Abstract

Second-order nonlinear metasurfaces have proven their ability to efficiently convert the frequency of incident signals over subwavelength thickness. However, the availability of second-order nonlinear materials for such metasurfaces has so far been limited to III-V semiconductors, which have low transparency in the visible and impose constraints on the excitation geometries due to the lack of diagonal second-order susceptibility components. Here we propose a new design concept for second-order nonlinear metasurfaces on a monolithic substrate, which is not limited by the availability of thin crystalline films and can be applied to any non-centrosymmetric material. We exemplify this concept in a monolithic Lithium Niobate metasurface with cylinder-shaped corrugations for enhanced field confinement. By optimizing the geometrical parameters, we show enhanced second harmonic generation from a near-infrared pump beam with conversion efficiency above 10−5 using 1 GW/cm2 pump intensity. Our approach enables new opportunities for practical designs of generic metasurfaces for nonlinear and quantum light sources.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (3)

J. D. Sautter, L. Xu, A. E. Miroshnichenko, M. Lysevych, I. Volkovskaya, D. A. Smirnova, R. Camacho-Morales, K. Z. Kamali, F. Karouta, K. Vora, H. H. Tan, M. Kauranen, I. Staude, C. Jagadish, D. N. Neshev, and M. Rahmani, “Tailoring Second-Harmonic Emission from (111)-GaAs Nanoantennas,” Nano Lett. 19(6), 3905–3911 (2019).
[Crossref]

B. Gao, M. Ren, W. Wu, H. Hu, W. Cai, and J. Xu, “Lithium Niobate Metasurfaces,” Laser Photonics Rev. 13(5), 1800312 (2019).
[Crossref]

F. Timpu, J. Sendra, C. Renaut, L. Lang, M. Timofeeva, M. T. Buscaglia, V. Buscaglia, and R. Grange, “Lithium Niobate Nanocubes as Linear and Nonlinear Ultraviolet Mie Resonators,” ACS Photonics 6(2), 545–552 (2019).
[Crossref]

2018 (4)

R. Alaee, C. Rockstuhl, and I. Fernandez-Corbaton, “An electromagnetic multipole expansion beyond the long-wavelength approximation,” Opt. Commun. 407, 17–21 (2018).
[Crossref]

C. Wang, M. Zhang, B. Stern, M. Lipson, and M. Lončar, “Nanophotonic lithium niobate electro-optic modulators,” Opt. Express 26(2), 1547–1555 (2018).
[Crossref]

P. P. Vabishchevich, S. Liu, M. B. Sinclair, G. A. Keeler, G. M. Peake, and I. Brener, “Enhanced Second-Harmonic Generation Using Broken Symmetry III–V Semiconductor Fano Metasurfaces,” ACS Photonics 5(5), 1685–1690 (2018).
[Crossref]

F. J. F. Löchner, A. N. Fedotova, S. Liu, G. A. Keeler, G. M. Peake, S. Saravi, M. R. Shcherbakov, S. Burger, A. A. Fedyanin, I. Brener, T. Pertsch, F. Setzpfandt, and I. Staude, “Polarization-Dependent Second Harmonic Diffraction from Resonant GaAs Metasurfaces,” ACS Photonics 5(5), 1786–1793 (2018).
[Crossref]

2017 (4)

L. Carletti, D. Rocco, A. Locatelli, C. De Angelis, V. F. Gili, M. Ravaro, I. Favero, G. Leo, M. Finazzi, L. Ghirardini, M. Celebrano, G. Marino, and A. V. Zayats, “Controlling Second-harmonic Generation at the Nanoscale with Monolithic AlGaAs-on-AlOx Antennas,” Nanotechnology 28(11), 114005 (2017).
[Crossref]

C. Wang, X. Xiong, N. Andrade, V. Venkataraman, X.-F. Ren, G.-C. Guo, and M. Lončar, “Second harmonic generation in nano-structured thin-film lithium niobate waveguides,” Opt. Express 25(6), 6963–6973 (2017).
[Crossref]

