Abstract

We analyze, theoretically and experimentally, the dynamics of the wavepackets in plasmonic beaming devices, and show that the beam evolution in this class of structures is a multiscale phenomenon, which initiates in the near-field proximity of the device, develops continuously over a new length scale many times the wavelength of the light, and is completed well into the far-field of the system. We develop a quantitative description of the light evolution in the beaming structures and verify our theoretical predictions with experiments. Our analytical results are utilized to develop plasmonic geometries for shaping the mid-field beam evolution, and experimental results from these structures are demonstrated.

© 2011 OSA

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  1. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the flow of light (Princeton U. Press, 1995).
  2. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
    [CrossRef] [PubMed]
  3. U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
    [CrossRef] [PubMed]
  4. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nature Photon. 1, 224–227 (2007).
    [CrossRef]
  5. 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, 820–822 (2002).
    [CrossRef] [PubMed]
  6. 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]
  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, 4500–4502 (2003).
    [CrossRef]
  8. D. C. Adams, S. Thongrattanasiri, T. Ribaudo, V. A. Podolskiy, and D. Wasserman, “Plasmonic mid-infrared beam steering,” Appl. Phys. Lett. 96, 201112 (2010).
  9. N. Yu, J. Fan, Q. J. Wang, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Small-divergence semiconductor lasers by plasmonic collimation,” Nature Photon. 2, 564–570 (2008).
    [CrossRef]
  10. M. Born and E. Wolf, Principles of Optics (Cambridge Univ., 1999).
  11. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).
  12. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508–511 (2006).
    [CrossRef] [PubMed]
  13. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
    [CrossRef] [PubMed]
  14. A. Krier, Mid-infrared Semiconductor Optoelectronics (Springer, 2006).
    [CrossRef]
  15. I. I. Smolyaninov, D. L. Mazzoni, and C. D. Davis, “Imaging of surface plasmon scattering by lithographically created individual surface defects,” Phys. Rev. Lett. 77, 3877–3880 (2003).
    [CrossRef]
  16. I. I. Smolyaninov, D. L. Mazzoni, J. Mait, and T. W. Ebbesen, “Experimental study of surface-plasmon scattering by individual surface defects,” Phys. Rev. B 56, 1601–1611 (2003).
    [CrossRef]
  17. A. V. Shchegrov, I. V. Novikov, and A. A. Maradudin, “Scattering of surface plasmon polaritons by a circularly symmetric surface defect,” Phys. Rev. Lett. 78, 4269–4272 (2003).
    [CrossRef]
  18. E.D. Palik, The Handbook of Optical Constants of Solids (Academic, 1997).
  19. M. A. Ordal, L. L. Long, R. J. Bell, R. R. Bell, R. W. Alexander, and C. A. Ward, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared,” Appl. Optics 22, 1099–1119 (1983).
    [CrossRef]
  20. For details see COMSOL Multiphysics 3.5a User’s Guide and RF Module User’s Guide, www.comsol.com .
  21. S. Thongrattanasiri, J. Elser, and V. A. Podolskiy, “Quasi-planar optics: computing light propagation and scattering in planar waveguide arrays,” J. Opt. Soc. Am. B 26, B102–B110 (2009).
    [CrossRef]
  22. M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, “Low-divergence single-mode terahertz quantum cascade lase,” Nature Photon. 3, 586–590 (2009)
    [CrossRef]

2011

D. C. Adams, S. Thongrattanasiri, T. Ribaudo, V. A. Podolskiy, and D. Wasserman, “Plasmonic mid-infrared beam steering,” Appl. Phys. Lett. 96, 201112 (2010).

