Abstract

For sensing and imaging applications of surface-enhanced Raman scattering (SERS), one needs a substrate with the capability of generating a consistent and uniform response and increased signal enhancement. To this goal, we propose a photonic-crystal (PC) structure capable of supporting large field enhancement due to its high quality-factor resonance. Moreover, we demonstrate that the interaction of two modes of this all-dielectric PC can provide an almost uniform field enhancement across the unit cell of the PC. This is of practical importance for SERS applications. The designed structure can support a maximum field enhancement of 70 and 97 percent of uniformity.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2019 (3)

2018 (3)

J. Černigoj, F. Silvestri, L. P. Stoevelaar, J. Berzinš, and G. Gerini, “Lattice resonances and local field enhancement in array of dielectric dimers for surface enhanced raman spectroscopy,” Sci. Rep. 8(1), 15706 (2018).
[Crossref]

M. Fränzl, S. Moras, O. D. Gordan, and D. R. Zahn, “Interaction of One-Dimensional Photonic Crystals and Metal Nanoparticle Arrays and Its Application for Surface-Enhanced Raman Spectroscopy,” J. Phys. Chem. C 122(18), 10153–10158 (2018).
[Crossref]

T. Lee, J.-S. Wi, A. Oh, H.-K. Na, J. Lee, K. Lee, T. G. Lee, and S. Haam, “Highly robust, uniform and ultra-sensitive surface-enhanced Raman scattering substrates for microRNA detection fabricated by using silver nanostructures grown in gold nanobowls,” Nanoscale 10(8), 3680–3687 (2018).
[Crossref]

2017 (4)

S. Jiang, J. Guo, C. Zhang, C. Li, M. Wang, Z. Li, S. Gao, P. Chen, H. Si, and S. Xu, “A sensitive, uniform, reproducible and stable SERS substrate has been presented based on MoS 2@ Ag nanoparticles@ pyramidal silicon,” RSC Adv. 7(10), 5764–5773 (2017).
[Crossref]

Z. Liu, J. Li, Z. Liu, W. Li, J. Li, C. Gu, and Z.-Y. Li, “Fano resonance Rabi splitting of surface plasmons,” Sci. Rep. 7(1), 8010 (2017).
[Crossref]

N. Michieli, R. Pilot, V. Russo, C. Scian, F. Todescato, R. Signorini, S. Agnoli, T. Cesca, R. Bozio, and G. Mattei, “Oxidation effects on the SERS response of silver nanoprism arrays,” RSC Adv. 7(1), 369–378 (2017).
[Crossref]

J.-N. Liu, Q. Huang, K.-K. Liu, S. Singamaneni, and B. T. Cunningham, “Nanoantenna–Microcavity Hybrids with Highly Cooperative Plasmonic–Photonic Coupling,” Nano Lett. 17(12), 7569–7577 (2017).
[Crossref]

2016 (3)

L. Zhang, C. Guan, Y. Wang, and J. Liao, “Highly effective and uniform SERS substrates fabricated by etching multi-layered gold nanoparticle arrays,” Nanoscale 8(11), 5928–5937 (2016).
[Crossref]

W. Zhu, R. Esteban, A. G. Borisov, J. J. Baumberg, P. Nordlander, H. J. Lezec, J. Aizpurua, and K. B. Crozier, “Quantum mechanical effects in plasmonic structures with subnanometre gaps,” Nat. Commun. 7(1), 11495 (2016).
[Crossref]

S.-Y. Ding, J. Yi, J.-F. Li, B. Ren, D.-Y. Wu, R. Panneerselvam, and Z.-Q. Tian, “Nanostructure-based plasmon-enhanced Raman spectroscopy for surface analysis of materials,” Nat. Rev. Mater. 1(6), 16021 (2016).
[Crossref]

2015 (2)

M. Caldarola, P. Albella, E. Cortés, M. Rahmani, T. Roschuk, G. Grinblat, R. F. Oulton, A. V. Bragas, and S. A. Maier, “Non-plasmonic nanoantennas for surface enhanced spectroscopies with ultra-low heat conversion,” Nat. Commun. 6(1), 7915 (2015).
[Crossref]

Z. Huang, J. Wang, Z. Liu, G. Xu, Y. Fan, H. Zhong, B. Cao, C. Wang, and K. Xu, “Strong-field-enhanced spectroscopy in silicon nanoparticle electric and magnetic dipole resonance near a metal surface,” J. Phys. Chem. C 119(50), 28127–28135 (2015).
[Crossref]

