Abstract

Bessel beams are of great potential applications in many fields due to their non-diffraction and self-reconstruction. Here we firstly present a type of nonlinear meta-axicon to generate second harmonic Bessel beams. The nonlinear meta-axicons are based on Au/WS2 hybrid nanostructures. Zero-order and first-order Bessel beams of second harmonic are generated under exciting of 810 nm femtosecond laser. In addition, the performances of the nonlinear meta-axicons, such as the second harmonic generation (SHG) efficiency, non-diffracting distance and full width at half maximum (FWHM) are analyzed theoretically and experimentally. The experimental results are consistent with the predicted, which can enable miniaturized nonlinear optical devices related to generate nonlinear Bessel beams, having potential application in nonlinear optical manipulation, imaging and tractor beams.

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

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References

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2020 (2)

Z. Yang, W. Cao, X. Chen, J. Zhang, Y. Mo, H. Xu, K. Mi, Q. Zhang, P. Lan, and P. Lu, “All-optical frequency resolved optical gating for isolated attosecond pulse reconstruction,” Opt. Lett. 45(2), 567–570 (2020).

X. H. Li, W. W. Liu, Y. L. Song, H. Long, K. Wang, B. Wang, and P. Lu, “Two-photon-pumped high-quality, single-mode vertical cavity lasing based on perovskite monocrystalline films,” Nano Energy 68, 104334 (2020).
[Crossref]

2019 (13)

X. H. Li, W. W. Liu, Y. L. Song, C. Zhang, H. Long, K. Wang, B. Wang, and P. X. Lu, “Enhancement of the second harmonic generation from WS2 monolayers by cooperating with dielectric microspheres,” Adv. Opt. Mater. 7(3), 1801270 (2019).
[Crossref]

G. W. Hu, X. M. Hong, K. Wang, W. J. Wang, H. X. Xu, W. C. Zhao, W. W. Liu, S. Zhang, F. Garcia-Vidal, B. Wang, P. X. Lu, and C. W. Qiu, “Coherent steering of nonlinear chiral valley photons with a synthetic Au–WS2 metasurface,” Nat. Photonics 13(7), 467–472 (2019).
[Crossref]

W. Zang, Z. Qin, X. Yang, Z. Chen, S. Wang, and Z. Wang, “Polarization Generation and Manipulation Based on Nonlinear Plasmonic Metasurfaces,” Adv. Opt. Mater. 7, 1801747 (2019).
[Crossref]

R. Sarma, D. Ceglia, N. Nookala, M. A. Vincenti, S. Campione, O. Wolf, M. Scalora, M. B. Sinclair, M. A. Belkin, and I. Brener, “Broadband and Efficient Second-Harmonic Generation from a Hybrid Dielectric Metasurface/Semiconductor Quantum-Well Structure,” ACS Photonics 6(6), 1458–1465 (2019).
[Crossref]

Y. L. Song, W. W. Liu, C. Fang, L. H. Li, and P. X. Lu, “Enhanced optoelectronic performance of 2D organic-inorganic hybrid perovskite through light-illumination,” Opt. Express 27(21), 30618–30628 (2019).
[Crossref]

J. V. Carrión, J. Albero, M. Baranski, C. Gorecki, and N. Passilly, “Microfabrication of axicons by glass blowing at a wafer-level,” Opt. Lett. 44(13), 3282–3285 (2019).
[Crossref]

S. Chowdhury, R. P. Roberts, G. Molina-Terriza, and X. Vidal, “Lens-axicon separation to tailor aberration free focused Bessel-Gaussian beams in the paraxial regime,” Opt. Express 27(8), 11160–11171 (2019).
[Crossref]

C. Holmes and P. G. R. Smith, “Self-assembled axicon lens in integrated optical fiber,” Opt. Lett. 44(14), 3506–3509 (2019).
[Crossref]

