Abstract

Two-dimensional materials are generating great interest due to their unique electrical and optical properties. In particular, transition metal dichalcogenides such as molybdenum disulfide (MoS2) are attractive materials due to the existence of a direct band gap in the monolayer limit that can be used to enhance nonlinear optical phenomena, such as Raman spectroscopy. Here, we have investigated four-wave mixing processes in bulk MoS2 using a multiplex coherent anti-Stokes Raman spectroscopy setup. The observed four-wave mixing signal has a resonance at approximately 680 nm, corresponding to the energy of the A excitonic transition of MoS2. This resonance can be attributed to the increased third-order nonlinear susceptibility at wavelengths near the excitonic transition. This phenomenon could open the path to using MoS2 as a substrate for enhancing four-wave mixing processes such as coherent anti-Stokes Raman spectroscopy.

© 2019 Chinese Laser Press

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References

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    [Crossref]
  11. K. Gołasa, M. Grzeszczyk, R. Bożek, P. Leszczyński, A. Wysmołek, M. Potemski, and A. Babiński, “Resonant Raman scattering in MoS2—from bulk to monolayer,” Solid State Commun. 197, 53–56 (2014).
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    [Crossref]
  19. K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim, “Two-dimensional atomic crystals,” Proc. Natl. Acad. Sci. USA 102, 10451–10453 (2005).
    [Crossref]
  20. H. Li, Q. Zhang, C. C. R. Yap, B. K. Tay, T. H. T. Edwin, A. Olivier, and D. Baillargeat, “From bulk to monolayer MoS2: evolution of Raman scattering,” Adv. Funct. Mater. 22, 1385–1390 (2012).
    [Crossref]
  21. J.-S. Park and T. Joo, “Nuclear dynamics in electronic ground and excited states probed by spectrally resolved four wave mixing,” J. Chem. Phys. 116, 10801–10808 (2002).
    [Crossref]
  22. C. Hirose, H. Ishida, K. Iwatsu, N. Watanabe, J. Kubota, A. Wada, and K. Domen, “In situ SFG spectroscopy of film growth. I. General formulation and the analysis of the signal observed during the deposition of formic acid on Pt(110)-(1×2) surface,” J. Chem. Phys. 108, 5948–5956 (1998).
    [Crossref]
  23. R. Coehoorn, C. Haas, and R. A. de Groot, “Electronic structure of MoSe2, MoS2, andWSe2. II. The nature of the optical band gaps,” Phys. Rev. B 35, 6203–6206 (1987).
    [Crossref]
  24. R. Wang, H. C. Chien, J. Kumar, N. Kumar, H. Y. Chiu, and H. Zhao, “Third-harmonic generation in ultrathin films of MoS2,” ACS Appl. Mater. Interface 6, 314–318 (2014).
    [Crossref]
  25. R. K. Jain and M. B. Klein, “Degenerate four‐wave mixing near the band gap of semiconductors,” Appl. Phys. Lett. 35, 454–456 (1979).
    [Crossref]
  26. K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, “Atomically thin MoS2: a new direct-gap semiconductor,” Phys. Rev. Lett. 105, 136805 (2010).
    [Crossref]
  27. S.-Y. Ding, J. Yi, J.-F. Li, B. Ren, D.-Y. Wu, R. Panneerselvam, and Z.-Q. Tian, “Nanostructure-based plasmon-enhanced Raman spectroscopy for surface analysis of materials,” Nat. Rev. Mater. 1, 16021 (2016).
    [Crossref]
  28. R. I. Woodward, R. T. Murray, C. F. Phelan, R. E. P. D. Oliveira, T. H. Runcorn, E. J. R. Kelleher, S. Li, E. C. D. Oliveira, G. J. M. Fechine, G. Eda, and C. J. S. D. Matos, “Characterization of the second- and third-order nonlinear optical susceptibilities of monolayer MoS2 using multiphoton microscopy,” 2D Mater. 4, 011006 (2016).
    [Crossref]
  29. D. B. S. Soh, C. Rogers, D. J. Gray, E. Chatterjee, and H. Mabuchi, “Optical nonlinearities of excitons in monolayer MoS2,” Phys. Rev. B 97, 165111 (2018).
    [Crossref]
  30. R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).
  31. F. Zahid, L. Liu, Y. Zhu, J. Wang, and H. Guo, “A generic tight-binding model for monolayer, bilayer and bulk MoS2,” AIP Adv. 3, 052111 (2013).
    [Crossref]
  32. A. R. Beal and H. P. Hughes, “Kramers-Kronig analysis of the reflectivity spectra of 2H-MoS2, 2H-MoSe2 and 2H-MoTe2,” J. Phys. C 12, 881–890 (1979).
    [Crossref]
  33. Z. Wang, Z. Dong, Y. Gu, Y. H. Chang, L. Zhang, L. J. Li, W. Zhao, G. Eda, W. Zhang, G. Grinblat, S. A. Maier, J. K. Yang, C. W. Qiu, and A. T. Wee, “Giant photoluminescence enhancement in tungsten-diselenide-gold plasmonic hybrid structures,” Nat. Commun. 7, 11283 (2016).
    [Crossref]

