Abstract

Monolayers of transition metal dichalcogenides have a strong second-order nonlinear response enabling second-harmonic generation. Here, we control the spatial radiation properties of the generated second harmonic by patterning MoS$_2$ monolayers using focused ion beam milling. We observe diffraction of the second harmonic into the zero and first diffraction orders via an inscribed one-dimensional grating. Additionally, we included a fork-like singularity into the grating to create a vortex beam in the first diffraction order.

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

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2019 (4)

T. Bucher, A. Vaskin, R. Mupparapu, F. J. F. Löchner, A. George, K. E. Chong, S. Fasold, C. Neumann, D.-Y. Choi, F. Eilenberger, F. Setzpfandt, Y. S. Kivshar, T. Pertsch, A. Turchanin, and I. Staude, “Tailoring photoluminescence from MoS$_2$2 monolayers by Mie-resonant metasurfaces,” ACS Photonics 6(4), 1002–1009 (2019).
[Crossref]

A. Dasgupta, J. Gao, and X. Yang, “Second-harmonic optical vortex conversion from WS$_2$2 monolayer,” Sci. Rep. 9(1), 8780 (2019).
[Crossref]

A. George, C. Neumann, D. Kaiser, R. Mupparapu, T. Lehnert, U. Hübner, Z. Tang, A. Winter, U. Kaiser, I. Staude, and A. Turchanin, “Controlled growth of transition metal dichalcogenide monolayers using Knudsen-type effusion cells for the precursors,” J. Phys. Mater. 2(1), 016001 (2019).
[Crossref]

A. Dasgupta, J. Gao, and X. Yang, “Atomically thin nonlinear transition metal dichalcogenide holograms,” Nano Lett. 19(9), 6511–6516 (2019).
[Crossref]

2018 (9)

A. Autere, H. Jussila, Y. Dai, Y. Wang, H. Lipsanen, and Z. Sun, “Nonlinear optics with 2D layered materials,” Adv. Mater. 30(24), 1705963 (2018).
[Crossref]

H. D. Saleh, S. Vezzoli, L. Caspani, A. Branny, S. Kumar, B. D. Gerardot, and D. Faccio, “Towards spontaneous parametric down conversion from monolayer MoS$_2$2,” Sci. Rep. 8(1), 3862 (2018).
[Crossref]

L. Marini, L. G. Helt, Y. Lu, B. J. Eggleton, and S. Palomba, “Constraints on downconversion in atomically thick films,” J. Opt. Soc. Am. B 35(4), 672–679 (2018).
[Crossref]

A. F. Cihan, A. G. Curto, S. Raza, P. G. Kik, and M. L. Brongersma, “Silicon Mie resonators for highly directional light emission from monolayer MoS$_2$2,” Nat. Photonics 12(5), 284–290 (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]

L. Wang, S. Kruk, K. Koshelev, I. Kravchenko, B. Luther-Davies, and Y. Kivshar, “Nonlinear wavefront control with all-dielectric metasurfaces,” Nano Lett. 18(6), 3978–3984 (2018).
[Crossref]

C. Schlickriede, N. Waterman, B. Reineke, P. Georgi, G. Li, S. Zhang, and T. Zentgraf, “Imaging through nonlinear metalens using second harmonic generation,” Adv. Mater. 30(8), 1703843 (2018).
[Crossref]

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

K.-I. Lin, Y.-H. Ho, S.-B. Liu, J.-J. Ciou, B.-T. Huang, C. Chen, H.-C. Chang, C.-L. Tu, and C.-H. Chen, “Atom-dependent edge-enhanced second-harmonic generation on MoS$_2$2 monolayers,” Nano Lett. 18(2), 793–797 (2018).
[Crossref]

2017 (6)

L. Karvonen, A. Säynätjoki, M. J. Huttunen, A. Autere, B. Amirsolaimani, S. Li, R. A. Norwood, N. Peyghambarian, H. Lipsanen, G. Eda, K. Kieu, and Z. Sun, “Rapid visualization of grain boundaries in monolayer MoS$_2$2 by multiphoton microscopy,” Nat. Commun. 8(1), 15714 (2017).
[Crossref]

H. Chen, V. Corboliou, A. S. Solntsev, D.-Y. Choi, M. A. Vincenti, D. D. Ceglia, C. D. Angelis, Y. Lu, and D. N. Neshev, “Enhanced second-harmonic generation from two-dimensional MoSe$_2$2 on a silicon waveguide,” Light: Sci. Appl. 6(10), e17060 (2017).
[Crossref]