C. Wang, Z. Li, M.-H. Kim, X. Xiong, X. Ren, G.-C. Guo, N. Yu, and M. Lončar, “Metasurface-assisted phase-matching-free second harmonic generation in lithium niobate waveguides,” Nat. Commun. 8(1), 2098 (2017).
[Crossref]

J. Cambiasso, G. Grinblat, Y. Li, A. Rakovich, E. Cortés, and S. A. Maier, “Bridging the Gap between Dielectric Nanophotonics and the Visible Regime with Effectively Lossless Gallium Phosphide Antennas,” Nano Lett. 17(2), 1219–1225 (2017).
[Crossref]

2016 (9)

M. Marciniak, M. Gębski, M. Dems, E. Haglund, A. Larsson, M. Riaziat, J. A. Lott, and T. Czyszanowski, “Optimal parameters of monolithic high-contrast grating mirrors,” Opt. Lett. 41(15), 3495–3498 (2016).
[Crossref]

S. Liu, M. B. Sinclair, S. Saravi, G. A. Keeler, Y. Yang, J. Reno, G. M. Peake, F. Setzpfandt, I. Staude, T. Pertsh, and I. Brener, “Resonantly Enhanced Second-Harmonic Generation Using III–V Semiconductor All-Dielectric Metasurfaces,” Nano Lett. 16(9), 5426–5432 (2016).
[Crossref]

D. Yudistira, A. Boes, B. Graczykowski, F. Alzina, L. Y. Yeo, C. M. S. Torres, and A. Mitchell, “Nanoscale pillar hypersonic surface phononic crystals,” Phys. Rev. B 94(9), 094304 (2016).
[Crossref]

D. Smirnova and Y. S. Kivshar, “Multipolar nonlinear nanophotonics,” Optica 3(11), 1241–1255 (2016).
[Crossref]

L. Chang, Y. Li, N. Volet, L. Wang, J. Peters, and J. E. Bowers, “Thin film wavelength converters for photonic integrated circuits,” Optica 3(5), 531–535 (2016).
[Crossref]

R. Camacho-Morales, M. Rahmani, S. Kruk, L. Wang, L. Xu, D. A. Smirnova, A. S. Solntsev, A. Miroshnichenko, H. H. Tan, F. Karouta, S. Naureen, K. Vora, L. Carletti, C. De Angelis, C. Jagadish, Y. S. Kivshar, and D. N. Neshev, “Nonlinear Generation of Vector Beams From AlGaAs Nanoantennas,” Nano Lett. 16(11), 7191–7197 (2016).
[Crossref]

L. Carletti, A. Locatelli, D. N. Neshev, and C. De Angelis, “Shaping the second harmonic radiation pattern from AlGaAs dielectric nanoantennas,” ACS Photonics 3(8), 1500–1507 (2016).
[Crossref]

V. F. Gili, L. Carletti, A. Locatelli, D. Rocco, M. Finazzi, L. Ghirardini, I. Favero, C. Gomez, A. Lemaître, M. Celebrano, C. De Angelis, and G. Leo, “Monolithic AlGaAs second-harmonic nanoantennas,” Opt. Express 24(14), 15965–15971 (2016).
[Crossref]

A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Y. S. Kivshar, and B. Luk’yanchuk, “Optically Resonant Dielectric Nanostructures,” Science 354(6314), aag2472 (2016).
[Crossref]

2015 (3)

2013 (2)

A. Sergeyev, R. Geiss, A. S. Solntsev, A. Steinbrück, F. Schrempel, E.-B. Kley, T. Pertsch, and R. Grange, “Second-harmonic generation in lithium niobate nanowires for local fluorescence excitation,” Opt. Express 21(16), 19012–19021 (2013).
[Crossref]

S. Buckley, M. Radulaski, K. Biermann, and J. Vučković, “Second harmonic generation in photonic crystal cavities in (111)-oriented GaAs,” Appl. Phys. Lett. 103(21), 211117 (2013).
[Crossref]

2012 (2)

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

P. Spinelli, M. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat. Commun. 3(1), 692 (2012).
[Crossref]

1998 (1)

S. Goeman, S. Boons, B. Dhoedt, K. Vandeputte, K. Caekebeke, P. Van Daele, and R. Baets, “First demonstration of highly reflective and highly polarization selective diffraction gratings (GIRO-gratings) for long-wavelength VCSEL's,” IEEE Photonics Technol. Lett. 10(9), 1205–1207 (1998).
[Crossref]

1997 (1)

Alaee, R.