2018 (1)

D. B. S. Soh, C. Rogers, D. J. Gray, E. Chatterjee, and H. Mabuchi, “Optical nonlinearities of excitons in monolayer MoS2,” Phys. Rev. B 97, 165111 (2018).
[Crossref]

2017 (1)

Z. He, D. V. Voronine, A. M. Sinyukov, Z. N. Liege, B. Birmingham, A. V. Sokolov, Z. Zhang, and M. O. Scully, “Tip-enhanced Raman scattering on bulk MoS2 substrate,” IEEE J. Sel. Top. Quantum Electron. 23, 113–118 (2017).
[Crossref]

2016 (4)

D. Li, W. Xiong, L. Jiang, Z. Xiao, H. R. Golgir, M. Wang, X. Huang, Y. Zhou, Z. Lin, J. Song, S. Ducharme, L. Jiang, J. F. Silvain, and Y. Lu, “Multimodal nonlinear optical imaging of MoS2 and MoS2-based van der Waals heterostructures,” ACS Nano 10, 3766–3775 (2016).
[Crossref]

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

R. I. Woodward, R. T. Murray, C. F. Phelan, R. E. P. D. Oliveira, T. H. Runcorn, E. J. R. Kelleher, S. Li, E. C. D. Oliveira, G. J. M. Fechine, G. Eda, and C. J. S. D. Matos, “Characterization of the second- and third-order nonlinear optical susceptibilities of monolayer MoS2 using multiphoton microscopy,” 2D Mater. 4, 011006 (2016).
[Crossref]

Z. Wang, Z. Dong, Y. Gu, Y. H. Chang, L. Zhang, L. J. Li, W. Zhao, G. Eda, W. Zhang, G. Grinblat, S. A. Maier, J. K. Yang, C. W. Qiu, and A. T. Wee, “Giant photoluminescence enhancement in tungsten-diselenide-gold plasmonic hybrid structures,” Nat. Commun. 7, 11283 (2016).
[Crossref]

2015 (1)

Y. Li, N. Dong, S. Zhang, X. Zhang, Y. Feng, K. Wang, L. Zhang, and J. Wang, “Giant two-photon absorption in monolayer MoS2,” Laser Photon. Rev. 9, 427–434 (2015).
[Crossref]

2014 (4)

K. Gołasa, M. Grzeszczyk, R. Bożek, P. Leszczyński, A. Wysmołek, M. Potemski, and A. Babiński, “Resonant Raman scattering in MoS2—from bulk to monolayer,” Solid State Commun. 197, 53–56 (2014).
[Crossref]

X. Ling, W. Fang, Y. H. Lee, P. T. Araujo, X. Zhang, J. F. Rodriguez-Nieva, Y. Lin, J. Zhang, J. Kong, and M. S. Dresselhaus, “Raman enhancement effect on two-dimensional layered materials: graphene, h-BN and MoS2,” Nano Lett. 14, 3033–3040 (2014).
[Crossref]

X. Yin, Z. Ye, D. A. Chenet, Y. Ye, K. O’Brien, J. C. Hone, and X. Zhang, “Edge nonlinear optics on a MoS2 atomic monolayer,” Science 344, 488–490 (2014).
[Crossref]

R. Wang, H. C. Chien, J. Kumar, N. Kumar, H. Y. Chiu, and H. Zhao, “Third-harmonic generation in ultrathin films of MoS2,” ACS Appl. Mater. Interface 6, 314–318 (2014).
[Crossref]

2013 (2)

F. Zahid, L. Liu, Y. Zhu, J. Wang, and H. Guo, “A generic tight-binding model for monolayer, bilayer and bulk MoS2,” AIP Adv. 3, 052111 (2013).
[Crossref]

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 MoS2 atomic crystals,” Phys. Rev. B 87, 201401 (2013).
[Crossref]

2012 (1)

H. Li, Q. Zhang, C. C. R. Yap, B. K. Tay, T. H. T. Edwin, A. Olivier, and D. Baillargeat, “From bulk to monolayer MoS2: evolution of Raman scattering,” Adv. Funct. Mater. 22, 1385–1390 (2012).
[Crossref]

