Abstract

We demonstrate the contribution of local electric near-field enhancement around convex and concave corners at resonant fundamental excitation to the second-harmonic (SH) emission intensity using complementary Au metasurfaces with triangular resonators (i.e., a square array of triangular particles and a square array of a thin film of Au with a triangular hole). It is demonstrated that for an electric near-field enhancement at normal incidence, the fundamental excitation around convex corners of a triangular particle is many times stronger than the one around concave corners of a complementary triangular hole. Notwithstanding, the SH emission intensity of the complementary structure is found to be comparable at their respective optimal resonant fundamental excitations. SH emission intensity is numerically estimated using mode overlap between the fundamental and SH waves. The comparable SH emission intensity is found to originate from the strong electric near-field enhancement on the sides of a triangular hole with zero curvature, which compensates for the field suppression around the concave corners of the triangular hole. In addition, the strong electric near-field enhancement around convex corners of a triangular particle (accompanied with suppression around the sides of the triangular particle) and field suppression around concave corners of a triangular hole (accompanied with strong field enhancement around the side of the triangular hole) are demonstrated using Babinet’s principle.

© 2019 Optical Society of America

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References

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2018 (2)

S. Chang, X. Guo, and X. Ni, “Optical metasurfaces: progress and applications,” Annu. Rev. Mater. Res. 48, 279–302 (2018).
[Crossref]

N. C. Panoiu, W. E. I. Sha, D. Y. Lei, and G.-C. Li, “Nonlinear optics in plasmonic nanostructures,” J. Opt. 20, 083001 (2018).
[Crossref]

2017 (1)

N. Zhang, Z. Ji, A. R. Cheney, H. Song, D. Ji, X. Zeng, B. Chen, T. Zhang, A. N. Cartwright, K. Shi, and Q. Gan, “Ultra-broadband enhancement of nonlinear optical processes from randomly patterned super absorbing metasurfaces,” Sci. Rep. 7, 4346 (2017).
[Crossref]

2016 (1)

2015 (1)

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14, 379–383 (2015).
[Crossref]

2014 (1)

S. W. Chen, Y.-H. Huang, B.-K. Chao, C.-H. Hsueh, and J.-H. Li, “Electric field enhancement and far-field radiation pattern of the nanoantenna with concentric rings,” Nanoscale Res. Lett. 9, 2405 (2014).
[Crossref]

2013 (1)

Y. Nakata, Y. Urade, T. Nakanishi, and M. Kitano, “Plane-wave scattering by self-complementary metasurfaces in terms of electromagnetic duality and Babinet’s principle,” Phys. Rev. B 88, 205138 (2013).
[Crossref]

2012 (5)

P. Ginzburg, A. Krasavin, Y. Sonnefraud, A. Murphy, R. J. Pollard, S. A. Maier, and A. V. Zayats, “Nonlinearly coupled localized plasmon resonances: resonant second-harmonic generation,” Phys. Rev. B 86, 085422 (2012).
[Crossref]

C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Second-harmonic generation in metallic nanoparticles: clarification of the role of the surface,” Phys. Rev. B 86, 115451 (2012).
[Crossref]

C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Origin of second-harmonic generation enhancement in optical split-ring resonators,” Phys. Rev. B 85, 201403 (2012).
[Crossref]

T. Hanke, J. Cesar, V. Knittel, A. Trügler, U. Hohenester, A. Leitenstorfer, and R. Bratschitsch, “Tailoring spatiotemporal light confinement in single plasmonic nanoantennas,” Nano Lett. 12, 992–996 (2012).
[Crossref]

V. K. Valev, “Characterization of nanostructured plasmonic surfaces with second harmonic generation,” Langmuir 28, 15454–15471 (2012).
[Crossref]

2011 (3)

C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics 5, 523–530 (2011).
[Crossref]

Y. Zhang, N. K. Grady, C. A. Orozco, and N. J. Halas, “Three-dimensional nanostructures as highly efficient generators of second harmonic light,” Nano Lett. 11, 5519–5523 (2011).
[Crossref]

J. Mäkitalo, S. Suuriniemi, and M. Kauranen, “Boundary element method for surface nonlinear optics of nanoparticles,” Opt. Express 19, 23386–23399 (2011).
[Crossref]

2008 (4)

2007 (2)

T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, and H. Giessen, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76, 033407 (2007).
[Crossref]

M. Yan and M. Qiu, “Guided plasmon polariton at 2D metal corners,” J. Opt. Soc. Am. B 24, 2333–2342 (2007).
[Crossref]

2004 (2)

F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, R. Marqués, F. Martın, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93, 197401 (2004).
[Crossref]

S. Roke, M. Bonn, and A. V. Petukhov, “Nonlinear optical scattering: the concept of effective susceptibility,” Phys. Rev. B 70, 115106 (2004).
[Crossref]

Bachelier, G.

