and M. L. Brongersma, “Design of midinfrared photodetectors enhanced by surface plasmons on grating structures,” Appl. Phys. Lett. 89, 151116 (2006).
[CrossRef]

G. Veronis and S. Fan, in Surface Plasmon Nanophotonics, M.L.Brongersma and P.G.Kik, eds. (Springer, 2007), p. 169.
[CrossRef]

Verslegers, L.

L. Verslegers, P. B. Catrysse, Z. Yu, W. Shin, Z. C. Ruan, and S. Fan, “Phase front design with metallic pillar arrays,” Opt. Lett. 35, 844–846 (2010).
[CrossRef] [PubMed]

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nano-scale slit arrays in a metallic film,” Nano Lett. 9, 235–238 (2009).
[CrossRef]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Planar metallic nanoscale slit lenses for angle compensation,” Appl. Phys. Lett. 95, 071112 (2009).
[CrossRef]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef] [PubMed]

Wang, C.

Wegener, M.

M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute extinction cross-section of individual magnetic split-ring resonators,” Nat. Photonics 2, 614–617 (2008).
[CrossRef]

White, J. S.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nano-scale slit arrays in a metallic film,” Nano Lett. 9, 235–238 (2009).
[CrossRef]

J. S. White, G. Veronis, Z. Yu, E. S. Barnard, A. Chandran, S. Fan, and M. L. Brongersma, “Extraordinary optical absorption through sub-wavelength slits,” Opt. Lett. 34, 686–688 (2009).
[CrossRef] [PubMed]

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Yang, F.

F. Yang and J. R. Sambles, “Resonant transmission of microwaves through a narrow metallic slit,” Phys. Rev. Lett. 89, 063901 (2002).
[CrossRef] [PubMed]

Yu, Z.

L. Verslegers, P. B. Catrysse, Z. Yu, W. Shin, Z. C. Ruan, and S. Fan, “Phase front design with metallic pillar arrays,” Opt. Lett. 35, 844–846 (2010).
[CrossRef] [PubMed]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Planar metallic nanoscale slit lenses for angle compensation,” Appl. Phys. Lett. 95, 071112 (2009).
[CrossRef]

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nano-scale slit arrays in a metallic film,” Nano Lett. 9, 235–238 (2009).
[CrossRef]

J. S. White, G. Veronis, Z. Yu, E. S. Barnard, A. Chandran, S. Fan, and M. L. Brongersma, “Extraordinary optical absorption through sub-wavelength slits,” Opt. Lett. 34, 686–688 (2009).
[CrossRef] [PubMed]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef] [PubMed]

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, “Single-molecule fluorescence enhancements produced by a Bowtie nanoantenna,” Nat. Photonics 3, 654–657 (2009).
[CrossRef]

Z. Yu, G. Veronis, S. Fan, and M. L. Brongersma, “Design of midinfrared photodetectors enhanced by surface plasmons on grating structures,” Appl. Phys. Lett. 89, 151116 (2006).
[CrossRef]

Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping for solar cells,” for Proc. Natl. Acad. Sci. (to be published).

Yuen, Y.

Zhao, L.

K. L. Kelly, E. Coronado, L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: The influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[CrossRef]

Adv. Opt. Photon.

Appl. Phys. Lett.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Planar metallic nanoscale slit lenses for angle compensation,” Appl. Phys. Lett. 95, 071112 (2009).
[CrossRef]

O. Muskens, N. Del Fatti, F. Vallee, J. R. Huntzinger, P. Billaud, and M. Boyer, “Single metal nanoparticle absorption spectroscopy and optical characterization,” Appl. Phys. Lett. 88, 063109 (2006).
[CrossRef]

F. J. García-Vidal, L. Martín-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83, 4500–4502 (2003).
[CrossRef]

Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett. 85, 642–644 (2004).
[CrossRef]

Z. Yu, G. Veronis, S. Fan, and M. L. Brongersma, “Design of midinfrared photodetectors enhanced by surface plasmons on grating structures,” Appl. Phys. Lett. 89, 151116 (2006).
[CrossRef]

J. Appl. Phys.

K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: Resonators for local field enhancement,” J. Appl. Phys. 94, 4632–4642 (2003).
[CrossRef]

J. Nanophotonics

P. B. Catrysse and S. Fan, “Propagating plasmonic mode in nanoscale apertures and its implications for extraordinary transmission,” J. Nanophotonics 2, 021790 (2008).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Phys. Chem. B

K. L. Kelly, E. Coronado, L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: The influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[CrossRef]