S. Manzeli, D. Ovchinnikov, D. Pasquier, O. V. Yazyev, and A. Kis, “2D transition metal dichalcogenides,” Nat. Rev. Mater. 2(8), 17033 (2017).
[Crossref]

F. Walter, G. Li, C. Meier, S. Zhang, and T. Zentgraf, “Ultrathin nonlinear metasurface for optical image encoding,” Nano Lett. 17(5), 3171–3175 (2017).
[Crossref]

G. Wei, D. A. Czaplewski, E. J. Lenferink, T. K. Stanev, I. W. Jung, and N. P. Stern, “Size-tunable lateral confinement in monolayer semiconductors,” Sci. Rep. 7(1), 3324 (2017).
[Crossref]

G. G. D. Han, K.-H. Tu, F. Niroui, W. Xu, S. Zhou, X. Wang, V. Bulović, C. A. Ross, J. H. Warner, and J. C. Grossman, “Photoluminescent arrays of nanopatterned monolayer MoS$_2$2,” Adv. Funct. Mater. 27(45), 1703688 (2017).
[Crossref]

2016 (7)

J. Yang, Z. Wang, F. Wang, R. Xu, J. Tao, S. Zhang, Q. Qin, B. Luther-Davies, C. Jagadish, Z. Yu, and Y. Lu, “Atomically thin optical lenses and gratings,” Light: Sci. Appl. 5(3), e16046 (2016).
[Crossref]

M. Weismann and N. C. Panoiu, “Theoretical and computational analysis of second-and third-harmonic generation in periodically patterned graphene and transition-metal dichalcogenide monolayers,” Phys. Rev. B 94(3), 035435 (2016).
[Crossref]

Y. P. V. Subbaiah, K. J. Saji, and A. Tiwari, “Atomically thin MoS$_2$2: A versatile nongraphene 2D material,” Adv. Funct. Mater. 26(13), 2046–2069 (2016).
[Crossref]

K. F. Mak and J. Shan, “Photonics and optoelectronics of 2D semiconductor transition metal dichalcogenides,” Nat. Photonics 10(4), 216–226 (2016).
[Crossref]

J. R. Schaibley, H. Yu, G. Clark, P. Rivera, J. S. Ross, K. L. Seyler, W. Yao, and X. Xu, “Valleytronics in 2D materials,” Nat. Rev. Mater. 1(11), 16055 (2016).
[Crossref]

W. Ye, F. Zeuner, X. Li, B. Reineke, S. He, C.-W. Qiu, J. Liu, Y. Wang, S. Zhang, and T. Zentgraf, “Spin and wavelength multiplexed nonlinear metasurface holography,” Nat. Commun. 7(1), 11930 (2016).
[Crossref]

E. Almeida, O. Bitton, and Y. Prior, “Nonlinear metamaterials for holography,” Nat. Commun. 7(1), 12533 (2016).
[Crossref]

2015 (12)

H. Zeng and X. Cui, “An optical spectroscopic study on two dimensional group-VI transition metal dichalcogenides,” Chem. Soc. Rev. 44(9), 2629–2642 (2015).
[Crossref]

K. L. Seyler, J. R. Schaibley, P. Gong, P. Rivera, A. M. Jones, S. Wu, J. Yan, D. G. Mandrus, W. Yao, and X. Xu, “Electrical control of second-harmonic generation in a WSe$_2$2 monolayer transistor,” Nat. Nanotechnol. 10(5), 407–411 (2015).
[Crossref]

H. Yu, D. Talukdar, W. Xu, J. B. Khurgin, and Q. Xiong, “Charge-induced second-harmonic generation in bilayer WSe$_2$2,” Nano Lett. 15(8), 5653–5657 (2015).
[Crossref]

J. Cheng, T. Jiang, Q. Ji, Y. Zhang, Z. Li, Y. Shan, Y. Zhang, X. Gong, W. Liu, and S. Wu, “Kinetic nature of grain boundary formation in as-grown MoS$_2$2 monolayers,” Adv. Mater. 27(27), 4069–4074 (2015).
[Crossref]

S. N. David, Y. Zhai, A. M. van der Zande, K. O’Brien, P. Y. Huang, D. A. Chenet, J. C. Hone, X. Zhang, and X. Yin, “Rapid, all-optical crystal orientation imaging of two-dimensional transition metal dichalcogenide monolayers,” Appl. Phys. Lett. 107(11), 111902 (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]

D. H. Kim and D. Lim, “Optical second-harmonic generation in few-layer MoSe$_2$2,” J. Korean Phys. Soc. 66(5), 816–820 (2015).
[Crossref]

