Abstract

We theoretically investigate the electromagnetic enhancement on a metallic surface patterned with periodic subwavelength structures. Fully-vectorial calculations show a large-area electromagnetic enhancement (LAEE) on the surface, which strongly contrasts with the previously reported “hot spots” that occur in specific tiny regions and which relieves the rigorous requirement of the nano-scale location of sample molecules. The LAEE allows for designing more practicable substrates for many enhanced-spectra applications. By building up microscopic models, the LAEE is shown due to a resonant excitation of surface waves that include both the surface plasmon polariton (SPP) and a quasi-cylindrical wave (QCW). The surface waves propagate on the substrate over a long distance and thus greatly enlarge the area of electromagnetic enhancement compared to the nano-sized hot spots caused by localized modes. Gain medium is introduced to further strengthen the large-area surface-wave resonance, with which an enhancement factor (EF) of electric-field intensity up to a few thousands is achieved.

© 2013 Optical Society of America

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2012 (3)

Z. W. Zeng and H. T. Liu, “Electromagnetic enhancement by a T-shaped metallic nano groove impact of surface plasmon polaritons and other surface waves,” IEEE J. Sel. Top. Quantum Electron. 18(6), 1669–1675 (2012).
[Crossref]

F. van Beijnum, C. Rétif, C. B. Smiet, H. T. Liu, P. Lalanne, and M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature 492(7429), 411–414 (2012).
[Crossref] [PubMed]

X. Zhang, H. T. Liu, and Y. Zhong, “Compensation of propagation loss of surface plasmon polaritons with a finite-thickness dielectric gain layer,” J. Opt. 14(12), 125003 (2012).
[Crossref]

2011 (3)

2010 (9)

N. Pazos-Pérez, W. Ni, A. Schweikart, R. A. Alvarez-Puebla, A. Fery, and L. M. Liz-Marzán, “Highly uniform SERS substrates formed by wrinkle-confined drying of gold colloids,” Chem. Sci. 1(2), 174–178 (2010).
[Crossref]

Z. Y. Li and Y. Xia, “Metal nanoparticles with gain toward single-molecule detection by surface-enhanced Raman scattering,” Nano Lett. 10(1), 243–249 (2010).
[Crossref] [PubMed]

D. K. Lim, K. S. Jeon, H. M. Kim, J. M. Nam, and Y. D. Suh, “Nanogap-engineerable Raman-active nanodumbbells for single-molecule detection,” Nat. Mater. 9(1), 60–67 (2010).
[Crossref] [PubMed]

S. L. Kleinman, J. M. Bingham, A. I. Henry, K. L. Wustholz, and R. P. Van Duyne, “Structural and optical characterization of single nanoparticles and single molecule SERS,” Proc. SPIE 7757, 77570J, 77570J-10 (2010).
[Crossref]

H. T. Liu and P. Lalanne, “Light scattering by metallic surfaces with subwavelength patterns,” Phys. Rev. B 82(11), 115418 (2010).
[Crossref]

A. Krishnan, S. P. Frisbie, L. Grave de Peralta, and A. A. Bernussi, “Plasmon stimulated emission in arrays of bimetallic structres coated with dye-doped dielectric,” Appl. Phys. Lett. 96(11), 111104 (2010).
[Crossref]

W. H. Park and Z. H. Kim, “Charge transfer enhancement in the SERS of a single molecule,” Nano Lett. 10(10), 4040–4048 (2010).
[Crossref] [PubMed]

Y. M. Hou, J. Xu, X. J. Zhang, and D. P. Yu, “SERS on periodic arrays of coupled quadrate-holes and squares,” Nanotechnology 21(19), 195203 (2010).
[Crossref] [PubMed]

H. T. Liu and P. Lalanne, “Comprehensive microscopic model of the extraordinary optical transmission,” J. Opt. Soc. Am. A 27(12), 2542–2550 (2010).
[Crossref] [PubMed]

2009 (3)

A. Kinkhabwala, Z. F. Yu, S. H. Fan, Y. Avlasevich, K. Müllen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photonics 3(11), 654–657 (2009).
[Crossref]

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, “A microscopic view of the electromagnetic properties of sub-lambda metallic surfaces,” Surf. Sci. Rep. 64(10), 453–469 (2009).
[Crossref]

S. S. Aćimović, M. P. Kreuzer, M. U. González, and R. Quidant, “Plasmon near-field coupling in metal dimers as a step toward single-molecule sensing,” ACS Nano 3(5), 1231–1237 (2009).
[Crossref] [PubMed]

2008 (7)

H. Ko and V. V. Tsukruk, “Nanoparticle-decorated nanocanals for surface-enhanced Raman scattering,” Small 4(11), 1980–1984 (2008).
[Crossref] [PubMed]

B. H. Zhang, H. S. Wang, L. H. Lu, K. L. Ai, G. Zhang, and X. L. Cheng, “Large area silver coated silicon nanowire arrays for molecular sensing using surface enhanced raman spectroscopy,” Adv. Funct. Mater. 18(16), 2348–2355 (2008).
[Crossref]

S. J. Lee, J. M. Baik, and M. Moskovits, “Polarization-dependent surface-enhanced Raman scattering from a silver-nanoparticle-decorated single silver nanowire,” Nano Lett. 8(10), 3244–3247 (2008).
[Crossref] [PubMed]

J. P. Camden, J. A. Dieringer, Y. M. Wang, D. J. Masiello, L. D. Marks, G. C. Schatz, and R. P. Van Duyne, “Probing the structure of single-molecule surface-enhanced Raman scattering hot spots,” J. Am. Chem. Soc. 130(38), 12616–12617 (2008).
[Crossref] [PubMed]

H. T. Miyazaki and Y. Kurokawa, “How can a resonant nanogap enhance optical fields by many orders of magnitude,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1565–1576 (2008).
[Crossref]

J. R. Anema, A. G. Brolo, P. Marthandam, and R. Gordon, “Enhanced Raman scattering from nanoholes in a copper film,” J. Phys. Chem. C 112(44), 17051–17055 (2008).
[Crossref]

H. T. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452(7188), 728–731 (2008).
[Crossref] [PubMed]

2007 (3)

F. Tam, G. P. Goodrich, B. R. Johnson, and N. J. Halas, “Plasmonic enhancement of molecular fluorescence,” Nano Lett. 7(2), 496–501 (2007).
[Crossref] [PubMed]

W. E. Doering, M. E. Piotti, M. J. Natan, and R. G. Freeman, “SERS as a foundation for nanoscale optically detected biological labels,” Adv. Mater. 19(20), 3100–3108 (2007).
[Crossref]

W. H. Zhang, B. S. Yeo, T. Schmid, and R. Zenobi, “Single molecule tip enhanced Raman spectroscopy with silver tips,” J. Phys. Chem. C 111(4), 1733–1738 (2007).
[Crossref]

2006 (6)

J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Ríos, “Controlling strong electromagnetic fields at subwavelength scales,” Phys. Rev. Lett. 97(3), 036405 (2006).
[Crossref] [PubMed]

H. Shen, B. Cheng, G. W. Lu, T. Y. Ning, D. Y. Guan, Y. L. Zhou, and Z. H. Chen, “Enhancement of optical nonlinearity in periodic gold nanoparticle arrays,” Nanotechnology 17(16), 4274–4277 (2006).
[Crossref] [PubMed]

F. Svedberg, Z. P. Li, H. X. Xu, and M. Käll, “Creating hot nanoparticle pairs for surface-enhanced Raman spectroscopy through optical manipulation,” Nano Lett. 6(12), 2639–2641 (2006).
[Crossref] [PubMed]

K. Zhao, H. X. Xu, B. H. Gu, and Z. Y. Zhang, “One-dimensional arrays of nanoshell dimers for single molecule spectroscopy via surface-enhanced raman scattering,” J. Chem. Phys. 125(8), 081102 (2006).
[Crossref] [PubMed]

S. Shanmukh, L. Jones, J. Driskell, Y. P. Zhao, R. Dluhy, and R. A. Tripp, “Rapid and sensitive detection of respiratory virus molecular signatures using a silver nanorod array SERS substrate,” Nano Lett. 6(11), 2630–2636 (2006).
[Crossref] [PubMed]

S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97(1), 017402 (2006).
[Crossref] [PubMed]

2005 (3)

2004 (2)

A. G. Brolo, E. Arctander, R. Gordon, B. Leathem, and K. L. Kavanagh, “Nanohole-enhanced Raman scattering,” Nano Lett. 4(10), 2015–2018 (2004).
[Crossref]

P. I. Geshev, S. Klein, T. Witting, K. Dickmann, and M. Hietschold, “Calculation of the electric-field enhancement at nanoparticles of arbitrary shape in close proximity to a metallic surface,” Phys. Rev. B 70(7), 075402 (2004).
[Crossref]