2009

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, “Low-divergence single-mode terahertz quantum cascade lase,” Nature Photon. 3, 586–590 (2009)
[CrossRef]

S. Thongrattanasiri, J. Elser, and V. A. Podolskiy, “Quasi-planar optics: computing light propagation and scattering in planar waveguide arrays,” J. Opt. Soc. Am. B 26, B102–B110 (2009).
[CrossRef]

2008

N. Yu, J. Fan, Q. J. Wang, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Small-divergence semiconductor lasers by plasmonic collimation,” Nature Photon. 2, 564–570 (2008).
[CrossRef]

2007

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nature Photon. 1, 224–227 (2007).
[CrossRef]

2006

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508–511 (2006).
[CrossRef] [PubMed]

2003

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

I. I. Smolyaninov, D. L. Mazzoni, and C. D. Davis, “Imaging of surface plasmon scattering by lithographically created individual surface defects,” Phys. Rev. Lett. 77, 3877–3880 (2003).
[CrossRef]

I. I. Smolyaninov, D. L. Mazzoni, J. Mait, and T. W. Ebbesen, “Experimental study of surface-plasmon scattering by individual surface defects,” Phys. Rev. B 56, 1601–1611 (2003).
[CrossRef]

A. V. Shchegrov, I. V. Novikov, and A. A. Maradudin, “Scattering of surface plasmon polaritons by a circularly symmetric surface defect,” Phys. Rev. Lett. 78, 4269–4272 (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, 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]

2002

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, 820–822 (2002).
[CrossRef] [PubMed]

2000

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef] [PubMed]

1983

M. A. Ordal, L. L. Long, R. J. Bell, R. R. Bell, R. W. Alexander, and C. A. Ward, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared,” Appl. Optics 22, 1099–1119 (1983).
[CrossRef]

Adams, D. C.

D. C. Adams, S. Thongrattanasiri, T. Ribaudo, V. A. Podolskiy, and D. Wasserman, “Plasmonic mid-infrared beam steering,” Appl. Phys. Lett. 96, 201112 (2010).

Alexander, R. W.

M. A. Ordal, L. L. Long, R. J. Bell, R. R. Bell, R. W. Alexander, and C. A. Ward, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared,” Appl. Optics 22, 1099–1119 (1983).
[CrossRef]

Amanti, M. I.

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, “Low-divergence single-mode terahertz quantum cascade lase,” Nature Photon. 3, 586–590 (2009)
[CrossRef]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

Beck, M.

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, “Low-divergence single-mode terahertz quantum cascade lase,” Nature Photon. 3, 586–590 (2009)
[CrossRef]

Bell, R. J.

M. A. Ordal, L. L. Long, R. J. Bell, R. R. Bell, R. W. Alexander, and C. A. Ward, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared,” Appl. Optics 22, 1099–1119 (1983).
[CrossRef]

Bell, R. R.

M. A. Ordal, L. L. Long, R. J. Bell, R. R. Bell, R. W. Alexander, and C. A. Ward, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared,” Appl. Optics 22, 1099–1119 (1983).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge Univ., 1999).

Bozhevolnyi, S. I.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508–511 (2006).
[CrossRef] [PubMed]

Cai, W.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nature Photon. 1, 224–227 (2007).
[CrossRef]

Capasso, F.

N. Yu, J. Fan, Q. J. Wang, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Small-divergence semiconductor lasers by plasmonic collimation,” Nature Photon. 2, 564–570 (2008).
[CrossRef]

Chettiar, U. K.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nature Photon. 1, 224–227 (2007).
[CrossRef]

Davis, C. D.

I. I. Smolyaninov, D. L. Mazzoni, and C. D. Davis, “Imaging of surface plasmon scattering by lithographically created individual surface defects,” Phys. Rev. Lett. 77, 3877–3880 (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]

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, 820–822 (2002).
[CrossRef] [PubMed]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

Devaux, E.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508–511 (2006).
[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, 820–822 (2002).
[CrossRef] [PubMed]

Diehl, L.

N. Yu, J. Fan, Q. J. Wang, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Small-divergence semiconductor lasers by plasmonic collimation,” Nature Photon. 2, 564–570 (2008).
[CrossRef]

Ebbesen, T. W.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508–511 (2006).
[CrossRef] [PubMed]

I. I. Smolyaninov, D. L. Mazzoni, J. Mait, and T. W. Ebbesen, “Experimental study of surface-plasmon scattering by individual surface defects,” Phys. Rev. B 56, 1601–1611 (2003).
[CrossRef]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (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]

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, 820–822 (2002).
[CrossRef] [PubMed]

Edamura, T.

N. Yu, J. Fan, Q. J. Wang, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Small-divergence semiconductor lasers by plasmonic collimation,” Nature Photon. 2, 564–570 (2008).
[CrossRef]

Elser, J.