Baena, J. D.

F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, R. Marqués, F. Martın, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93, 197401 (2004).
[Crossref]

Benichou, E.

Bonache, J.

F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, R. Marqués, F. Martın, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93, 197401 (2004).
[Crossref]

Bonn, M.

S. Roke, M. Bonn, and A. V. Petukhov, “Nonlinear optical scattering: the concept of effective susceptibility,” Phys. Rev. B 70, 115106 (2004).
[Crossref]

Bratschitsch, R.

T. Hanke, J. Cesar, V. Knittel, A. Trügler, U. Hohenester, A. Leitenstorfer, and R. Bratschitsch, “Tailoring spatiotemporal light confinement in single plasmonic nanoantennas,” Nano Lett. 12, 992–996 (2012).
[Crossref]

Brevet, P.-F.

Butet, J.

Cartwright, A. N.

N. Zhang, Z. Ji, A. R. Cheney, H. Song, D. Ji, X. Zeng, B. Chen, T. Zhang, A. N. Cartwright, K. Shi, and Q. Gan, “Ultra-broadband enhancement of nonlinear optical processes from randomly patterned super absorbing metasurfaces,” Sci. Rep. 7, 4346 (2017).
[Crossref]

Cesar, J.

T. Hanke, J. Cesar, V. Knittel, A. Trügler, U. Hohenester, A. Leitenstorfer, and R. Bratschitsch, “Tailoring spatiotemporal light confinement in single plasmonic nanoantennas,” Nano Lett. 12, 992–996 (2012).
[Crossref]

Chang, S.

S. Chang, X. Guo, and X. Ni, “Optical metasurfaces: progress and applications,” Annu. Rev. Mater. Res. 48, 279–302 (2018).
[Crossref]

Chao, B.-K.

S. W. Chen, Y.-H. Huang, B.-K. Chao, C.-H. Hsueh, and J.-H. Li, “Electric field enhancement and far-field radiation pattern of the nanoantenna with concentric rings,” Nanoscale Res. Lett. 9, 2405 (2014).
[Crossref]

Chen, B.

N. Zhang, Z. Ji, A. R. Cheney, H. Song, D. Ji, X. Zeng, B. Chen, T. Zhang, A. N. Cartwright, K. Shi, and Q. Gan, “Ultra-broadband enhancement of nonlinear optical processes from randomly patterned super absorbing metasurfaces,” Sci. Rep. 7, 4346 (2017).
[Crossref]

Chen, S. W.

S. W. Chen, Y.-H. Huang, B.-K. Chao, C.-H. Hsueh, and J.-H. Li, “Electric field enhancement and far-field radiation pattern of the nanoantenna with concentric rings,” Nanoscale Res. Lett. 9, 2405 (2014).
[Crossref]

Cheney, A. R.

N. Zhang, Z. Ji, A. R. Cheney, H. Song, D. Ji, X. Zeng, B. Chen, T. Zhang, A. N. Cartwright, K. Shi, and Q. Gan, “Ultra-broadband enhancement of nonlinear optical processes from randomly patterned super absorbing metasurfaces,” Sci. Rep. 7, 4346 (2017).
[Crossref]

Cheng, X.

X. Cheng and C. Fang, “Metamaterial design applying Babinet’s principle,” in XXXIth URSI General Assembly and Scientific Symposium (IEEE, 2014), pp. 1–4.

Ciracì, C.

C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Second-harmonic generation in metallic nanoparticles: clarification of the role of the surface,” Phys. Rev. B 86, 115451 (2012).
[Crossref]

C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Origin of second-harmonic generation enhancement in optical split-ring resonators,” Phys. Rev. B 85, 201403 (2012).
[Crossref]

de Lustrac, A.