2002 (1)

D. Pisignano, M. Anni, G. Gigli, R. Cingolani, M. Zavelani-Rossi, G. Lanzani, G. Barbarella, and L. Favaretto, “Amplified spontaneous emission and efficient tunable laser emission,” Appl. Phys. Lett. 81(19), 3534–3536 (2002).
[Crossref]

2001 (1)

N. Hayazawa, Y. Inouye, Z. Sekkat, and S. Kawata, “Near-field Raman scattering enhanced by a metallized tip,” Chem. Phys. Lett. 335(5-6), 369–374 (2001).
[Crossref]

2000 (1)

H. X. Xu, J. Aizpurua, M. Käll, and P. Apell, “Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(33 Pt B), 4318–4324 (2000).
[Crossref] [PubMed]

1997 (2)

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, “Single molecule detection using surface enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78(9), 1667–1670 (1997).
[Crossref]

L. F. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A 14(10), 2758–2767 (1997).
[Crossref]

1996 (2)

A. P. Alivisatos, “Semiconductor clusters, nanocrystals, and quantum dots,” Science 271(5251), 933–937 (1996).
[Crossref]

F. J. García-Vidal and J. B. Pendry, “Collective theory for surface enhanced Raman scattering,” Phys. Rev. Lett. 77(6), 1163–1166 (1996).
[Crossref] [PubMed]

1995 (1)

1974 (1)

M. Fleischmann, P. J. Hendra, and A. J. McQuillan, “Raman spectra of pyridine adsorbed at a silver electrode,” Chem. Phys. Lett. 26(2), 163–166 (1974).
[Crossref]

1941 (1)

1902 (1)

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag. 4, 396–402 (1902).

Acimovic, S. S.

S. S. Aćimović, M. P. Kreuzer, M. U. González, and R. Quidant, “Plasmon near-field coupling in metal dimers as a step toward single-molecule sensing,” ACS Nano 3(5), 1231–1237 (2009).
[Crossref] [PubMed]

Ai, K. L.

B. H. Zhang, H. S. Wang, L. H. Lu, K. L. Ai, G. Zhang, and X. L. Cheng, “Large area silver coated silicon nanowire arrays for molecular sensing using surface enhanced raman spectroscopy,” Adv. Funct. Mater. 18(16), 2348–2355 (2008).
[Crossref]

Aizpurua, J.

H. X. Xu, J. Aizpurua, M. Käll, and P. Apell, “Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(33 Pt B), 4318–4324 (2000).
[Crossref] [PubMed]

Alivisatos, A. P.

A. P. Alivisatos, “Semiconductor clusters, nanocrystals, and quantum dots,” Science 271(5251), 933–937 (1996).
[Crossref]

Alvarez-Puebla, R. A.

N. Pazos-Pérez, W. Ni, A. Schweikart, R. A. Alvarez-Puebla, A. Fery, and L. M. Liz-Marzán, “Highly uniform SERS substrates formed by wrinkle-confined drying of gold colloids,” Chem. Sci. 1(2), 174–178 (2010).
[Crossref]

Anema, J. R.

J. R. Anema, A. G. Brolo, P. Marthandam, and R. Gordon, “Enhanced Raman scattering from nanoholes in a copper film,” J. Phys. Chem. C 112(44), 17051–17055 (2008).
[Crossref]

Anni, M.

D. Pisignano, M. Anni, G. Gigli, R. Cingolani, M. Zavelani-Rossi, G. Lanzani, G. Barbarella, and L. Favaretto, “Amplified spontaneous emission and efficient tunable laser emission,” Appl. Phys. Lett. 81(19), 3534–3536 (2002).
[Crossref]

Apell, P.

H. X. Xu, J. Aizpurua, M. Käll, and P. Apell, “Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(33 Pt B), 4318–4324 (2000).
[Crossref] [PubMed]

Arctander, E.

A. G. Brolo, E. Arctander, R. Gordon, B. Leathem, and K. L. Kavanagh, “Nanohole-enhanced Raman scattering,” Nano Lett. 4(10), 2015–2018 (2004).
[Crossref]

Avlasevich, Y.

A. Kinkhabwala, Z. F. Yu, S. H. Fan, Y. Avlasevich, K. Müllen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photonics 3(11), 654–657 (2009).
[Crossref]

Baik, J. M.

S. J. Lee, J. M. Baik, and M. Moskovits, “Polarization-dependent surface-enhanced Raman scattering from a silver-nanoparticle-decorated single silver nanowire,” Nano Lett. 8(10), 3244–3247 (2008).
[Crossref] [PubMed]

Barbara, A.

J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Ríos, “Controlling strong electromagnetic fields at subwavelength scales,” Phys. Rev. Lett. 97(3), 036405 (2006).
[Crossref] [PubMed]

Barbarella, G.

D. Pisignano, M. Anni, G. Gigli, R. Cingolani, M. Zavelani-Rossi, G. Lanzani, G. Barbarella, and L. Favaretto, “Amplified spontaneous emission and efficient tunable laser emission,” Appl. Phys. Lett. 81(19), 3534–3536 (2002).
[Crossref]

Bernussi, A. A.

A. Krishnan, S. P. Frisbie, L. Grave de Peralta, and A. A. Bernussi, “Plasmon stimulated emission in arrays of bimetallic structres coated with dye-doped dielectric,” Appl. Phys. Lett. 96(11), 111104 (2010).
[Crossref]

Bingham, J. M.

S. L. Kleinman, J. M. Bingham, A. I. Henry, K. L. Wustholz, and R. P. Van Duyne, “Structural and optical characterization of single nanoparticles and single molecule SERS,” Proc. SPIE 7757, 77570J, 77570J-10 (2010).
[Crossref]

Brolo, A. G.

J. R. Anema, A. G. Brolo, P. Marthandam, and R. Gordon, “Enhanced Raman scattering from nanoholes in a copper film,” J. Phys. Chem. C 112(44), 17051–17055 (2008).
[Crossref]

A. G. Brolo, E. Arctander, R. Gordon, B. Leathem, and K. L. Kavanagh, “Nanohole-enhanced Raman scattering,” Nano Lett. 4(10), 2015–2018 (2004).
[Crossref]

Camden, J. P.

J. P. Camden, J. A. Dieringer, Y. M. Wang, D. J. Masiello, L. D. Marks, G. C. Schatz, and R. P. Van Duyne, “Probing the structure of single-molecule surface-enhanced Raman scattering hot spots,” J. Am. Chem. Soc. 130(38), 12616–12617 (2008).
[Crossref] [PubMed]

Chen, Z. H.

H. Shen, B. Cheng, G. W. Lu, T. Y. Ning, D. Y. Guan, Y. L. Zhou, and Z. H. Chen, “Enhancement of optical nonlinearity in periodic gold nanoparticle arrays,” Nanotechnology 17(16), 4274–4277 (2006).
[Crossref] [PubMed]

Cheng, B.

H. Shen, B. Cheng, G. W. Lu, T. Y. Ning, D. Y. Guan, Y. L. Zhou, and Z. H. Chen, “Enhancement of optical nonlinearity in periodic gold nanoparticle arrays,” Nanotechnology 17(16), 4274–4277 (2006).
[Crossref] [PubMed]

Cheng, X. L.

B. H. Zhang, H. S. Wang, L. H. Lu, K. L. Ai, G. Zhang, and X. L. Cheng, “Large area silver coated silicon nanowire arrays for molecular sensing using surface enhanced raman spectroscopy,” Adv. Funct. Mater. 18(16), 2348–2355 (2008).
[Crossref]

Chung, A. J.

A. J. Chung, Y. S. Huh, and D. Erickson, “Large area flexible SERS active substrates using engineered nanostructures,” Nanoscale 3(7), 2903–2908 (2011).
[Crossref] [PubMed]

Cingolani, R.

D. Pisignano, M. Anni, G. Gigli, R. Cingolani, M. Zavelani-Rossi, G. Lanzani, G. Barbarella, and L. Favaretto, “Amplified spontaneous emission and efficient tunable laser emission,” Appl. Phys. Lett. 81(19), 3534–3536 (2002).
[Crossref]

Dai, D. X.

Dasari, R. R.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, “Single molecule detection using surface enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78(9), 1667–1670 (1997).
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Dickmann, K.

P. I. Geshev, S. Klein, T. Witting, K. Dickmann, and M. Hietschold, “Calculation of the electric-field enhancement at nanoparticles of arbitrary shape in close proximity to a metallic surface,” Phys. Rev. B 70(7), 075402 (2004).
[Crossref]

Dieringer, J. A.

J. P. Camden, J. A. Dieringer, Y. M. Wang, D. J. Masiello, L. D. Marks, G. C. Schatz, and R. P. Van Duyne, “Probing the structure of single-molecule surface-enhanced Raman scattering hot spots,” J. Am. Chem. Soc. 130(38), 12616–12617 (2008).
[Crossref] [PubMed]

Dluhy, R.

