Abstract

A cathodoluminescence technique using a 200-keV transmission electron microscope revealed the dispersion patterns of surface plasmon polaritons (SPPs) in a two- dimensional plasmonic crystal with cylindrical hole arrays. The dispersion curves of the SPP modes involving the Γ point were derived from the angle-resolved spectrum patterns. The contrast along the dispersion curves changed with the polarization direction of the emitted light due to the property of the SPP modes. The SPP modes at the Γ point were identified from the photon maps, which mimicked standing SPP waves in a real space. The beam-scan spectral images across the plasmonic crystal edge clearly demonstrated the dependence of the SPP to light conversion efficiency on the emission angle and polarization of light.

© 2011 OSA

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  20. J. J. Cha, Z. Yu, E. Smith, M. Couillard, S. Fan, and D. A. Muller, “Mapping local optical densities of states in silicon photonic structures with nanoscale electron spectroscopy,” Phys. Rev. B 81(11), 113102 (2010).
    [CrossRef]

2011

N. Yamamoto, S. Ohtani, and F. J. García de Abajo, “Gap and Mie plasmons in individual silver nanospheres near a silver surface,” Nano Lett. 11(1), 91–95 (2011).
[CrossRef]

2010

G. Boudarham, N. Feth, V. Myroshnychenko, S. Linden, J. García de Abajo, M. Wegener, and M. Kociak, “Spectral imaging of individual split-ring resonators,” Phys. Rev. Lett. 105(25), 255501 (2010).
[CrossRef]

J. J. Cha, Z. Yu, E. Smith, M. Couillard, S. Fan, and D. A. Muller, “Mapping local optical densities of states in silicon photonic structures with nanoscale electron spectroscopy,” Phys. Rev. B 81(11), 113102 (2010).
[CrossRef]

2009

M. Kuttge, E. J. R. Vesseur, A. F. Koenderink, H. Lezec, H. Atwater, F. García de Abajo, and A. Polman, “Local density of states, spectrum, and far-field interference of surface plasmon polaritons probed by cathodoluminescence,” Phys. Rev. B 79(11), 113405 (2009).
[CrossRef]

T. T. Truong, J. Maria, J. Yao, M. E. Stewart, T.-W. Lee, S. K. Gray, R. G. Nuzzo, and J. A. Rogers, “Nanopost plasmonic crystals,” Nanotechnology 20(43), 434011 (2009).
[CrossRef] [PubMed]

T. Suzuki and N. Yamamoto, “Cathodoluminescent spectroscopic imaging of surface plasmon polaritons in a 1-dimensional plasmonic crystal,” Opt. Express 17(26), 23664–23671 (2009).
[CrossRef]

2008

F. J. García de Abajo and M. Kociak, “Probing the photonic local density of states with electron energy loss spectroscopy,” Phys. Rev. Lett. 100(10), 106804 (2008).
[CrossRef] [PubMed]

H. Ditlbacher, N. Galler, D. M. Koller, A. Hohenau, A. Leitner, F. R. Aussenegg, and J. R. Krenn, “Coupling dielectric waveguide modes to surface plasmon polaritons,” Opt. Express 16(14), 10455–10464 (2008).
[CrossRef] [PubMed]

J. Homola, “Surface plasmon resonance sensors for detection of chemical and biological species,” Chem. Rev. 108(2), 462–493 (2008).
[CrossRef] [PubMed]

N. Yamamoto and T. Suzuki, “Conversion of surface plasmon polaritons to light by a surface step,” Appl. Phys. Lett. 93(9), 093114 (2008).
[CrossRef]

2007

M. V. Bashevoy, F. Jonsson, K. F. Macdonald, Y. Chen, and N. I. Zheludev, “Hyperspectral imaging of plasmonic nanostructures with nanoscale resolution,” Opt. Express 15(18), 11313–11320 (2007).
[CrossRef] [PubMed]

J.-C. Weeber, A. Bouhelier, G. Colas des Francs, L. Markey, and A. Dereux, “Submicrometer in-plane integrated surface plasmon cavities,” Nano Lett. 7(5), 1352–1359 (2007).
[CrossRef] [PubMed]

2006

J. T. van Wijngaarden, E. Verhagen, A. Polman, C. E. Ross, H. J. Lezec, and H. A. Atwater, “Direct imaging of propagation and damping of near-resonance surface plasmon polaritons using cathodoluminescence spectroscopy,” Appl. Phys. Lett. 88(22), 221111 (2006).
[CrossRef]