2014 (2)

P. Albella, R. Alcaraz de la Osa, F. Moreno, and S. A. Maier, “Electric and magnetic field enhancement with ultralow heat radiation dielectric nanoantennas: considerations for surface-enhanced spectroscopies,” ACS Photonics 1(6), 524–529 (2014).
[Crossref]

W. Zhu and K. B. Crozier, “Quantum mechanical limit to plasmonic enhancement as observed by surface-enhanced Raman scattering,” Nat. Commun. 5(1), 5228 (2014).
[Crossref]

2013 (5)

S. L. Kleinman, R. R. Frontiera, A.-I. Henry, J. A. Dieringer, and R. P. Van Duyne, “Creating, characterizing, and controlling chemistry with SERS hot spots,” Phys. Chem. Chem. Phys. 15(1), 21–36 (2013).
[Crossref]

S. L. Kleinman, B. Sharma, M. G. Blaber, A.-I. Henry, N. Valley, R. G. Freeman, M. J. Natan, G. C. Schatz, and R. P. Van Duyne, “Structure enhancement factor relationships in single gold nanoantennas by surface-enhanced Raman excitation spectroscopy,” J. Am. Chem. Soc. 135(1), 301–308 (2013).
[Crossref]

A. Pokhriyal, M. Lu, V. Chaudhery, S. George, and B. T. Cunningham, “Enhanced fluorescence emission using a photonic crystal coupled to an optical cavity,” Appl. Phys. Lett. 102(22), 221114 (2013).
[Crossref]

M. Radulaski, T. M. Babinec, S. Buckley, A. Rundquist, J. Provine, K. Alassaad, G. Ferro, and J. Vučković, “Photonic crystal cavities in cubic (3C) polytype silicon carbide films,” Opt. Express 21(26), 32623–32629 (2013).
[Crossref]

S. Pirotta, X. Xu, A. Delfan, S. Mysore, S. Maiti, G. Dacarro, M. Patrini, M. Galli, G. Guizzetti, and D. Bajoni, “Surface-enhanced Raman scattering in purely dielectric structures via Bloch surface waves,” J. Phys. Chem. C 117(13), 6821–6825 (2013).
[Crossref]

2012 (4)

M. A. Schmidt, D. Y. Lei, L. Wondraczek, V. Nazabal, and S. A. Maier, “Hybrid nanoparticle–microcavity-based plasmonic nanosensors with improved detection resolution and extended remote-sensing ability,” Nat. Commun. 3(1), 1108 (2012).
[Crossref]

J. M. McMahon, S. Li, L. K. Ausman, and G. C. Schatz, “Modeling the effect of small gaps in surface-enhanced Raman spectroscopy,” J. Phys. Chem. C 116(2), 1627–1637 (2012).
[Crossref]

A. Ahmed and R. Gordon, “Single molecule directivity enhanced Raman scattering using nanoantennas,” Nano Lett. 12(5), 2625–2630 (2012).
[Crossref]

A. Delfan, M. Liscidini, and J. E. Sipe, “Surface enhanced Raman scattering in the presence of multilayer dielectric structures,” J. Opt. Soc. Am. B 29(8), 1863–1874 (2012).
[Crossref]

2011 (1)

D.-K. Lim, K.-S. Jeon, J.-H. Hwang, H. Kim, S. Kwon, Y. D. Suh, and J.-M. Nam, “Highly uniform and reproducible surface-enhanced Raman scattering from DNA-tailorable nanoparticles with 1-nm interior gap,” Nat. Nanotechnol. 6(7), 452–460 (2011).
[Crossref]

2010 (3)

2008 (3)

X.-M. Qian and S. M. Nie, “Single-molecule and single-nanoparticle SERS: from fundamental mechanisms to biomedical applications,” Chem. Soc. Rev. 37(5), 912–920 (2008).
[Crossref]

P. G. Etchegoin and E. Le Ru, “A perspective on single molecule SERS: current status and future challenges,” Phys. Chem. Chem. Phys. 10(40), 6079–6089 (2008).
[Crossref]

H. Wei, U. Håkanson, Z. Yang, F. Höök, and H. Xu, “Individual Nanometer Hole–Particle Pairs for Surface-Enhanced Raman Scattering,” Small 4(9), 1296–1300 (2008).
[Crossref]

2007 (1)

E. Le Ru, E. Blackie, M. Meyer, and P. G. Etchegoin, “Surface enhanced Raman scattering enhancement factors: a comprehensive study,” J. Phys. Chem. C 111(37), 13794–13803 (2007).
[Crossref]

2002 (1)

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
[Crossref]

1999 (1)

H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, “Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering,” Phys. Rev. Lett. 83(21), 4357–4360 (1999).
[Crossref]

1997 (1)

S. Nie and S. R. Emory, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science 275(5303), 1102–1106 (1997).
[Crossref]

1951 (1)

Agnoli, S.