G. Wang, X. Marie, I. Gerber, T. Amand, D. Lagarde, L. Bouet, M. Vidal, A. Balocchi, and B. Urbaszek, “Giant enhancement of the optical second-harmonic emission of WSe$_2$2 monolayers by laser excitation at exciton resonances,” Phys. Rev. Lett. 114(9), 097403 (2015).
[Crossref]

J. Ribeiro-Soares, C. Janisch, Z. Liu, A. L. Elías, M. S. Dresselhaus, M. Terrones, L. G. Cancado, and A. Jorio, “Second harmonic generation in WSe$_2$2,” 2D Mater. 2(4), 045015 (2015).
[Crossref]

D. J. Clark, C. T. Le, V. Senthilkumar, F. Ullah, H.-Y. Cho, Y. Sim, M.-J. Seong, K.-H. Chung, Y. S. Kim, and J. I. Jang, “Near bandgap second-order nonlinear optical characteristics of MoS$_2$2 monolayer transferred on transparent substrates,” Appl. Phys. Lett. 107(13), 131113 (2015).
[Crossref]

N. Segal, S. Keren-Zur, N. Hendler, and T. Ellenbogen, “Controlling light with metamaterial-based nonlinear photonic crystals,” Nat. Photonics 9(3), 180–184 (2015).
[Crossref]

D. S. Fox, Y. Zhou, P. Maguire, A. O’Neill, C. Ó’Coileáin, R. Gatensby, A. M. Glushenkov, T. Tao, G. S. Duesberg, I. V. Shvets, M. Abid, M. Abid, H.-C. Wu, Y. Chen, J. N. Coleman, J. F. Donegan, and H. Zhang, “Nanopatterning and electrical tuning of MoS$_2$2 layers with a subnanometer helium ion beam,” Nano Lett. 15(8), 5307–5313 (2015).
[Crossref]

2014 (6)

W.-T. Hsu, Z.-A. Zhao, L.-J. Li, C.-H. Chen, M.-H. Chiu, P.-S. Chang, Y.-C. Chou, and W.-H. Chang, “Second harmonic generation from artificially stacked transition metal dichalcogenide twisted bilayers,” ACS Nano 8(3), 2951–2958 (2014).
[Crossref]

G. X. Li, S. M. Chen, Y. Cai, S. Zhang, and K. W. Cheah, “Third harmonic generation of optical vortices using holography-based gold-fork microstructure,” Adv. Opt. Mater. 2(4), 389–393 (2014).
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D. J. Clark, V. Senthilkumar, C. T. Le, D. L. Weerawarne, B. Shim, J. I. Jang, J. H. Shim, J. Cho, Y. Sim, M.-J. Seong, S. H. Rhim, A. J. Freeman, K.-H. Chung, and Y. S. Kim, “Strong optical nonlinearity of CVD-grown MoS$_2$2 monolayer as probed by wavelength-dependent second-harmonic generation; (R),” Phys. Rev. B 90(12), 121409 (2014).
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M. L. Trolle, G. Seifert, and T. G. Pedersen, “Theory of excitonic second-harmonic generation in monolayer MoS$_2$2,” Phys. Rev. B 89(23), 235410 (2014).
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M. Grüning and C. Attaccalite, “Second harmonic generation in h-BN and MoS$_2$2 monolayers: Role of electron-hole interaction,” Phys. Rev. B 89(8), 081102 (2014).
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X. Yin, Z. Ye, D. A. Chenet, Y. Ye, K. O’Brien, J. C. Hone, and X. Zhang, “Edge nonlinear optics on a MoS$_2$2 atomic monolayer,” Science 344(6183), 488–490 (2014).
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2013 (4)

L. M. Malard, T. V. Alencar, A. P. M. Barboza, K. F. Mak, and A. M. de Paula, “Observation of intense second harmonic generation from MoS$_2$2 atomic crystals; (R),” Phys. Rev. B 87(20), 201401 (2013).
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N. Kumar, S. Najmaei, Q. Cui, F. Ceballos, P. M. Ajayan, J. Lou, and H. Zhao, “Second harmonic microscopy of monolayer MoS$_2$2; (R),” Phys. Rev. B 87(16), 161403 (2013).
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S. Li and Z. Wang, “Generation of optical vortex based on computer-generated holographic gratings by photolithography,” Appl. Phys. Lett. 103(14), 141110 (2013).
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Y. Li, Y. Rao, K. F. Mak, Y. You, S. Wang, C. R. Dean, and T. F. Heinz, “Probing symmetry properties of few-layer MoS$_2$2 and h-BN by optical second-harmonic generation,” Nano Lett. 13(7), 3329–3333 (2013).
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2012 (2)

