Abstract

It is demonstrated that multiple directional beaming effect can be realized by a metallic subwavelength slit surrounded by finite number of grooves based on mode expansion method. Each of the directional beaming is formed by superimposing two diffraction orders of spoof surface plasmon excited on the two corrugated sides of the slit. This delivers high contrast and considerably uniform energy distribution for the beaming directions.

© 2008 Optical Society of America

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  1. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 820 (2002).
    [CrossRef] [PubMed]
  2. 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]
  3. 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]
  4. M. J. Lockyear, A. P. Hibbins, J. Roy Sambles and C. R. Lawrence, "Surface-topography-induced enhanced transmission and directivity of microwave radiation through a subwavelength circular metal aperture." Appl. Phys. Lett. 84, 2040 (2004).
    [CrossRef]
  5. C. Wang, C. Du, and X. Luo, "Refining the model of light diffraction from a subwavelength slit surrounded by grooves on a metallic film," Phys. Rev. B 74, 245403 (2006).
    [CrossRef]
  6. C. Wang, C. Du, Y. Lv, and X. Luo, "Surface electromagnetic wave excitation and diffraction by subwavelength slit with periodically patterned metallic grooves," Opt. Express 14, 5671 (2006).
    [CrossRef] [PubMed]
  7. 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 (2003).
    [CrossRef]
  8. H. Shi, C. Du, and X. Luo, "Focal length modulation based on a metallic slit surrounded with grooves in curved depths," Appl. Phys. Lett. 91, 093111 (2007).
    [CrossRef]
  9. C. Huang, C. Du, and X. Luo, "A waveguide slit array antenna fabricated with subwavelength periodic grooves," Appl. Phys. Lett. 91, 143512 (2007).
    [CrossRef]
  10. W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Science 424, 824 (2003).
  11. O. T. A. Janssen, H. P. Urbach, and G. W. Hooft, "Giant optical transmission of a subwavelength slit optimized using the magnetic field phase," Phys. Rev. Lett. 99, 043902 (2007)
    [CrossRef] [PubMed]
  12. L.-B. Yu, D.-Z. Lin, Y.-C. Chen, Y.-C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, "Physical origin of directional beaming emitted from a subwavelength slit," Phys. Rev. B 71, 041405 (2005).
    [CrossRef]
  13. F. J. García-Vidal, L. Martín-Moreno, and J. B. Pendry, "Surface with holes in them: new plasmatic metamaterials," J. Opt. A 7, S91 (2005).

2007 (3)

H. Shi, C. Du, and X. Luo, "Focal length modulation based on a metallic slit surrounded with grooves in curved depths," Appl. Phys. Lett. 91, 093111 (2007).
[CrossRef]

C. Huang, C. Du, and X. Luo, "A waveguide slit array antenna fabricated with subwavelength periodic grooves," Appl. Phys. Lett. 91, 143512 (2007).
[CrossRef]

O. T. A. Janssen, H. P. Urbach, and G. W. Hooft, "Giant optical transmission of a subwavelength slit optimized using the magnetic field phase," Phys. Rev. Lett. 99, 043902 (2007)
[CrossRef] [PubMed]

2006 (2)

C. Wang, C. Du, and X. Luo, "Refining the model of light diffraction from a subwavelength slit surrounded by grooves on a metallic film," Phys. Rev. B 74, 245403 (2006).
[CrossRef]

C. Wang, C. Du, Y. Lv, and X. Luo, "Surface electromagnetic wave excitation and diffraction by subwavelength slit with periodically patterned metallic grooves," Opt. Express 14, 5671 (2006).
[CrossRef] [PubMed]

2005 (2)

L.-B. Yu, D.-Z. Lin, Y.-C. Chen, Y.-C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, "Physical origin of directional beaming emitted from a subwavelength slit," Phys. Rev. B 71, 041405 (2005).
[CrossRef]

F. J. García-Vidal, L. Martín-Moreno, and J. B. Pendry, "Surface with holes in them: new plasmatic metamaterials," J. Opt. A 7, S91 (2005).