N. Michieli, R. Pilot, V. Russo, C. Scian, F. Todescato, R. Signorini, S. Agnoli, T. Cesca, R. Bozio, and G. Mattei, “Oxidation effects on the SERS response of silver nanoprism arrays,” RSC Adv. 7(1), 369–378 (2017).
[Crossref]

Ahmed, A.

A. Ahmed and R. Gordon, “Single molecule directivity enhanced Raman scattering using nanoantennas,” Nano Lett. 12(5), 2625–2630 (2012).
[Crossref]

Aizpurua, J.

W. Zhu, R. Esteban, A. G. Borisov, J. J. Baumberg, P. Nordlander, H. J. Lezec, J. Aizpurua, and K. B. Crozier, “Quantum mechanical effects in plasmonic structures with subnanometre gaps,” Nat. Commun. 7(1), 11495 (2016).
[Crossref]

Alassaad, K.

Albella, P.

M. Caldarola, P. Albella, E. Cortés, M. Rahmani, T. Roschuk, G. Grinblat, R. F. Oulton, A. V. Bragas, and S. A. Maier, “Non-plasmonic nanoantennas for surface enhanced spectroscopies with ultra-low heat conversion,” Nat. Commun. 6(1), 7915 (2015).
[Crossref]

P. Albella, R. Alcaraz de la Osa, F. Moreno, and S. A. Maier, “Electric and magnetic field enhancement with ultralow heat radiation dielectric nanoantennas: considerations for surface-enhanced spectroscopies,” ACS Photonics 1(6), 524–529 (2014).
[Crossref]

Alcaraz de la Osa, R.

P. Albella, R. Alcaraz de la Osa, F. Moreno, and S. A. Maier, “Electric and magnetic field enhancement with ultralow heat radiation dielectric nanoantennas: considerations for surface-enhanced spectroscopies,” ACS Photonics 1(6), 524–529 (2014).
[Crossref]

Ausman, L. K.

J. M. McMahon, S. Li, L. K. Ausman, and G. C. Schatz, “Modeling the effect of small gaps in surface-enhanced Raman spectroscopy,” J. Phys. Chem. C 116(2), 1627–1637 (2012).
[Crossref]

Ayliffe, P.

J. J. Baumberg, M. Netti, S. Mahnkopf, J. Lincoln, M. Charlton, S. Cox, P. Ayliffe, M. Zoorob, J. Wilkinson, and N. Perney, “Metallo-dielectric photonic crystals for reproducible surface-enhanced Raman substrates,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2005), p. CTuH6.

Babinec, T. M.

Bajoni, D.

S. Pirotta, X. Xu, A. Delfan, S. Mysore, S. Maiti, G. Dacarro, M. Patrini, M. Galli, G. Guizzetti, and D. Bajoni, “Surface-enhanced Raman scattering in purely dielectric structures via Bloch surface waves,” J. Phys. Chem. C 117(13), 6821–6825 (2013).
[Crossref]

Baumberg, J. J.

W. Zhu, R. Esteban, A. G. Borisov, J. J. Baumberg, P. Nordlander, H. J. Lezec, J. Aizpurua, and K. B. Crozier, “Quantum mechanical effects in plasmonic structures with subnanometre gaps,” Nat. Commun. 7(1), 11495 (2016).
[Crossref]

J. J. Baumberg, M. Netti, S. Mahnkopf, J. Lincoln, M. Charlton, S. Cox, P. Ayliffe, M. Zoorob, J. Wilkinson, and N. Perney, “Metallo-dielectric photonic crystals for reproducible surface-enhanced Raman substrates,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2005), p. CTuH6.

Berzinš, J.

J. Černigoj, F. Silvestri, L. P. Stoevelaar, J. Berzinš, and G. Gerini, “Lattice resonances and local field enhancement in array of dielectric dimers for surface enhanced raman spectroscopy,” Sci. Rep. 8(1), 15706 (2018).
[Crossref]

Bjerneld, E. J.

