Abstract

A scanning transmission electron microscope (STEM) -cathodoluminescence (CL) technique is used to investigate the size dependence of the band structures in two-dimensional plasmonic crystals with a square lattice (SQ-PlCs) composed of cylindrical pillars and holes. The experimentally determined and calculated dependences of the band edge energies of the three SPP modes at the Γ point on the diameter of the cylindrical structure agree well. The photon maps reveal the field strength distributions of the standing SPP waves of the three eigenmodes. Additionally, a mechanism is proposed to explain the dependence of the contrast on the detected light polarization.

© 2014 Optical Society of America

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    [Crossref] [PubMed]
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  38. M. Kuttge, E. J. R. Vesseur, A. F. Koenderink, H. J. Lezec, H. A. Atwater, F. J. 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).
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    [Crossref] [PubMed]

2014 (1)

2013 (5)

C. Valsecchi and A. G. Brolo, “Periodic metallic nanostructures as plasmonic chemical sensors,” Langmuir 29(19), 5638–5649 (2013).
[Crossref] [PubMed]

W. Zhou, M. Dridi, J. Y. Suh, C. H. Kim, D. T. Co, M. R. Wasielewski, G. C. Schatz, and T. W. Odom, “Lasing action in strongly coupled plasmonic nanocavity arrays,” Nat. Nanotechnol. 8(7), 506–511 (2013).
[Crossref] [PubMed]

F. van Beijnum, P. J. van Veldhoven, E. J. Geluk, M. J. A. de Dood, G. W. ’t Hooft, and M. P. van Exter, “Surface plasmon lasing observed in metal hole arrays,” Phys. Rev. Lett. 110(20), 206802 (2013).
[Crossref] [PubMed]

S. Y. Chou and W. Ding, “Ultrathin, high-efficiency, broad-band, omniacceptance, organic solar cells enhanced by plasmonic cavity with subwavelength hole array,” Opt. Express 21(S1Suppl 1), A60–A76 (2013).
[Crossref] [PubMed]

M. Honda and N. Yamamoto, “Size dependence of surface plasmon modes in one-dimensional plasmonic crystal cavities,” Opt. Express 21(10), 11973–11983 (2013).
[Crossref] [PubMed]

2012 (3)

2011 (4)

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] [PubMed]

K. Takeuchi and N. Yamamoto, “Visualization of surface plasmon polariton waves in two-dimensional plasmonic crystal by cathodoluminescence,” Opt. Express 19(13), 12365–12374 (2011).
[Crossref] [PubMed]

A. M. Lakhani, M. K. Kim, E. K. Lau, and M. C. Wu, “Plasmonic crystal defect nanolaser,” Opt. Express 19(19), 18237–18245 (2011).
[Crossref] [PubMed]

P. Senanayake, C.-H. Hung, J. Shapiro, A. Lin, B. Liang, B. S. Williams, and D. L. Huffaker, “Surface plasmon-enhanced nanopillar photodetectors,” Nano Lett. 11(12), 5279–5283 (2011).
[Crossref] [PubMed]

2010 (5)

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[Crossref] [PubMed]

M. Iwanaga, “Polarization-selective transmission in stacked two-dimensional complementary plasmonic crystal slabs,” Appl. Phys. Lett. 96(8), 083106 (2010).
[Crossref]

W. Zhou, H. Gao, and T. W. Odom, “Toward broadband plasmonics: Tuning dispersion in rhombic plasmonic crystals,” ACS Nano 4(2), 1241–1247 (2010).
[Crossref] [PubMed]

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

J. Rosenberg, R. V. Shenoi, S. Krishna, and O. Painter, “Design of plasmonic photonic crystal resonant cavities for polarization sensitive infrared photodetectors,” Opt. Express 18(4), 3672–3686 (2010).
[Crossref] [PubMed]

2009 (3)

M. Kuttge, E. J. R. Vesseur, A. F. Koenderink, H. J. Lezec, H. A. Atwater, F. J. 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. 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] [PubMed]

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]

2008 (4)

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[Crossref] [PubMed]

T. Okamoto, J. Simonen, and S. Kawata, “Plasmonic band gaps of structured metallic thin films evaluated for a surface plasmon laser using the coupled-wave approach,” Phys. Rev. B 77(11), 115425 (2008).
[Crossref]