2011 (2)

B. Radisavljevic, A. Radenovic, J. Brivio, V. Giacometti, and A. Kis, “Single-layer MoS2 transistors,” Nat. Nanotechnol. 6, 147–150 (2011).
[Crossref]

B. Radisavljevic, M. B. Whitwick, and A. Kis, “Integrated circuits and logic operations based on single-layer MoS2,” ACS Nano 5, 9934–9938 (2011).
[Crossref]

2010 (2)

A. Splendiani, L. Sun, Y. Zhang, T. Li, J. Kim, C. Y. Chim, G. Galli, and F. Wang, “Emerging photoluminescence in monolayer MoS2,” Nano Lett. 10, 1271–1275 (2010).
[Crossref]

K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, “Atomically thin MoS2: a new direct-gap semiconductor,” Phys. Rev. Lett. 105, 136805 (2010).
[Crossref]

2005 (1)

K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim, “Two-dimensional atomic crystals,” Proc. Natl. Acad. Sci. USA 102, 10451–10453 (2005).
[Crossref]

2002 (1)

J.-S. Park and T. Joo, “Nuclear dynamics in electronic ground and excited states probed by spectrally resolved four wave mixing,” J. Chem. Phys. 116, 10801–10808 (2002).
[Crossref]

2000 (1)

N. M. Renevier, N. Lobiondo, V. C. Fox, D. G. Teer, and J. Hampshire, “Performance of MoS2/metal composite coatings used for dry machining and other industrial applications,” Surf. Coat. Technol. 123, 84–91 (2000).
[Crossref]

1998 (1)

C. Hirose, H. Ishida, K. Iwatsu, N. Watanabe, J. Kubota, A. Wada, and K. Domen, “In situ SFG spectroscopy of film growth. I. General formulation and the analysis of the signal observed during the deposition of formic acid on Pt(110)-(1×2) surface,” J. Chem. Phys. 108, 5948–5956 (1998).
[Crossref]

1993 (1)

J. Rechberger, P. Brunner, and R. Dubach, “High performance cutting tools with a solid lubricant physically vapour-deposited coating,” Surf. Coat. Technol. 62, 393–398 (1993).
[Crossref]

1991 (1)

J. Strempel and W. Kiefer, “Polarized and depolarized continuum resonance Raman scattering of molecular iodine: accurate determination of repulsive states,” Can. J. Chem. 69, 1732–1739 (1991).
[Crossref]

1987 (1)

R. Coehoorn, C. Haas, and R. A. de Groot, “Electronic structure of MoSe2, MoS2, andWSe2. II. The nature of the optical band gaps,” Phys. Rev. B 35, 6203–6206 (1987).
[Crossref]

1979 (2)

R. K. Jain and M. B. Klein, “Degenerate four‐wave mixing near the band gap of semiconductors,” Appl. Phys. Lett. 35, 454–456 (1979).
[Crossref]

A. R. Beal and H. P. Hughes, “Kramers-Kronig analysis of the reflectivity spectra of 2H-MoS2, 2H-MoSe2 and 2H-MoTe2,” J. Phys. C 12, 881–890 (1979).
[Crossref]

1973 (3)

R. V. Kasowski, “Band structure of MoS2 and NbS2,” Phys. Rev. Lett. 30, 1175–1178 (1973).
[Crossref]

L. F. Mattheiss, “Energy bands for 2H-NbSe2 and 2H–MoS2,” Phys. Rev. Lett. 30, 784–787 (1973).
[Crossref]

L. F. Mattheiss, “Band structures of transition-metal-dichalcogenide layer compounds,” Phys. Rev. B 8, 3719–3740 (1973).
[Crossref]

1972 (1)

R. A. Bromley, R. B. Murray, and A. D. Yoffe, “The band structures of some transition metal dichalcogenides. III. Group VIA: trigonal prism materials,” J. Phys. C 5, 759–778 (1972).
[Crossref]

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 MoS2 atomic crystals,” Phys. Rev. B 87, 201401 (2013).
[Crossref]

Araujo, P. T.

X. Ling, W. Fang, Y. H. Lee, P. T. Araujo, X. Zhang, J. F. Rodriguez-Nieva, Y. Lin, J. Zhang, J. Kong, and M. S. Dresselhaus, “Raman enhancement effect on two-dimensional layered materials: graphene, h-BN and MoS2,” Nano Lett. 14, 3033–3040 (2014).
[Crossref]

Babinski, A.