S. Shanmukh, L. Jones, J. Driskell, Y. P. Zhao, R. Dluhy, and R. A. Tripp, “Rapid and sensitive detection of respiratory virus molecular signatures using a silver nanorod array SERS substrate,” Nano Lett. 6(11), 2630–2636 (2006).
[Crossref] [PubMed]

Doering, W. E.

W. E. Doering, M. E. Piotti, M. J. Natan, and R. G. Freeman, “SERS as a foundation for nanoscale optically detected biological labels,” Adv. Mater. 19(20), 3100–3108 (2007).
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Driskell, J.

S. Shanmukh, L. Jones, J. Driskell, Y. P. Zhao, R. Dluhy, and R. A. Tripp, “Rapid and sensitive detection of respiratory virus molecular signatures using a silver nanorod array SERS substrate,” Nano Lett. 6(11), 2630–2636 (2006).
[Crossref] [PubMed]

Eisler, H. J.

P. Mühlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308(5728), 1607–1609 (2005).
[Crossref] [PubMed]

Erickson, D.

A. J. Chung, Y. S. Huh, and D. Erickson, “Large area flexible SERS active substrates using engineered nanostructures,” Nanoscale 3(7), 2903–2908 (2011).
[Crossref] [PubMed]

Fan, S. H.

A. Kinkhabwala, Z. F. Yu, S. H. Fan, Y. Avlasevich, K. Müllen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photonics 3(11), 654–657 (2009).
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Fano, U.

Favaretto, L.

D. Pisignano, M. Anni, G. Gigli, R. Cingolani, M. Zavelani-Rossi, G. Lanzani, G. Barbarella, and L. Favaretto, “Amplified spontaneous emission and efficient tunable laser emission,” Appl. Phys. Lett. 81(19), 3534–3536 (2002).
[Crossref]

Feld, M. S.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, “Single molecule detection using surface enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78(9), 1667–1670 (1997).
[Crossref]

Fery, A.

N. Pazos-Pérez, W. Ni, A. Schweikart, R. A. Alvarez-Puebla, A. Fery, and L. M. Liz-Marzán, “Highly uniform SERS substrates formed by wrinkle-confined drying of gold colloids,” Chem. Sci. 1(2), 174–178 (2010).
[Crossref]

Fleischmann, M.

M. Fleischmann, P. J. Hendra, and A. J. McQuillan, “Raman spectra of pyridine adsorbed at a silver electrode,” Chem. Phys. Lett. 26(2), 163–166 (1974).
[Crossref]

Freeman, R. G.

W. E. Doering, M. E. Piotti, M. J. Natan, and R. G. Freeman, “SERS as a foundation for nanoscale optically detected biological labels,” Adv. Mater. 19(20), 3100–3108 (2007).
[Crossref]

Frisbie, S. P.

A. Krishnan, S. P. Frisbie, L. Grave de Peralta, and A. A. Bernussi, “Plasmon stimulated emission in arrays of bimetallic structres coated with dye-doped dielectric,” Appl. Phys. Lett. 96(11), 111104 (2010).
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F. J. García-Vidal and J. B. Pendry, “Collective theory for surface enhanced Raman scattering,” Phys. Rev. Lett. 77(6), 1163–1166 (1996).
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Gaylord, T. K.

Geshev, P. I.

P. I. Geshev, S. Klein, T. Witting, K. Dickmann, and M. Hietschold, “Calculation of the electric-field enhancement at nanoparticles of arbitrary shape in close proximity to a metallic surface,” Phys. Rev. B 70(7), 075402 (2004).
[Crossref]

Gigli, G.

D. Pisignano, M. Anni, G. Gigli, R. Cingolani, M. Zavelani-Rossi, G. Lanzani, G. Barbarella, and L. Favaretto, “Amplified spontaneous emission and efficient tunable laser emission,” Appl. Phys. Lett. 81(19), 3534–3536 (2002).
[Crossref]

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S. S. Aćimović, M. P. Kreuzer, M. U. González, and R. Quidant, “Plasmon near-field coupling in metal dimers as a step toward single-molecule sensing,” ACS Nano 3(5), 1231–1237 (2009).
[Crossref] [PubMed]

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F. Tam, G. P. Goodrich, B. R. Johnson, and N. J. Halas, “Plasmonic enhancement of molecular fluorescence,” Nano Lett. 7(2), 496–501 (2007).
[Crossref] [PubMed]

Gordon, R.

J. R. Anema, A. G. Brolo, P. Marthandam, and R. Gordon, “Enhanced Raman scattering from nanoholes in a copper film,” J. Phys. Chem. C 112(44), 17051–17055 (2008).
[Crossref]

A. G. Brolo, E. Arctander, R. Gordon, B. Leathem, and K. L. Kavanagh, “Nanohole-enhanced Raman scattering,” Nano Lett. 4(10), 2015–2018 (2004).
[Crossref]

Grann, E. B.

Grave de Peralta, L.

A. Krishnan, S. P. Frisbie, L. Grave de Peralta, and A. A. Bernussi, “Plasmon stimulated emission in arrays of bimetallic structres coated with dye-doped dielectric,” Appl. Phys. Lett. 96(11), 111104 (2010).
[Crossref]

Gu, B. H.

K. Zhao, H. X. Xu, B. H. Gu, and Z. Y. Zhang, “One-dimensional arrays of nanoshell dimers for single molecule spectroscopy via surface-enhanced raman scattering,” J. Chem. Phys. 125(8), 081102 (2006).
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H. Shen, B. Cheng, G. W. Lu, T. Y. Ning, D. Y. Guan, Y. L. Zhou, and Z. H. Chen, “Enhancement of optical nonlinearity in periodic gold nanoparticle arrays,” Nanotechnology 17(16), 4274–4277 (2006).
[Crossref] [PubMed]

Håkanson, U.

S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97(1), 017402 (2006).
[Crossref] [PubMed]

Halas, N. J.

F. Tam, G. P. Goodrich, B. R. Johnson, and N. J. Halas, “Plasmonic enhancement of molecular fluorescence,” Nano Lett. 7(2), 496–501 (2007).
[Crossref] [PubMed]

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N. Hayazawa, Y. Inouye, Z. Sekkat, and S. Kawata, “Near-field Raman scattering enhanced by a metallized tip,” Chem. Phys. Lett. 335(5-6), 369–374 (2001).
[Crossref]

He, S. L.

Hecht, B.

P. Mühlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308(5728), 1607–1609 (2005).
[Crossref] [PubMed]

Hendra, P. J.

M. Fleischmann, P. J. Hendra, and A. J. McQuillan, “Raman spectra of pyridine adsorbed at a silver electrode,” Chem. Phys. Lett. 26(2), 163–166 (1974).
[Crossref]

Henry, A. I.

S. L. Kleinman, J. M. Bingham, A. I. Henry, K. L. Wustholz, and R. P. Van Duyne, “Structural and optical characterization of single nanoparticles and single molecule SERS,” Proc. SPIE 7757, 77570J, 77570J-10 (2010).
[Crossref]

Hietschold, M.

P. I. Geshev, S. Klein, T. Witting, K. Dickmann, and M. Hietschold, “Calculation of the electric-field enhancement at nanoparticles of arbitrary shape in close proximity to a metallic surface,” Phys. Rev. B 70(7), 075402 (2004).
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Hou, Y. M.

Y. M. Hou, J. Xu, X. J. Zhang, and D. P. Yu, “SERS on periodic arrays of coupled quadrate-holes and squares,” Nanotechnology 21(19), 195203 (2010).
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Huang, J. P.

Hugonin, J. P.

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, “A microscopic view of the electromagnetic properties of sub-lambda metallic surfaces,” Surf. Sci. Rep. 64(10), 453–469 (2009).
[Crossref]

J. P. Hugonin and P. Lalanne, “Perfectly matched layers as nonlinear coordinate transforms: a generalized formalization,” J. Opt. Soc. Am. A 22(9), 1844–1849 (2005).
[Crossref] [PubMed]

Huh, Y. S.

A. J. Chung, Y. S. Huh, and D. Erickson, “Large area flexible SERS active substrates using engineered nanostructures,” Nanoscale 3(7), 2903–2908 (2011).
[Crossref] [PubMed]

Inouye, Y.

N. Hayazawa, Y. Inouye, Z. Sekkat, and S. Kawata, “Near-field Raman scattering enhanced by a metallized tip,” Chem. Phys. Lett. 335(5-6), 369–374 (2001).
[Crossref]

Itzkan, I.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, “Single molecule detection using surface enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78(9), 1667–1670 (1997).
[Crossref]

Jeon, K. S.