C. Billaudeau, S. Collin, C. Sauvan, N. Bardou, F. Pardo, and J.-L. Pelouard, “Angle-resolved transmission measurements through anisotropic two-dimensional plasmonic crystals,” Opt. Lett. 33(2), 165–167 (2008).
[Crossref] [PubMed]

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]

2007 (3)

F. J. Garcia de Abajo, “Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79(4), 1267–1290 (2007).
[Crossref]

M. Davanco, Y. Urzhumov, and G. Shvets, “The complex Bloch bands of a 2D plasmonic crystal displaying isotropic negative refraction,” Opt. Express 15(15), 9681–9691 (2007).
[Crossref] [PubMed]

Y. Gong and J. Vučković, “Design of plasmon cavities for solid-state cavity quantum electrodynamics applications,” Appl. Phys. Lett. 90(3), 033113 (2007).
[Crossref]

2006 (1)

M. U. González, J.-C. Weeber, A.-L. Baudrion, A. Dereux, A. L. Stepanov, J. R. Krenn, E. Devaux, and T. W. Ebbesen, “Design, near-field characterization, and modeling of 45° surface-plasmon Bragg mirrors,” Phys. Rev. B 73(15), 155416 (2006).
[Crossref]

2005 (2)

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408(3–4), 131–314 (2005).
[Crossref]

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408(3–4), 131–314 (2005).
[Crossref]

2004 (1)

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92(10), 107401 (2004).
[Crossref] [PubMed]

2001 (1)

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]

1998 (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission throughsub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[Crossref]

1996 (1)

S. C. Kitson, W. L. Barnes, and J. R. Sambles, “Full photonic band gap for surface modes in the visible,” Phys. Rev. Lett. 77(13), 2670–2673 (1996).
[Crossref] [PubMed]

’t Hooft, G. W.

F. van Beijnum, P. J. van Veldhoven, E. J. Geluk, M. J. A. de Dood, G. W. ’t Hooft, and M. P. van Exter, “Surface plasmon lasing observed in metal hole arrays,” Phys. Rev. Lett. 110(20), 206802 (2013).
[Crossref] [PubMed]

Anker, J. N.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[Crossref] [PubMed]

Atwater, H. A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[Crossref] [PubMed]

M. Kuttge, E. J. R. Vesseur, A. F. Koenderink, H. J. Lezec, H. A. Atwater, F. J. 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]

Bardou, N.

Barnes, W. L.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92(10), 107401 (2004).
[Crossref] [PubMed]

S. C. Kitson, W. L. Barnes, and J. R. Sambles, “Full photonic band gap for surface modes in the visible,” Phys. Rev. Lett. 77(13), 2670–2673 (1996).
[Crossref] [PubMed]

Baudrion, A.-L.

M. U. González, J.-C. Weeber, A.-L. Baudrion, A. Dereux, A. L. Stepanov, J. R. Krenn, E. Devaux, and T. W. Ebbesen, “Design, near-field characterization, and modeling of 45° surface-plasmon Bragg mirrors,” Phys. Rev. B 73(15), 155416 (2006).
[Crossref]

Billaudeau, C.

Boudarham, G.

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

Brolo, A. G.

C. Valsecchi and A. G. Brolo, “Periodic metallic nanostructures as plasmonic chemical sensors,” Langmuir 29(19), 5638–5649 (2013).
[Crossref] [PubMed]

Chou, S. Y.

Co, D. T.

W. Zhou, M. Dridi, J. Y. Suh, C. H. Kim, D. T. Co, M. R. Wasielewski, G. C. Schatz, and T. W. Odom, “Lasing action in strongly coupled plasmonic nanocavity arrays,” Nat. Nanotechnol. 8(7), 506–511 (2013).
[Crossref] [PubMed]

Collin, S.

Davanco, M.

de Abajo, F. J. G.

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

de Dood, M. J. A.

F. van Beijnum, P. J. van Veldhoven, E. J. Geluk, M. J. A. de Dood, G. W. ’t Hooft, and M. P. van Exter, “Surface plasmon lasing observed in metal hole arrays,” Phys. Rev. Lett. 110(20), 206802 (2013).
[Crossref] [PubMed]

Dereux, A.