2004

A. Degiron, H. J. Lezec, N. Yamamoto, and T. W. Ebbesen, “Optical transmission properties of a single subwavelength aperture in a real metal,” Opt. Commun. 239(1-3), 61–66 (2004).
[CrossRef]

2001

N. Yamamoto, K. Araya, and F. J. García de Abajo, “Photon emission from silver particles induced by high energy electron beam,” Phys. Rev. B 64(20), 205419 (2001).
[CrossRef]

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, “Waveguiding in surface plasmon polariton band gap structures,” Phys. Rev. Lett. 86(14), 3008–3011 (2001).
[CrossRef] [PubMed]

1977

D. Heitmann, “Radiative decay of surface plasmons excited by fast electrons on periodically modulated silver surfaces,” J. Phys. Chem. 10, 397–405 (1977).

1968

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, “Surface plasmon resonance effect in grating diffraction,” Phys. Rev. Lett. 21(22), 1530–1533 (1968).
[CrossRef]

Arakawa, E. T.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, “Surface plasmon resonance effect in grating diffraction,” Phys. Rev. Lett. 21(22), 1530–1533 (1968).
[CrossRef]

Araya, K.

N. Yamamoto, K. Araya, and F. J. García de Abajo, “Photon emission from silver particles induced by high energy electron beam,” Phys. Rev. B 64(20), 205419 (2001).
[CrossRef]

Atwater, H.

M. Kuttge, E. J. R. Vesseur, A. F. Koenderink, H. Lezec, H. Atwater, F. García de Abajo, and A. Polman, “Local density of states, spectrum, and far-field interference of surface plasmon polaritons probed by cathodoluminescence,” Phys. Rev. B 79(11), 113405 (2009).
[CrossRef]

Atwater, H. A.

J. T. van Wijngaarden, E. Verhagen, A. Polman, C. E. Ross, H. J. Lezec, and H. A. Atwater, “Direct imaging of propagation and damping of near-resonance surface plasmon polaritons using cathodoluminescence spectroscopy,” Appl. Phys. Lett. 88(22), 221111 (2006).
[CrossRef]

Aussenegg, F. R.

Bashevoy, M. V.

Boudarham, G.

G. Boudarham, N. Feth, V. Myroshnychenko, S. Linden, J. García de Abajo, M. Wegener, and M. Kociak, “Spectral imaging of individual split-ring resonators,” Phys. Rev. Lett. 105(25), 255501 (2010).
[CrossRef]

Bouhelier, A.

J.-C. Weeber, A. Bouhelier, G. Colas des Francs, L. Markey, and A. Dereux, “Submicrometer in-plane integrated surface plasmon cavities,” Nano Lett. 7(5), 1352–1359 (2007).
[CrossRef] [PubMed]

Bozhevolnyi, S. I.

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, “Waveguiding in surface plasmon polariton band gap structures,” Phys. Rev. Lett. 86(14), 3008–3011 (2001).
[CrossRef] [PubMed]

Cha, J. J.

J. J. Cha, Z. Yu, E. Smith, M. Couillard, S. Fan, and D. A. Muller, “Mapping local optical densities of states in silicon photonic structures with nanoscale electron spectroscopy,” Phys. Rev. B 81(11), 113102 (2010).
[CrossRef]

Chen, Y.

Colas des Francs, G.

J.-C. Weeber, A. Bouhelier, G. Colas des Francs, L. Markey, and A. Dereux, “Submicrometer in-plane integrated surface plasmon cavities,” Nano Lett. 7(5), 1352–1359 (2007).
[CrossRef] [PubMed]

Couillard, M.

J. J. Cha, Z. Yu, E. Smith, M. Couillard, S. Fan, and D. A. Muller, “Mapping local optical densities of states in silicon photonic structures with nanoscale electron spectroscopy,” Phys. Rev. B 81(11), 113102 (2010).
[CrossRef]

Cowan, J. J.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, “Surface plasmon resonance effect in grating diffraction,” Phys. Rev. Lett. 21(22), 1530–1533 (1968).
[CrossRef]

Degiron, A.

A. Degiron, H. J. Lezec, N. Yamamoto, and T. W. Ebbesen, “Optical transmission properties of a single subwavelength aperture in a real metal,” Opt. Commun. 239(1-3), 61–66 (2004).
[CrossRef]

Dereux, A.

J.-C. Weeber, A. Bouhelier, G. Colas des Francs, L. Markey, and A. Dereux, “Submicrometer in-plane integrated surface plasmon cavities,” Nano Lett. 7(5), 1352–1359 (2007).
[CrossRef] [PubMed]

Ditlbacher, H.