Faist, J.

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, “Low-divergence single-mode terahertz quantum cascade lase,” Nature Photon. 3, 586–590 (2009)
[CrossRef]

Fan, J.

N. Yu, J. Fan, Q. J. Wang, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Small-divergence semiconductor lasers by plasmonic collimation,” Nature Photon. 2, 564–570 (2008).
[CrossRef]

Fischer, M.

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, “Low-divergence single-mode terahertz quantum cascade lase,” Nature Photon. 3, 586–590 (2009)
[CrossRef]

García-Vidal, F. 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, 4500–4502 (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]

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, 820–822 (2002).
[CrossRef] [PubMed]

Joannopoulos, J. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the flow of light (Princeton U. Press, 1995).

Kan, H.

N. Yu, J. Fan, Q. J. Wang, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Small-divergence semiconductor lasers by plasmonic collimation,” Nature Photon. 2, 564–570 (2008).
[CrossRef]

Kildishev, A. V.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nature Photon. 1, 224–227 (2007).
[CrossRef]

Krier, A.

A. Krier, Mid-infrared Semiconductor Optoelectronics (Springer, 2006).
[CrossRef]

Laluet, J.-Y.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508–511 (2006).
[CrossRef] [PubMed]

Leonhardt, U.

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
[CrossRef] [PubMed]

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, 4500–4502 (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]

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, 820–822 (2002).
[CrossRef] [PubMed]

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, 820–822 (2002).
[CrossRef] [PubMed]

Long, L. L.

M. A. Ordal, L. L. Long, R. J. Bell, R. R. Bell, R. W. Alexander, and C. A. Ward, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared,” Appl. Optics 22, 1099–1119 (1983).
[CrossRef]

Mait, J.

I. I. Smolyaninov, D. L. Mazzoni, J. Mait, and T. W. Ebbesen, “Experimental study of surface-plasmon scattering by individual surface defects,” Phys. Rev. B 56, 1601–1611 (2003).
[CrossRef]

Maradudin, A. A.

A. V. Shchegrov, I. V. Novikov, and A. A. Maradudin, “Scattering of surface plasmon polaritons by a circularly symmetric surface defect,” Phys. Rev. Lett. 78, 4269–4272 (2003).
[CrossRef]

Martín-Moreno, L.

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]

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, 820–822 (2002).
[CrossRef] [PubMed]

Mazzoni, D. L.

I. I. Smolyaninov, D. L. Mazzoni, J. Mait, and T. W. Ebbesen, “Experimental study of surface-plasmon scattering by individual surface defects,” Phys. Rev. B 56, 1601–1611 (2003).
[CrossRef]

I. I. Smolyaninov, D. L. Mazzoni, and C. D. Davis, “Imaging of surface plasmon scattering by lithographically created individual surface defects,” Phys. Rev. Lett. 77, 3877–3880 (2003).
[CrossRef]

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the flow of light (Princeton U. Press, 1995).

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef] [PubMed]

Novikov, I. V.

A. V. Shchegrov, I. V. Novikov, and A. A. Maradudin, “Scattering of surface plasmon polaritons by a circularly symmetric surface defect,” Phys. Rev. Lett. 78, 4269–4272 (2003).
[CrossRef]

Ordal, M. A.

M. A. Ordal, L. L. Long, R. J. Bell, R. R. Bell, R. W. Alexander, and C. A. Ward, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared,” Appl. Optics 22, 1099–1119 (1983).
[CrossRef]

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef] [PubMed]

Palik, E.D.

E.D. Palik, The Handbook of Optical Constants of Solids (Academic, 1997).

Pflügl, C.

N. Yu, J. Fan, Q. J. Wang, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Small-divergence semiconductor lasers by plasmonic collimation,” Nature Photon. 2, 564–570 (2008).
[CrossRef]

Podolskiy, V. A.

D. C. Adams, S. Thongrattanasiri, T. Ribaudo, V. A. Podolskiy, and D. Wasserman, “Plasmonic mid-infrared beam steering,” Appl. Phys. Lett. 96, 201112 (2010).