2004 (1)

M. J. Lockyear, A. P. Hibbins, J. Roy Sambles and C. R. Lawrence, "Surface-topography-induced enhanced transmission and directivity of microwave radiation through a subwavelength circular metal aperture." Appl. Phys. Lett. 84, 2040 (2004).
[CrossRef]

2003 (4)

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]

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 (2003).
[CrossRef]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Science 424, 824 (2003).

2002 (1)

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 820 (2002).
[CrossRef] [PubMed]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Science 424, 824 (2003).

Chang, Y.-C.

L.-B. Yu, D.-Z. Lin, Y.-C. Chen, Y.-C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, "Physical origin of directional beaming emitted from a subwavelength slit," Phys. Rev. B 71, 041405 (2005).
[CrossRef]

Chen, Y.-C.

L.-B. Yu, D.-Z. Lin, Y.-C. Chen, Y.-C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, "Physical origin of directional beaming emitted from a subwavelength slit," Phys. Rev. B 71, 041405 (2005).
[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]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 820 (2002).
[CrossRef] [PubMed]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Science 424, 824 (2003).

Devaux, E.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 820 (2002).
[CrossRef] [PubMed]

Du, C.

H. Shi, C. Du, and X. Luo, "Focal length modulation based on a metallic slit surrounded with grooves in curved depths," Appl. Phys. Lett. 91, 093111 (2007).
[CrossRef]

C. Huang, C. Du, and X. Luo, "A waveguide slit array antenna fabricated with subwavelength periodic grooves," Appl. Phys. Lett. 91, 143512 (2007).
[CrossRef]

C. Wang, C. Du, and X. Luo, "Refining the model of light diffraction from a subwavelength slit surrounded by grooves on a metallic film," Phys. Rev. B 74, 245403 (2006).
[CrossRef]

C. Wang, C. Du, Y. Lv, and X. Luo, "Surface electromagnetic wave excitation and diffraction by subwavelength slit with periodically patterned metallic grooves," Opt. Express 14, 5671 (2006).
[CrossRef] [PubMed]

Ebbesen, T. W.

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 (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]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Science 424, 824 (2003).

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 820 (2002).
[CrossRef] [PubMed]

García-Vidal, F. J.

F. J. García-Vidal, L. Martín-Moreno, and J. B. Pendry, "Surface with holes in them: new plasmatic metamaterials," J. Opt. A 7, S91 (2005).

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]

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 (2003).
[CrossRef]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 820 (2002).
[CrossRef] [PubMed]

Hibbins, A. P.

M. J. Lockyear, A. P. Hibbins, J. Roy Sambles and C. R. Lawrence, "Surface-topography-induced enhanced transmission and directivity of microwave radiation through a subwavelength circular metal aperture." Appl. Phys. Lett. 84, 2040 (2004).
[CrossRef]

Hooft, G. W.

O. T. A. Janssen, H. P. Urbach, and G. W. Hooft, "Giant optical transmission of a subwavelength slit optimized using the magnetic field phase," Phys. Rev. Lett. 99, 043902 (2007)
[CrossRef] [PubMed]

Huang, C.

C. Huang, C. Du, and X. Luo, "A waveguide slit array antenna fabricated with subwavelength periodic grooves," Appl. Phys. Lett. 91, 143512 (2007).
[CrossRef]

Huang, K.-T.

L.-B. Yu, D.-Z. Lin, Y.-C. Chen, Y.-C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, "Physical origin of directional beaming emitted from a subwavelength slit," Phys. Rev. B 71, 041405 (2005).
[CrossRef]

Janssen, O. T. A.

O. T. A. Janssen, H. P. Urbach, and G. W. Hooft, "Giant optical transmission of a subwavelength slit optimized using the magnetic field phase," Phys. Rev. Lett. 99, 043902 (2007)
[CrossRef] [PubMed]

Lee, C.-K.

L.-B. Yu, D.-Z. Lin, Y.-C. Chen, Y.-C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, "Physical origin of directional beaming emitted from a subwavelength slit," Phys. Rev. B 71, 041405 (2005).
[CrossRef]

Lezec, H. J.