Q. H. Ke, Y. M. Zhou, J. Tan, M. R. He, J. T. Liang, Y. Zhao, M. Li, and P. X. Lu, “Two-dimensional photoelectron holography in strong-field tunneling ionization by counter rotating two-color circularly polarized laser pulses,” Opt. Express 27(22), 32193–32209 (2019).
[Crossref]

B. N. Wang, L. X. He, Y. Q. He, Y. F. Zhang, R. Z. Shao, P. F. Lan, and P. X. Lu, “All-optical measurement of high-order fractional molecular echoes by high-order harmonic generation,” Opt. Express 27(21), 30172–30181 (2019).
[Crossref]

M. R. Akram, M. Q. Mehmood, X. Bai, R. Jin, M. Premaratne, and W. Zhu, “High efficiency ultrathin transmissive metasurfaces,” Adv. Opt. Mater. 7(11), 1801628 (2019).
[Crossref]

M. R. Akram, M. Q. Mehmood, T. Tauqeer, A. S. Rana, I. D. Rukhlenko, and W. Zhu, “Highly efficient generation of Bessel beams with polarization insensitive metasurfaces,” Opt. Express 27(7), 9467 (2019).
[Crossref]

W. Wei, X. Jiang, L. Dong, W. Liu, X. Han, Y. Qin, K. Li, W. Li, Z. Lin, and P. Lu, “Regulating second-harmonic generation by Van der Waals Interactions in 2D lead halide perovskite nanosheets,” J. Am. Chem. Soc. 141(23), 9134–9139 (2019).
[Crossref]

2018 (2)

Y. Zhu, D. Wei, Z. Kuang, Q. Wang, Y. Wang, X. Huang, Y. Zhang, and M. Xiao, “Broadband Variable Meta-Axicons Based on Nano-Aperture Arrays in a Metallic Film,” Sci. Rep. 8(1), 11591 (2018).
[Crossref]

J. W. Chen, K. Wang, H. Long, X. B. Han, H. B. Hu, W. W. Liu, B. Wang, and P. X. Lu, “Tungsten disulfide−gold nanohole hybrid metasurfaces for nonlinear metalenses in the visible region,” Nano Lett. 18(2), 1344–1350 (2018).
[Crossref]

2017 (5)

2016 (2)

N. M. Estakhri and A. Alù, “Recent progress in gradient metasurfaces,” J. Opt. Soc. Am. B 33(2), A21–A30 (2016).
[Crossref]

S. Liu, A. Noor, L. L. Du, L. Zhang, Q. Xu, K. Luan, T. Q. Wang, Z. Tian, W. X. Tang, J. G. Han, W. L. Zhang, X. Y. Zhou, Q. Cheng, and T. J. Cui, “Anomalous Refraction and Nondiffractive Bessel-Beam Generation of Terahertz Waves through Transmission-Type Coding Metasurfaces,” ACS Photonics 3(10), 1968–1977 (2016).
[Crossref]

2015 (3)

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
[Crossref]

C. Janisch, Y. Wang, D. Ma, N. Mehta, A. L. Elías, N. Perea-López, M. Terrones, V. Crespi, and Z. Liu, “Extraordinary second harmonic generation in Tungsten Disulfide monolayers,” Sci. Rep. 4(1), 5530 (2015).
[Crossref]

J. Butet, P. F. Brevet, and O. J. Martin, “Optical second harmonic generation in plasmonic nanostructures: From fundamental principles to advanced applications,” ACS Nano 9(11), 10545–10562 (2015).
[Crossref]

2014 (2)

J. Lee, M. Tymchenko, C. Argyropoulos, P. Y. Chen, P. Y. Lu, F. Demmerle, G. Boehm, M. C. Amann, A. Alu, and M. A. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511(7507), 65–69 (2014).
[Crossref]

C. Pfeiffer and A. Grbic, “Controlling Vector Bessel Beams with Metasurfaces,” Phys. Rev. Appl. 2(4), 044012 (2014).
[Crossref]

2013 (1)

N. Kumar, S. Najmaei, Q. Cui, F. Ceballos, P. M. Ajayan, J. Lou, and H. Zhao, “Second harmonic microscopy of monolayer MoS2,” Phys. Rev. B 87(16), 161403 (2013).
[Crossref]