N. V. Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting light by nonlinear photonic crystals,” Phys. Rev. Lett. 108(23), 233902 (2012).
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A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Two-dimensional nonlinear beam shaping,” Opt. Lett. 37(11), 2136–2138 (2012).
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2011 (1)

2007 (1)

D. S. Hum and M. M. Fejer, “Quasi-phasematching,” C. R. Phys. 8(2), 180–198 (2007).
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2003 (1)

A. Lugstein, B. Basnar, J. Smoliner, and E. Bertagnolli, “FIB processing of silicon in the nanoscale regime,” Appl. Phys. A 76(4), 545–548 (2003).
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2000 (1)

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett. 84(19), 4345–4348 (2000).
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1973 (1)

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D. S. Fox, Y. Zhou, P. Maguire, A. O’Neill, C. Ó’Coileáin, R. Gatensby, A. M. Glushenkov, T. Tao, G. S. Duesberg, I. V. Shvets, M. Abid, M. Abid, H.-C. Wu, Y. Chen, J. N. Coleman, J. F. Donegan, and H. Zhang, “Nanopatterning and electrical tuning of MoS$_2$2 layers with a subnanometer helium ion beam,” Nano Lett. 15(8), 5307–5313 (2015).
[Crossref]

D. S. Fox, Y. Zhou, P. Maguire, A. O’Neill, C. Ó’Coileáin, R. Gatensby, A. M. Glushenkov, T. Tao, G. S. Duesberg, I. V. Shvets, M. Abid, M. Abid, H.-C. Wu, Y. Chen, J. N. Coleman, J. F. Donegan, and H. Zhang, “Nanopatterning and electrical tuning of MoS$_2$2 layers with a subnanometer helium ion beam,” Nano Lett. 15(8), 5307–5313 (2015).
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Ajayan, P. M.

N. Kumar, S. Najmaei, Q. Cui, F. Ceballos, P. M. Ajayan, J. Lou, and H. Zhao, “Second harmonic microscopy of monolayer MoS$_2$2; (R),” Phys. Rev. B 87(16), 161403 (2013).
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Alencar, T. V.

L. M. Malard, T. V. Alencar, A. P. M. Barboza, K. F. Mak, and A. M. de Paula, “Observation of intense second harmonic generation from MoS$_2$2 atomic crystals; (R),” Phys. Rev. B 87(20), 201401 (2013).
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Almeida, E.

E. Almeida, O. Bitton, and Y. Prior, “Nonlinear metamaterials for holography,” Nat. Commun. 7(1), 12533 (2016).
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Amand, T.

G. Wang, X. Marie, I. Gerber, T. Amand, D. Lagarde, L. Bouet, M. Vidal, A. Balocchi, and B. Urbaszek, “Giant enhancement of the optical second-harmonic emission of WSe$_2$2 monolayers by laser excitation at exciton resonances,” Phys. Rev. Lett. 114(9), 097403 (2015).
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Amirsolaimani, B.

L. Karvonen, A. Säynätjoki, M. J. Huttunen, A. Autere, B. Amirsolaimani, S. Li, R. A. Norwood, N. Peyghambarian, H. Lipsanen, G. Eda, K. Kieu, and Z. Sun, “Rapid visualization of grain boundaries in monolayer MoS$_2$2 by multiphoton microscopy,” Nat. Commun. 8(1), 15714 (2017).
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Angelis, C. D.

H. Chen, V. Corboliou, A. S. Solntsev, D.-Y. Choi, M. A. Vincenti, D. D. Ceglia, C. D. Angelis, Y. Lu, and D. N. Neshev, “Enhanced second-harmonic generation from two-dimensional MoSe$_2$2 on a silicon waveguide,” Light: Sci. Appl. 6(10), e17060 (2017).
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Arie, A.

Attaccalite, C.

M. Grüning and C. Attaccalite, “Second harmonic generation in h-BN and MoS$_2$2 monolayers: Role of electron-hole interaction,” Phys. Rev. B 89(8), 081102 (2014).
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A. Autere, H. Jussila, Y. Dai, Y. Wang, H. Lipsanen, and Z. Sun, “Nonlinear optics with 2D layered materials,” Adv. Mater. 30(24), 1705963 (2018).
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L. Karvonen, A. Säynätjoki, M. J. Huttunen, A. Autere, B. Amirsolaimani, S. Li, R. A. Norwood, N. Peyghambarian, H. Lipsanen, G. Eda, K. Kieu, and Z. Sun, “Rapid visualization of grain boundaries in monolayer MoS$_2$2 by multiphoton microscopy,” Nat. Commun. 8(1), 15714 (2017).
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Balocchi, A.