M. U. González, J.-C. Weeber, A.-L. Baudrion, A. Dereux, A. L. Stepanov, J. R. Krenn, E. Devaux, and T. W. Ebbesen, “Design, near-field characterization, and modeling of 45° surface-plasmon Bragg mirrors,” Phys. Rev. B 73(15), 155416 (2006).
[Crossref]

Devaux, E.

M. U. González, J.-C. Weeber, A.-L. Baudrion, A. Dereux, A. L. Stepanov, J. R. Krenn, E. Devaux, and T. W. Ebbesen, “Design, near-field characterization, and modeling of 45° surface-plasmon Bragg mirrors,” Phys. Rev. B 73(15), 155416 (2006).
[Crossref]

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92(10), 107401 (2004).
[Crossref] [PubMed]

Ding, W.

Dintinger, J.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92(10), 107401 (2004).
[Crossref] [PubMed]

Dridi, M.

W. Zhou, M. Dridi, J. Y. Suh, C. H. Kim, D. T. Co, M. R. Wasielewski, G. C. Schatz, and T. W. Odom, “Lasing action in strongly coupled plasmonic nanocavity arrays,” Nat. Nanotechnol. 8(7), 506–511 (2013).
[Crossref] [PubMed]

Ebbesen, T. W.

M. U. González, J.-C. Weeber, A.-L. Baudrion, A. Dereux, A. L. Stepanov, J. R. Krenn, E. Devaux, and T. W. Ebbesen, “Design, near-field characterization, and modeling of 45° surface-plasmon Bragg mirrors,” Phys. Rev. B 73(15), 155416 (2006).
[Crossref]

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92(10), 107401 (2004).
[Crossref] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission throughsub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[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]

Feth, N.

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

Gao, H.

W. Zhou, H. Gao, and T. W. Odom, “Toward broadband plasmonics: Tuning dispersion in rhombic plasmonic crystals,” ACS Nano 4(2), 1241–1247 (2010).
[Crossref] [PubMed]

Garcia de Abajo, F. J.

F. J. Garcia de Abajo, “Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79(4), 1267–1290 (2007).
[Crossref]

García de Abajo, F. J.

M. Kociak and F. J. García de Abajo, “Nanoscale mapping of plasmons, photons, and excitons,” MRS Bull. 37(01), 39–46 (2012).
[Crossref]

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] [PubMed]

M. Kuttge, E. J. R. Vesseur, A. F. Koenderink, H. J. Lezec, H. A. Atwater, F. J. 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]

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]

Geluk, E. J.

F. van Beijnum, P. J. van Veldhoven, E. J. Geluk, M. J. A. de Dood, G. W. ’t Hooft, and M. P. van Exter, “Surface plasmon lasing observed in metal hole arrays,” Phys. Rev. Lett. 110(20), 206802 (2013).
[Crossref] [PubMed]

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission throughsub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[Crossref]

Gong, Y.

Y. Gong and J. Vučković, “Design of plasmon cavities for solid-state cavity quantum electrodynamics applications,” Appl. Phys. Lett. 90(3), 033113 (2007).
[Crossref]

González, M. U.

M. U. González, J.-C. Weeber, A.-L. Baudrion, A. Dereux, A. L. Stepanov, J. R. Krenn, E. Devaux, and T. W. Ebbesen, “Design, near-field characterization, and modeling of 45° surface-plasmon Bragg mirrors,” Phys. Rev. B 73(15), 155416 (2006).
[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]

Hall, W. P.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[Crossref] [PubMed]

Honda, M.

Huffaker, D. L.

P. Senanayake, C.-H. Hung, J. Shapiro, A. Lin, B. Liang, B. S. Williams, and D. L. Huffaker, “Surface plasmon-enhanced nanopillar photodetectors,” Nano Lett. 11(12), 5279–5283 (2011).
[Crossref] [PubMed]

Hung, C.-H.

P. Senanayake, C.-H. Hung, J. Shapiro, A. Lin, B. Liang, B. S. Williams, and D. L. Huffaker, “Surface plasmon-enhanced nanopillar photodetectors,” Nano Lett. 11(12), 5279–5283 (2011).
[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]

Iwanaga, M.

M. Iwanaga, “Polarization-selective transmission in stacked two-dimensional complementary plasmonic crystal slabs,” Appl. Phys. Lett. 96(8), 083106 (2010).
[Crossref]

Kawata, S.