2012 (1)

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
[Crossref]

2011 (1)

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
[Crossref]

2004 (1)

V. Pyragaite, A. Piskarskas, K. Regelskis, V. Smilgevicius, A. Stabinis, and S. Mikalauskas, “Parametric down-conversion of higher-order Bessel optical beams in quadratic nonlinear medium,” Opt. Commun. 240(1-3), 191–200 (2004).
[Crossref]

1998 (1)

I. Manek, Y. B. Ovchinnikov, and R. Grimm, “Generation of a hollow laser beam for atom trapping using an axicon,” Opt. Commun. 147(1-3), 67–70 (1998).
[Crossref]

Aieta, F.

P. Genevet, F. Capasso, F. Aieta, M. Khorasaninejad, and R. Devlin, “Recent advances in planar optics: from plasmonic to dielectric metasurfaces,” Optica 4(1), 139–152 (2017).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
[Crossref]

Ajayan, P. M.

N. Kumar, S. Najmaei, Q. Cui, F. Ceballos, P. M. Ajayan, J. Lou, and H. Zhao, “Second harmonic microscopy of monolayer MoS2,” Phys. Rev. B 87(16), 161403 (2013).
[Crossref]

Akram, M. R.

M. R. Akram, M. Q. Mehmood, X. Bai, R. Jin, M. Premaratne, and W. Zhu, “High efficiency ultrathin transmissive metasurfaces,” Adv. Opt. Mater. 7(11), 1801628 (2019).
[Crossref]

M. R. Akram, M. Q. Mehmood, T. Tauqeer, A. S. Rana, I. D. Rukhlenko, and W. Zhu, “Highly efficient generation of Bessel beams with polarization insensitive metasurfaces,” Opt. Express 27(7), 9467 (2019).
[Crossref]

Albero, J.

Alu, A.

J. Lee, M. Tymchenko, C. Argyropoulos, P. Y. Chen, P. Y. Lu, F. Demmerle, G. Boehm, M. C. Amann, A. Alu, and M. A. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511(7507), 65–69 (2014).
[Crossref]

Alù, A.

Amann, M. C.

J. Lee, M. Tymchenko, C. Argyropoulos, P. Y. Chen, P. Y. Lu, F. Demmerle, G. Boehm, M. C. Amann, A. Alu, and M. A. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511(7507), 65–69 (2014).
[Crossref]

Arbabi, A.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
[Crossref]

Argyropoulos, C.

J. Lee, M. Tymchenko, C. Argyropoulos, P. Y. Chen, P. Y. Lu, F. Demmerle, G. Boehm, M. C. Amann, A. Alu, and M. A. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511(7507), 65–69 (2014).
[Crossref]

Bagheri, M.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
[Crossref]

Bai, X.

M. R. Akram, M. Q. Mehmood, X. Bai, R. Jin, M. Premaratne, and W. Zhu, “High efficiency ultrathin transmissive metasurfaces,” Adv. Opt. Mater. 7(11), 1801628 (2019).
[Crossref]

Baranski, M.

Belkin, M. A.

R. Sarma, D. Ceglia, N. Nookala, M. A. Vincenti, S. Campione, O. Wolf, M. Scalora, M. B. Sinclair, M. A. Belkin, and I. Brener, “Broadband and Efficient Second-Harmonic Generation from a Hybrid Dielectric Metasurface/Semiconductor Quantum-Well Structure,” ACS Photonics 6(6), 1458–1465 (2019).
[Crossref]

J. Lee, M. Tymchenko, C. Argyropoulos, P. Y. Chen, P. Y. Lu, F. Demmerle, G. Boehm, M. C. Amann, A. Alu, and M. A. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511(7507), 65–69 (2014).
[Crossref]

Boehm, G.

J. Lee, M. Tymchenko, C. Argyropoulos, P. Y. Chen, P. Y. Lu, F. Demmerle, G. Boehm, M. C. Amann, A. Alu, and M. A. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511(7507), 65–69 (2014).
[Crossref]

Brener, I.