D. K. Lim, K. S. Jeon, H. M. Kim, J. M. Nam, and Y. D. Suh, “Nanogap-engineerable Raman-active nanodumbbells for single-molecule detection,” Nat. Mater. 9(1), 60–67 (2010).
[Crossref] [PubMed]

Johnson, B. R.

F. Tam, G. P. Goodrich, B. R. Johnson, and N. J. Halas, “Plasmonic enhancement of molecular fluorescence,” Nano Lett. 7(2), 496–501 (2007).
[Crossref] [PubMed]

Jones, L.

S. Shanmukh, L. Jones, J. Driskell, Y. P. Zhao, R. Dluhy, and R. A. Tripp, “Rapid and sensitive detection of respiratory virus molecular signatures using a silver nanorod array SERS substrate,” Nano Lett. 6(11), 2630–2636 (2006).
[Crossref] [PubMed]

Käll, M.

F. Svedberg, Z. P. Li, H. X. Xu, and M. Käll, “Creating hot nanoparticle pairs for surface-enhanced Raman spectroscopy through optical manipulation,” Nano Lett. 6(12), 2639–2641 (2006).
[Crossref] [PubMed]

H. X. Xu, J. Aizpurua, M. Käll, and P. Apell, “Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(33 Pt B), 4318–4324 (2000).
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Kavanagh, K. L.

A. G. Brolo, E. Arctander, R. Gordon, B. Leathem, and K. L. Kavanagh, “Nanohole-enhanced Raman scattering,” Nano Lett. 4(10), 2015–2018 (2004).
[Crossref]

Kawata, S.

N. Hayazawa, Y. Inouye, Z. Sekkat, and S. Kawata, “Near-field Raman scattering enhanced by a metallized tip,” Chem. Phys. Lett. 335(5-6), 369–374 (2001).
[Crossref]

Kim, H. M.

D. K. Lim, K. S. Jeon, H. M. Kim, J. M. Nam, and Y. D. Suh, “Nanogap-engineerable Raman-active nanodumbbells for single-molecule detection,” Nat. Mater. 9(1), 60–67 (2010).
[Crossref] [PubMed]

Kim, Z. H.

W. H. Park and Z. H. Kim, “Charge transfer enhancement in the SERS of a single molecule,” Nano Lett. 10(10), 4040–4048 (2010).
[Crossref] [PubMed]

Kinkhabwala, A.

A. Kinkhabwala, Z. F. Yu, S. H. Fan, Y. Avlasevich, K. Müllen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photonics 3(11), 654–657 (2009).
[Crossref]

Klein, S.

P. I. Geshev, S. Klein, T. Witting, K. Dickmann, and M. Hietschold, “Calculation of the electric-field enhancement at nanoparticles of arbitrary shape in close proximity to a metallic surface,” Phys. Rev. B 70(7), 075402 (2004).
[Crossref]

Kleinman, S. L.

S. L. Kleinman, J. M. Bingham, A. I. Henry, K. L. Wustholz, and R. P. Van Duyne, “Structural and optical characterization of single nanoparticles and single molecule SERS,” Proc. SPIE 7757, 77570J, 77570J-10 (2010).
[Crossref]

Kneipp, H.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, “Single molecule detection using surface enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78(9), 1667–1670 (1997).
[Crossref]

Kneipp, K.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, “Single molecule detection using surface enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78(9), 1667–1670 (1997).
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H. Ko and V. V. Tsukruk, “Nanoparticle-decorated nanocanals for surface-enhanced Raman scattering,” Small 4(11), 1980–1984 (2008).
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S. S. Aćimović, M. P. Kreuzer, M. U. González, and R. Quidant, “Plasmon near-field coupling in metal dimers as a step toward single-molecule sensing,” ACS Nano 3(5), 1231–1237 (2009).
[Crossref] [PubMed]

Krishnan, A.

A. Krishnan, S. P. Frisbie, L. Grave de Peralta, and A. A. Bernussi, “Plasmon stimulated emission in arrays of bimetallic structres coated with dye-doped dielectric,” Appl. Phys. Lett. 96(11), 111104 (2010).
[Crossref]

Kühn, S.

S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97(1), 017402 (2006).
[Crossref] [PubMed]

Kurokawa, Y.

H. T. Miyazaki and Y. Kurokawa, “How can a resonant nanogap enhance optical fields by many orders of magnitude,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1565–1576 (2008).
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Lalanne, P.

F. van Beijnum, C. Rétif, C. B. Smiet, H. T. Liu, P. Lalanne, and M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature 492(7429), 411–414 (2012).
[Crossref] [PubMed]

H. T. Liu and P. Lalanne, “Light scattering by metallic surfaces with subwavelength patterns,” Phys. Rev. B 82(11), 115418 (2010).
[Crossref]

H. T. Liu and P. Lalanne, “Comprehensive microscopic model of the extraordinary optical transmission,” J. Opt. Soc. Am. A 27(12), 2542–2550 (2010).
[Crossref] [PubMed]

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, “A microscopic view of the electromagnetic properties of sub-lambda metallic surfaces,” Surf. Sci. Rep. 64(10), 453–469 (2009).
[Crossref]

H. T. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452(7188), 728–731 (2008).
[Crossref] [PubMed]

J. P. Hugonin and P. Lalanne, “Perfectly matched layers as nonlinear coordinate transforms: a generalized formalization,” J. Opt. Soc. Am. A 22(9), 1844–1849 (2005).
[Crossref] [PubMed]

Lanzani, G.

D. Pisignano, M. Anni, G. Gigli, R. Cingolani, M. Zavelani-Rossi, G. Lanzani, G. Barbarella, and L. Favaretto, “Amplified spontaneous emission and efficient tunable laser emission,” Appl. Phys. Lett. 81(19), 3534–3536 (2002).
[Crossref]

Le Perchec, J.

J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Ríos, “Controlling strong electromagnetic fields at subwavelength scales,” Phys. Rev. Lett. 97(3), 036405 (2006).
[Crossref] [PubMed]

Leathem, B.

A. G. Brolo, E. Arctander, R. Gordon, B. Leathem, and K. L. Kavanagh, “Nanohole-enhanced Raman scattering,” Nano Lett. 4(10), 2015–2018 (2004).
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Lee, S. J.

S. J. Lee, J. M. Baik, and M. Moskovits, “Polarization-dependent surface-enhanced Raman scattering from a silver-nanoparticle-decorated single silver nanowire,” Nano Lett. 8(10), 3244–3247 (2008).
[Crossref] [PubMed]

Li, L. F.

Li, Z. P.

F. Svedberg, Z. P. Li, H. X. Xu, and M. Käll, “Creating hot nanoparticle pairs for surface-enhanced Raman spectroscopy through optical manipulation,” Nano Lett. 6(12), 2639–2641 (2006).
[Crossref] [PubMed]

Li, Z. Y.

Z. Y. Li and Y. Xia, “Metal nanoparticles with gain toward single-molecule detection by surface-enhanced Raman scattering,” Nano Lett. 10(1), 243–249 (2010).
[Crossref] [PubMed]

Lim, D. K.

D. K. Lim, K. S. Jeon, H. M. Kim, J. M. Nam, and Y. D. Suh, “Nanogap-engineerable Raman-active nanodumbbells for single-molecule detection,” Nat. Mater. 9(1), 60–67 (2010).
[Crossref] [PubMed]

Liu, H. T.

Z. W. Zeng and H. T. Liu, “Electromagnetic enhancement by a T-shaped metallic nano groove impact of surface plasmon polaritons and other surface waves,” IEEE J. Sel. Top. Quantum Electron. 18(6), 1669–1675 (2012).
[Crossref]

F. van Beijnum, C. Rétif, C. B. Smiet, H. T. Liu, P. Lalanne, and M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature 492(7429), 411–414 (2012).
[Crossref] [PubMed]

X. Zhang, H. T. Liu, and Y. Zhong, “Compensation of propagation loss of surface plasmon polaritons with a finite-thickness dielectric gain layer,” J. Opt. 14(12), 125003 (2012).
[Crossref]

S. W. Zhang, H. T. Liu, and G. G. Mu, “Electromagnetic enhancement by a periodic array of nanogrooves in a metallic substrate,” J. Opt. Soc. Am. A 28(5), 879–886 (2011).
[Crossref] [PubMed]

H. T. Liu and P. Lalanne, “Light scattering by metallic surfaces with subwavelength patterns,” Phys. Rev. B 82(11), 115418 (2010).
[Crossref]

H. T. Liu and P. Lalanne, “Comprehensive microscopic model of the extraordinary optical transmission,” J. Opt. Soc. Am. A 27(12), 2542–2550 (2010).
[Crossref] [PubMed]

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, “A microscopic view of the electromagnetic properties of sub-lambda metallic surfaces,” Surf. Sci. Rep. 64(10), 453–469 (2009).
[Crossref]

H. T. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452(7188), 728–731 (2008).
[Crossref] [PubMed]

Liz-Marzán, L. M.