T. Okamoto and S. Kawata, “Dispersion relation and radiation properties of plasmonic crystals with triangular lattices,” Opt. Express 20(5), 5168–5177 (2012).
[Crossref] [PubMed]

T. Okamoto, J. Simonen, and S. Kawata, “Plasmonic band gaps of structured metallic thin films evaluated for a surface plasmon laser using the coupled-wave approach,” Phys. Rev. B 77(11), 115425 (2008).
[Crossref]

Kim, C. H.

W. Zhou, M. Dridi, J. Y. Suh, C. H. Kim, D. T. Co, M. R. Wasielewski, G. C. Schatz, and T. W. Odom, “Lasing action in strongly coupled plasmonic nanocavity arrays,” Nat. Nanotechnol. 8(7), 506–511 (2013).
[Crossref] [PubMed]

Kim, M. K.

Kitson, S. C.

S. C. Kitson, W. L. Barnes, and J. R. Sambles, “Full photonic band gap for surface modes in the visible,” Phys. Rev. Lett. 77(13), 2670–2673 (1996).
[Crossref] [PubMed]

Kociak, M.

M. Kociak and F. J. García de Abajo, “Nanoscale mapping of plasmons, photons, and excitons,” MRS Bull. 37(01), 39–46 (2012).
[Crossref]

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

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. J. Lezec, H. A. Atwater, F. J. 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]

Krenn, J. R.

M. U. González, J.-C. Weeber, A.-L. Baudrion, A. Dereux, A. L. Stepanov, J. R. Krenn, E. Devaux, and T. W. Ebbesen, “Design, near-field characterization, and modeling of 45° surface-plasmon Bragg mirrors,” Phys. Rev. B 73(15), 155416 (2006).
[Crossref]

Krishna, S.

Kuttge, M.

M. Kuttge, E. J. R. Vesseur, A. F. Koenderink, H. J. Lezec, H. A. Atwater, F. J. 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]

Lakhani, A. M.

Lau, E. K.

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]

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. J.

M. Kuttge, E. J. R. Vesseur, A. F. Koenderink, H. J. Lezec, H. A. Atwater, F. J. 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. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission throughsub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[Crossref]

Liang, B.

P. Senanayake, C.-H. Hung, J. Shapiro, A. Lin, B. Liang, B. S. Williams, and D. L. Huffaker, “Surface plasmon-enhanced nanopillar photodetectors,” Nano Lett. 11(12), 5279–5283 (2011).
[Crossref] [PubMed]

Lin, A.

P. Senanayake, C.-H. Hung, J. Shapiro, A. Lin, B. Liang, B. S. Williams, and D. L. Huffaker, “Surface plasmon-enhanced nanopillar photodetectors,” Nano Lett. 11(12), 5279–5283 (2011).
[Crossref] [PubMed]

Linden, S.

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

Lyandres, O.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[Crossref] [PubMed]

Maradudin, A. A.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408(3–4), 131–314 (2005).
[Crossref]

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408(3–4), 131–314 (2005).
[Crossref]

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]

Murray, W. A.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92(10), 107401 (2004).
[Crossref] [PubMed]

Myroshnychenko, V.

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

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]

Odom, T. W.

W. Zhou, M. Dridi, J. Y. Suh, C. H. Kim, D. T. Co, M. R. Wasielewski, G. C. Schatz, and T. W. Odom, “Lasing action in strongly coupled plasmonic nanocavity arrays,” Nat. Nanotechnol. 8(7), 506–511 (2013).
[Crossref] [PubMed]

W. Zhou, H. Gao, and T. W. Odom, “Toward broadband plasmonics: Tuning dispersion in rhombic plasmonic crystals,” ACS Nano 4(2), 1241–1247 (2010).
[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] [PubMed]

Okamoto, T.

T. Okamoto and S. Kawata, “Dispersion relation and radiation properties of plasmonic crystals with triangular lattices,” Opt. Express 20(5), 5168–5177 (2012).
[Crossref] [PubMed]

T. Okamoto, J. Simonen, and S. Kawata, “Plasmonic band gaps of structured metallic thin films evaluated for a surface plasmon laser using the coupled-wave approach,” Phys. Rev. B 77(11), 115425 (2008).
[Crossref]

Painter, O.

Pardo, F.