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 (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]

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]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 820 (2002).
[CrossRef] [PubMed]

Liaw, J.-W.

L.-B. Yu, D.-Z. Lin, Y.-C. Chen, Y.-C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, "Physical origin of directional beaming emitted from a subwavelength slit," Phys. Rev. B 71, 041405 (2005).
[CrossRef]

Lin, D.-Z.

L.-B. Yu, D.-Z. Lin, Y.-C. Chen, Y.-C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, "Physical origin of directional beaming emitted from a subwavelength slit," Phys. Rev. B 71, 041405 (2005).
[CrossRef]

Linke, R. A.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 820 (2002).
[CrossRef] [PubMed]

Liu, J.-M.

L.-B. Yu, D.-Z. Lin, Y.-C. Chen, Y.-C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, "Physical origin of directional beaming emitted from a subwavelength slit," Phys. Rev. B 71, 041405 (2005).
[CrossRef]

Lockyear, M. J.

M. J. Lockyear, A. P. Hibbins, J. Roy Sambles and C. R. Lawrence, "Surface-topography-induced enhanced transmission and directivity of microwave radiation through a subwavelength circular metal aperture." Appl. Phys. Lett. 84, 2040 (2004).
[CrossRef]

Luo, X.

H. Shi, C. Du, and X. Luo, "Focal length modulation based on a metallic slit surrounded with grooves in curved depths," Appl. Phys. Lett. 91, 093111 (2007).
[CrossRef]

C. Huang, C. Du, and X. Luo, "A waveguide slit array antenna fabricated with subwavelength periodic grooves," Appl. Phys. Lett. 91, 143512 (2007).
[CrossRef]

C. Wang, C. Du, Y. Lv, and X. Luo, "Surface electromagnetic wave excitation and diffraction by subwavelength slit with periodically patterned metallic grooves," Opt. Express 14, 5671 (2006).
[CrossRef] [PubMed]

C. Wang, C. Du, and X. Luo, "Refining the model of light diffraction from a subwavelength slit surrounded by grooves on a metallic film," Phys. Rev. B 74, 245403 (2006).
[CrossRef]

Lv, Y.

Martín-Moreno, L.

F. J. García-Vidal, L. Martín-Moreno, and J. B. Pendry, "Surface with holes in them: new plasmatic metamaterials," J. Opt. A 7, S91 (2005).

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 (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]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 820 (2002).
[CrossRef] [PubMed]

Pendry, J. B.

F. J. García-Vidal, L. Martín-Moreno, and J. B. Pendry, "Surface with holes in them: new plasmatic metamaterials," J. Opt. A 7, S91 (2005).

Shi, H.

H. Shi, C. Du, and X. Luo, "Focal length modulation based on a metallic slit surrounded with grooves in curved depths," Appl. Phys. Lett. 91, 093111 (2007).
[CrossRef]

Urbach, H. P.

O. T. A. Janssen, H. P. Urbach, and G. W. Hooft, "Giant optical transmission of a subwavelength slit optimized using the magnetic field phase," Phys. Rev. Lett. 99, 043902 (2007)
[CrossRef] [PubMed]

Wang, C.

C. Wang, C. Du, Y. Lv, and X. Luo, "Surface electromagnetic wave excitation and diffraction by subwavelength slit with periodically patterned metallic grooves," Opt. Express 14, 5671 (2006).
[CrossRef] [PubMed]

C. Wang, C. Du, and X. Luo, "Refining the model of light diffraction from a subwavelength slit surrounded by grooves on a metallic film," Phys. Rev. B 74, 245403 (2006).
[CrossRef]

Yeh, C.-S.

L.-B. Yu, D.-Z. Lin, Y.-C. Chen, Y.-C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, "Physical origin of directional beaming emitted from a subwavelength slit," Phys. Rev. B 71, 041405 (2005).
[CrossRef]

Yeh, J.-T.

L.-B. Yu, D.-Z. Lin, Y.-C. Chen, Y.-C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, "Physical origin of directional beaming emitted from a subwavelength slit," Phys. Rev. B 71, 041405 (2005).
[CrossRef]

Yu, L.-B.