S. Thongrattanasiri, J. Elser, and V. A. Podolskiy, “Quasi-planar optics: computing light propagation and scattering in planar waveguide arrays,” J. Opt. Soc. Am. B 26, B102–B110 (2009).
[CrossRef]

Raether, H.

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).

Ribaudo, T.

D. C. Adams, S. Thongrattanasiri, T. Ribaudo, V. A. Podolskiy, and D. Wasserman, “Plasmonic mid-infrared beam steering,” Appl. Phys. Lett. 96, 201112 (2010).

Scalari, G.

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, “Low-divergence single-mode terahertz quantum cascade lase,” Nature Photon. 3, 586–590 (2009)
[CrossRef]

Schultz, S.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef] [PubMed]

Shalaev, V. M.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nature Photon. 1, 224–227 (2007).
[CrossRef]

Shchegrov, A. V.

A. V. Shchegrov, I. V. Novikov, and A. A. Maradudin, “Scattering of surface plasmon polaritons by a circularly symmetric surface defect,” Phys. Rev. Lett. 78, 4269–4272 (2003).
[CrossRef]

Smith, D. R.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef] [PubMed]

Smolyaninov, I. I.

I. I. Smolyaninov, D. L. Mazzoni, and C. D. Davis, “Imaging of surface plasmon scattering by lithographically created individual surface defects,” Phys. Rev. Lett. 77, 3877–3880 (2003).
[CrossRef]

I. I. Smolyaninov, D. L. Mazzoni, J. Mait, and T. W. Ebbesen, “Experimental study of surface-plasmon scattering by individual surface defects,” Phys. Rev. B 56, 1601–1611 (2003).
[CrossRef]

Thongrattanasiri, S.

D. C. Adams, S. Thongrattanasiri, T. Ribaudo, V. A. Podolskiy, and D. Wasserman, “Plasmonic mid-infrared beam steering,” Appl. Phys. Lett. 96, 201112 (2010).

S. Thongrattanasiri, J. Elser, and V. A. Podolskiy, “Quasi-planar optics: computing light propagation and scattering in planar waveguide arrays,” J. Opt. Soc. Am. B 26, B102–B110 (2009).
[CrossRef]

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef] [PubMed]

Volkov, V. S.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508–511 (2006).
[CrossRef] [PubMed]

Wang, Q. J.

N. Yu, J. Fan, Q. J. Wang, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Small-divergence semiconductor lasers by plasmonic collimation,” Nature Photon. 2, 564–570 (2008).
[CrossRef]

Ward, C. A.

M. A. Ordal, L. L. Long, R. J. Bell, R. R. Bell, R. W. Alexander, and C. A. Ward, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared,” Appl. Optics 22, 1099–1119 (1983).
[CrossRef]

Wasserman, D.

D. C. Adams, S. Thongrattanasiri, T. Ribaudo, V. A. Podolskiy, and D. Wasserman, “Plasmonic mid-infrared beam steering,” Appl. Phys. Lett. 96, 201112 (2010).

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the flow of light (Princeton U. Press, 1995).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge Univ., 1999).

Yamanishi, M.

N. Yu, J. Fan, Q. J. Wang, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Small-divergence semiconductor lasers by plasmonic collimation,” Nature Photon. 2, 564–570 (2008).
[CrossRef]

Yu, N.

N. Yu, J. Fan, Q. J. Wang, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Small-divergence semiconductor lasers by plasmonic collimation,” Nature Photon. 2, 564–570 (2008).
[CrossRef]

Appl. Optics

M. A. Ordal, L. L. Long, R. J. Bell, R. R. Bell, R. W. Alexander, and C. A. Ward, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared,” Appl. Optics 22, 1099–1119 (1983).
[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, 4500–4502 (2003).
[CrossRef]

D. C. Adams, S. Thongrattanasiri, T. Ribaudo, V. A. Podolskiy, and D. Wasserman, “Plasmonic mid-infrared beam steering,” Appl. Phys. Lett. 96, 201112 (2010).

J. Opt. Soc. Am. B

Nature

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508–511 (2006).
[CrossRef] [PubMed]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

Nature Photon.