J. Phys. Chem. C

Z. Ruan and S. Fan, “Temporal coupled-mode theory for Fano resonance in light scattering by a single obstacle,” J. Phys. Chem. C 114, 7324–7329 (2010).
[CrossRef]

Nano Lett.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nano-scale slit arrays in a metallic film,” Nano Lett. 9, 235–238 (2009).
[CrossRef]

Nat. Photonics

M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute extinction cross-section of individual magnetic split-ring resonators,” Nat. Photonics 2, 614–617 (2008).
[CrossRef]

L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D.-S. Ly-Gagnon, K. C. Saraswat, and D. A. B. Miller, “Nanometer-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat. Photonics 2, 226–229 (2008).
[CrossRef]

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, “Single-molecule fluorescence enhancements produced by a Bowtie nanoantenna,” Nat. Photonics 3, 654–657 (2009).
[CrossRef]

A. Alu and N. Engheta, “Tuning the scattering response of optical nanoantennas with nanocircuit loads,” Nat. Photonics 2, 307–310 (2008).
[CrossRef]

Nature

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Rev. A

R. E. Hamam, A. Karalis, J. D. Joannopoulos, and M. Soljacic, “Coupled-mode theory for general free-space resonant scattering of waves,” Phys. Rev. A 75, 053801 (2007).
[CrossRef]

Phys. Rev. B

R. Gordon, “Light in a subwavelength slit in a metal: Propagation and reflection,” Phys. Rev. B 73, 153405 (2006).
[CrossRef]

F. J. García-Vidal, L. Martín-Moreno, E. Moreno, L. K. S. Kumar, and R. Gordon, “Transmission of light through a single rectangular hole in a real metal,” Phys. Rev. B 74, 153411 (2006).
[CrossRef]

Phys. Rev. E

J. Bravo-Abad, L. Martín-Moreno, and F. J. García-Vidal, “Transmission properties of a single metallic slit: From the subwavelength regime to the geometrical-optics limit,” Phys. Rev. E 69, 026601 (2004).
[CrossRef]

Phys. Rev. Lett.

F. J. García-Vidal, E. Moreno, J. A. Porto, and L. Martín-Moreno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett. 95, 103901 (2005).
[CrossRef] [PubMed]

A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett. 93, 127401 (2004).
[CrossRef] [PubMed]

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, “Multiple paths to enhance optical transmission through a single subwavelength slit,” Phys. Rev. Lett. 90, 213901 (2003).
[CrossRef] [PubMed]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett. 95, 263902 (2005).
[CrossRef]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef] [PubMed]

Z. C. Ruan and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: The role of localized waveguide resonances,” Phys. Rev. Lett. 96, 233901 (2006).
[CrossRef] [PubMed]

F. Yang and J. R. Sambles, “Resonant transmission of microwaves through a narrow metallic slit,” Phys. Rev. Lett. 89, 063901 (2002).
[CrossRef] [PubMed]

Y. Takakura, “Optical resonance in a narrow slit in a thick metallic screen,” Phys. Rev. Lett. 86, 5601–5603 (2001).
[CrossRef] [PubMed]

J. R. Suckling, A. P. Hibbins, M. J. Lockyear, T. W. Preist, J. R. Sambles, and C. R. Lawrence, “Finite conductance governs the resonance transmission of thin metal slits at microwave frequencies,” Phys. Rev. Lett. 92, 147401 (2004).
[CrossRef] [PubMed]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef] [PubMed]

Science

P. Muhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[CrossRef] [PubMed]

Other

Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping for solar cells,” for Proc. Natl. Acad. Sci. (to be published).

G. Veronis and S. Fan, in Surface Plasmon Nanophotonics, M.L.Brongersma and P.G.Kik, eds. (Springer, 2007), p. 169.
[CrossRef]

The directivity, as we defined it, is analogous to the directivity in antenna theory, defined as the ratio of U(θ), the radiation intensity in a certain direction, to Uave, the average radiation intensity: D(θ)=U(θ)/Uave (two-dimensional case).

The factor G is called the (power) gain in antenna theory . We do not adopt this name since in the optics literature gain is commonly related to amplification, which is not the case here.

D.R.Lide, ed., CRC Handbook of Chemistry and Physics, 88th ed. (CRC, 2007).

W. L. Stutzman and G. A. Thiele, Antenna Theory and Design, 2nd ed. (Wiley, 1998).

S. Drabowitch, A. Papiernik, H. Griffiths, J. Encinas, and B. L. Smith, Modern Antennas (Chapman & Hall, 1998).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

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Figures (8)

Fig. 1
Fig. 1

CMT of a slit in an optically thick metallic film. The slit couples with free-space channels above (with amplitudes s T , n + and s T , n ) and below (with amplitudes s B , n + and s B , n ) the film, as well as with the surface plasmon channels (with amplitudes s T , s p + , s T , s p , s B , s p + , and s B , s p ). The channels are shown as discrete modes.