R. Alaee, C. Rockstuhl, and I. Fernandez-Corbaton, “An electromagnetic multipole expansion beyond the long-wavelength approximation,” Opt. Commun. 407, 17–21 (2018).
[Crossref]

Alzina, F.

D. Yudistira, A. Boes, B. Graczykowski, F. Alzina, L. Y. Yeo, C. M. S. Torres, and A. Mitchell, “Nanoscale pillar hypersonic surface phononic crystals,” Phys. Rev. B 94(9), 094304 (2016).
[Crossref]

Andrade, N.

Baets, R.

S. Goeman, S. Boons, B. Dhoedt, K. Vandeputte, K. Caekebeke, P. Van Daele, and R. Baets, “First demonstration of highly reflective and highly polarization selective diffraction gratings (GIRO-gratings) for long-wavelength VCSEL's,” IEEE Photonics Technol. Lett. 10(9), 1205–1207 (1998).
[Crossref]

Biermann, K.

S. Buckley, M. Radulaski, K. Biermann, and J. Vučković, “Second harmonic generation in photonic crystal cavities in (111)-oriented GaAs,” Appl. Phys. Lett. 103(21), 211117 (2013).
[Crossref]

Boes, A.

D. Yudistira, A. Boes, B. Graczykowski, F. Alzina, L. Y. Yeo, C. M. S. Torres, and A. Mitchell, “Nanoscale pillar hypersonic surface phononic crystals,” Phys. Rev. B 94(9), 094304 (2016).
[Crossref]

Boons, S.

S. Goeman, S. Boons, B. Dhoedt, K. Vandeputte, K. Caekebeke, P. Van Daele, and R. Baets, “First demonstration of highly reflective and highly polarization selective diffraction gratings (GIRO-gratings) for long-wavelength VCSEL's,” IEEE Photonics Technol. Lett. 10(9), 1205–1207 (1998).
[Crossref]

Bowers, J. E.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, (Elsevier, 2003).

Brener, I.

P. P. Vabishchevich, S. Liu, M. B. Sinclair, G. A. Keeler, G. M. Peake, and I. Brener, “Enhanced Second-Harmonic Generation Using Broken Symmetry III–V Semiconductor Fano Metasurfaces,” ACS Photonics 5(5), 1685–1690 (2018).
[Crossref]

F. J. F. Löchner, A. N. Fedotova, S. Liu, G. A. Keeler, G. M. Peake, S. Saravi, M. R. Shcherbakov, S. Burger, A. A. Fedyanin, I. Brener, T. Pertsch, F. Setzpfandt, and I. Staude, “Polarization-Dependent Second Harmonic Diffraction from Resonant GaAs Metasurfaces,” ACS Photonics 5(5), 1786–1793 (2018).
[Crossref]

S. Liu, M. B. Sinclair, S. Saravi, G. A. Keeler, Y. Yang, J. Reno, G. M. Peake, F. Setzpfandt, I. Staude, T. Pertsh, and I. Brener, “Resonantly Enhanced Second-Harmonic Generation Using III–V Semiconductor All-Dielectric Metasurfaces,” Nano Lett. 16(9), 5426–5432 (2016).
[Crossref]

Brongersma, M. L.

A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Y. S. Kivshar, and B. Luk’yanchuk, “Optically Resonant Dielectric Nanostructures,” Science 354(6314), aag2472 (2016).
[Crossref]

Buckley, S.