Decker, M.

Falcone, F.

F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, R. Marqués, F. Martın, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93, 197401 (2004).
[Crossref]

Fang, C.

X. Cheng and C. Fang, “Metamaterial design applying Babinet’s principle,” in XXXIth URSI General Assembly and Scientific Symposium (IEEE, 2014), pp. 1–4.

Feth, N.

Gadot, F.

Gan, Q.

N. Zhang, Z. Ji, A. R. Cheney, H. Song, D. Ji, X. Zeng, B. Chen, T. Zhang, A. N. Cartwright, K. Shi, and Q. Gan, “Ultra-broadband enhancement of nonlinear optical processes from randomly patterned super absorbing metasurfaces,” Sci. Rep. 7, 4346 (2017).
[Crossref]

Giessen, H.

C. Rockstuhl, T. Zentgraf, T. P. Meyrath, H. Giessen, and F. Lederer, “Resonances in complementary metamaterials and nanoapertures,” Opt. Express 16, 2080–2090 (2008).
[Crossref]

T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, and H. Giessen, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76, 033407 (2007).
[Crossref]

Ginzburg, P.

P. Ginzburg, A. Krasavin, Y. Sonnefraud, A. Murphy, R. J. Pollard, S. A. Maier, and A. V. Zayats, “Nonlinearly coupled localized plasmon resonances: resonant second-harmonic generation,” Phys. Rev. B 86, 085422 (2012).
[Crossref]

Grady, N. K.

Y. Zhang, N. K. Grady, C. A. Orozco, and N. J. Halas, “Three-dimensional nanostructures as highly efficient generators of second harmonic light,” Nano Lett. 11, 5519–5523 (2011).
[Crossref]

Guo, X.

S. Chang, X. Guo, and X. Ni, “Optical metasurfaces: progress and applications,” Annu. Rev. Mater. Res. 48, 279–302 (2018).
[Crossref]

Halas, N. J.

Y. Zhang, N. K. Grady, C. A. Orozco, and N. J. Halas, “Three-dimensional nanostructures as highly efficient generators of second harmonic light,” Nano Lett. 11, 5519–5523 (2011).
[Crossref]

Hanke, T.

T. Hanke, J. Cesar, V. Knittel, A. Trügler, U. Hohenester, A. Leitenstorfer, and R. Bratschitsch, “Tailoring spatiotemporal light confinement in single plasmonic nanoantennas,” Nano Lett. 12, 992–996 (2012).
[Crossref]

Hohenester, U.

T. Hanke, J. Cesar, V. Knittel, A. Trügler, U. Hohenester, A. Leitenstorfer, and R. Bratschitsch, “Tailoring spatiotemporal light confinement in single plasmonic nanoantennas,” Nano Lett. 12, 992–996 (2012).
[Crossref]

Hoyer, W.

Hsueh, C.-H.

S. W. Chen, Y.-H. Huang, B.-K. Chao, C.-H. Hsueh, and J.-H. Li, “Electric field enhancement and far-field radiation pattern of the nanoantenna with concentric rings,” Nanoscale Res. Lett. 9, 2405 (2014).
[Crossref]

Huang, Y.-H.

S. W. Chen, Y.-H. Huang, B.-K. Chao, C.-H. Hsueh, and J.-H. Li, “Electric field enhancement and far-field radiation pattern of the nanoantenna with concentric rings,” Nanoscale Res. Lett. 9, 2405 (2014).
[Crossref]

Ji, D.

N. Zhang, Z. Ji, A. R. Cheney, H. Song, D. Ji, X. Zeng, B. Chen, T. Zhang, A. N. Cartwright, K. Shi, and Q. Gan, “Ultra-broadband enhancement of nonlinear optical processes from randomly patterned super absorbing metasurfaces,” Sci. Rep. 7, 4346 (2017).
[Crossref]

Ji, Z.

N. Zhang, Z. Ji, A. R. Cheney, H. Song, D. Ji, X. Zeng, B. Chen, T. Zhang, A. N. Cartwright, K. Shi, and Q. Gan, “Ultra-broadband enhancement of nonlinear optical processes from randomly patterned super absorbing metasurfaces,” Sci. Rep. 7, 4346 (2017).
[Crossref]

Jonin, C.