K. Gołasa, M. Grzeszczyk, R. Bożek, P. Leszczyński, A. Wysmołek, M. Potemski, and A. Babiński, “Resonant Raman scattering in MoS2—from bulk to monolayer,” Solid State Commun. 197, 53–56 (2014).
[Crossref]

Baillargeat, D.

H. Li, Q. Zhang, C. C. R. Yap, B. K. Tay, T. H. T. Edwin, A. Olivier, and D. Baillargeat, “From bulk to monolayer MoS2: evolution of Raman scattering,” Adv. Funct. Mater. 22, 1385–1390 (2012).
[Crossref]

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 MoS2 atomic crystals,” Phys. Rev. B 87, 201401 (2013).
[Crossref]

Beal, A. R.

A. R. Beal and H. P. Hughes, “Kramers-Kronig analysis of the reflectivity spectra of 2H-MoS2, 2H-MoSe2 and 2H-MoTe2,” J. Phys. C 12, 881–890 (1979).
[Crossref]

Birmingham, B.

Z. He, D. V. Voronine, A. M. Sinyukov, Z. N. Liege, B. Birmingham, A. V. Sokolov, Z. Zhang, and M. O. Scully, “Tip-enhanced Raman scattering on bulk MoS2 substrate,” IEEE J. Sel. Top. Quantum Electron. 23, 113–118 (2017).
[Crossref]

Booth, T. J.

K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim, “Two-dimensional atomic crystals,” Proc. Natl. Acad. Sci. USA 102, 10451–10453 (2005).
[Crossref]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).

Bozek, R.

K. Gołasa, M. Grzeszczyk, R. Bożek, P. Leszczyński, A. Wysmołek, M. Potemski, and A. Babiński, “Resonant Raman scattering in MoS2—from bulk to monolayer,” Solid State Commun. 197, 53–56 (2014).
[Crossref]

Brivio, J.

B. Radisavljevic, A. Radenovic, J. Brivio, V. Giacometti, and A. Kis, “Single-layer MoS2 transistors,” Nat. Nanotechnol. 6, 147–150 (2011).
[Crossref]

Bromley, R. A.

R. A. Bromley, R. B. Murray, and A. D. Yoffe, “The band structures of some transition metal dichalcogenides. III. Group VIA: trigonal prism materials,” J. Phys. C 5, 759–778 (1972).
[Crossref]

Brunner, P.

J. Rechberger, P. Brunner, and R. Dubach, “High performance cutting tools with a solid lubricant physically vapour-deposited coating,” Surf. Coat. Technol. 62, 393–398 (1993).
[Crossref]

Chang, Y. H.

Z. Wang, Z. Dong, Y. Gu, Y. H. Chang, L. Zhang, L. J. Li, W. Zhao, G. Eda, W. Zhang, G. Grinblat, S. A. Maier, J. K. Yang, C. W. Qiu, and A. T. Wee, “Giant photoluminescence enhancement in tungsten-diselenide-gold plasmonic hybrid structures,” Nat. Commun. 7, 11283 (2016).
[Crossref]

Chatterjee, E.

D. B. S. Soh, C. Rogers, D. J. Gray, E. Chatterjee, and H. Mabuchi, “Optical nonlinearities of excitons in monolayer MoS2,” Phys. Rev. B 97, 165111 (2018).
[Crossref]

Chenet, D. A.

X. Yin, Z. Ye, D. A. Chenet, Y. Ye, K. O’Brien, J. C. Hone, and X. Zhang, “Edge nonlinear optics on a MoS2 atomic monolayer,” Science 344, 488–490 (2014).
[Crossref]

Chien, H. C.

R. Wang, H. C. Chien, J. Kumar, N. Kumar, H. Y. Chiu, and H. Zhao, “Third-harmonic generation in ultrathin films of MoS2,” ACS Appl. Mater. Interface 6, 314–318 (2014).
[Crossref]

Chim, C. Y.

A. Splendiani, L. Sun, Y. Zhang, T. Li, J. Kim, C. Y. Chim, G. Galli, and F. Wang, “Emerging photoluminescence in monolayer MoS2,” Nano Lett. 10, 1271–1275 (2010).
[Crossref]

Chiu, H. Y.

R. Wang, H. C. Chien, J. Kumar, N. Kumar, H. Y. Chiu, and H. Zhao, “Third-harmonic generation in ultrathin films of MoS2,” ACS Appl. Mater. Interface 6, 314–318 (2014).
[Crossref]

Coehoorn, R.

R. Coehoorn, C. Haas, and R. A. de Groot, “Electronic structure of MoSe2, MoS2, andWSe2. II. The nature of the optical band gaps,” Phys. Rev. B 35, 6203–6206 (1987).
[Crossref]

de Groot, R. A.