Parisi, G.

Pelouard, J.-L.

Polman, A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[Crossref] [PubMed]

M. Kuttge, E. J. R. Vesseur, A. F. Koenderink, H. J. Lezec, H. A. Atwater, F. J. 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]

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]

Romanato, F.

Rosenberg, J.

Sambles, J. R.

S. C. Kitson, W. L. Barnes, and J. R. Sambles, “Full photonic band gap for surface modes in the visible,” Phys. Rev. Lett. 77(13), 2670–2673 (1996).
[Crossref] [PubMed]

Sauvan, C.

Schatz, G. C.

W. Zhou, M. Dridi, J. Y. Suh, C. H. Kim, D. T. Co, M. R. Wasielewski, G. C. Schatz, and T. W. Odom, “Lasing action in strongly coupled plasmonic nanocavity arrays,” Nat. Nanotechnol. 8(7), 506–511 (2013).
[Crossref] [PubMed]

Senanayake, P.

P. Senanayake, C.-H. Hung, J. Shapiro, A. Lin, B. Liang, B. S. Williams, and D. L. Huffaker, “Surface plasmon-enhanced nanopillar photodetectors,” Nano Lett. 11(12), 5279–5283 (2011).
[Crossref] [PubMed]

Shah, N. C.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[Crossref] [PubMed]

Shapiro, J.

P. Senanayake, C.-H. Hung, J. Shapiro, A. Lin, B. Liang, B. S. Williams, and D. L. Huffaker, “Surface plasmon-enhanced nanopillar photodetectors,” Nano Lett. 11(12), 5279–5283 (2011).
[Crossref] [PubMed]

Shenoi, R. V.

Shvets, G.

Simonen, J.

T. Okamoto, J. Simonen, and S. Kawata, “Plasmonic band gaps of structured metallic thin films evaluated for a surface plasmon laser using the coupled-wave approach,” Phys. Rev. B 77(11), 115425 (2008).
[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]

Smolyaninov, I. I.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408(3–4), 131–314 (2005).
[Crossref]

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408(3–4), 131–314 (2005).
[Crossref]

Stepanov, A. L.

M. U. González, J.-C. Weeber, A.-L. Baudrion, A. Dereux, A. L. Stepanov, J. R. Krenn, E. Devaux, and T. W. Ebbesen, “Design, near-field characterization, and modeling of 45° surface-plasmon Bragg mirrors,” Phys. Rev. B 73(15), 155416 (2006).
[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]

Suh, J. Y.

W. Zhou, M. Dridi, J. Y. Suh, C. H. Kim, D. T. Co, M. R. Wasielewski, G. C. Schatz, and T. W. Odom, “Lasing action in strongly coupled plasmonic nanocavity arrays,” Nat. Nanotechnol. 8(7), 506–511 (2013).
[Crossref] [PubMed]

Suzuki, T.

Takeuchi, K.

Thio, T.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission throughsub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[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]

Urzhumov, Y.

Valsecchi, C.

C. Valsecchi and A. G. Brolo, “Periodic metallic nanostructures as plasmonic chemical sensors,” Langmuir 29(19), 5638–5649 (2013).
[Crossref] [PubMed]

van Beijnum, F.

F. van Beijnum, P. J. van Veldhoven, E. J. Geluk, M. J. A. de Dood, G. W. ’t Hooft, and M. P. van Exter, “Surface plasmon lasing observed in metal hole arrays,” Phys. Rev. Lett. 110(20), 206802 (2013).
[Crossref] [PubMed]

Van Duyne, R. P.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[Crossref] [PubMed]

van Exter, M. P.

F. van Beijnum, P. J. van Veldhoven, E. J. Geluk, M. J. A. de Dood, G. W. ’t Hooft, and M. P. van Exter, “Surface plasmon lasing observed in metal hole arrays,” Phys. Rev. Lett. 110(20), 206802 (2013).
[Crossref] [PubMed]

van Veldhoven, P. J.

F. van Beijnum, P. J. van Veldhoven, E. J. Geluk, M. J. A. de Dood, G. W. ’t Hooft, and M. P. van Exter, “Surface plasmon lasing observed in metal hole arrays,” Phys. Rev. Lett. 110(20), 206802 (2013).
[Crossref] [PubMed]

Vesseur, E. J. R.