Kaiser, S.

T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, and H. Giessen, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76, 033407 (2007).
[Crossref]

Kante, B.

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14, 379–383 (2015).
[Crossref]

Kanté, B.

Karampour, N.

N. Karampour and N. Nozhat, “Triple-band metamaterial absorber based on electric excitation of split ring resonator magnetic resonance,” in Fourth International Conference on Millimeter-Wave and Terahertz Technologies (IEEE, 2016), pp. 37–40.

Kauranen, M.

Kitano, M.

Y. Nakata, Y. Urade, T. Nakanishi, and M. Kitano, “Plane-wave scattering by self-complementary metasurfaces in terms of electromagnetic duality and Babinet’s principle,” Phys. Rev. B 88, 205138 (2013).
[Crossref]

Klein, M. W.

Knittel, V.

T. Hanke, J. Cesar, V. Knittel, A. Trügler, U. Hohenester, A. Leitenstorfer, and R. Bratschitsch, “Tailoring spatiotemporal light confinement in single plasmonic nanoantennas,” Nano Lett. 12, 992–996 (2012).
[Crossref]

Koch, S. W.

Krasavin, A.

P. Ginzburg, A. Krasavin, Y. Sonnefraud, A. Murphy, R. J. Pollard, S. A. Maier, and A. V. Zayats, “Nonlinearly coupled localized plasmon resonances: resonant second-harmonic generation,” Phys. Rev. B 86, 085422 (2012).
[Crossref]

Laso, M. A. G.

F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, R. Marqués, F. Martın, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93, 197401 (2004).
[Crossref]

Lederer, F.

Lei, D. Y.

N. C. Panoiu, W. E. I. Sha, D. Y. Lei, and G.-C. Li, “Nonlinear optics in plasmonic nanostructures,” J. Opt. 20, 083001 (2018).
[Crossref]

Leitenstorfer, A.

T. Hanke, J. Cesar, V. Knittel, A. Trügler, U. Hohenester, A. Leitenstorfer, and R. Bratschitsch, “Tailoring spatiotemporal light confinement in single plasmonic nanoantennas,” Nano Lett. 12, 992–996 (2012).
[Crossref]

Li, G.-C.

N. C. Panoiu, W. E. I. Sha, D. Y. Lei, and G.-C. Li, “Nonlinear optics in plasmonic nanostructures,” J. Opt. 20, 083001 (2018).
[Crossref]

Li, J.-H.

S. W. Chen, Y.-H. Huang, B.-K. Chao, C.-H. Hsueh, and J.-H. Li, “Electric field enhancement and far-field radiation pattern of the nanoantenna with concentric rings,” Nanoscale Res. Lett. 9, 2405 (2014).
[Crossref]

Linden, S.

Liu, J.

Lopetegi, T.

F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, R. Marqués, F. Martın, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93, 197401 (2004).
[Crossref]

Lourtioz, J. M.

Maier, S. A.

P. Ginzburg, A. Krasavin, Y. Sonnefraud, A. Murphy, R. J. Pollard, S. A. Maier, and A. V. Zayats, “Nonlinearly coupled localized plasmon resonances: resonant second-harmonic generation,” Phys. Rev. B 86, 085422 (2012).
[Crossref]

S. A. Maier, “Surface plasmon polaritons at metal/insulator interfaces,” in Plasmonics: Fundamentals and Applications (Springer, 2007).

Mäkitalo, J.

Marqués, R.

F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, R. Marqués, F. Martın, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93, 197401 (2004).
[Crossref]

Martin, F.

F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, R. Marqués, F. Martın, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93, 197401 (2004).
[Crossref]

Martin, O. J. F.

Meyrath, T. P.

C. Rockstuhl, T. Zentgraf, T. P. Meyrath, H. Giessen, and F. Lederer, “Resonances in complementary metamaterials and nanoapertures,” Opt. Express 16, 2080–2090 (2008).
[Crossref]

T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, and H. Giessen, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76, 033407 (2007).
[Crossref]

Moloney, J. V.

Murphy, A.