N. Pazos-Pérez, W. Ni, A. Schweikart, R. A. Alvarez-Puebla, A. Fery, and L. M. Liz-Marzán, “Highly uniform SERS substrates formed by wrinkle-confined drying of gold colloids,” Chem. Sci. 1(2), 174–178 (2010).
[Crossref]

López-Ríos, T.

J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Ríos, “Controlling strong electromagnetic fields at subwavelength scales,” Phys. Rev. Lett. 97(3), 036405 (2006).
[Crossref] [PubMed]

Lu, G. W.

H. Shen, B. Cheng, G. W. Lu, T. Y. Ning, D. Y. Guan, Y. L. Zhou, and Z. H. Chen, “Enhancement of optical nonlinearity in periodic gold nanoparticle arrays,” Nanotechnology 17(16), 4274–4277 (2006).
[Crossref] [PubMed]

Lu, L. H.

B. H. Zhang, H. S. Wang, L. H. Lu, K. L. Ai, G. Zhang, and X. L. Cheng, “Large area silver coated silicon nanowire arrays for molecular sensing using surface enhanced raman spectroscopy,” Adv. Funct. Mater. 18(16), 2348–2355 (2008).
[Crossref]

Marks, L. D.

J. P. Camden, J. A. Dieringer, Y. M. Wang, D. J. Masiello, L. D. Marks, G. C. Schatz, and R. P. Van Duyne, “Probing the structure of single-molecule surface-enhanced Raman scattering hot spots,” J. Am. Chem. Soc. 130(38), 12616–12617 (2008).
[Crossref] [PubMed]

Marthandam, P.

J. R. Anema, A. G. Brolo, P. Marthandam, and R. Gordon, “Enhanced Raman scattering from nanoholes in a copper film,” J. Phys. Chem. C 112(44), 17051–17055 (2008).
[Crossref]

Martin, O. J. F.

P. Mühlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308(5728), 1607–1609 (2005).
[Crossref] [PubMed]

Masiello, D. J.

J. P. Camden, J. A. Dieringer, Y. M. Wang, D. J. Masiello, L. D. Marks, G. C. Schatz, and R. P. Van Duyne, “Probing the structure of single-molecule surface-enhanced Raman scattering hot spots,” J. Am. Chem. Soc. 130(38), 12616–12617 (2008).
[Crossref] [PubMed]

McQuillan, A. J.

M. Fleischmann, P. J. Hendra, and A. J. McQuillan, “Raman spectra of pyridine adsorbed at a silver electrode,” Chem. Phys. Lett. 26(2), 163–166 (1974).
[Crossref]

Miyazaki, H. T.

H. T. Miyazaki and Y. Kurokawa, “How can a resonant nanogap enhance optical fields by many orders of magnitude,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1565–1576 (2008).
[Crossref]

Moerner, W. E.

A. Kinkhabwala, Z. F. Yu, S. H. Fan, Y. Avlasevich, K. Müllen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photonics 3(11), 654–657 (2009).
[Crossref]

Moharam, M. G.

Moskovits, M.

S. J. Lee, J. M. Baik, and M. Moskovits, “Polarization-dependent surface-enhanced Raman scattering from a silver-nanoparticle-decorated single silver nanowire,” Nano Lett. 8(10), 3244–3247 (2008).
[Crossref] [PubMed]

Mu, G. G.

Mühlschlegel, P.

P. Mühlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308(5728), 1607–1609 (2005).
[Crossref] [PubMed]

Müllen, K.

A. Kinkhabwala, Z. F. Yu, S. H. Fan, Y. Avlasevich, K. Müllen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photonics 3(11), 654–657 (2009).
[Crossref]

Nam, J. M.

D. K. Lim, K. S. Jeon, H. M. Kim, J. M. Nam, and Y. D. Suh, “Nanogap-engineerable Raman-active nanodumbbells for single-molecule detection,” Nat. Mater. 9(1), 60–67 (2010).
[Crossref] [PubMed]

Natan, M. J.

W. E. Doering, M. E. Piotti, M. J. Natan, and R. G. Freeman, “SERS as a foundation for nanoscale optically detected biological labels,” Adv. Mater. 19(20), 3100–3108 (2007).
[Crossref]

Ni, W.

N. Pazos-Pérez, W. Ni, A. Schweikart, R. A. Alvarez-Puebla, A. Fery, and L. M. Liz-Marzán, “Highly uniform SERS substrates formed by wrinkle-confined drying of gold colloids,” Chem. Sci. 1(2), 174–178 (2010).
[Crossref]

Ning, T. Y.

H. Shen, B. Cheng, G. W. Lu, T. Y. Ning, D. Y. Guan, Y. L. Zhou, and Z. H. Chen, “Enhancement of optical nonlinearity in periodic gold nanoparticle arrays,” Nanotechnology 17(16), 4274–4277 (2006).
[Crossref] [PubMed]

Park, W. H.

W. H. Park and Z. H. Kim, “Charge transfer enhancement in the SERS of a single molecule,” Nano Lett. 10(10), 4040–4048 (2010).
[Crossref] [PubMed]

Pazos-Pérez, N.

N. Pazos-Pérez, W. Ni, A. Schweikart, R. A. Alvarez-Puebla, A. Fery, and L. M. Liz-Marzán, “Highly uniform SERS substrates formed by wrinkle-confined drying of gold colloids,” Chem. Sci. 1(2), 174–178 (2010).
[Crossref]

Pendry, J. B.

F. J. García-Vidal and J. B. Pendry, “Collective theory for surface enhanced Raman scattering,” Phys. Rev. Lett. 77(6), 1163–1166 (1996).
[Crossref] [PubMed]

Perelman, L. T.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, “Single molecule detection using surface enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78(9), 1667–1670 (1997).
[Crossref]

Piotti, M. E.

W. E. Doering, M. E. Piotti, M. J. Natan, and R. G. Freeman, “SERS as a foundation for nanoscale optically detected biological labels,” Adv. Mater. 19(20), 3100–3108 (2007).
[Crossref]

Pisignano, D.

D. Pisignano, M. Anni, G. Gigli, R. Cingolani, M. Zavelani-Rossi, G. Lanzani, G. Barbarella, and L. Favaretto, “Amplified spontaneous emission and efficient tunable laser emission,” Appl. Phys. Lett. 81(19), 3534–3536 (2002).
[Crossref]

Pohl, D. W.

P. Mühlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308(5728), 1607–1609 (2005).
[Crossref] [PubMed]

Pommet, D. A.

Quémerais, P.

J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Ríos, “Controlling strong electromagnetic fields at subwavelength scales,” Phys. Rev. Lett. 97(3), 036405 (2006).
[Crossref] [PubMed]

Quidant, R.

S. S. Aćimović, M. P. Kreuzer, M. U. González, and R. Quidant, “Plasmon near-field coupling in metal dimers as a step toward single-molecule sensing,” ACS Nano 3(5), 1231–1237 (2009).
[Crossref] [PubMed]

Rétif, C.

F. van Beijnum, C. Rétif, C. B. Smiet, H. T. Liu, P. Lalanne, and M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature 492(7429), 411–414 (2012).
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S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97(1), 017402 (2006).
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S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97(1), 017402 (2006).
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J. P. Camden, J. A. Dieringer, Y. M. Wang, D. J. Masiello, L. D. Marks, G. C. Schatz, and R. P. Van Duyne, “Probing the structure of single-molecule surface-enhanced Raman scattering hot spots,” J. Am. Chem. Soc. 130(38), 12616–12617 (2008).
[Crossref] [PubMed]

Schmid, T.

W. H. Zhang, B. S. Yeo, T. Schmid, and R. Zenobi, “Single molecule tip enhanced Raman spectroscopy with silver tips,” J. Phys. Chem. C 111(4), 1733–1738 (2007).
[Crossref]

Schweikart, A.

N. Pazos-Pérez, W. Ni, A. Schweikart, R. A. Alvarez-Puebla, A. Fery, and L. M. Liz-Marzán, “Highly uniform SERS substrates formed by wrinkle-confined drying of gold colloids,” Chem. Sci. 1(2), 174–178 (2010).
[Crossref]

Sekkat, Z.

N. Hayazawa, Y. Inouye, Z. Sekkat, and S. Kawata, “Near-field Raman scattering enhanced by a metallized tip,” Chem. Phys. Lett. 335(5-6), 369–374 (2001).
[Crossref]

Shanmukh, S.

S. Shanmukh, L. Jones, J. Driskell, Y. P. Zhao, R. Dluhy, and R. A. Tripp, “Rapid and sensitive detection of respiratory virus molecular signatures using a silver nanorod array SERS substrate,” Nano Lett. 6(11), 2630–2636 (2006).
[Crossref] [PubMed]

Shen, H.