G. Wang, X. Marie, I. Gerber, T. Amand, D. Lagarde, L. Bouet, M. Vidal, A. Balocchi, and B. Urbaszek, “Giant enhancement of the optical second-harmonic emission of WSe$_2$2 monolayers by laser excitation at exciton resonances,” Phys. Rev. Lett. 114(9), 097403 (2015).
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Barboza, A. P. M.

L. M. Malard, T. V. Alencar, A. P. M. Barboza, K. F. Mak, and A. M. de Paula, “Observation of intense second harmonic generation from MoS$_2$2 atomic crystals; (R),” Phys. Rev. B 87(20), 201401 (2013).
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Basnar, B.

A. Lugstein, B. Basnar, J. Smoliner, and E. Bertagnolli, “FIB processing of silicon in the nanoscale regime,” Appl. Phys. A 76(4), 545–548 (2003).
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Bertagnolli, E.

A. Lugstein, B. Basnar, J. Smoliner, and E. Bertagnolli, “FIB processing of silicon in the nanoscale regime,” Appl. Phys. A 76(4), 545–548 (2003).
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Bitton, O.

E. Almeida, O. Bitton, and Y. Prior, “Nonlinear metamaterials for holography,” Nat. Commun. 7(1), 12533 (2016).
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N. V. Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting light by nonlinear photonic crystals,” Phys. Rev. Lett. 108(23), 233902 (2012).
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G. Wang, X. Marie, I. Gerber, T. Amand, D. Lagarde, L. Bouet, M. Vidal, A. Balocchi, and B. Urbaszek, “Giant enhancement of the optical second-harmonic emission of WSe$_2$2 monolayers by laser excitation at exciton resonances,” Phys. Rev. Lett. 114(9), 097403 (2015).
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H. D. Saleh, S. Vezzoli, L. Caspani, A. Branny, S. Kumar, B. D. Gerardot, and D. Faccio, “Towards spontaneous parametric down conversion from monolayer MoS$_2$2,” Sci. Rep. 8(1), 3862 (2018).
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N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett. 84(19), 4345–4348 (2000).
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A. F. Cihan, A. G. Curto, S. Raza, P. G. Kik, and M. L. Brongersma, “Silicon Mie resonators for highly directional light emission from monolayer MoS$_2$2,” Nat. Photonics 12(5), 284–290 (2018).
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T. Bucher, A. Vaskin, R. Mupparapu, F. J. F. Löchner, A. George, K. E. Chong, S. Fasold, C. Neumann, D.-Y. Choi, F. Eilenberger, F. Setzpfandt, Y. S. Kivshar, T. Pertsch, A. Turchanin, and I. Staude, “Tailoring photoluminescence from MoS$_2$2 monolayers by Mie-resonant metasurfaces,” ACS Photonics 6(4), 1002–1009 (2019).
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G. G. D. Han, K.-H. Tu, F. Niroui, W. Xu, S. Zhou, X. Wang, V. Bulović, C. A. Ross, J. H. Warner, and J. C. Grossman, “Photoluminescent arrays of nanopatterned monolayer MoS$_2$2,” Adv. Funct. Mater. 27(45), 1703688 (2017).
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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).
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Cai, Y.

G. X. Li, S. M. Chen, Y. Cai, S. Zhang, and K. W. Cheah, “Third harmonic generation of optical vortices using holography-based gold-fork microstructure,” Adv. Opt. Mater. 2(4), 389–393 (2014).
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J. Ribeiro-Soares, C. Janisch, Z. Liu, A. L. Elías, M. S. Dresselhaus, M. Terrones, L. G. Cancado, and A. Jorio, “Second harmonic generation in WSe$_2$2,” 2D Mater. 2(4), 045015 (2015).
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Caspani, L.

H. D. Saleh, S. Vezzoli, L. Caspani, A. Branny, S. Kumar, B. D. Gerardot, and D. Faccio, “Towards spontaneous parametric down conversion from monolayer MoS$_2$2,” Sci. Rep. 8(1), 3862 (2018).
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Ceballos, F.

N. Kumar, S. Najmaei, Q. Cui, F. Ceballos, P. M. Ajayan, J. Lou, and H. Zhao, “Second harmonic microscopy of monolayer MoS$_2$2; (R),” Phys. Rev. B 87(16), 161403 (2013).
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Ceglia, D. D.

H. Chen, V. Corboliou, A. S. Solntsev, D.-Y. Choi, M. A. Vincenti, D. D. Ceglia, C. D. Angelis, Y. Lu, and D. N. Neshev, “Enhanced second-harmonic generation from two-dimensional MoSe$_2$2 on a silicon waveguide,” Light: Sci. Appl. 6(10), e17060 (2017).
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Chang, H.-C.

