Abstract

Based on the theoretical formalism derived from the diffraction theory and electromagnetic boundary condition (Phys. Rev. Lett. 167401(2003)), we investigate numerically the diffraction behavior of light passing through a subwavelength metallic slit-grooves structure, slit surrounded symmetrically by a finite array of grooves at the output surface. The diffraction dependence with the geometrical parameters, groove depth, width and number is analyzed in detail. It is found that variant profile of angle spectra and beaming intensity can be obtained in the far field by tuning the geometrical parameters. Numerical analysis shows that these diffraction behaviors are associated with different excitation states of surface electromagnetic wave.

© 2006 Optical Society of America

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  1. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, F. Martín-Moreno, L. J. García-Vidal, and T. W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 820 (2002).
    [CrossRef] [PubMed]
  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]
  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]
  4. 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]
  5. P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, "Highly directional emission from photonic crystal waveguides of subwavelength width," Phys. Rev. Lett. 92, 113903(2004).
    [CrossRef] [PubMed]
  6. E. Moreno, F. J. García-Vidal, L. Martín-Moreno, "Enhanced transmission and beaming of light via photonic crystal surface modes," Phys. Rev. B. 69,121402 (2004).
    [CrossRef]
  7. L. A. Blanco and F. J. García de Abajo, "Control of spontaneous emission by complex nanostructures," Opt. Lett. 29, 1494 (2004).
    [CrossRef] [PubMed]
  8. J. B. Pendry, L. Martín-Moreno, F. J. García-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847(2004).
    [CrossRef] [PubMed]
  9. The approximation of fails when a=b. You should refer to the original integral definition in Ref. 3. Here we do the calculation by the method of Montecarlo.

2005

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]

2004

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, "Highly directional emission from photonic crystal waveguides of subwavelength width," Phys. Rev. Lett. 92, 113903(2004).
[CrossRef] [PubMed]

E. Moreno, F. J. García-Vidal, L. Martín-Moreno, "Enhanced transmission and beaming of light via photonic crystal surface modes," Phys. Rev. B. 69,121402 (2004).
[CrossRef]

J. B. Pendry, L. Martín-Moreno, F. J. García-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847(2004).
[CrossRef] [PubMed]

L. A. Blanco and F. J. García de Abajo, "Control of spontaneous emission by complex nanostructures," Opt. Lett. 29, 1494 (2004).
[CrossRef] [PubMed]

2003

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 (2003).
[CrossRef]

2002

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

Agio, M.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, "Highly directional emission from photonic crystal waveguides of subwavelength width," Phys. Rev. Lett. 92, 113903(2004).
[CrossRef] [PubMed]

Birner, A.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, "Highly directional emission from photonic crystal waveguides of subwavelength width," Phys. Rev. Lett. 92, 113903(2004).
[CrossRef] [PubMed]

Blanco, L. A.

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, F. Martín-Moreno, L. J. García-Vidal, and T. W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 820 (2002).
[CrossRef] [PubMed]

Devaux, E.

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

Ebbesen, T. W.

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 (2003).
[CrossRef]

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

García de Abajo, F. J.

García-Vidal, F. J.

E. Moreno, F. J. García-Vidal, L. Martín-Moreno, "Enhanced transmission and beaming of light via photonic crystal surface modes," Phys. Rev. B. 69,121402 (2004).
[CrossRef]

J. B. Pendry, L. Martín-Moreno, F. J. García-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847(2004).
[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]

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]

García-Vidal, L. J.

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

Gösele, U.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, "Highly directional emission from photonic crystal waveguides of subwavelength width," Phys. Rev. Lett. 92, 113903(2004).
[CrossRef] [PubMed]

Kramper, P.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, "Highly directional emission from photonic crystal waveguides of subwavelength width," Phys. Rev. Lett. 92, 113903(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 (2003).
[CrossRef]

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

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, F. Martín-Moreno, L. J. García-Vidal, and T. W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 820 (2002).
[CrossRef] [PubMed]

Martín-Moreno, F.

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

Martín-Moreno, L.