R. Sarma, D. Ceglia, N. Nookala, M. A. Vincenti, S. Campione, O. Wolf, M. Scalora, M. B. Sinclair, M. A. Belkin, and I. Brener, “Broadband and Efficient Second-Harmonic Generation from a Hybrid Dielectric Metasurface/Semiconductor Quantum-Well Structure,” ACS Photonics 6(6), 1458–1465 (2019).
[Crossref]

Brevet, P. F.

J. Butet, P. F. Brevet, and O. J. Martin, “Optical second harmonic generation in plasmonic nanostructures: From fundamental principles to advanced applications,” ACS Nano 9(11), 10545–10562 (2015).
[Crossref]

Butet, J.

J. Butet, P. F. Brevet, and O. J. Martin, “Optical second harmonic generation in plasmonic nanostructures: From fundamental principles to advanced applications,” ACS Nano 9(11), 10545–10562 (2015).
[Crossref]

Cai, W.

M. Ren, W. Cai, and J. Xu, “Tailorable Dynamics in Nonlinear Optical Metasurfaces,” Adv. Mater.1806317 (2019).

Campione, S.

R. Sarma, D. Ceglia, N. Nookala, M. A. Vincenti, S. Campione, O. Wolf, M. Scalora, M. B. Sinclair, M. A. Belkin, and I. Brener, “Broadband and Efficient Second-Harmonic Generation from a Hybrid Dielectric Metasurface/Semiconductor Quantum-Well Structure,” ACS Photonics 6(6), 1458–1465 (2019).
[Crossref]

Cao, W.

Capasso, F.

W. T. Chen, M. Khorasaninejad, A. Y. Zhu, J. Oh, R. C. Devlin, A. Zaidi, and F. Capasso, “Generation of wavelength-independent subwavelength Bessel beams using metasurfaces,” Light: Sci. Appl. 6(5), e16259 (2017).
[Crossref]

P. Genevet, F. Capasso, F. Aieta, M. Khorasaninejad, and R. Devlin, “Recent advances in planar optics: from plasmonic to dielectric metasurfaces,” Optica 4(1), 139–152 (2017).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
[Crossref]

Carrión, J. V.

Ceballos, F.

N. Kumar, S. Najmaei, Q. Cui, F. Ceballos, P. M. Ajayan, J. Lou, and H. Zhao, “Second harmonic microscopy of monolayer MoS2,” Phys. Rev. B 87(16), 161403 (2013).
[Crossref]

Ceglia, D.

R. Sarma, D. Ceglia, N. Nookala, M. A. Vincenti, S. Campione, O. Wolf, M. Scalora, M. B. Sinclair, M. A. Belkin, and I. Brener, “Broadband and Efficient Second-Harmonic Generation from a Hybrid Dielectric Metasurface/Semiconductor Quantum-Well Structure,” ACS Photonics 6(6), 1458–1465 (2019).
[Crossref]

Chen, H. M.

Chen, J. W.

J. W. Chen, K. Wang, H. Long, X. B. Han, H. B. Hu, W. W. Liu, B. Wang, and P. X. Lu, “Tungsten disulfide−gold nanohole hybrid metasurfaces for nonlinear metalenses in the visible region,” Nano Lett. 18(2), 1344–1350 (2018).
[Crossref]

Chen, P. Y.

J. Lee, M. Tymchenko, C. Argyropoulos, P. Y. Chen, P. Y. Lu, F. Demmerle, G. Boehm, M. C. Amann, A. Alu, and M. A. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511(7507), 65–69 (2014).
[Crossref]

Chen, W. T.

W. T. Chen, M. Khorasaninejad, A. Y. Zhu, J. Oh, R. C. Devlin, A. Zaidi, and F. Capasso, “Generation of wavelength-independent subwavelength Bessel beams using metasurfaces,” Light: Sci. Appl. 6(5), e16259 (2017).
[Crossref]

Chen, X.