Ebbesen, T. W.

A. Degiron, H. J. Lezec, N. Yamamoto, and T. W. Ebbesen, “Optical transmission properties of a single subwavelength aperture in a real metal,” Opt. Commun. 239(1-3), 61–66 (2004).
[CrossRef]

Erland, J.

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, “Waveguiding in surface plasmon polariton band gap structures,” Phys. Rev. Lett. 86(14), 3008–3011 (2001).
[CrossRef] [PubMed]

Fan, S.

J. J. Cha, Z. Yu, E. Smith, M. Couillard, S. Fan, and D. A. Muller, “Mapping local optical densities of states in silicon photonic structures with nanoscale electron spectroscopy,” Phys. Rev. B 81(11), 113102 (2010).
[CrossRef]

Feth, N.

G. Boudarham, N. Feth, V. Myroshnychenko, S. Linden, J. García de Abajo, M. Wegener, and M. Kociak, “Spectral imaging of individual split-ring resonators,” Phys. Rev. Lett. 105(25), 255501 (2010).
[CrossRef]

Galler, N.

García de Abajo, F.

M. Kuttge, E. J. R. Vesseur, A. F. Koenderink, H. Lezec, H. Atwater, F. García de Abajo, and A. Polman, “Local density of states, spectrum, and far-field interference of surface plasmon polaritons probed by cathodoluminescence,” Phys. Rev. B 79(11), 113405 (2009).
[CrossRef]

García de Abajo, F. J.

N. Yamamoto, S. Ohtani, and F. J. García de Abajo, “Gap and Mie plasmons in individual silver nanospheres near a silver surface,” Nano Lett. 11(1), 91–95 (2011).
[CrossRef]

F. J. García de Abajo and M. Kociak, “Probing the photonic local density of states with electron energy loss spectroscopy,” Phys. Rev. Lett. 100(10), 106804 (2008).
[CrossRef] [PubMed]

N. Yamamoto, K. Araya, and F. J. García de Abajo, “Photon emission from silver particles induced by high energy electron beam,” Phys. Rev. B 64(20), 205419 (2001).
[CrossRef]

García de Abajo, J.

G. Boudarham, N. Feth, V. Myroshnychenko, S. Linden, J. García de Abajo, M. Wegener, and M. Kociak, “Spectral imaging of individual split-ring resonators,” Phys. Rev. Lett. 105(25), 255501 (2010).
[CrossRef]

Gray, S. K.

T. T. Truong, J. Maria, J. Yao, M. E. Stewart, T.-W. Lee, S. K. Gray, R. G. Nuzzo, and J. A. Rogers, “Nanopost plasmonic crystals,” Nanotechnology 20(43), 434011 (2009).
[CrossRef] [PubMed]

Hamm, R. N.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, “Surface plasmon resonance effect in grating diffraction,” Phys. Rev. Lett. 21(22), 1530–1533 (1968).
[CrossRef]

Heitmann, D.

D. Heitmann, “Radiative decay of surface plasmons excited by fast electrons on periodically modulated silver surfaces,” J. Phys. Chem. 10, 397–405 (1977).

Hohenau, A.

Homola, J.

J. Homola, “Surface plasmon resonance sensors for detection of chemical and biological species,” Chem. Rev. 108(2), 462–493 (2008).
[CrossRef] [PubMed]

Hvam, J. M.

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, “Waveguiding in surface plasmon polariton band gap structures,” Phys. Rev. Lett. 86(14), 3008–3011 (2001).
[CrossRef] [PubMed]

Jonsson, F.

Kociak, M.

G. Boudarham, N. Feth, V. Myroshnychenko, S. Linden, J. García de Abajo, M. Wegener, and M. Kociak, “Spectral imaging of individual split-ring resonators,” Phys. Rev. Lett. 105(25), 255501 (2010).
[CrossRef]

F. J. García de Abajo and M. Kociak, “Probing the photonic local density of states with electron energy loss spectroscopy,” Phys. Rev. Lett. 100(10), 106804 (2008).
[CrossRef] [PubMed]

Koenderink, A. F.

M. Kuttge, E. J. R. Vesseur, A. F. Koenderink, H. Lezec, H. Atwater, F. García de Abajo, and A. Polman, “Local density of states, spectrum, and far-field interference of surface plasmon polaritons probed by cathodoluminescence,” Phys. Rev. B 79(11), 113405 (2009).
[CrossRef]

Koller, D. M.