S. Buckley, M. Radulaski, K. Biermann, and J. Vučković, “Second harmonic generation in photonic crystal cavities in (111)-oriented GaAs,” Appl. Phys. Lett. 103(21), 211117 (2013).
[Crossref]

Bugajski, M.

Burger, S.

F. J. F. Löchner, A. N. Fedotova, S. Liu, G. A. Keeler, G. M. Peake, S. Saravi, M. R. Shcherbakov, S. Burger, A. A. Fedyanin, I. Brener, T. Pertsch, F. Setzpfandt, and I. Staude, “Polarization-Dependent Second Harmonic Diffraction from Resonant GaAs Metasurfaces,” ACS Photonics 5(5), 1786–1793 (2018).
[Crossref]

Buscaglia, M. T.

F. Timpu, J. Sendra, C. Renaut, L. Lang, M. Timofeeva, M. T. Buscaglia, V. Buscaglia, and R. Grange, “Lithium Niobate Nanocubes as Linear and Nonlinear Ultraviolet Mie Resonators,” ACS Photonics 6(2), 545–552 (2019).
[Crossref]

Buscaglia, V.

F. Timpu, J. Sendra, C. Renaut, L. Lang, M. Timofeeva, M. T. Buscaglia, V. Buscaglia, and R. Grange, “Lithium Niobate Nanocubes as Linear and Nonlinear Ultraviolet Mie Resonators,” ACS Photonics 6(2), 545–552 (2019).
[Crossref]

Caekebeke, K.

S. Goeman, S. Boons, B. Dhoedt, K. Vandeputte, K. Caekebeke, P. Van Daele, and R. Baets, “First demonstration of highly reflective and highly polarization selective diffraction gratings (GIRO-gratings) for long-wavelength VCSEL's,” IEEE Photonics Technol. Lett. 10(9), 1205–1207 (1998).
[Crossref]

Cai, W.

B. Gao, M. Ren, W. Wu, H. Hu, W. Cai, and J. Xu, “Lithium Niobate Metasurfaces,” Laser Photonics Rev. 13(5), 1800312 (2019).
[Crossref]

Camacho-Morales, R.

J. D. Sautter, L. Xu, A. E. Miroshnichenko, M. Lysevych, I. Volkovskaya, D. A. Smirnova, R. Camacho-Morales, K. Z. Kamali, F. Karouta, K. Vora, H. H. Tan, M. Kauranen, I. Staude, C. Jagadish, D. N. Neshev, and M. Rahmani, “Tailoring Second-Harmonic Emission from (111)-GaAs Nanoantennas,” Nano Lett. 19(6), 3905–3911 (2019).
[Crossref]

R. Camacho-Morales, M. Rahmani, S. Kruk, L. Wang, L. Xu, D. A. Smirnova, A. S. Solntsev, A. Miroshnichenko, H. H. Tan, F. Karouta, S. Naureen, K. Vora, L. Carletti, C. De Angelis, C. Jagadish, Y. S. Kivshar, and D. N. Neshev, “Nonlinear Generation of Vector Beams From AlGaAs Nanoantennas,” Nano Lett. 16(11), 7191–7197 (2016).
[Crossref]

Cambiasso, J.

J. Cambiasso, G. Grinblat, Y. Li, A. Rakovich, E. Cortés, and S. A. Maier, “Bridging the Gap between Dielectric Nanophotonics and the Visible Regime with Effectively Lossless Gallium Phosphide Antennas,” Nano Lett. 17(2), 1219–1225 (2017).
[Crossref]

Carletti, L.