K.-I. Lin, Y.-H. Ho, S.-B. Liu, J.-J. Ciou, B.-T. Huang, C. Chen, H.-C. Chang, C.-L. Tu, and C.-H. Chen, “Atom-dependent edge-enhanced second-harmonic generation on MoS$_2$2 monolayers,” Nano Lett. 18(2), 793–797 (2018).
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Chang, P.-S.

W.-T. Hsu, Z.-A. Zhao, L.-J. Li, C.-H. Chen, M.-H. Chiu, P.-S. Chang, Y.-C. Chou, and W.-H. Chang, “Second harmonic generation from artificially stacked transition metal dichalcogenide twisted bilayers,” ACS Nano 8(3), 2951–2958 (2014).
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Chang, W.-H.

W.-T. Hsu, Z.-A. Zhao, L.-J. Li, C.-H. Chen, M.-H. Chiu, P.-S. Chang, Y.-C. Chou, and W.-H. Chang, “Second harmonic generation from artificially stacked transition metal dichalcogenide twisted bilayers,” ACS Nano 8(3), 2951–2958 (2014).
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Cheah, K. W.

G. X. Li, S. M. Chen, Y. Cai, S. Zhang, and K. W. Cheah, “Third harmonic generation of optical vortices using holography-based gold-fork microstructure,” Adv. Opt. Mater. 2(4), 389–393 (2014).
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Chen, C.

K.-I. Lin, Y.-H. Ho, S.-B. Liu, J.-J. Ciou, B.-T. Huang, C. Chen, H.-C. Chang, C.-L. Tu, and C.-H. Chen, “Atom-dependent edge-enhanced second-harmonic generation on MoS$_2$2 monolayers,” Nano Lett. 18(2), 793–797 (2018).
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Chen, C.-H.

K.-I. Lin, Y.-H. Ho, S.-B. Liu, J.-J. Ciou, B.-T. Huang, C. Chen, H.-C. Chang, C.-L. Tu, and C.-H. Chen, “Atom-dependent edge-enhanced second-harmonic generation on MoS$_2$2 monolayers,” Nano Lett. 18(2), 793–797 (2018).
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W.-T. Hsu, Z.-A. Zhao, L.-J. Li, C.-H. Chen, M.-H. Chiu, P.-S. Chang, Y.-C. Chou, and W.-H. Chang, “Second harmonic generation from artificially stacked transition metal dichalcogenide twisted bilayers,” ACS Nano 8(3), 2951–2958 (2014).
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Chen, H.

H. Chen, V. Corboliou, A. S. Solntsev, D.-Y. Choi, M. A. Vincenti, D. D. Ceglia, C. D. Angelis, Y. Lu, and D. N. Neshev, “Enhanced second-harmonic generation from two-dimensional MoSe$_2$2 on a silicon waveguide,” Light: Sci. Appl. 6(10), e17060 (2017).
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Chen, J.

J. Chen, K. Wang, H. Long, X. Han, H. Hu, W. Liu, B. Wang, and P. 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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Chen, S. M.

G. X. Li, S. M. Chen, Y. Cai, S. Zhang, and K. W. Cheah, “Third harmonic generation of optical vortices using holography-based gold-fork microstructure,” Adv. Opt. Mater. 2(4), 389–393 (2014).
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Chen, Y.

D. S. Fox, Y. Zhou, P. Maguire, A. O’Neill, C. Ó’Coileáin, R. Gatensby, A. M. Glushenkov, T. Tao, G. S. Duesberg, I. V. Shvets, M. Abid, M. Abid, H.-C. Wu, Y. Chen, J. N. Coleman, J. F. Donegan, and H. Zhang, “Nanopatterning and electrical tuning of MoS$_2$2 layers with a subnanometer helium ion beam,” Nano Lett. 15(8), 5307–5313 (2015).
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Chenet, D. A.

S. N. David, Y. Zhai, A. M. van der Zande, K. O’Brien, P. Y. Huang, D. A. Chenet, J. C. Hone, X. Zhang, and X. Yin, “Rapid, all-optical crystal orientation imaging of two-dimensional transition metal dichalcogenide monolayers,” Appl. Phys. Lett. 107(11), 111902 (2015).
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X. Yin, Z. Ye, D. A. Chenet, Y. Ye, K. O’Brien, J. C. Hone, and X. Zhang, “Edge nonlinear optics on a MoS$_2$2 atomic monolayer,” Science 344(6183), 488–490 (2014).
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Cheng, J.