Krenn, J. R.

Kuttge, M.

M. Kuttge, E. J. R. Vesseur, A. F. Koenderink, H. Lezec, H. Atwater, F. García de Abajo, and A. Polman, “Local density of states, spectrum, and far-field interference of surface plasmon polaritons probed by cathodoluminescence,” Phys. Rev. B 79(11), 113405 (2009).
[CrossRef]

Lee, T.-W.

T. T. Truong, J. Maria, J. Yao, M. E. Stewart, T.-W. Lee, S. K. Gray, R. G. Nuzzo, and J. A. Rogers, “Nanopost plasmonic crystals,” Nanotechnology 20(43), 434011 (2009).
[CrossRef] [PubMed]

Leitner, A.

Leosson, K.

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, “Waveguiding in surface plasmon polariton band gap structures,” Phys. Rev. Lett. 86(14), 3008–3011 (2001).
[CrossRef] [PubMed]

Lezec, H.

M. Kuttge, E. J. R. Vesseur, A. F. Koenderink, H. Lezec, H. Atwater, F. García de Abajo, and A. Polman, “Local density of states, spectrum, and far-field interference of surface plasmon polaritons probed by cathodoluminescence,” Phys. Rev. B 79(11), 113405 (2009).
[CrossRef]

Lezec, H. J.

J. T. van Wijngaarden, E. Verhagen, A. Polman, C. E. Ross, H. J. Lezec, and H. A. Atwater, “Direct imaging of propagation and damping of near-resonance surface plasmon polaritons using cathodoluminescence spectroscopy,” Appl. Phys. Lett. 88(22), 221111 (2006).
[CrossRef]

A. Degiron, H. J. Lezec, N. Yamamoto, and T. W. Ebbesen, “Optical transmission properties of a single subwavelength aperture in a real metal,” Opt. Commun. 239(1-3), 61–66 (2004).
[CrossRef]

Linden, S.

G. Boudarham, N. Feth, V. Myroshnychenko, S. Linden, J. García de Abajo, M. Wegener, and M. Kociak, “Spectral imaging of individual split-ring resonators,” Phys. Rev. Lett. 105(25), 255501 (2010).
[CrossRef]

Macdonald, K. F.

Maria, J.

T. T. Truong, J. Maria, J. Yao, M. E. Stewart, T.-W. Lee, S. K. Gray, R. G. Nuzzo, and J. A. Rogers, “Nanopost plasmonic crystals,” Nanotechnology 20(43), 434011 (2009).
[CrossRef] [PubMed]

Markey, L.

J.-C. Weeber, A. Bouhelier, G. Colas des Francs, L. Markey, and A. Dereux, “Submicrometer in-plane integrated surface plasmon cavities,” Nano Lett. 7(5), 1352–1359 (2007).
[CrossRef] [PubMed]

Muller, D. A.

J. J. Cha, Z. Yu, E. Smith, M. Couillard, S. Fan, and D. A. Muller, “Mapping local optical densities of states in silicon photonic structures with nanoscale electron spectroscopy,” Phys. Rev. B 81(11), 113102 (2010).
[CrossRef]

Myroshnychenko, V.

G. Boudarham, N. Feth, V. Myroshnychenko, S. Linden, J. García de Abajo, M. Wegener, and M. Kociak, “Spectral imaging of individual split-ring resonators,” Phys. Rev. Lett. 105(25), 255501 (2010).
[CrossRef]

Nuzzo, R. G.

T. T. Truong, J. Maria, J. Yao, M. E. Stewart, T.-W. Lee, S. K. Gray, R. G. Nuzzo, and J. A. Rogers, “Nanopost plasmonic crystals,” Nanotechnology 20(43), 434011 (2009).
[CrossRef] [PubMed]

Ohtani, S.

N. Yamamoto, S. Ohtani, and F. J. García de Abajo, “Gap and Mie plasmons in individual silver nanospheres near a silver surface,” Nano Lett. 11(1), 91–95 (2011).
[CrossRef]

Polman, A.

M. Kuttge, E. J. R. Vesseur, A. F. Koenderink, H. Lezec, H. Atwater, F. García de Abajo, and A. Polman, “Local density of states, spectrum, and far-field interference of surface plasmon polaritons probed by cathodoluminescence,” Phys. Rev. B 79(11), 113405 (2009).
[CrossRef]

J. T. van Wijngaarden, E. Verhagen, A. Polman, C. E. Ross, H. J. Lezec, and H. A. Atwater, “Direct imaging of propagation and damping of near-resonance surface plasmon polaritons using cathodoluminescence spectroscopy,” Appl. Phys. Lett. 88(22), 221111 (2006).
[CrossRef]

Ritchie, R. H.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, “Surface plasmon resonance effect in grating diffraction,” Phys. Rev. Lett. 21(22), 1530–1533 (1968).
[CrossRef]

Rogers, J. A.