H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, “Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering,” Phys. Rev. Lett. 83(21), 4357–4360 (1999).
[Crossref]

Blaber, M. G.

S. L. Kleinman, B. Sharma, M. G. Blaber, A.-I. Henry, N. Valley, R. G. Freeman, M. J. Natan, G. C. Schatz, and R. P. Van Duyne, “Structure enhancement factor relationships in single gold nanoantennas by surface-enhanced Raman excitation spectroscopy,” J. Am. Chem. Soc. 135(1), 301–308 (2013).
[Crossref]

Blackie, E.

E. Le Ru, E. Blackie, M. Meyer, and P. G. Etchegoin, “Surface enhanced Raman scattering enhancement factors: a comprehensive study,” J. Phys. Chem. C 111(37), 13794–13803 (2007).
[Crossref]

Borisov, A. G.

W. Zhu, R. Esteban, A. G. Borisov, J. J. Baumberg, P. Nordlander, H. J. Lezec, J. Aizpurua, and K. B. Crozier, “Quantum mechanical effects in plasmonic structures with subnanometre gaps,” Nat. Commun. 7(1), 11495 (2016).
[Crossref]

Börjesson, L.

H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, “Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering,” Phys. Rev. Lett. 83(21), 4357–4360 (1999).
[Crossref]

Bosnick, K.

J. Jiang, K. Bosnick, M. Maillard, and L. Brus, “Single molecule Raman spectroscopy at the junctions of large Ag nanocrystals,” (ACS Publications, 2003).

Bozio, R.

N. Michieli, R. Pilot, V. Russo, C. Scian, F. Todescato, R. Signorini, S. Agnoli, T. Cesca, R. Bozio, and G. Mattei, “Oxidation effects on the SERS response of silver nanoprism arrays,” RSC Adv. 7(1), 369–378 (2017).
[Crossref]

Bragas, A. V.

M. Caldarola, P. Albella, E. Cortés, M. Rahmani, T. Roschuk, G. Grinblat, R. F. Oulton, A. V. Bragas, and S. A. Maier, “Non-plasmonic nanoantennas for surface enhanced spectroscopies with ultra-low heat conversion,” Nat. Commun. 6(1), 7915 (2015).
[Crossref]

Brus, L.

J. Jiang, K. Bosnick, M. Maillard, and L. Brus, “Single molecule Raman spectroscopy at the junctions of large Ag nanocrystals,” (ACS Publications, 2003).

Buckley, S.

Caldarola, M.

M. Caldarola, P. Albella, E. Cortés, M. Rahmani, T. Roschuk, G. Grinblat, R. F. Oulton, A. V. Bragas, and S. A. Maier, “Non-plasmonic nanoantennas for surface enhanced spectroscopies with ultra-low heat conversion,” Nat. Commun. 6(1), 7915 (2015).
[Crossref]

Cao, B.

Z. Huang, J. Wang, Z. Liu, G. Xu, Y. Fan, H. Zhong, B. Cao, C. Wang, and K. Xu, “Strong-field-enhanced spectroscopy in silicon nanoparticle electric and magnetic dipole resonance near a metal surface,” J. Phys. Chem. C 119(50), 28127–28135 (2015).
[Crossref]

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Liu, J.-N.

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P. Albella, R. Alcaraz de la Osa, F. Moreno, and S. A. Maier, “Electric and magnetic field enhancement with ultralow heat radiation dielectric nanoantennas: considerations for surface-enhanced spectroscopies,” ACS Photonics 1(6), 524–529 (2014).
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D.-K. Lim, K.-S. Jeon, J.-H. Hwang, H. Kim, S. Kwon, Y. D. Suh, and J.-M. Nam, “Highly uniform and reproducible surface-enhanced Raman scattering from DNA-tailorable nanoparticles with 1-nm interior gap,” Nat. Nanotechnol. 6(7), 452–460 (2011).
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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).
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Zahn, D. R.

M. Fränzl, S. Moras, O. D. Gordan, and D. R. Zahn, “Interaction of One-Dimensional Photonic Crystals and Metal Nanoparticle Arrays and Its Application for Surface-Enhanced Raman Spectroscopy,” J. Phys. Chem. C 122(18), 10153–10158 (2018).
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Zhang, L.