H. Shen, B. Cheng, G. W. Lu, T. Y. Ning, D. Y. Guan, Y. L. Zhou, and Z. H. Chen, “Enhancement of optical nonlinearity in periodic gold nanoparticle arrays,” Nanotechnology 17(16), 4274–4277 (2006).
[Crossref] [PubMed]

Shi, Y. C.

Smiet, C. B.

F. van Beijnum, C. Rétif, C. B. Smiet, H. T. Liu, P. Lalanne, and M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature 492(7429), 411–414 (2012).
[Crossref] [PubMed]

Suh, Y. D.

D. K. Lim, K. S. Jeon, H. M. Kim, J. M. Nam, and Y. D. Suh, “Nanogap-engineerable Raman-active nanodumbbells for single-molecule detection,” Nat. Mater. 9(1), 60–67 (2010).
[Crossref] [PubMed]

Svedberg, F.

F. Svedberg, Z. P. Li, H. X. Xu, and M. Käll, “Creating hot nanoparticle pairs for surface-enhanced Raman spectroscopy through optical manipulation,” Nano Lett. 6(12), 2639–2641 (2006).
[Crossref] [PubMed]

Tam, F.

F. Tam, G. P. Goodrich, B. R. Johnson, and N. J. Halas, “Plasmonic enhancement of molecular fluorescence,” Nano Lett. 7(2), 496–501 (2007).
[Crossref] [PubMed]

Thylen, L.

Tripp, R. A.

S. Shanmukh, L. Jones, J. Driskell, Y. P. Zhao, R. Dluhy, and R. A. Tripp, “Rapid and sensitive detection of respiratory virus molecular signatures using a silver nanorod array SERS substrate,” Nano Lett. 6(11), 2630–2636 (2006).
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H. Ko and V. V. Tsukruk, “Nanoparticle-decorated nanocanals for surface-enhanced Raman scattering,” Small 4(11), 1980–1984 (2008).
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F. van Beijnum, C. Rétif, C. B. Smiet, H. T. Liu, P. Lalanne, and M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature 492(7429), 411–414 (2012).
[Crossref] [PubMed]

Van Duyne, R. P.

S. L. Kleinman, J. M. Bingham, A. I. Henry, K. L. Wustholz, and R. P. Van Duyne, “Structural and optical characterization of single nanoparticles and single molecule SERS,” Proc. SPIE 7757, 77570J, 77570J-10 (2010).
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J. P. Camden, J. A. Dieringer, Y. M. Wang, D. J. Masiello, L. D. Marks, G. C. Schatz, and R. P. Van Duyne, “Probing the structure of single-molecule surface-enhanced Raman scattering hot spots,” J. Am. Chem. Soc. 130(38), 12616–12617 (2008).
[Crossref] [PubMed]

van Exter, M. P.

F. van Beijnum, C. Rétif, C. B. Smiet, H. T. Liu, P. Lalanne, and M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature 492(7429), 411–414 (2012).
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Wang, B.

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, “A microscopic view of the electromagnetic properties of sub-lambda metallic surfaces,” Surf. Sci. Rep. 64(10), 453–469 (2009).
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Wang, H. S.

B. H. Zhang, H. S. Wang, L. H. Lu, K. L. Ai, G. Zhang, and X. L. Cheng, “Large area silver coated silicon nanowire arrays for molecular sensing using surface enhanced raman spectroscopy,” Adv. Funct. Mater. 18(16), 2348–2355 (2008).
[Crossref]

Wang, Y.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, “Single molecule detection using surface enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78(9), 1667–1670 (1997).
[Crossref]

Wang, Y. M.

J. P. Camden, J. A. Dieringer, Y. M. Wang, D. J. Masiello, L. D. Marks, G. C. Schatz, and R. P. Van Duyne, “Probing the structure of single-molecule surface-enhanced Raman scattering hot spots,” J. Am. Chem. Soc. 130(38), 12616–12617 (2008).
[Crossref] [PubMed]

Witting, T.

P. I. Geshev, S. Klein, T. Witting, K. Dickmann, and M. Hietschold, “Calculation of the electric-field enhancement at nanoparticles of arbitrary shape in close proximity to a metallic surface,” Phys. Rev. B 70(7), 075402 (2004).
[Crossref]

Wood, R. W.

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag. 4, 396–402 (1902).

Wosinski, L.

Wustholz, K. L.

S. L. Kleinman, J. M. Bingham, A. I. Henry, K. L. Wustholz, and R. P. Van Duyne, “Structural and optical characterization of single nanoparticles and single molecule SERS,” Proc. SPIE 7757, 77570J, 77570J-10 (2010).
[Crossref]

Xia, Y.

Z. Y. Li and Y. Xia, “Metal nanoparticles with gain toward single-molecule detection by surface-enhanced Raman scattering,” Nano Lett. 10(1), 243–249 (2010).
[Crossref] [PubMed]

Xu, H. X.

K. Zhao, H. X. Xu, B. H. Gu, and Z. Y. Zhang, “One-dimensional arrays of nanoshell dimers for single molecule spectroscopy via surface-enhanced raman scattering,” J. Chem. Phys. 125(8), 081102 (2006).
[Crossref] [PubMed]

F. Svedberg, Z. P. Li, H. X. Xu, and M. Käll, “Creating hot nanoparticle pairs for surface-enhanced Raman spectroscopy through optical manipulation,” Nano Lett. 6(12), 2639–2641 (2006).
[Crossref] [PubMed]

H. X. Xu, J. Aizpurua, M. Käll, and P. Apell, “Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(33 Pt B), 4318–4324 (2000).
[Crossref] [PubMed]

Xu, J.

Y. M. Hou, J. Xu, X. J. Zhang, and D. P. Yu, “SERS on periodic arrays of coupled quadrate-holes and squares,” Nanotechnology 21(19), 195203 (2010).
[Crossref] [PubMed]

Yeo, B. S.

W. H. Zhang, B. S. Yeo, T. Schmid, and R. Zenobi, “Single molecule tip enhanced Raman spectroscopy with silver tips,” J. Phys. Chem. C 111(4), 1733–1738 (2007).
[Crossref]

Yu, D. P.

Y. M. Hou, J. Xu, X. J. Zhang, and D. P. Yu, “SERS on periodic arrays of coupled quadrate-holes and squares,” Nanotechnology 21(19), 195203 (2010).
[Crossref] [PubMed]

Yu, K. W.

Yu, Z. F.

A. Kinkhabwala, Z. F. Yu, S. H. Fan, Y. Avlasevich, K. Müllen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photonics 3(11), 654–657 (2009).
[Crossref]

Zavelani-Rossi, M.

D. Pisignano, M. Anni, G. Gigli, R. Cingolani, M. Zavelani-Rossi, G. Lanzani, G. Barbarella, and L. Favaretto, “Amplified spontaneous emission and efficient tunable laser emission,” Appl. Phys. Lett. 81(19), 3534–3536 (2002).
[Crossref]

Zeng, Z. W.

Z. W. Zeng and H. T. Liu, “Electromagnetic enhancement by a T-shaped metallic nano groove impact of surface plasmon polaritons and other surface waves,” IEEE J. Sel. Top. Quantum Electron. 18(6), 1669–1675 (2012).
[Crossref]

Zenobi, R.

W. H. Zhang, B. S. Yeo, T. Schmid, and R. Zenobi, “Single molecule tip enhanced Raman spectroscopy with silver tips,” J. Phys. Chem. C 111(4), 1733–1738 (2007).
[Crossref]

Zhang, B. H.

B. H. Zhang, H. S. Wang, L. H. Lu, K. L. Ai, G. Zhang, and X. L. Cheng, “Large area silver coated silicon nanowire arrays for molecular sensing using surface enhanced raman spectroscopy,” Adv. Funct. Mater. 18(16), 2348–2355 (2008).
[Crossref]

Zhang, G.

B. H. Zhang, H. S. Wang, L. H. Lu, K. L. Ai, G. Zhang, and X. L. Cheng, “Large area silver coated silicon nanowire arrays for molecular sensing using surface enhanced raman spectroscopy,” Adv. Funct. Mater. 18(16), 2348–2355 (2008).
[Crossref]

Zhang, S. W.

Zhang, W. H.

W. H. Zhang, B. S. Yeo, T. Schmid, and R. Zenobi, “Single molecule tip enhanced Raman spectroscopy with silver tips,” J. Phys. Chem. C 111(4), 1733–1738 (2007).
[Crossref]

Zhang, X.

X. Zhang, H. T. Liu, and Y. Zhong, “Compensation of propagation loss of surface plasmon polaritons with a finite-thickness dielectric gain layer,” J. Opt. 14(12), 125003 (2012).
[Crossref]

Zhang, X. J.