N. Yu, J. Fan, Q. J. Wang, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Small-divergence semiconductor lasers by plasmonic collimation,” Nature Photon. 2, 564–570 (2008).
[CrossRef]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nature Photon. 1, 224–227 (2007).
[CrossRef]

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, “Low-divergence single-mode terahertz quantum cascade lase,” Nature Photon. 3, 586–590 (2009)
[CrossRef]

Phys. Rev. B

I. I. Smolyaninov, D. L. Mazzoni, J. Mait, and T. W. Ebbesen, “Experimental study of surface-plasmon scattering by individual surface defects,” Phys. Rev. B 56, 1601–1611 (2003).
[CrossRef]

Phys. Rev. Lett.

A. V. Shchegrov, I. V. Novikov, and A. A. Maradudin, “Scattering of surface plasmon polaritons by a circularly symmetric surface defect,” Phys. Rev. Lett. 78, 4269–4272 (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]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef] [PubMed]

I. I. Smolyaninov, D. L. Mazzoni, and C. D. Davis, “Imaging of surface plasmon scattering by lithographically created individual surface defects,” Phys. Rev. Lett. 77, 3877–3880 (2003).
[CrossRef]

Science

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
[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, 820–822 (2002).
[CrossRef] [PubMed]

Other

M. Born and E. Wolf, Principles of Optics (Cambridge Univ., 1999).

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the flow of light (Princeton U. Press, 1995).

A. Krier, Mid-infrared Semiconductor Optoelectronics (Springer, 2006).
[CrossRef]

E.D. Palik, The Handbook of Optical Constants of Solids (Academic, 1997).

For details see COMSOL Multiphysics 3.5a User’s Guide and RF Module User’s Guide, www.comsol.com .

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Figures (9)

Fig. 1
Fig. 1

Schematics of the beam steering structures studied in this work. In (a), SPPs are excited at the GaAs/metal interface and the transmitted beams develop through the GaAs substrate into free space. In (b), SPPs are excited at the air/metal interface. For both structures, do is the central slit width, Λ the corrugation period, and h and L the corrugation height and width, respectively. λo is the free space wavelength of the incident light. Here we show only the incident light, the more complex behavior of the fields on the backside of the structure are the focus of the remainder of the paper.

Fig. 2
Fig. 2

Schematic view of the plasmonic beaming structure, superimposed on top of the typical intensity distribution of the transitted light. Here s is the substrate thickness and f is the length of the focal range (to be discussed in greater length below). Note that the beams (dashed lines), resulting from the interference of the SPPs scattered by the periodic surface corrugations with the light directly transmitted through the subwavelength slit, appear to curve away from the central slit, asymptotically approaching the straight lines, described by Eq.(1).

Fig. 3
Fig. 3

(a) Depiction of an individual scattering event of a SPP propagating across the small bump on the otherwise smooth plasmonic surface. As result of this scattering, a (small) portion of the SPP energy is converted into free-space radiation, seen as the beam propagating upward (dashed white curves). The amplitude of the SPP whose field profile is schematically shown as the red shaded region is reduced, and its phase is (slightly) advanced. (b)Transmission and phase shift of SPP propagating through dielectric inserts. Note that more than 90 % of the SPP’s energy transfers through the insert. The phase of SPP is slightly advanced during the process. The 5 sets of solid (transmission) and dotted (phase shift) lines correspond to transmission though 1 to 5 inserts, t 1 ...t 5; the lines of different color almost overlap, indicating that multiple-scattering can be omitted.

Fig. 4
Fig. 4

Position of the extent of the focal range (f max) as a function of incident wavelength λ for a beaming structure with corrugation period Λ = 2.8μm. The discontinuity of fmax at λ 0 ≃ 9.2μm corresponds to a single beam emitted normal to the device surface.

Fig. 5
Fig. 5

Field profile, calculated with FEM simulations (top panels) and using the semi-analytical calculations (bottom) described in subsection 2.2; The parts of the spectrum corresponding to propagation parallel to the structure, included in the calculations, are omitted from the plotting procedure to minimize fringing.