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W. Zang, Z. Qin, X. Yang, Z. Chen, S. Wang, and Z. Wang, “Polarization Generation and Manipulation Based on Nonlinear Plasmonic Metasurfaces,” Adv. Opt. Mater. 7, 1801747 (2019).
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G. W. Hu, X. M. Hong, K. Wang, W. J. Wang, H. X. Xu, W. C. Zhao, W. W. Liu, S. Zhang, F. Garcia-Vidal, B. Wang, P. X. Lu, and C. W. Qiu, “Coherent steering of nonlinear chiral valley photons with a synthetic Au–WS2 metasurface,” Nat. Photonics 13(7), 467–472 (2019).
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Regelskis, K.

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M. Ren, W. Cai, and J. Xu, “Tailorable Dynamics in Nonlinear Optical Metasurfaces,” Adv. Mater.1806317 (2019).

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Sarma, R.

R. Sarma, D. Ceglia, N. Nookala, M. A. Vincenti, S. Campione, O. Wolf, M. Scalora, M. B. Sinclair, M. A. Belkin, and I. Brener, “Broadband and Efficient Second-Harmonic Generation from a Hybrid Dielectric Metasurface/Semiconductor Quantum-Well Structure,” ACS Photonics 6(6), 1458–1465 (2019).
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V. Pyragaite, A. Piskarskas, K. Regelskis, V. Smilgevicius, A. Stabinis, and S. Mikalauskas, “Parametric down-conversion of higher-order Bessel optical beams in quadratic nonlinear medium,” Opt. Commun. 240(1-3), 191–200 (2004).
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V. Pyragaite, A. Piskarskas, K. Regelskis, V. Smilgevicius, A. Stabinis, and S. Mikalauskas, “Parametric down-conversion of higher-order Bessel optical beams in quadratic nonlinear medium,” Opt. Commun. 240(1-3), 191–200 (2004).
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Terrones, M.

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N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
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X. H. Li, W. W. Liu, Y. L. Song, H. Long, K. Wang, B. Wang, and P. Lu, “Two-photon-pumped high-quality, single-mode vertical cavity lasing based on perovskite monocrystalline films,” Nano Energy 68, 104334 (2020).
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Wang, K.

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J. W. Chen, K. Wang, H. Long, X. B. Han, H. B. Hu, W. W. Liu, B. Wang, and P. X. Lu, “Tungsten disulfide−gold nanohole hybrid metasurfaces for nonlinear metalenses in the visible region,” Nano Lett. 18(2), 1344–1350 (2018).
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W. Zang, Z. Qin, X. Yang, Z. Chen, S. Wang, and Z. Wang, “Polarization Generation and Manipulation Based on Nonlinear Plasmonic Metasurfaces,” Adv. Opt. Mater. 7, 1801747 (2019).
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S. Liu, A. Noor, L. L. Du, L. Zhang, Q. Xu, K. Luan, T. Q. Wang, Z. Tian, W. X. Tang, J. G. Han, W. L. Zhang, X. Y. Zhou, Q. Cheng, and T. J. Cui, “Anomalous Refraction and Nondiffractive Bessel-Beam Generation of Terahertz Waves through Transmission-Type Coding Metasurfaces,” ACS Photonics 3(10), 1968–1977 (2016).
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W. Zang, Z. Qin, X. Yang, Z. Chen, S. Wang, and Z. Wang, “Polarization Generation and Manipulation Based on Nonlinear Plasmonic Metasurfaces,” Adv. Opt. Mater. 7, 1801747 (2019).
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Wolf, O.

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Y. Zhu, D. Wei, Z. Kuang, Q. Wang, Y. Wang, X. Huang, Y. Zhang, and M. Xiao, “Broadband Variable Meta-Axicons Based on Nano-Aperture Arrays in a Metallic Film,” Sci. Rep. 8(1), 11591 (2018).
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M. Ren, W. Cai, and J. Xu, “Tailorable Dynamics in Nonlinear Optical Metasurfaces,” Adv. Mater.1806317 (2019).