M. Kuttge, E. J. R. Vesseur, A. F. Koenderink, H. J. Lezec, H. A. Atwater, F. J. 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]

Vuckovic, J.

Y. Gong and J. Vučković, “Design of plasmon cavities for solid-state cavity quantum electrodynamics applications,” Appl. Phys. Lett. 90(3), 033113 (2007).
[Crossref]

Wasielewski, M. R.

W. Zhou, M. Dridi, J. Y. Suh, C. H. Kim, D. T. Co, M. R. Wasielewski, G. C. Schatz, and T. W. Odom, “Lasing action in strongly coupled plasmonic nanocavity arrays,” Nat. Nanotechnol. 8(7), 506–511 (2013).
[Crossref] [PubMed]

Watanabe, H.

Weeber, J.-C.

M. U. González, J.-C. Weeber, A.-L. Baudrion, A. Dereux, A. L. Stepanov, J. R. Krenn, E. Devaux, and T. W. Ebbesen, “Design, near-field characterization, and modeling of 45° surface-plasmon Bragg mirrors,” Phys. Rev. B 73(15), 155416 (2006).
[Crossref]

Wegener, M.

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

Williams, B. S.

P. Senanayake, C.-H. Hung, J. Shapiro, A. Lin, B. Liang, B. S. Williams, and D. L. Huffaker, “Surface plasmon-enhanced nanopillar photodetectors,” Nano Lett. 11(12), 5279–5283 (2011).
[Crossref] [PubMed]

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission throughsub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[Crossref]

Wu, M. C.

Yamamoto, N.

Yao, 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]

Zayats, A. V.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408(3–4), 131–314 (2005).
[Crossref]

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408(3–4), 131–314 (2005).
[Crossref]

Zhao, J.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[Crossref] [PubMed]

Zhou, W.

W. Zhou, M. Dridi, J. Y. Suh, C. H. Kim, D. T. Co, M. R. Wasielewski, G. C. Schatz, and T. W. Odom, “Lasing action in strongly coupled plasmonic nanocavity arrays,” Nat. Nanotechnol. 8(7), 506–511 (2013).
[Crossref] [PubMed]

W. Zhou, H. Gao, and T. W. Odom, “Toward broadband plasmonics: Tuning dispersion in rhombic plasmonic crystals,” ACS Nano 4(2), 1241–1247 (2010).
[Crossref] [PubMed]

Zilio, P.

ACS Nano (1)

W. Zhou, H. Gao, and T. W. Odom, “Toward broadband plasmonics: Tuning dispersion in rhombic plasmonic crystals,” ACS Nano 4(2), 1241–1247 (2010).
[Crossref] [PubMed]

Appl. Phys. Lett. (2)

M. Iwanaga, “Polarization-selective transmission in stacked two-dimensional complementary plasmonic crystal slabs,” Appl. Phys. Lett. 96(8), 083106 (2010).
[Crossref]

Y. Gong and J. Vučković, “Design of plasmon cavities for solid-state cavity quantum electrodynamics applications,” Appl. Phys. Lett. 90(3), 033113 (2007).
[Crossref]

Langmuir (1)

C. Valsecchi and A. G. Brolo, “Periodic metallic nanostructures as plasmonic chemical sensors,” Langmuir 29(19), 5638–5649 (2013).
[Crossref] [PubMed]

MRS Bull. (1)

M. Kociak and F. J. García de Abajo, “Nanoscale mapping of plasmons, photons, and excitons,” MRS Bull. 37(01), 39–46 (2012).
[Crossref]

Nano Lett. (2)

P. Senanayake, C.-H. Hung, J. Shapiro, A. Lin, B. Liang, B. S. Williams, and D. L. Huffaker, “Surface plasmon-enhanced nanopillar photodetectors,” Nano Lett. 11(12), 5279–5283 (2011).
[Crossref] [PubMed]

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] [PubMed]

Nanotechnology (1)

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]

Nat. Mater. (2)

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[Crossref] [PubMed]

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[Crossref] [PubMed]

Nat. Nanotechnol. (1)

W. Zhou, M. Dridi, J. Y. Suh, C. H. Kim, D. T. Co, M. R. Wasielewski, G. C. Schatz, and T. W. Odom, “Lasing action in strongly coupled plasmonic nanocavity arrays,” Nat. Nanotechnol. 8(7), 506–511 (2013).
[Crossref] [PubMed]