L. Zhang, C. Guan, Y. Wang, and J. Liao, “Highly effective and uniform SERS substrates fabricated by etching multi-layered gold nanoparticle arrays,” Nanoscale 8(11), 5928–5937 (2016).
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Zhang, Z.

Zhao, C.

Zhong, H.

Z. Huang, J. Wang, Z. Liu, G. Xu, Y. Fan, H. Zhong, B. Cao, C. Wang, and K. Xu, “Strong-field-enhanced spectroscopy in silicon nanoparticle electric and magnetic dipole resonance near a metal surface,” J. Phys. Chem. C 119(50), 28127–28135 (2015).
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Zhu, W.

W. Zhu, R. Esteban, A. G. Borisov, J. J. Baumberg, P. Nordlander, H. J. Lezec, J. Aizpurua, and K. B. Crozier, “Quantum mechanical effects in plasmonic structures with subnanometre gaps,” Nat. Commun. 7(1), 11495 (2016).
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W. Zhu and K. B. Crozier, “Quantum mechanical limit to plasmonic enhancement as observed by surface-enhanced Raman scattering,” Nat. Commun. 5(1), 5228 (2014).
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Zhu, Y.

Zoorob, M.

J. J. Baumberg, M. Netti, S. Mahnkopf, J. Lincoln, M. Charlton, S. Cox, P. Ayliffe, M. Zoorob, J. Wilkinson, and N. Perney, “Metallo-dielectric photonic crystals for reproducible surface-enhanced Raman substrates,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2005), p. CTuH6.

ACS Photonics (1)

P. Albella, R. Alcaraz de la Osa, F. Moreno, and S. A. Maier, “Electric and magnetic field enhancement with ultralow heat radiation dielectric nanoantennas: considerations for surface-enhanced spectroscopies,” ACS Photonics 1(6), 524–529 (2014).
[Crossref]

Appl. Phys. Lett. (1)

A. Pokhriyal, M. Lu, V. Chaudhery, S. George, and B. T. Cunningham, “Enhanced fluorescence emission using a photonic crystal coupled to an optical cavity,” Appl. Phys. Lett. 102(22), 221114 (2013).
[Crossref]

Chem. Soc. Rev. (1)

X.-M. Qian and S. M. Nie, “Single-molecule and single-nanoparticle SERS: from fundamental mechanisms to biomedical applications,” Chem. Soc. Rev. 37(5), 912–920 (2008).
[Crossref]

J. Am. Chem. Soc. (1)

S. L. Kleinman, B. Sharma, M. G. Blaber, A.-I. Henry, N. Valley, R. G. Freeman, M. J. Natan, G. C. Schatz, and R. P. Van Duyne, “Structure enhancement factor relationships in single gold nanoantennas by surface-enhanced Raman excitation spectroscopy,” J. Am. Chem. Soc. 135(1), 301–308 (2013).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (1)

J. Phys. Chem. C (5)

Z. Huang, J. Wang, Z. Liu, G. Xu, Y. Fan, H. Zhong, B. Cao, C. Wang, and K. Xu, “Strong-field-enhanced spectroscopy in silicon nanoparticle electric and magnetic dipole resonance near a metal surface,” J. Phys. Chem. C 119(50), 28127–28135 (2015).
[Crossref]

M. Fränzl, S. Moras, O. D. Gordan, and D. R. Zahn, “Interaction of One-Dimensional Photonic Crystals and Metal Nanoparticle Arrays and Its Application for Surface-Enhanced Raman Spectroscopy,” J. Phys. Chem. C 122(18), 10153–10158 (2018).
[Crossref]

S. Pirotta, X. Xu, A. Delfan, S. Mysore, S. Maiti, G. Dacarro, M. Patrini, M. Galli, G. Guizzetti, and D. Bajoni, “Surface-enhanced Raman scattering in purely dielectric structures via Bloch surface waves,” J. Phys. Chem. C 117(13), 6821–6825 (2013).
[Crossref]

E. Le Ru, E. Blackie, M. Meyer, and P. G. Etchegoin, “Surface enhanced Raman scattering enhancement factors: a comprehensive study,” J. Phys. Chem. C 111(37), 13794–13803 (2007).
[Crossref]

J. M. McMahon, S. Li, L. K. Ausman, and G. C. Schatz, “Modeling the effect of small gaps in surface-enhanced Raman spectroscopy,” J. Phys. Chem. C 116(2), 1627–1637 (2012).
[Crossref]