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S. Liu, A. Noor, L. L. Du, L. Zhang, Q. Xu, K. Luan, T. Q. Wang, Z. Tian, W. X. Tang, J. G. Han, W. L. Zhang, X. Y. Zhou, Q. Cheng, and T. J. Cui, “Anomalous Refraction and Nondiffractive Bessel-Beam Generation of Terahertz Waves through Transmission-Type Coding Metasurfaces,” ACS Photonics 3(10), 1968–1977 (2016).
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W. Zang, Z. Qin, X. Yang, Z. Chen, S. Wang, and Z. Wang, “Polarization Generation and Manipulation Based on Nonlinear Plasmonic Metasurfaces,” Adv. Opt. Mater. 7, 1801747 (2019).
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N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
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W. Zang, Z. Qin, X. Yang, Z. Chen, S. Wang, and Z. Wang, “Polarization Generation and Manipulation Based on Nonlinear Plasmonic Metasurfaces,” Adv. Opt. Mater. 7, 1801747 (2019).
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Zhang, L.

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Zhang, S.

G. W. Hu, X. M. Hong, K. Wang, W. J. Wang, H. X. Xu, W. C. Zhao, W. W. Liu, S. Zhang, F. Garcia-Vidal, B. Wang, P. X. Lu, and C. W. Qiu, “Coherent steering of nonlinear chiral valley photons with a synthetic Au–WS2 metasurface,” Nat. Photonics 13(7), 467–472 (2019).
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Y. Zhu, D. Wei, Z. Kuang, Q. Wang, Y. Wang, X. Huang, Y. Zhang, and M. Xiao, “Broadband Variable Meta-Axicons Based on Nano-Aperture Arrays in a Metallic Film,” Sci. Rep. 8(1), 11591 (2018).
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Zhao, Z.

Zhou, X. Y.

S. Liu, A. Noor, L. L. Du, L. Zhang, Q. Xu, K. Luan, T. Q. Wang, Z. Tian, W. X. Tang, J. G. Han, W. L. Zhang, X. Y. Zhou, Q. Cheng, and T. J. Cui, “Anomalous Refraction and Nondiffractive Bessel-Beam Generation of Terahertz Waves through Transmission-Type Coding Metasurfaces,” ACS Photonics 3(10), 1968–1977 (2016).
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Zhu, A. Y.

W. T. Chen, M. Khorasaninejad, A. Y. Zhu, J. Oh, R. C. Devlin, A. Zaidi, and F. Capasso, “Generation of wavelength-independent subwavelength Bessel beams using metasurfaces,” Light: Sci. Appl. 6(5), e16259 (2017).
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M. R. Akram, M. Q. Mehmood, X. Bai, R. Jin, M. Premaratne, and W. Zhu, “High efficiency ultrathin transmissive metasurfaces,” Adv. Opt. Mater. 7(11), 1801628 (2019).
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M. R. Akram, M. Q. Mehmood, T. Tauqeer, A. S. Rana, I. D. Rukhlenko, and W. Zhu, “Highly efficient generation of Bessel beams with polarization insensitive metasurfaces,” Opt. Express 27(7), 9467 (2019).
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Y. Zhu, D. Wei, Z. Kuang, Q. Wang, Y. Wang, X. Huang, Y. Zhang, and M. Xiao, “Broadband Variable Meta-Axicons Based on Nano-Aperture Arrays in a Metallic Film,” Sci. Rep. 8(1), 11591 (2018).
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J. Butet, P. F. Brevet, and O. J. Martin, “Optical second harmonic generation in plasmonic nanostructures: From fundamental principles to advanced applications,” ACS Nano 9(11), 10545–10562 (2015).
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R. Sarma, D. Ceglia, N. Nookala, M. A. Vincenti, S. Campione, O. Wolf, M. Scalora, M. B. Sinclair, M. A. Belkin, and I. Brener, “Broadband and Efficient Second-Harmonic Generation from a Hybrid Dielectric Metasurface/Semiconductor Quantum-Well Structure,” ACS Photonics 6(6), 1458–1465 (2019).
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M. R. Akram, M. Q. Mehmood, X. Bai, R. Jin, M. Premaratne, and W. Zhu, “High efficiency ultrathin transmissive metasurfaces,” Adv. Opt. Mater. 7(11), 1801628 (2019).
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J. W. Chen, K. Wang, H. Long, X. B. Han, H. B. Hu, W. W. Liu, B. Wang, and P. X. Lu, “Tungsten disulfide−gold nanohole hybrid metasurfaces for nonlinear metalenses in the visible region,” Nano Lett. 18(2), 1344–1350 (2018).
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V. Pyragaite, A. Piskarskas, K. Regelskis, V. Smilgevicius, A. Stabinis, and S. Mikalauskas, “Parametric down-conversion of higher-order Bessel optical beams in quadratic nonlinear medium,” Opt. Commun. 240(1-3), 191–200 (2004).
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N. M. Jassim, K. Wang, X. Han, H. Long, B. Wang, and P. X. Lu, “Plasmon assisted enhanced second-harmonic generation in singlehybrid Au/ZnS nanowires,” Opt. Mater. 64, 257–261 (2017).
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Sci. Rep. (2)