T. T. Truong, J. Maria, J. Yao, M. E. Stewart, T.-W. Lee, S. K. Gray, R. G. Nuzzo, and J. A. Rogers, “Nanopost plasmonic crystals,” Nanotechnology 20(43), 434011 (2009).
[CrossRef] [PubMed]

Ross, C. E.

J. T. van Wijngaarden, E. Verhagen, A. Polman, C. E. Ross, H. J. Lezec, and H. A. Atwater, “Direct imaging of propagation and damping of near-resonance surface plasmon polaritons using cathodoluminescence spectroscopy,” Appl. Phys. Lett. 88(22), 221111 (2006).
[CrossRef]

Skovgaard, P. M. W.

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, “Waveguiding in surface plasmon polariton band gap structures,” Phys. Rev. Lett. 86(14), 3008–3011 (2001).
[CrossRef] [PubMed]

Smith, E.

J. J. Cha, Z. Yu, E. Smith, M. Couillard, S. Fan, and D. A. Muller, “Mapping local optical densities of states in silicon photonic structures with nanoscale electron spectroscopy,” Phys. Rev. B 81(11), 113102 (2010).
[CrossRef]

Stewart, M. E.

T. T. Truong, J. Maria, J. Yao, M. E. Stewart, T.-W. Lee, S. K. Gray, R. G. Nuzzo, and J. A. Rogers, “Nanopost plasmonic crystals,” Nanotechnology 20(43), 434011 (2009).
[CrossRef] [PubMed]

Suzuki, T.

T. Suzuki and N. Yamamoto, “Cathodoluminescent spectroscopic imaging of surface plasmon polaritons in a 1-dimensional plasmonic crystal,” Opt. Express 17(26), 23664–23671 (2009).
[CrossRef]

N. Yamamoto and T. Suzuki, “Conversion of surface plasmon polaritons to light by a surface step,” Appl. Phys. Lett. 93(9), 093114 (2008).
[CrossRef]

Truong, T. T.

T. T. Truong, J. Maria, J. Yao, M. E. Stewart, T.-W. Lee, S. K. Gray, R. G. Nuzzo, and J. A. Rogers, “Nanopost plasmonic crystals,” Nanotechnology 20(43), 434011 (2009).
[CrossRef] [PubMed]

van Wijngaarden, J. T.

J. T. van Wijngaarden, E. Verhagen, A. Polman, C. E. Ross, H. J. Lezec, and H. A. Atwater, “Direct imaging of propagation and damping of near-resonance surface plasmon polaritons using cathodoluminescence spectroscopy,” Appl. Phys. Lett. 88(22), 221111 (2006).
[CrossRef]

Verhagen, E.

J. T. van Wijngaarden, E. Verhagen, A. Polman, C. E. Ross, H. J. Lezec, and H. A. Atwater, “Direct imaging of propagation and damping of near-resonance surface plasmon polaritons using cathodoluminescence spectroscopy,” Appl. Phys. Lett. 88(22), 221111 (2006).
[CrossRef]

Vesseur, E. J. R.

M. Kuttge, E. J. R. Vesseur, A. F. Koenderink, H. Lezec, H. Atwater, F. García de Abajo, and A. Polman, “Local density of states, spectrum, and far-field interference of surface plasmon polaritons probed by cathodoluminescence,” Phys. Rev. B 79(11), 113405 (2009).
[CrossRef]

Weeber, J.-C.

J.-C. Weeber, A. Bouhelier, G. Colas des Francs, L. Markey, and A. Dereux, “Submicrometer in-plane integrated surface plasmon cavities,” Nano Lett. 7(5), 1352–1359 (2007).
[CrossRef] [PubMed]

Wegener, M.

G. Boudarham, N. Feth, V. Myroshnychenko, S. Linden, J. García de Abajo, M. Wegener, and M. Kociak, “Spectral imaging of individual split-ring resonators,” Phys. Rev. Lett. 105(25), 255501 (2010).
[CrossRef]

Yamamoto, N.