L.-B. Yu, D.-Z. Lin, Y.-C. Chen, Y.-C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, "Physical origin of directional beaming emitted from a subwavelength slit," Phys. Rev. B 71, 041405 (2005).
[CrossRef]

Appl. Phys. Lett. (4)

M. J. Lockyear, A. P. Hibbins, J. Roy Sambles and C. R. Lawrence, "Surface-topography-induced enhanced transmission and directivity of microwave radiation through a subwavelength circular metal aperture." Appl. Phys. Lett. 84, 2040 (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 (2003).
[CrossRef]

H. Shi, C. Du, and X. Luo, "Focal length modulation based on a metallic slit surrounded with grooves in curved depths," Appl. Phys. Lett. 91, 093111 (2007).
[CrossRef]

C. Huang, C. Du, and X. Luo, "A waveguide slit array antenna fabricated with subwavelength periodic grooves," Appl. Phys. Lett. 91, 143512 (2007).
[CrossRef]

J. Opt. A (1)

F. J. García-Vidal, L. Martín-Moreno, and J. B. Pendry, "Surface with holes in them: new plasmatic metamaterials," J. Opt. A 7, S91 (2005).

Opt. Express (1)

Phys. Rev. B (2)

L.-B. Yu, D.-Z. Lin, Y.-C. Chen, Y.-C. Chang, K.-T. Huang, J.-W. Liaw, J.-T. Yeh, J.-M. Liu, C.-S. Yeh, and C.-K. Lee, "Physical origin of directional beaming emitted from a subwavelength slit," Phys. Rev. B 71, 041405 (2005).
[CrossRef]

C. Wang, C. Du, and X. Luo, "Refining the model of light diffraction from a subwavelength slit surrounded by grooves on a metallic film," Phys. Rev. B 74, 245403 (2006).
[CrossRef]

Phys. Rev. Lett. (3)

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]

O. T. A. Janssen, H. P. Urbach, and G. W. Hooft, "Giant optical transmission of a subwavelength slit optimized using the magnetic field phase," Phys. Rev. Lett. 99, 043902 (2007)
[CrossRef] [PubMed]

Science (2)

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 820 (2002).
[CrossRef] [PubMed]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Science 424, 824 (2003).

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Figures (6)

Fig. 1.
Fig. 1.

Schematic diagram of the slit-grooves structure with radiation angle θ at exit plane.

Fig. 2.
Fig. 2.

Diffraction angular spectra as a function of λ/d, ranging from 0.1d to 2.2d for a slitgrooves structure configured with a=0.11λ, h=0.145λ and N=10. The y axis represents the farfield angle distribution.

Fig. 3.
Fig. 3.

Angular spectra of multiple beaming effect for the slit-grooves structures. The parameter λ/d are those listed in Table 1 with the same number of peaks and other geometrical parameters are those in Fig. 2.

Fig. 4.
Fig. 4.

Time averaged |Hy |2 in space behind the exit surface of the slit-groove structures. The geometrical parameters are as same as those in Table 1 and Fig. 2.

Fig. 5.
Fig. 5.

The relationship between beaming conditions for λ/d, beaming angle θ and the corresponding diffraction orders (n, m) for multiple directional beaming effect. The structure parameters are calculated from grating equation (GE) and mode expansion method (MEM), respectively. The inset is the calculated error of beaming positions with GE and MEM (black points) and □λ/d derived from equation (3) (blue line).

Fig. 6.
Fig. 6.

The diffraction efficiency and the beaming intensity for multiple directional beaming.

Tables (1)

Tables Icon

Table 1. The corresponding values of λ/d for the highlight spots in Fig. 2.

Equations (3)

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

{ k 0 sin θ = k sp n 2 π d k 0 sin θ = k sp m 2 π d
d = ( n m ) 2 λ sp ( n = 1 , 2 , 3 , , m = 1 , 2 , 3 ) ,
Δ ( λ d ) = λ d λ SP d = ( a 2 λ 2 d 3 ) tan 2 ( 2 π h λ )

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