Fig. 6
Fig. 6

Analytical description of SPP scattering and beam formation in the system with periodic dielectric inserts as discussed in the text. (a) Intensity and (c) wavevector distribution of the light behind the system for incident light with λ = 7μm. (b) Intensity and (d) wavevector distribution of the light behind the system for incident light with λ = 12μm. For the particular structure, the phase of beams produced by the SPPs is opposite to the phase of light emitted by the central slit so that the beams manifest themselves as intensity minima [dotted lines in panels (a,b)]. Dashed lines illustrate the main point of this work: the beams asymptotically approach the straight lines that can be traced back to the last focal spot of the corrugated surface. The position of the cross is given by Eq.(4), the direction of the dashed lines in (c,e) [and the position of the dashed lines in (d,f)] is given by Eq.(1).

Fig. 7
Fig. 7

Formation of the beams in a structure with Λ = 2.8μm, L = 100nm,h = 250nm, and λ 0 = 12μm, with (a) 10, and (b) 20 bumps. Since L,hλ 0, the SPP scattering is extremely small (|t| ≃ 0.99), so that evolution of the beams is determined by the number of the scatterers in the structure. The position of the cross corresponds to (a) f 10 (10 scattering bumps) and (b) f 20 (20 scattering bumps) [Eq.(3)]; the dashed lines depict the expected far-field steering angle calculated from Eq.(1).

Fig. 8
Fig. 8

(a) Experimental set-up for mid-field beam intensity measurements. Mid- to far-field intensity for (b) 9.3 μm and (c) 9.4 μm light transmitted through our beaming structure (note that y=0 on the two contour plots corresponds to the surface of the GaAs substrate, approximately 200μm above the structure slit). As explained in the text, the far field pattern of the beaming structure contains two symmetric beams; these beams, however, emerge from the end of the extended focal range, whose length is determined by Eq.(4). The focal range and the eventual divergence of the beams are clearly seen in this figure, where the position of the overlaid circle and the direction of the overlaid dashed lines are given by Eqs.(4, 1) respectively.

Fig. 9
Fig. 9

The evolution of light in the mid-field of the device can be engineered by arranging the scatterers in a pre-designed manner. The bumps [black dots in panels (a) and (c)] were arranged to produce a well-defined focal spots above a metal/air device subwavelength slit according to Eq.(9). Panel (a) shows the designed mid-field beam profile for a device designed to focus light 250μm above a 1.4μm central slit flanked by a non-periodic ridge pattern. Panel (b) represents the same data, averaged across 25 – μm area corresponding to the resolution of experimental sequp. Panel (c) show the experimental mid-field data from the fabricated device, and demonstrates a clear focal spot approximately 250μm above the metal/air interface. Panels (c)–(f) show similar results for a sample designed to focus light 500μm above the central slit.

Equations (8)

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k 0 sin θ = k SPP ( 2 π δ ) / Λ ,
Δ i δ + ( x i x i 1 ) [ k SPP + k 0 x i + x i 1 2 y ] ,
f i = k 0 Λ 2 ( 2 i max + 1 ) 2 ( 2 π k SPP Λ δ ) .
f max f i max ,
H z ref = m r m e i q y m y cos ( q x m x ) , E x ref = m c ω q y m r m e i q y m y cos ( q x m x ) ,
H z sc = a ( k x ) e i k x x + i k y y d k x n a ( k x n ) w n e i k x n x + i k y n y , E x sc = a ( k x ) c ɛ GaAs ω k y e i k x x + i k y y d k x n a ( k x n ) w n c ɛ GaAs ω k y n e i k x n x + i k y n y ,
n a ( k x n ) w n e i k x n x = { i 0 + Σ m r m cos ( q x m x ) | x | < d 0 / 2 Σ n a ( k x n ) w n ɛ b ( x ) k y n ɛ GaAs k b n e i k x n x | x | d 0 / 2 , n a ( k x n ) k y n ɛ GaAs w n e i k x n x = { i 0 ω c Σ m r m q y m cos ( q x m x ) | x | < d 0 / 2 Σ n a ( k x n ) w n k b n ɛ b ( x ) e i k x n x | x | d 0 / 2 ,
x i = x i 1 + d x i , d x i = f 0 k 0 [ κ i + κ i 2 + 2 k 0 f 0 ( 2 π δ ) ] 2 π δ κ i ,

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