J. B. Pendry, L. Martín-Moreno, F. J. García-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847(2004).
[CrossRef] [PubMed]

E. Moreno, F. J. García-Vidal, L. Martín-Moreno, "Enhanced transmission and beaming of light via photonic crystal surface modes," Phys. Rev. B. 69,121402 (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]

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]

Moreno, E.

E. Moreno, F. J. García-Vidal, L. Martín-Moreno, "Enhanced transmission and beaming of light via photonic crystal surface modes," Phys. Rev. B. 69,121402 (2004).
[CrossRef]

Müller, F.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, "Highly directional emission from photonic crystal waveguides of subwavelength width," Phys. Rev. Lett. 92, 113903(2004).
[CrossRef] [PubMed]

Pendry, J. B.

J. B. Pendry, L. Martín-Moreno, F. J. García-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847(2004).
[CrossRef] [PubMed]

Sandoghdar, V.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, "Highly directional emission from photonic crystal waveguides of subwavelength width," Phys. Rev. Lett. 92, 113903(2004).
[CrossRef] [PubMed]

Soukoulis, C. M.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, "Highly directional emission from photonic crystal waveguides of subwavelength width," Phys. Rev. Lett. 92, 113903(2004).
[CrossRef] [PubMed]

Wehrspohn, R. B.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, "Highly directional emission from photonic crystal waveguides of subwavelength width," Phys. Rev. Lett. 92, 113903(2004).
[CrossRef] [PubMed]

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.

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]

Opt. Lett.

Phys. Rev. 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]

Phys. Rev. B.

E. Moreno, F. J. García-Vidal, L. Martín-Moreno, "Enhanced transmission and beaming of light via photonic crystal surface modes," Phys. Rev. B. 69,121402 (2004).
[CrossRef]

Phys. Rev. Lett.

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]

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, "Highly directional emission from photonic crystal waveguides of subwavelength width," Phys. Rev. Lett. 92, 113903(2004).
[CrossRef] [PubMed]

Science

J. B. Pendry, L. Martín-Moreno, F. J. García-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847(2004).
[CrossRef] [PubMed]

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

Other

The approximation of fails when a=b. You should refer to the original integral definition in Ref. 3. Here we do the calculation by the method of Montecarlo.

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Figures (8)

Fig. 1.
Fig. 1.

Schematic of slit-grooves structure for surface EM wave excitation and diffraction

Fig. 2.
Fig. 2.

Diffraction angular spectra for variant wavelength ranging from 0.4d to 2.4d for a slit-grooves structure configured with a=0.1λ, h=λ/7, and N=10.

Fig. 3.
Fig. 3.

Evolution of angular spectra for variant groove depth ranging from 0 to 0.5λ. Here (a) λ=1.6d and (b) λ=0.8d. The other parameters are a=0.1λ and N=10.

Fig. 4.
Fig. 4.

Excited electric field E α (amplitude (a) and argument (b)) at groove openings for variant groove depth. The other parameters of calculation is the same as that of Fig. 3(a).

Fig. 5.
Fig. 5.

Groove depth dependence of (a) surface EM mode excitation efficiency and (b) the phase deviation of slit from the linear distribution of grooves’ phases for the structure defined in Fig. 3(a).

Fig. 6.
Fig. 6.

Contour plots of functions of angular spectra with groove depth for variant groove width, (a) a=0.01λ, (b) a=0.06λ, (c) a=0.12λ, (d) a=0.3λ. Here λ=1.6d and N=10.

Fig. 7.
Fig. 7.

Angular spectra of light beaming for variant groove numbers. (a) and (b) h=0.1λ, (c) h=0.2λ, (d) h=0.3λ. The other parameters are λ=1.6d, a=0.1d.

Fig. 8.
Fig. 8.

Beaming intensity (a) and divergence (FWHM) (b) for groove number ranging from 0 to 200 with a step of 20. The other parameters here are λ=1.6d, a=0.1d and h=0.125λ.

Equations (3)

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G α α E α + β α G α β E β = 2 i A 0 δ α 0 + ε α E α .
H y N ( r , θ ) = 1 μ 0 c N N E α ϕ α ( x ) H 0 ( 1 ) ( k r x x ) d x .
H y N ( θ ) = a μ 0 c 2 π k r exp ( i k r i π / 4 ) N N E α exp ( i k α d sin θ ) .

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