Fig. 2
Fig. 2

Channels in k space for a slit in a metallic film with periodic boundary condition (PBC). k x and k z are the spatial frequencies in the x and z directions. The CMT explicitly makes the conversion from discrete modes to a continuous spatial spectrum by assuming a periodic boundary condition and letting the spatial period L, and consequently N, go to infinity at the end of the calculation. Under this assumption, channels are equally spaced in spatial frequency k x , but not in angle.

Fig. 3
Fig. 3

Single slit in a PEC. (a) The theoretical normalized transmission cross section spectrum (green curve) and from FDFD simulations (blue dots). The straight red line indicates the maximal transmission cross section of an isotropic radiator. (b) Contour plot of the magnetic field intensity for the single slit excited at 1.176 μ m .

Fig. 4
Fig. 4

Slit with surface corrugation. (a) The theoretical normalized transmission cross section spectrum (green curve) and from FDFD simulations (blue dots). The straight red line shows the maximal transmission cross section of an isotropic radiator. (b) Contour plot of the magnetic field intensity for the structure excited at 1.168 μ m shows directional emission.

Fig. 5
Fig. 5

Slit with wider slits at its ends. (a) The theoretical normalized transmission cross section spectrum (green curve) and from FDFD simulations (blue dots). The straight red line shows the maximal transmission cross section of an isotropic radiator. (b) Contour plot of the magnetic field intensity for the structure excited at 2.370 μ m shows directional emission.

Fig. 6
Fig. 6

Single slit in real metal (gold). (a) The theoretical normalized transmission cross section spectrum (green curve) and from FDFD simulations (blue dots). The straight red line indicates the maximal transmission cross section of an isotropic radiator. (b) Contour plot of the magnetic field intensity for the single slit excited at 0.676 μ m shows strong excitation of the surface plasmon.

Fig. 7
Fig. 7

Single slit in a PEC, containing an absorbing material. The theoretical normalized transmission cross section spectrum (green curve) and from FDFD simulations (blue dots). The straight red line indicates the maximal transmission cross section of an isotropic radiator.

Fig. 8
Fig. 8

Absorption cross section of the slit. The theoretical normalized absorption cross section (green curve) and from FDFD simulations (blue dots) for non-critical coupling and for critical coupling (orange curve with purple triangles). The straight red line indicates the maximal absorption cross section of an isotropic radiator.

Equations (34)