L. Carletti, D. Rocco, A. Locatelli, C. De Angelis, V. F. Gili, M. Ravaro, I. Favero, G. Leo, M. Finazzi, L. Ghirardini, M. Celebrano, G. Marino, and A. V. Zayats, “Controlling Second-harmonic Generation at the Nanoscale with Monolithic AlGaAs-on-AlOx Antennas,” Nanotechnology 28(11), 114005 (2017).
[Crossref]

R. Camacho-Morales, M. Rahmani, S. Kruk, L. Wang, L. Xu, D. A. Smirnova, A. S. Solntsev, A. Miroshnichenko, H. H. Tan, F. Karouta, S. Naureen, K. Vora, L. Carletti, C. De Angelis, C. Jagadish, Y. S. Kivshar, and D. N. Neshev, “Nonlinear Generation of Vector Beams From AlGaAs Nanoantennas,” Nano Lett. 16(11), 7191–7197 (2016).
[Crossref]

L. Carletti, A. Locatelli, D. N. Neshev, and C. De Angelis, “Shaping the second harmonic radiation pattern from AlGaAs dielectric nanoantennas,” ACS Photonics 3(8), 1500–1507 (2016).
[Crossref]

V. F. Gili, L. Carletti, A. Locatelli, D. Rocco, M. Finazzi, L. Ghirardini, I. Favero, C. Gomez, A. Lemaître, M. Celebrano, C. De Angelis, and G. Leo, “Monolithic AlGaAs second-harmonic nanoantennas,” Opt. Express 24(14), 15965–15971 (2016).
[Crossref]

L. Carletti, A. Locatelli, O. Stepanenko, G. Leo, and C. De Angelis, “Enhanced second-harmonic generation from magnetic resonance in AlGaAs nanoantennas,” Opt. Express 23(20), 26544–26550 (2015).
[Crossref]

Celebrano, M.

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[Crossref]

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D. Yudistira, A. Boes, B. Graczykowski, F. Alzina, L. Y. Yeo, C. M. S. Torres, and A. Mitchell, “Nanoscale pillar hypersonic surface phononic crystals,” Phys. Rev. B 94(9), 094304 (2016).
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Figures (5)

Fig. 1.
Fig. 1. (a) Schematic design of the monolithic metasurface for second harmonic generation. Incident plane wave is polarized along the y-axis. The pump beam direction and electric field are indicated in terms of k and E. (b) Schematic of the metasurface unit cell. The pillar-shaped nanoantenna has a radius r and a height h. The pitch of the squire unit cell is p.
Fig. 2.
Fig. 2. (a) Reflectivity and multipolar analysis of the fields generated in the nanopillar as a function of wavelength, calculated for r = 150 nm, p = 590 nm and h = 440 nm. Rx stands for reflectivity, MD for magnetic dipole, ED for electric dipole, MQ for magnetic quadrupole, EQ for electric quadrupole, and FE for field intensity enhancement. (b) Cross-section of the electric field intensity enhancement (|E|/E0)2 in the yz plane through the axis of the cylinder at a wavelength of 815 nm. E0 is the amplitude of the incident plane wave. The arrows represent the E-field vector components in the same yz plane.
Fig. 3.
Fig. 3. Average E-field intensity enhancement spectra as a function of (a) pillar radius (p = 600 nm, h = 500 nm), (b) metasurface pitch (r = 150 nm, h = 500 nm), and (c) pillar height (p = 590 nm, r = 150 nm). The dashed line on (a) shows the MD peak as a function of radius and wavelength.
Fig. 4.
Fig. 4. Total SH conversion efficiency as a function of the pump wavelength and (a) pillar radius (p = 600 nm, h = 500 nm), (b) array pitch (r = 150 nm, h = 500 nm), and (c) pillar height (r = 150 nm, p = 590 nm). The dashed line on (a) shows the MD peak as a function of radius and wavelength.
Fig. 5.
Fig. 5. (a) Total SH conversion efficiency as a function of the pump wavelength and geometry for a fixed ratio between radius, pitch, and height of 150 nm: 590 nm: 440 nm. (b) SH conversion efficiency for FW at 815 nm as a function of polarization angle of input electric field calculated for r = 150 nm, p = 590 nm and h = 440 nm.

Equations (3)

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F E a v g = F E d V V = ( E / E E 0 E 0 ) 2 d V V ,
[ 0 0 0 0 d 31 d 22 d 22 d 22 0 d 31 0 0 d 31 d 31 d 33 0 0 0 ] ,
η = P 2 ω P i n = ( S n ^ ) d A I i n p 2 ,

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