Y. M. Hou, J. Xu, X. J. Zhang, and D. P. Yu, “SERS on periodic arrays of coupled quadrate-holes and squares,” Nanotechnology 21(19), 195203 (2010).
[Crossref] [PubMed]

Zhang, Z. Y.

K. Zhao, H. X. Xu, B. H. Gu, and Z. Y. Zhang, “One-dimensional arrays of nanoshell dimers for single molecule spectroscopy via surface-enhanced raman scattering,” J. Chem. Phys. 125(8), 081102 (2006).
[Crossref] [PubMed]

Zhao, K.

K. Zhao, H. X. Xu, B. H. Gu, and Z. Y. Zhang, “One-dimensional arrays of nanoshell dimers for single molecule spectroscopy via surface-enhanced raman scattering,” J. Chem. Phys. 125(8), 081102 (2006).
[Crossref] [PubMed]

Zhao, Y. P.

S. Shanmukh, L. Jones, J. Driskell, Y. P. Zhao, R. Dluhy, and R. A. Tripp, “Rapid and sensitive detection of respiratory virus molecular signatures using a silver nanorod array SERS substrate,” Nano Lett. 6(11), 2630–2636 (2006).
[Crossref] [PubMed]

Zhong, Y.

X. Zhang, H. T. Liu, and Y. Zhong, “Compensation of propagation loss of surface plasmon polaritons with a finite-thickness dielectric gain layer,” J. Opt. 14(12), 125003 (2012).
[Crossref]

Zhou, Y. L.

H. Shen, B. Cheng, G. W. Lu, T. Y. Ning, D. Y. Guan, Y. L. Zhou, and Z. H. Chen, “Enhancement of optical nonlinearity in periodic gold nanoparticle arrays,” Nanotechnology 17(16), 4274–4277 (2006).
[Crossref] [PubMed]

ACS Nano (1)

S. S. Aćimović, M. P. Kreuzer, M. U. González, and R. Quidant, “Plasmon near-field coupling in metal dimers as a step toward single-molecule sensing,” ACS Nano 3(5), 1231–1237 (2009).
[Crossref] [PubMed]

Adv. Funct. Mater. (1)

B. H. Zhang, H. S. Wang, L. H. Lu, K. L. Ai, G. Zhang, and X. L. Cheng, “Large area silver coated silicon nanowire arrays for molecular sensing using surface enhanced raman spectroscopy,” Adv. Funct. Mater. 18(16), 2348–2355 (2008).
[Crossref]

Adv. Mater. (1)

W. E. Doering, M. E. Piotti, M. J. Natan, and R. G. Freeman, “SERS as a foundation for nanoscale optically detected biological labels,” Adv. Mater. 19(20), 3100–3108 (2007).
[Crossref]

Appl. Phys. Lett. (2)

D. Pisignano, M. Anni, G. Gigli, R. Cingolani, M. Zavelani-Rossi, G. Lanzani, G. Barbarella, and L. Favaretto, “Amplified spontaneous emission and efficient tunable laser emission,” Appl. Phys. Lett. 81(19), 3534–3536 (2002).
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A. Krishnan, S. P. Frisbie, L. Grave de Peralta, and A. A. Bernussi, “Plasmon stimulated emission in arrays of bimetallic structres coated with dye-doped dielectric,” Appl. Phys. Lett. 96(11), 111104 (2010).
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Chem. Phys. Lett. (2)

M. Fleischmann, P. J. Hendra, and A. J. McQuillan, “Raman spectra of pyridine adsorbed at a silver electrode,” Chem. Phys. Lett. 26(2), 163–166 (1974).
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N. Hayazawa, Y. Inouye, Z. Sekkat, and S. Kawata, “Near-field Raman scattering enhanced by a metallized tip,” Chem. Phys. Lett. 335(5-6), 369–374 (2001).
[Crossref]

Chem. Sci. (1)

N. Pazos-Pérez, W. Ni, A. Schweikart, R. A. Alvarez-Puebla, A. Fery, and L. M. Liz-Marzán, “Highly uniform SERS substrates formed by wrinkle-confined drying of gold colloids,” Chem. Sci. 1(2), 174–178 (2010).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

H. T. Miyazaki and Y. Kurokawa, “How can a resonant nanogap enhance optical fields by many orders of magnitude,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1565–1576 (2008).
[Crossref]

Z. W. Zeng and H. T. Liu, “Electromagnetic enhancement by a T-shaped metallic nano groove impact of surface plasmon polaritons and other surface waves,” IEEE J. Sel. Top. Quantum Electron. 18(6), 1669–1675 (2012).
[Crossref]

J. Am. Chem. Soc. (1)

J. P. Camden, J. A. Dieringer, Y. M. Wang, D. J. Masiello, L. D. Marks, G. C. Schatz, and R. P. Van Duyne, “Probing the structure of single-molecule surface-enhanced Raman scattering hot spots,” J. Am. Chem. Soc. 130(38), 12616–12617 (2008).
[Crossref] [PubMed]

J. Chem. Phys. (1)

K. Zhao, H. X. Xu, B. H. Gu, and Z. Y. Zhang, “One-dimensional arrays of nanoshell dimers for single molecule spectroscopy via surface-enhanced raman scattering,” J. Chem. Phys. 125(8), 081102 (2006).
[Crossref] [PubMed]

J. Opt. (1)

X. Zhang, H. T. Liu, and Y. Zhong, “Compensation of propagation loss of surface plasmon polaritons with a finite-thickness dielectric gain layer,” J. Opt. 14(12), 125003 (2012).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (5)

J. Phys. Chem. C (2)

J. R. Anema, A. G. Brolo, P. Marthandam, and R. Gordon, “Enhanced Raman scattering from nanoholes in a copper film,” J. Phys. Chem. C 112(44), 17051–17055 (2008).
[Crossref]

W. H. Zhang, B. S. Yeo, T. Schmid, and R. Zenobi, “Single molecule tip enhanced Raman spectroscopy with silver tips,” J. Phys. Chem. C 111(4), 1733–1738 (2007).
[Crossref]

Nano Lett. (7)

Z. Y. Li and Y. Xia, “Metal nanoparticles with gain toward single-molecule detection by surface-enhanced Raman scattering,” Nano Lett. 10(1), 243–249 (2010).
[Crossref] [PubMed]

S. Shanmukh, L. Jones, J. Driskell, Y. P. Zhao, R. Dluhy, and R. A. Tripp, “Rapid and sensitive detection of respiratory virus molecular signatures using a silver nanorod array SERS substrate,” Nano Lett. 6(11), 2630–2636 (2006).
[Crossref] [PubMed]

W. H. Park and Z. H. Kim, “Charge transfer enhancement in the SERS of a single molecule,” Nano Lett. 10(10), 4040–4048 (2010).
[Crossref] [PubMed]

F. Tam, G. P. Goodrich, B. R. Johnson, and N. J. Halas, “Plasmonic enhancement of molecular fluorescence,” Nano Lett. 7(2), 496–501 (2007).
[Crossref] [PubMed]

S. J. Lee, J. M. Baik, and M. Moskovits, “Polarization-dependent surface-enhanced Raman scattering from a silver-nanoparticle-decorated single silver nanowire,” Nano Lett. 8(10), 3244–3247 (2008).
[Crossref] [PubMed]

F. Svedberg, Z. P. Li, H. X. Xu, and M. Käll, “Creating hot nanoparticle pairs for surface-enhanced Raman spectroscopy through optical manipulation,” Nano Lett. 6(12), 2639–2641 (2006).
[Crossref] [PubMed]

A. G. Brolo, E. Arctander, R. Gordon, B. Leathem, and K. L. Kavanagh, “Nanohole-enhanced Raman scattering,” Nano Lett. 4(10), 2015–2018 (2004).
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Nanoscale (1)

A. J. Chung, Y. S. Huh, and D. Erickson, “Large area flexible SERS active substrates using engineered nanostructures,” Nanoscale 3(7), 2903–2908 (2011).
[Crossref] [PubMed]

Nanotechnology (2)

Y. M. Hou, J. Xu, X. J. Zhang, and D. P. Yu, “SERS on periodic arrays of coupled quadrate-holes and squares,” Nanotechnology 21(19), 195203 (2010).
[Crossref] [PubMed]

H. Shen, B. Cheng, G. W. Lu, T. Y. Ning, D. Y. Guan, Y. L. Zhou, and Z. H. Chen, “Enhancement of optical nonlinearity in periodic gold nanoparticle arrays,” Nanotechnology 17(16), 4274–4277 (2006).
[Crossref] [PubMed]

Nat. Mater. (1)

D. K. Lim, K. S. Jeon, H. M. Kim, J. M. Nam, and Y. D. Suh, “Nanogap-engineerable Raman-active nanodumbbells for single-molecule detection,” Nat. Mater. 9(1), 60–67 (2010).
[Crossref] [PubMed]

Nat. Photonics (1)

A. Kinkhabwala, Z. F. Yu, S. H. Fan, Y. Avlasevich, K. Müllen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photonics 3(11), 654–657 (2009).
[Crossref]

Nature (2)

H. T. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452(7188), 728–731 (2008).
[Crossref] [PubMed]

F. van Beijnum, C. Rétif, C. B. Smiet, H. T. Liu, P. Lalanne, and M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature 492(7429), 411–414 (2012).
[Crossref] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Philos. Mag. (1)

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag. 4, 396–402 (1902).