Nature (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission throughsub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
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Opt. Express (10)

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).
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J. Rosenberg, R. V. Shenoi, S. Krishna, and O. Painter, “Design of plasmonic photonic crystal resonant cavities for polarization sensitive infrared photodetectors,” Opt. Express 18(4), 3672–3686 (2010).
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K. Takeuchi and N. Yamamoto, “Visualization of surface plasmon polariton waves in two-dimensional plasmonic crystal by cathodoluminescence,” Opt. Express 19(13), 12365–12374 (2011).
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A. M. Lakhani, M. K. Kim, E. K. Lau, and M. C. Wu, “Plasmonic crystal defect nanolaser,” Opt. Express 19(19), 18237–18245 (2011).
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T. Okamoto and S. Kawata, “Dispersion relation and radiation properties of plasmonic crystals with triangular lattices,” Opt. Express 20(5), 5168–5177 (2012).
[Crossref] [PubMed]

G. Parisi, P. Zilio, and F. Romanato, “Complex Bloch-modes calculation of plasmonic crystal slabs by means of finite elements method,” Opt. Express 20(15), 16690–16703 (2012).
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S. Y. Chou and W. Ding, “Ultrathin, high-efficiency, broad-band, omniacceptance, organic solar cells enhanced by plasmonic cavity with subwavelength hole array,” Opt. Express 21(S1Suppl 1), A60–A76 (2013).
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M. Honda and N. Yamamoto, “Size dependence of surface plasmon modes in one-dimensional plasmonic crystal cavities,” Opt. Express 21(10), 11973–11983 (2013).
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H. Watanabe, M. Honda, and N. Yamamoto, “Size dependence of band-gaps in a one-dimensional plasmonic crystal,” Opt. Express 22(5), 5155–5165 (2014).
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M. Davanco, Y. Urzhumov, and G. Shvets, “The complex Bloch bands of a 2D plasmonic crystal displaying isotropic negative refraction,” Opt. Express 15(15), 9681–9691 (2007).
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Opt. Lett. (1)

Phys. Rep. (2)

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408(3–4), 131–314 (2005).
[Crossref]

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408(3–4), 131–314 (2005).
[Crossref]

Phys. Rev. B (3)

M. U. González, J.-C. Weeber, A.-L. Baudrion, A. Dereux, A. L. Stepanov, J. R. Krenn, E. Devaux, and T. W. Ebbesen, “Design, near-field characterization, and modeling of 45° surface-plasmon Bragg mirrors,” Phys. Rev. B 73(15), 155416 (2006).
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Figures (12)