J. Cheng, T. Jiang, Q. Ji, Y. Zhang, Z. Li, Y. Shan, Y. Zhang, X. Gong, W. Liu, and S. Wu, “Kinetic nature of grain boundary formation in as-grown MoS$_2$2 monolayers,” Adv. Mater. 27(27), 4069–4074 (2015).
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W.-T. Hsu, Z.-A. Zhao, L.-J. Li, C.-H. Chen, M.-H. Chiu, P.-S. Chang, Y.-C. Chou, and W.-H. Chang, “Second harmonic generation from artificially stacked transition metal dichalcogenide twisted bilayers,” ACS Nano 8(3), 2951–2958 (2014).
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Cho, H.-Y.

D. J. Clark, C. T. Le, V. Senthilkumar, F. Ullah, H.-Y. Cho, Y. Sim, M.-J. Seong, K.-H. Chung, Y. S. Kim, and J. I. Jang, “Near bandgap second-order nonlinear optical characteristics of MoS$_2$2 monolayer transferred on transparent substrates,” Appl. Phys. Lett. 107(13), 131113 (2015).
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Cho, J.

D. J. Clark, V. Senthilkumar, C. T. Le, D. L. Weerawarne, B. Shim, J. I. Jang, J. H. Shim, J. Cho, Y. Sim, M.-J. Seong, S. H. Rhim, A. J. Freeman, K.-H. Chung, and Y. S. Kim, “Strong optical nonlinearity of CVD-grown MoS$_2$2 monolayer as probed by wavelength-dependent second-harmonic generation; (R),” Phys. Rev. B 90(12), 121409 (2014).
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Choi, D.-Y.

T. Bucher, A. Vaskin, R. Mupparapu, F. J. F. Löchner, A. George, K. E. Chong, S. Fasold, C. Neumann, D.-Y. Choi, F. Eilenberger, F. Setzpfandt, Y. S. Kivshar, T. Pertsch, A. Turchanin, and I. Staude, “Tailoring photoluminescence from MoS$_2$2 monolayers by Mie-resonant metasurfaces,” ACS Photonics 6(4), 1002–1009 (2019).
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H. Chen, V. Corboliou, A. S. Solntsev, D.-Y. Choi, M. A. Vincenti, D. D. Ceglia, C. D. Angelis, Y. Lu, and D. N. Neshev, “Enhanced second-harmonic generation from two-dimensional MoSe$_2$2 on a silicon waveguide,” Light: Sci. Appl. 6(10), e17060 (2017).
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T. Bucher, A. Vaskin, R. Mupparapu, F. J. F. Löchner, A. George, K. E. Chong, S. Fasold, C. Neumann, D.-Y. Choi, F. Eilenberger, F. Setzpfandt, Y. S. Kivshar, T. Pertsch, A. Turchanin, and I. Staude, “Tailoring photoluminescence from MoS$_2$2 monolayers by Mie-resonant metasurfaces,” ACS Photonics 6(4), 1002–1009 (2019).
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Chou, Y.-C.

W.-T. Hsu, Z.-A. Zhao, L.-J. Li, C.-H. Chen, M.-H. Chiu, P.-S. Chang, Y.-C. Chou, and W.-H. Chang, “Second harmonic generation from artificially stacked transition metal dichalcogenide twisted bilayers,” ACS Nano 8(3), 2951–2958 (2014).
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D. J. Clark, C. T. Le, V. Senthilkumar, F. Ullah, H.-Y. Cho, Y. Sim, M.-J. Seong, K.-H. Chung, Y. S. Kim, and J. I. Jang, “Near bandgap second-order nonlinear optical characteristics of MoS$_2$2 monolayer transferred on transparent substrates,” Appl. Phys. Lett. 107(13), 131113 (2015).
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D. J. Clark, V. Senthilkumar, C. T. Le, D. L. Weerawarne, B. Shim, J. I. Jang, J. H. Shim, J. Cho, Y. Sim, M.-J. Seong, S. H. Rhim, A. J. Freeman, K.-H. Chung, and Y. S. Kim, “Strong optical nonlinearity of CVD-grown MoS$_2$2 monolayer as probed by wavelength-dependent second-harmonic generation; (R),” Phys. Rev. B 90(12), 121409 (2014).
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A. F. Cihan, A. G. Curto, S. Raza, P. G. Kik, and M. L. Brongersma, “Silicon Mie resonators for highly directional light emission from monolayer MoS$_2$2,” Nat. Photonics 12(5), 284–290 (2018).
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Ciou, J.-J.

K.-I. Lin, Y.-H. Ho, S.-B. Liu, J.-J. Ciou, B.-T. Huang, C. Chen, H.-C. Chang, C.-L. Tu, and C.-H. Chen, “Atom-dependent edge-enhanced second-harmonic generation on MoS$_2$2 monolayers,” Nano Lett. 18(2), 793–797 (2018).
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Clark, D. J.