N. Yamamoto, S. Ohtani, and F. J. García de Abajo, “Gap and Mie plasmons in individual silver nanospheres near a silver surface,” Nano Lett. 11(1), 91–95 (2011).
[CrossRef]

T. Suzuki and N. Yamamoto, “Cathodoluminescent spectroscopic imaging of surface plasmon polaritons in a 1-dimensional plasmonic crystal,” Opt. Express 17(26), 23664–23671 (2009).
[CrossRef]

N. Yamamoto and T. Suzuki, “Conversion of surface plasmon polaritons to light by a surface step,” Appl. Phys. Lett. 93(9), 093114 (2008).
[CrossRef]

A. Degiron, H. J. Lezec, N. Yamamoto, and T. W. Ebbesen, “Optical transmission properties of a single subwavelength aperture in a real metal,” Opt. Commun. 239(1-3), 61–66 (2004).
[CrossRef]

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[CrossRef]

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Yu, Z.

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[CrossRef]

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[CrossRef] [PubMed]

Nanotechnology

T. T. Truong, J. Maria, J. Yao, M. E. Stewart, T.-W. Lee, S. K. Gray, R. G. Nuzzo, and J. A. Rogers, “Nanopost plasmonic crystals,” Nanotechnology 20(43), 434011 (2009).
[CrossRef] [PubMed]

Opt. Commun.

A. Degiron, H. J. Lezec, N. Yamamoto, and T. W. Ebbesen, “Optical transmission properties of a single subwavelength aperture in a real metal,” Opt. Commun. 239(1-3), 61–66 (2004).
[CrossRef]

Opt. Express

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[CrossRef]

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[CrossRef]

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[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

(a) SEM image of a specimen with a periodic array of cylindrical holes and a period of 600 nm, and a diagram of the cross-section. Hole diameter and depth are 300 nm and 100 nm, respectively. InP substrate is coated by a 200-nm thick silver layer. (b) SPP to photon conversion process on the 2D-plasmonic crystal after excitation by an electron beam. (c) Geometry of the angle resolved measurement with a parabolic mirror. (d) Relation among the wave vectors of an emitting photon and associated SPPs.

Fig. 2
Fig. 2

Conversion of the intensity distribution from (a) the original data acquired by changing the hole position, to (b) an ARS pattern and (c) dispersion pattern. Each square indicates an interval between neighboring data points corresponding to the original ones in (a).

Fig. 3
Fig. 3

Dispersion patterns along the ΓX direction derived from the ARS patterns for (a) p-polarized and (b) s-polarized emissions, and along the ΓM direction for (c) p-polarized and (d) s-polarized emissions. Green lines indicate the SPP dispersion curves of the plasmonic crystal in the empty lattice approximation.

Fig. 4
Fig. 4

(a) Four reciprocal lattice points associated with the first-order Bloch states at the Γ point. (b)−(e) represent the Bloch wave patterns of the four SPP modes at the Γ point. Solid circles indicate holes and squares indicate a unit cell.

Fig. 5
Fig. 5

ARS patterns near the Γ point taken by (a) p-polarized and (b) s-polarized emissions. (c) Schematic diagram of the dispersion curves along the ΓX direction. Photon maps taken by the p-polarized emission at peak energies of (d) 2.067 eV, (e) 2.002 eV, (f) 1.944 eV, and by the s-polarized emission at (g) 2.002 eV and (h) 1.944 eV. (i)−(k) show patterns of the time-averaged square modulus of the field amplitude associated with the SPP modes at the Γ point. Red circles indicate holes.

Fig. 6
Fig. 6

(a) ARS pattern taken with a fixed electron beam outside the plasmonic crystal under the arrangement illustrated in Fig. 1(b). (b) and (c) are beam-scan spectral images across the plasmonic crystal edge taken by p-polarized emission in the surface normal direction and a tilted direction indicated by arrows 1 and 2 in (a), respectively. (d)–(f) are the ARS pattern and beam-scan spectral images for the s-polarized emission corresponding to (a)–(c).

Equations (7)

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I ( θ ) = I ( z ) p 2 ( 1 + ( z 2 p ) 2 ) 2 ,
k / / = | k | sin θ = E p h c sin θ ,
I ( k / / ) = I ( θ ) 1 k 2 sin θ cos θ .
k / / k p = G ,
E S P P = E p h ,
ψ n k p ( r ) = exp i ( k p r ) u ( r ) = G C G n exp i ( k p + G ) r ,
ψ n Γ ( r ) = C 1 n exp ( i a * r ) + C 2 n exp ( i b * r ) + C 3 n exp ( i a * r ) + C 4 n exp ( i b * r ) .

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