Fig. 1
Fig. 1 (a) Setup for an angle-resolved measurement, and (b) angular map in a parabolic mirror with respect to a tilted specimen. Red circle indicates a pinhole moving along the broken red line. (c) Two linear paths on a SQ-PlC along which the electron beam is scanned to acquire the BSS images.
Fig. 2
Fig. 2 (a) Reciprocal lattice and (b) dispersion relation of a SQ-PlC. (c) Electric field and (d) field strength distribution of the three band edge modes at the Γ point. Square in the middle of each pattern indicates a unit cell.
Fig. 3
Fig. 3 Emission spectra for the SQ-PlCs with various diameters of (a) cylindrical pillars and (b) cylindrical holes taken in the surface normal direction. (P = 600 nm, h = 100 nm).
Fig. 4
Fig. 4 ARS patterns from the SQ-PlCs with various diameters of cylindrical pillars acquired with [(a)–(e)] p-polarized and [(f)–(j)] s-polarized light. (k) Illustration of the sample. (l) and (m) Schematic dispersion curves for D = 200 nm and D = 500 nm, respectively. (P = 600 nm, h = 100 nm).
Fig. 5
Fig. 5 BSS images of the SQ-PlCs with pillar diameters between 200 nm and 500 nm taken by non-polarized light emitted in the surface normal direction. Images in the upper row are taken along the L1 line, while those in the lower row are along the L2 line. (P = 600 nm, h = 100 nm).
Fig. 6
Fig. 6 (a)–(e) Photon maps of the SQ-PlCs of the pillars with D = 200 nm and (f)–(i) those with D = 500 nm taken by non-polarized light emitted in the surface normal direction. (a) and (f) are panchromatic photon maps, and the others are monochromatic ones at the mode energies shown. (P = 600 nm, h = 100 nm).
Fig. 7
Fig. 7 (a)–(d) ARS patterns from the SQ-PlCs of cylindrical holes acquired using p-polarized light and (e)–(h) those taken by s-polarized light. (i)–(k) Schematic drawings of the band structures along the Γ–X line for D = 200 nm, 400 nm, and 500 nm, respectively. (P = 600 nm, h = 100 nm).
Fig. 8
Fig. 8 BSS images of the SQ-PlCs with hole diameters ranging from 200 nm to 500 nm taken by scanning the electron beam along (a)–(e) the L1 line and (f)–(j) the L2 line using non-polarized light emitted in the surface normal direction. (P = 600 nm, h = 100 nm).
Fig. 9
Fig. 9 (a)–(d) Photon maps of the SQ-PlCs of cylindrical holes with D = 300 nm and (e)–(h) those with D = 500 nm acquired using non-polarized light emitted in the surface normal direction. (a) and (e) are panchromatic photon maps, and the others are monochromatic ones at the mode energies shown. (P = 600 nm, h = 100 nm).
Fig. 10
Fig. 10 Size dependence of the band edge energies at the Γ point of the SQ-PlCs with cylindrical pillars and holes. Pillar height is (a) h = 50 nm and (b) h = 100 nm, and the hole depth is (c) h = 50 nm and (d) h = 100 nm. (P = 600 nm).
Fig. 11
Fig. 11 Size dependence of the band edge energies and the Q-factors of the SQ-PlCs of (a), (b), (d), (e) pillars and (c), (f) holes calculated by FDTD. Pillar height is h = 30 nm for (a) and (d), and h = 50 nm for (b) and (e), and the hole depth is h = 50 nm for (c) and (f).
Fig. 12
Fig. 12 Photon maps of the SQ-PlCs of the cylindrical pillars with D = 500 nm and h = 50 nm taken by (a) non-polarized light and (c) polarized light emitted in the surface normal direction. From left to right, the photon maps correspond to the E, B, and A modes. Field strength distributions of the three modes calculated (b) by group theory and (d) by the FDTD method.

Tables (1)

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Table 1 Character table for C4v point symmetry.

Equations (15)

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Ψ n (r,t)= ψ n (r) e iωt ,
ψ n (r)= e i kr ϕ n (r)= e i k.r g C g n e i gr
ψ A1 (x,y)=cos2πx+cosπy, ψ B1 (x,y)=cos2πxcosπy, ψ E(1) (x,y)=sin2πx, ψ E(2) (x,y)=sin2πy,
A 1 mode: (cos2πx+cos2πy) 2 , B 1 mode: (cos2πxcos2πy) 2 , E(1) mode: sin 2 2πx, E(2) mode: sin 2 2πy.
h 2 =πh ( D 2P ) 2 2 J 1 ( X ) X ,
I PM (R) η ex ( E n ,R) η SPPphoton ( E n ,0,0).
I n//e (R) | C n (R)(e p n ) | 2 | C n (R) (er) ψ n (r) dr | 2 ,
p n r σ n (r) dr r ψ n (r) dr
ψ E (r,R)= C 1 (R) ψ E(1) (r)+ C 2 (R) ψ E(2) (r) ,
p E (R) r σ E (r) dr r ψ E (r,R) dr= C 1 (R) p 1 + C 2 (R) p 2
p = 1 r ψ E(1) (r) dr=( p x 0 ) , p = 2 r ψ E(2) (r) dr=( 0 p y ) ,
p x x ψ E(1) (r) dr, p y y ψ E(2) (r) dr
I E//e (R) | e p E (R) | 2 = | C 1 (R)(e p 1 )+ C 2 (R)(e p 2 ) | 2
I E//x (R) | C 1 (R)(e p 1 ) | 2 p 2 | ψ E(1) (R) | 2 p 2 sin 2 2πX.
I E,NP (R) 0 2π | ψ E(1) (R)pcosθ+ ψ E(2) (R)psinθ | 2 dθ p 2 { | ψ E(1) (R) | 2 + | ψ E(2) (R) | 2 } p 2 ( sin 2 2πX+ sin 2 2πY )

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