D. J. Clark, C. T. Le, V. Senthilkumar, F. Ullah, H.-Y. Cho, Y. Sim, M.-J. Seong, K.-H. Chung, Y. S. Kim, and J. I. Jang, “Near bandgap second-order nonlinear optical characteristics of MoS$_2$2 monolayer transferred on transparent substrates,” Appl. Phys. Lett. 107(13), 131113 (2015).
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D. J. Clark, V. Senthilkumar, C. T. Le, D. L. Weerawarne, B. Shim, J. I. Jang, J. H. Shim, J. Cho, Y. Sim, M.-J. Seong, S. H. Rhim, A. J. Freeman, K.-H. Chung, and Y. S. Kim, “Strong optical nonlinearity of CVD-grown MoS$_2$2 monolayer as probed by wavelength-dependent second-harmonic generation; (R),” Phys. Rev. B 90(12), 121409 (2014).
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D. S. Fox, Y. Zhou, P. Maguire, A. O’Neill, C. Ó’Coileáin, R. Gatensby, A. M. Glushenkov, T. Tao, G. S. Duesberg, I. V. Shvets, M. Abid, M. Abid, H.-C. Wu, Y. Chen, J. N. Coleman, J. F. Donegan, and H. Zhang, “Nanopatterning and electrical tuning of MoS$_2$2 layers with a subnanometer helium ion beam,” Nano Lett. 15(8), 5307–5313 (2015).
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Corboliou, V.

H. Chen, V. Corboliou, A. S. Solntsev, D.-Y. Choi, M. A. Vincenti, D. D. Ceglia, C. D. Angelis, Y. Lu, and D. N. Neshev, “Enhanced second-harmonic generation from two-dimensional MoSe$_2$2 on a silicon waveguide,” Light: Sci. Appl. 6(10), e17060 (2017).
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C. Janisch, Y. Wang, D. Ma, N. Mehta, A. L. Elías, N. Perea-López, M. Terrones, V. Crespi, and Z. Liu, “Extraordinary second harmonic generation in tungsten disulfide monolayers,” Sci. Rep. 4(1), 5530 (2015).
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N. Kumar, S. Najmaei, Q. Cui, F. Ceballos, P. M. Ajayan, J. Lou, and H. Zhao, “Second harmonic microscopy of monolayer MoS$_2$2; (R),” Phys. Rev. B 87(16), 161403 (2013).
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H. Zeng and X. Cui, “An optical spectroscopic study on two dimensional group-VI transition metal dichalcogenides,” Chem. Soc. Rev. 44(9), 2629–2642 (2015).
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A. F. Cihan, A. G. Curto, S. Raza, P. G. Kik, and M. L. Brongersma, “Silicon Mie resonators for highly directional light emission from monolayer MoS$_2$2,” Nat. Photonics 12(5), 284–290 (2018).
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Figures (4)

Fig. 1.
Fig. 1. a) Schematic representation showing the excitation of the patterned MoS $_2$ ML flake and the radiation of the generated second harmonic (SH). b) Fabrication scheme: (i) CVD growth of MoS $_2$ ML on SiO $_2$ /Si substrate and (ii) focused ion beam milling. c) Atomic force microscope measurement of an inscribed grating. The blue dotted line indicates the line where the height profile plotted below with the blue line is taken.
Fig. 2.
Fig. 2. a) Contrast-enhanced optical microscope image of a patterned flake with a one-dimensional grating. b) Map of SH signal scanned over the patterned flake. c) SH signal at 0 $^\circ$ polarization from the structured and unstructured areas of the monolayer flake dependent on the input polarization. d) Dependence of the SH power measured at one position on the unstructured MoS $_2$ on the FW power $P_{\mathrm {FW}}$ .
Fig. 3.
Fig. 3. a) Spatial distribution of the second-harmonic (SH) signal from the patterned flake using an excitation spot of 7 $\mu$ m diameter. b) Contrast enhanced optical microscope image of the investigated monolayer flake. c) Back-focal plane image (angular spectrum) of the SH signal from the patterned flake showing the zero and the first diffraction orders. d) Angle of the first diffraction order for different periods of the grating.
Fig. 4.
Fig. 4. a) Design of the inscribed pattern with an introduced defect providing a fork-like structure. b) Optical microscope image of the structure with contrast-enhanced zoomed-in inset of the defect singularity. c) Back-focal plane image (angular spectrum) of the SH signal from the structure showing the zero and the first diffraction orders, where the latter show a zero-intensity center (ring shape).

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