P. Ginzburg, A. Krasavin, Y. Sonnefraud, A. Murphy, R. J. Pollard, S. A. Maier, and A. V. Zayats, “Nonlinearly coupled localized plasmon resonances: resonant second-harmonic generation,” Phys. Rev. B 86, 085422 (2012).
[Crossref]

Nakanishi, T.

Y. Nakata, Y. Urade, T. Nakanishi, and M. Kitano, “Plane-wave scattering by self-complementary metasurfaces in terms of electromagnetic duality and Babinet’s principle,” Phys. Rev. B 88, 205138 (2013).
[Crossref]

Nakata, Y.

Y. Nakata, Y. Urade, T. Nakanishi, and M. Kitano, “Plane-wave scattering by self-complementary metasurfaces in terms of electromagnetic duality and Babinet’s principle,” Phys. Rev. B 88, 205138 (2013).
[Crossref]

Ni, X.

S. Chang, X. Guo, and X. Ni, “Optical metasurfaces: progress and applications,” Annu. Rev. Mater. Res. 48, 279–302 (2018).
[Crossref]

Niesler, F. B. P.

Nozhat, N.

N. Karampour and N. Nozhat, “Triple-band metamaterial absorber based on electric excitation of split ring resonator magnetic resonance,” in Fourth International Conference on Millimeter-Wave and Terahertz Technologies (IEEE, 2016), pp. 37–40.

O’Brien, K.

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14, 379–383 (2015).
[Crossref]

O’Brien, K. P.

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N. C. Panoiu, W. E. I. Sha, D. Y. Lei, and G.-C. Li, “Nonlinear optics in plasmonic nanostructures,” J. Opt. 20, 083001 (2018).
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J. Opt. Soc. Am. B (3)

Langmuir (1)

V. K. Valev, “Characterization of nanostructured plasmonic surfaces with second harmonic generation,” Langmuir 28, 15454–15471 (2012).
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Nano Lett. (2)

Y. Zhang, N. K. Grady, C. A. Orozco, and N. J. Halas, “Three-dimensional nanostructures as highly efficient generators of second harmonic light,” Nano Lett. 11, 5519–5523 (2011).
[Crossref]

T. Hanke, J. Cesar, V. Knittel, A. Trügler, U. Hohenester, A. Leitenstorfer, and R. Bratschitsch, “Tailoring spatiotemporal light confinement in single plasmonic nanoantennas,” Nano Lett. 12, 992–996 (2012).
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S. W. Chen, Y.-H. Huang, B.-K. Chao, C.-H. Hsueh, and J.-H. Li, “Electric field enhancement and far-field radiation pattern of the nanoantenna with concentric rings,” Nanoscale Res. Lett. 9, 2405 (2014).
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K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14, 379–383 (2015).
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Nat. Photonics (1)

C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics 5, 523–530 (2011).
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Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. B (6)

T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, and H. Giessen, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76, 033407 (2007).
[Crossref]

P. Ginzburg, A. Krasavin, Y. Sonnefraud, A. Murphy, R. J. Pollard, S. A. Maier, and A. V. Zayats, “Nonlinearly coupled localized plasmon resonances: resonant second-harmonic generation,” Phys. Rev. B 86, 085422 (2012).
[Crossref]

S. Roke, M. Bonn, and A. V. Petukhov, “Nonlinear optical scattering: the concept of effective susceptibility,” Phys. Rev. B 70, 115106 (2004).
[Crossref]

C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Second-harmonic generation in metallic nanoparticles: clarification of the role of the surface,” Phys. Rev. B 86, 115451 (2012).
[Crossref]

C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Origin of second-harmonic generation enhancement in optical split-ring resonators,” Phys. Rev. B 85, 201403 (2012).
[Crossref]

Y. Nakata, Y. Urade, T. Nakanishi, and M. Kitano, “Plane-wave scattering by self-complementary metasurfaces in terms of electromagnetic duality and Babinet’s principle,” Phys. Rev. B 88, 205138 (2013).
[Crossref]

Phys. Rev. Lett. (1)

F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, R. Marqués, F. Martın, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93, 197401 (2004).
[Crossref]

Sci. Rep. (1)

N. Zhang, Z. Ji, A. R. Cheney, H. Song, D. Ji, X. Zeng, B. Chen, T. Zhang, A. N. Cartwright, K. Shi, and Q. Gan, “Ultra-broadband enhancement of nonlinear optical processes from randomly patterned super absorbing metasurfaces,” Sci. Rep. 7, 4346 (2017).
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S. A. Maier, “Surface plasmon polaritons at metal/insulator interfaces,” in Plasmonics: Fundamentals and Applications (Springer, 2007).