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Science (1)

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Figures (7)

Fig. 1.
Fig. 1. The schematic sketch of (a) the Au/WS2 hybrid nonlinear meta-axicon and (b) the generation of SHG Bessel beam through the nonlinear meta-axicon
Fig. 2.
Fig. 2. (a) The geometry of the unit cell of the designed Au metasurfaces. The size of unit cell is 330 nm. The nanohole has length of L = 185 nm and width of W = 80 nm, and it rotates in the x-y plane with an orientation angle, θ. (c) The optical image of WS2/Au hybrid metasurface. (b) and (d) SEM images of the Au nanohole arrays.
Fig. 3.
Fig. 3. The schematic sketch of the experiment setup for the emitted second harmonic signal profiles and the SHG spectra measurements.
Fig. 4.
Fig. 4. (a) SHG enhancement in the hybrid metalens. Comparison of the SHG spectra of WS2/Au hybrid metasurface and the bare WS2 monolayer. (b) The simulated absorption spectra of the unit cell structure with different oriental nano-holes of θ=0° and θ=45°, excited by circularly polarized fundamental beams. The dashed curve is the measured spectra with the nanoholes array. (c) and (d) The simulated electric field distribution on the intersurface of Au and air, for nanoholes of θ=0° and θ=45°, respectively. Excited by 810 nm plane wave.
Fig. 5.
Fig. 5. Electric field intensity profile in xz plane of SHG for the zero-order Bessel beam hybrid metasurfaces with (a) R = 15 µm and (b) R = 20 µm, respectively.
Fig. 6.
Fig. 6. (a) SHG intensity distributions in the xy plane at z = 28µm. (b) The SHG intensity distribution along x = 0 in the xy plane. The dotted curve is the results of Bessel function fitting.
Fig. 7.
Fig. 7. (a) Electric field intensity profile in xz plane of SHG for the first-order Bessel beam hybrid metasurface with R = 20 µm. (b) SHG intensity distributions in the xy plane at z = 25 µm. (c) The SHG intensity distribution along x = 0 in the xy plane. The dotted curve is the results of Bessel function fitting.

Equations (9)

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E ( r , ϕ , z ) = A exp ( i k z z ) J n ( k r r ) exp ( ± i n ϕ )
k r 2 + k r 2 = k = 2 π / λ
2 π λ S H G sin α = d ψ d r
k S H G sin α = 2 π Γ
ψ ( x , y ) = 2 π ( 2 π / λ S H G ) x 2 + y 2 0.9
ψ ( x , y ) = 2 π ( 2 π / λ S H G ) × x 2 + y 2 × 0.9 + ϕ
Z max = R tan α
F W H M = 0.358 λ S H G sin α
F W H M = 0.292 λ S H G sin α

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