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| n | N ω 0 L 2 π c = L λ 0 ,
d A d t + ( i ω 0 + n = N N γ T , n + n = N N γ B , n + γ T , s p + γ B , s p + γ a ) A = 2 γ T , 0 s T , 0 + ,
s B , n = 2 γ B , n A ,
s B , s p = 2 γ B , s p A .
T ( ω ) = n = N N | s B , n | 2 + | s B , s p | 2 | s T , 0 + | 2 = 2 γ T , 0 ( 2 n = N N γ B , n + 2 γ B , s p ) ( ω ω 0 ) 2 + ( n = N N γ T , n + n = N N γ B , n + γ T , s p + γ B , s p + γ a ) 2 = 2 γ 0 ( 2 n = N N γ n + 2 γ s p ) ( ω ω 0 ) 2 + ( 2 n = N N γ n + 2 γ s p + γ a ) 2 .
T ( ω , θ m ) = 2 γ m ( 2 n = N N γ n + 2 γ s p ) ( ω ω 0 ) 2 + ( 2 n = N N γ n + 2 γ s p + γ a ) 2 .
σ T ( ω ) = n = N N | s B , n | 2 + | s B , s p | 2 | s T , 0 + | 2 / L = T ( ω ) L ,
σ T ( ω , θ m ) = n = N N | s B , n | 2 + | s B , s p | 2 | s T , m + | 2 / ( L   cos   θ m ) = T ( ω , θ m ) L   cos   θ m .
γ n = γ 0 cos   θ n .
n = N N γ n = γ 0 n = N N 1 cos   θ n = N π γ 0 .
σ T , isotropic ( ω , θ m ) = 2 γ m L   cos   θ m ( 2 n = N N γ n ) ( ω ω 0 ) 2 + ( 2 n = N N γ n ) 2 = 2 γ 0 L ( 2 n = N N γ n ) ( ω ω 0 ) 2 + ( 2 n = N N γ n ) 2 = λ 0 π 1 4 Q 2 ( ω ω 0 ω 0 ) 2 + 1 4 Q 2 ,
Q = ω 0 4 n = N N γ n .
σ T , isotropic ( ω 0 , θ m ) = λ 0 π
σ T ( ω ) = i λ 0 , i π 1 4 Q i 2 ( ω ω 0 , i ω 0 , i ) 2 + 1 4 Q i 2 = i σ T , i ( ω ) .
D = γ 0 N π n = N N γ n .
σ T ( ω ) = D λ 0 π 1 4 Q 2 ( ω ω 0 ω 0 ) 2 + 1 4 Q 2 = D σ T , isotropic ( ω ) .
D ( θ m ) = γ m N π   cos ( θ m ) n = N N γ n ,
σ T ( ω , θ m ) = T ( ω , θ m ) L   cos ( θ m ) = 2 γ m L   cos ( θ m ) ( 2 n = N N γ n ) ( ω ω 0 ) 2 + ( 2 n = N N γ n ) 2 = D ( θ m ) λ 0 π 1 4 Q 2 ( ω ω 0 ω 0 ) 2 + 1 4 Q 2 = D ( θ m ) σ T , isotropic ( ω ) .
π / 2 π / 2 σ T ( ω 0 , θ ) d θ = m = N N σ T ( ω 0 , θ m ) 1 N   cos   θ m = λ 0 π m = N N D ( θ m ) 1 N   cos   θ m = λ 0 π m = N N γ m π n = N N γ n = λ 0 .
σ T ( ω ) = 2 γ 0 L ( 2 n = N N γ n + 2 γ s p ) ( ω ω 0 ) 2 + ( 2 n = N N γ n + 2 γ s p ) 2 = 2 γ 0 L 2 n = N N γ n + 2 γ s p ( 2 n = N N γ n + 2 γ s p ) 2 ( ω ω 0 ) 2 + ( 2 n = N N γ n + 2 γ s p ) 2 = D λ 0 π 2 n = N N γ n 2 n = N N γ n + 2 γ s p ( 2 n = N N γ n + 2 γ s p ) 2 ( ω ω 0 ) 2 + ( 2 n = N N γ n + 2 γ s p ) 2 = G λ 0 π 1 4 Q 2 ( ω ω 0 ω 0 ) 2 + 1 4 Q 2 = G σ T , isotropic ( ω ) ,
G = 2 n = N N γ n 2 n = N N γ n + 2 γ s p D = e r D ,
Q = ω 0 4 ( n = N N γ n + γ s p ) .
σ T ( ω ) = 2 γ 0 L ( 2 n = N N γ n ) ( ω ω 0 ) 2 + ( 2 n = N N γ n + γ a ) 2 = D λ 0 π ( 2 n = N N γ n ) 2 ( ω ω 0 ) 2 + ( 2 n = N N γ n + γ a ) 2 .
γ a = c n i k 0 n r ,
σ A ( ω ) = P A ( ω ) F inc ( ω ) ,
σ A ( ω ) = 4 γ a γ 0 L ( ω ω 0 ) 2 + ( n = N N γ n + γ a ) 2 = D λ 0 π 2 γ a ( 2 n = N N γ n ) ( ω ω 0 ) 2 + ( n = N N γ n + γ a ) 2 .
n = N N γ n = γ a ,
σ A ( ω 0 ) = D λ 0 π .
T ( ω ) = m , n = N N | s m , n | 2 | s 0 , 0 + | 2 = 2 γ 0 , 0 ( 2 m , n = N N γ m , n ) ( ω ω 0 ) 2 + ( 2 m , n = N N γ m , n ) 2 ,
m , n = N N γ m , n = γ 0 , 0 m , n = N N 1 cos   θ n   cos   θ m = 2 N 2 π γ 0 , 0 ,
σ T , isotropic ( ω ) = 2 γ 0 , 0 L 2 ( 2 m , n = N N γ m , n ) ( ω ω 0 ) 2 + ( 2 m , n = N N γ m , n ) 2 = L 2 2 N 2 π ( 2 m , n = N N γ m , n ) 2 ( ω ω 0 ) 2 + ( 2 m , n = N N γ m , n ) 2 = λ 0 2 2 π 1 4 Q 2 ( ω ω 0 ω 0 ) 2 + 1 4 Q 2 .
σ T , isotropic ( ω 0 ) = λ 0 2 2 π .
exp ( 2 γ a n r Δ c ) = exp ( 2 n i k 0 Δ ) ,
γ a = c n i k 0 n r .

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