X. Cheng and C. Fang, “Metamaterial design applying Babinet’s principle,” in XXXIth URSI General Assembly and Scientific Symposium (IEEE, 2014), pp. 1–4.

K. P. O’Brien, “Nonlinear light-matter interactions in metamaterials,” Ph.D. thesis (University of California, 2016).

N. Karampour and N. Nozhat, “Triple-band metamaterial absorber based on electric excitation of split ring resonator magnetic resonance,” in Fourth International Conference on Millimeter-Wave and Terahertz Technologies (IEEE, 2016), pp. 37–40.

A. Pramanik, Electromagnetism—Vol.  2: Theory (Prentice-Hall of India Pvt. Ltd, 2014).

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Figures (10)

Fig. 1.
Fig. 1. Au metasurface with (a) triangular particles, (b) triangular holes. Front view of unit cell of (c) the Au metasurface with a triangular particle and (d) Au metasurface with triangular holes.
Fig. 2.
Fig. 2. Normal incidence transmission spectra for different sizes of (a) a particle upon x polarization, (b) a particle upon y polarization, (c) a hole upon x polarization, (d) a hole upon y polarization.
Fig. 3.
Fig. 3. Schematic showing excitation configuration for nonlinear scattering theory.
Fig. 4.
Fig. 4. SH emission spectra for complementary Au triangular resonators with varied structural sizes.
Fig. 5.
Fig. 5. Real part of modal field profile around the particle surface for (a) XXX, (b) XYY, (c) YXX, (d) YYY, where the first letter specifies the polarization direction of SH excitation and the following two letters are those for the fundamental excitation.
Fig. 6.
Fig. 6. Imaginary part of modal field profile around particle surface for (a) XXX, (b) XYY, (c) YXX, (d) YYY, where the first letter specifies the polarization direction of SH excitation and the following two letters are those for the fundamental excitation.
Fig. 7.
Fig. 7. Comparison of optimum SH emission intensity of particle and hole for K=150, 200, 250, and 300 nm (a) with XXX and XYY excitation, respectively, where the first letter specifies the polarization direction of SH excitation and the following two letters are those for the fundamental excitation and (b) with XYY and XXX excitation, respectively. Comparison of optimum SH wavelength of particles and holes for K=150, 200, 250, and 300 (c) with XXX and XYY excitation, respectively and (d) with XYY and XXX excitation, respectively.
Fig. 8.
Fig. 8. Real part of field enhancement along the hole surface for (a) XXX, (b) XYY, (c) YXX, (d) YYY, where the first letter specifies the polarization direction of SH excitation and the following two letters are those for the fundamental excitation.
Fig. 9.
Fig. 9. Electric field along the surface of the particle upon SH wave excitation. This was evaluated for four different SH wave excitations as specified in the figure.
Fig. 10.
Fig. 10. (a) Particle with the electric near-field distribution upon x-polarized electric field excitation and its complementary. (b) Hole with the magnetic near-field distribution upon y-polarized electric field excitation. (c) Hole with the magnetic near-field distribution upon y-polarized electric field excitation. (d) Particle with the electric near-field distribution upon y-polarized electric field excitation. (e) Particle with the electric near-field distribution upon x-polarized electric field excitation. (f) Hole with the magnetic near-field distribution upon x-polarized electric field excitation.

Equations (5)

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EijkSHGEi,n2ω(r)χnnn(2)Ej,nω(r)Ek,nω(r)dS,
EijjSHGχnnn(2)Ei,n2ω(r)Ej,nω(r)Ej,nω(r)dS=[Ei,n2ω(r)cos(2ωt)+Ej,n2ω(r)sin(2ωt)][Ei,nω(r)cos(ωt)+Ej,nω(r)sin(ωt)]2dS=14[Ei,n2ω(r)(Ej,nω(r))2+Ei,n2ω(r)(Ej,nω(r))2]dS,
IijjSHG|EijjSHG|2.
EC=E0CcB,
BC=B0C+Ec,