Phys. Rev. B (2)

P. I. Geshev, S. Klein, T. Witting, K. Dickmann, and M. Hietschold, “Calculation of the electric-field enhancement at nanoparticles of arbitrary shape in close proximity to a metallic surface,” Phys. Rev. B 70(7), 075402 (2004).
[Crossref]

H. T. Liu and P. Lalanne, “Light scattering by metallic surfaces with subwavelength patterns,” Phys. Rev. B 82(11), 115418 (2010).
[Crossref]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (1)

H. X. Xu, J. Aizpurua, M. Käll, and P. Apell, “Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(33 Pt B), 4318–4324 (2000).
[Crossref] [PubMed]

Phys. Rev. Lett. (4)

F. J. García-Vidal and J. B. Pendry, “Collective theory for surface enhanced Raman scattering,” Phys. Rev. Lett. 77(6), 1163–1166 (1996).
[Crossref] [PubMed]

J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Ríos, “Controlling strong electromagnetic fields at subwavelength scales,” Phys. Rev. Lett. 97(3), 036405 (2006).
[Crossref] [PubMed]

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, “Single molecule detection using surface enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78(9), 1667–1670 (1997).
[Crossref]

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S. L. Kleinman, J. M. Bingham, A. I. Henry, K. L. Wustholz, and R. P. Van Duyne, “Structural and optical characterization of single nanoparticles and single molecule SERS,” Proc. SPIE 7757, 77570J, 77570J-10 (2010).
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Figures (6)

Fig. 1
Fig. 1

(a) Two-dimensional array of blind holes drilled in a gold substrate illuminated by a normally-incident x-polarized plane wave from air. The array period is a = 1μm and the hole side length and depth are 0.2μm. (b) Reflectance spectra (green triangles) and the enhanced factor of the hole array. EF obtained with the RCWA, the HW model and the SPP model are shown with the red circles, the black solid curve, and the blue dash-dot curve, respectively. (c1)-(c2) Moduli and phases of τ + ρ (red dashed curves), 1/ΣHHW + 1 (black solid curves) and 1/ΣHSPP + 1 = exp(−ikSPPa) (blue dash-dot curves). The phase-matching conditions for the SPP model and for the HW model are labeled by the two vertical dashed lines at the intersections in (c2). (c3) Moduli of the HW excitation coefficient β under plane-wave illumination [see Fig. 3(c), for the calculated β the incident plane wave and the SPP contained in the HW are normalized to have unitary magnetic field Hy at the center of holes]. (d) Normalized electric-field intensity |Ez|2/|(E)inc|2 of the dominant z-component on the metal surface (d1) and on the cross section y = 0 (d2)-(d4), which are obtained with the RCWA (d1)-(d2), the SPP model (d3) and the HW model (d4) under the phase-matching condition (λ = 1.0153μm).

Fig. 2
Fig. 2

(a) Two-dimensional array of gold cubes on a gold substrate illuminated by a normally-incident x-polarized plane wave from air. The array period is a = 1μm and the cube side length is 0.2μm. (b) Enhancement factor of the cube array obtained with the RCWA (red circles) and the HW model (black solid curve). (c1)-(c2) Moduli and phases of τ + ρ (red dashed curves) and 1/ΣHHW + 1 (black solid curves). The phase-matching condition for the HW model is labeled by the vertical dashed line at the intersection in (c2). (c3) Moduli of β. (d) Normalized electric-field intensity |Ez|2/|(E)inc|2 of the dominant z-component on the cross section y = 0, which is obtained with the RCWA (d1) and the HW model (d2) at the resonance wavelength (λ = 1.0029μm).

Fig. 3
Fig. 3

(a) Coefficients P0 and Q0 of the right-going and the left-going HWs that originate from every y-periodic chain of subwavelength indentations in the array. The indentation array is illuminated by a normally-incident x-polarized plane wave. (b1)-(b3) HW, its SPP component and the residual QCW component, launched on an air-gold interface at λ = 1μm by a subwavelength line scatterer at x = z = 0. Analytical expressions of the HW, SPP and QCW can be found in [41], and their descriptions are provided in chapter 3. The refractive index of gold at λ = 1μm is 0.25 + 6.84i. The dominant electric-field component Ez is shown. (c)-(d) Scattering coefficients β, ρ and τ that characterize the excitation, reflection and transmission of HWs at a chain of indentations that are assumed to be symmetric about x = 0.

Fig. 4
Fig. 4

(a) One-dimensional periodic array of slits in a gold substrate. The slit array is illuminated by a normally-incident x-polarized plane wave from air. The array period is a = 1μm and the slit width is 0.2μm. (b) Enhancement factor of the slit array obtained with the RCWA (red circles) and the HW model (black solid curve). (c1)-(c2) Moduli and phases of τ + ρ (red dashed curves) and of 1/ΣHHW + 1 (black solid curves). The phase-matching condition is labeled with the vertical dashed line at the intersection in (c2). (c3) Moduli of β. (d) Normalized electric-field intensity |Ez|2/|(E)inc|2 of the dominant z-component on the cross section y = 0, which is obtained with the RCWA under the phase-matching condition (λ = 1.0001μm).

Fig. 5
Fig. 5

(a) Two-dimensional array of blind holes in gold substrate filled with materials with or without gain [refractive index nhole = 1.5−0.15i for (b), (c) and (f), and nhole = 1.5−0i for (d), (e) and (g)]. The hole array is illuminated by a normally-incident x-polarized plane wave from air. The array period is a = 1μm and the hole side length and depth are 0.2μm. (b) Enhancement factor of the gain-filled hole array obtained with the RCWA (red circles) and the HW model (black solid curve). (c1)-(c2) Moduli and phases of τ + ρ (red dashed curves) and of 1/ΣHHW + 1 (black solid curves) obtained for nhole = 1.5−0.15i. The phase-matching condition is labeled by the vertical dashed line at the intersection in (c2). (c3) Moduli of β for nhole = 1.5−0.15i. (d)-(e) the same as (b)-(c) but for nhole = 1.5−0i without gain. (f) Normalized electric-field intensity |Ez|2/|(E)inc|2 of the dominant z-component on the cross section y = 0, which is obtained for nhole = 1.5−0.15i with the RCWA under the phase-matching condition (λ = 1.0175μm). (g) the same as (f) but for nhole = 1.5−0i.

Fig. 6
Fig. 6

(a) Two-dimensional array of dielectric cubes [refractive index ncube = 1.5−0.15i for (b), (c) and (f), and ncube = 1.5−0i for (d), (e) and (g)] on a gold substrate. The cube array is illuminated by a normally-incident x-polarized plane wave from air. The array period is a = 1μm and the cube side length is 0.2μm. (b) Enhancement factor of the gain cube array obtained with the RCWA (red circles) and the HW model (black solid curve). (c1)-(c2) Moduli and phases of τ + ρ (red dashed curves) and of 1/ΣHHW + 1 (black solid curves) for ncube = 1.5−0.15i. The phase-matching condition is labeled with the vertical dashed line at the intersection in (c2). (c3) Moduli of β for ncube = 1.5−0.15i. (d)-(e) the same as (b)-(c) but for ncube = 1.5-0i without gain. (f) Normalized electric-field intensity |Ez|2/|(E)inc|2 of the dominant z-component on the cross section y = 0, which is obtained for ncube = 1.5−0.15i with the RCWA under the phase-matching condition (λ = 1.0128μm). (g) the same as (f) but for ncube = 1.5−0i.

Equations (8)

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EF= | E(x=a/4,y=0,z=0) | 2 / | E inc | 2 ,
ψ(x,z)= n=0 P 0 ψ HW + (xna,z) + n=1 + Q 0 ψ HW (xna,z) ,
P 0 =β+(τ1)Σ H HW P 0 +ρΣ H HW Q 0 ,
Q 0 =β+ρΣ H HW P 0 +(τ1)Σ H HW Q 0 .
P 0 = Q 0 = β/Σ H HW (1/Σ H HW +1)(τ+ρ) .
arg(1/Σ H HW +1)=arg(τ+ρ) modulo 2π
| P 0 | λ= λ res = [ |β|/|Σ H HW | | |1/Σ H HW +1||τ+ρ| | ] λ= λ res
Re( k SPP )a+arg(τ+ρ)=0 modulo 2π,   

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