Nano Lett. (2)

A. Ahmed and R. Gordon, “Single molecule directivity enhanced Raman scattering using nanoantennas,” Nano Lett. 12(5), 2625–2630 (2012).
[Crossref]

J.-N. Liu, Q. Huang, K.-K. Liu, S. Singamaneni, and B. T. Cunningham, “Nanoantenna–Microcavity Hybrids with Highly Cooperative Plasmonic–Photonic Coupling,” Nano Lett. 17(12), 7569–7577 (2017).
[Crossref]

Nanoscale (2)

T. Lee, J.-S. Wi, A. Oh, H.-K. Na, J. Lee, K. Lee, T. G. Lee, and S. Haam, “Highly robust, uniform and ultra-sensitive surface-enhanced Raman scattering substrates for microRNA detection fabricated by using silver nanostructures grown in gold nanobowls,” Nanoscale 10(8), 3680–3687 (2018).
[Crossref]

L. Zhang, C. Guan, Y. Wang, and J. Liao, “Highly effective and uniform SERS substrates fabricated by etching multi-layered gold nanoparticle arrays,” Nanoscale 8(11), 5928–5937 (2016).
[Crossref]

Nat. Commun. (4)

M. Caldarola, P. Albella, E. Cortés, M. Rahmani, T. Roschuk, G. Grinblat, R. F. Oulton, A. V. Bragas, and S. A. Maier, “Non-plasmonic nanoantennas for surface enhanced spectroscopies with ultra-low heat conversion,” Nat. Commun. 6(1), 7915 (2015).
[Crossref]

W. Zhu, R. Esteban, A. G. Borisov, J. J. Baumberg, P. Nordlander, H. J. Lezec, J. Aizpurua, and K. B. Crozier, “Quantum mechanical effects in plasmonic structures with subnanometre gaps,” Nat. Commun. 7(1), 11495 (2016).
[Crossref]

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Figures (10)

Fig. 1.
Fig. 1. Schematic of the 2D PC surrounded by water media under the illumination of an x-polarized normally incident plane wave.
Fig. 2.
Fig. 2. Reflectance of the 2D PC for a normal x-polarized plane wave with the structural parameters of $R = 20nm$, and ${P_x} = {P_y} = 400nm$.
Fig. 3.
Fig. 3. Electric field distribution inside the 2D PC at the wavelengths of (a) 598.79 nm, and (b) 646.66 nm. The bottom figures are the cross section along the dash-dot line on the surface. Four unit cells are included in this representation.
Fig. 4.
Fig. 4. Electric field distribution in the structure of (a) 1D corrugated PC and (b) the 1D resonance of 2D PC. Four unit cells of the structures can be seen in this figure. As can be inferred from the figure (b), the electric field pattern of the proposed structure within a period has slight variation along the y-direction while it fluctuates along the x-direction. This is comparable to the field variation in the one-dimensional grating structure of (a).
Fig. 5.
Fig. 5. Hole radius effect on the (a) resonances and (b) maximum enhancement factor of the electric field inside the hot spots.
Fig. 6.
Fig. 6. Effect of ${P_y}$ variation on the PC resonances. It changes only the 2D resonance position.
Fig. 7.
Fig. 7. Maximum enhancement of the electric field at the points of (a) a, (b) b, and (c) c.
Fig. 8.
Fig. 8. Electric field distribution on the surface of the PC. The bottom figure is the cross section along the dash-dot line on the surface. Four unit cells are included in this illustration.
Fig. 9.
Fig. 9. Instantaneous electric field distribution on the surface of the PC at various phases. The associated parameters are ${P_x} = 400nm$, ${P_y} = 508.04nm$, and $R = 20nm$. The PC is illuminated by an x-polarized normally incident plane wave.
Fig. 10.
Fig. 10. Typical local field enhancement on the surface of the structure for ${P_x} = 400nm$, and ${P_y} = 508.04nm$.

Equations (2)

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U F = P d c P t o t = | c 00 | 2 m n | c m n | 2 = 1 ( P x P y ) 2 | 0 P y 0 P x E ( x , y ) d x d y | 2 1 ( P x P y ) 0 P y 0 P x | E ( x , y ) | 2 d x d y
E S E R S = ( | E | | E 0 | ) λ R a y l e i g h 2 × ( | E | | E 0 | ) λ R a m a n 2