R. Coehoorn, C. Haas, and R. A. de Groot, “Electronic structure of MoSe2, MoS2, andWSe2. II. The nature of the optical band gaps,” Phys. Rev. B 35, 6203–6206 (1987).
[Crossref]

de Paula, A. 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 MoS2 atomic crystals,” Phys. Rev. B 87, 201401 (2013).
[Crossref]

Ding, S.-Y.

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

Domen, K.

C. Hirose, H. Ishida, K. Iwatsu, N. Watanabe, J. Kubota, A. Wada, and K. Domen, “In situ SFG spectroscopy of film growth. I. General formulation and the analysis of the signal observed during the deposition of formic acid on Pt(110)-(1×2) surface,” J. Chem. Phys. 108, 5948–5956 (1998).
[Crossref]

Dong, N.

Y. Li, N. Dong, S. Zhang, X. Zhang, Y. Feng, K. Wang, L. Zhang, and J. Wang, “Giant two-photon absorption in monolayer MoS2,” Laser Photon. Rev. 9, 427–434 (2015).
[Crossref]

Dong, Z.

Z. Wang, Z. Dong, Y. Gu, Y. H. Chang, L. Zhang, L. J. Li, W. Zhao, G. Eda, W. Zhang, G. Grinblat, S. A. Maier, J. K. Yang, C. W. Qiu, and A. T. Wee, “Giant photoluminescence enhancement in tungsten-diselenide-gold plasmonic hybrid structures,” Nat. Commun. 7, 11283 (2016).
[Crossref]

Dresselhaus, M. S.

X. Ling, W. Fang, Y. H. Lee, P. T. Araujo, X. Zhang, J. F. Rodriguez-Nieva, Y. Lin, J. Zhang, J. Kong, and M. S. Dresselhaus, “Raman enhancement effect on two-dimensional layered materials: graphene, h-BN and MoS2,” Nano Lett. 14, 3033–3040 (2014).
[Crossref]

Dubach, R.

J. Rechberger, P. Brunner, and R. Dubach, “High performance cutting tools with a solid lubricant physically vapour-deposited coating,” Surf. Coat. Technol. 62, 393–398 (1993).
[Crossref]

Ducharme, S.

D. Li, W. Xiong, L. Jiang, Z. Xiao, H. R. Golgir, M. Wang, X. Huang, Y. Zhou, Z. Lin, J. Song, S. Ducharme, L. Jiang, J. F. Silvain, and Y. Lu, “Multimodal nonlinear optical imaging of MoS2 and MoS2-based van der Waals heterostructures,” ACS Nano 10, 3766–3775 (2016).
[Crossref]

Eda, G.

R. I. Woodward, R. T. Murray, C. F. Phelan, R. E. P. D. Oliveira, T. H. Runcorn, E. J. R. Kelleher, S. Li, E. C. D. Oliveira, G. J. M. Fechine, G. Eda, and C. J. S. D. Matos, “Characterization of the second- and third-order nonlinear optical susceptibilities of monolayer MoS2 using multiphoton microscopy,” 2D Mater. 4, 011006 (2016).
[Crossref]

Z. Wang, Z. Dong, Y. Gu, Y. H. Chang, L. Zhang, L. J. Li, W. Zhao, G. Eda, W. Zhang, G. Grinblat, S. A. Maier, J. K. Yang, C. W. Qiu, and A. T. Wee, “Giant photoluminescence enhancement in tungsten-diselenide-gold plasmonic hybrid structures,” Nat. Commun. 7, 11283 (2016).
[Crossref]

Edwin, T. H. T.

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N. M. Renevier, N. Lobiondo, V. C. Fox, D. G. Teer, and J. Hampshire, “Performance of MoS2/metal composite coatings used for dry machining and other industrial applications,” Surf. Coat. Technol. 123, 84–91 (2000).
[Crossref]

Rodriguez-Nieva, J. F.

X. Ling, W. Fang, Y. H. Lee, P. T. Araujo, X. Zhang, J. F. Rodriguez-Nieva, Y. Lin, J. Zhang, J. Kong, and M. S. Dresselhaus, “Raman enhancement effect on two-dimensional layered materials: graphene, h-BN and MoS2,” Nano Lett. 14, 3033–3040 (2014).
[Crossref]

Rogers, C.

D. B. S. Soh, C. Rogers, D. J. Gray, E. Chatterjee, and H. Mabuchi, “Optical nonlinearities of excitons in monolayer MoS2,” Phys. Rev. B 97, 165111 (2018).
[Crossref]

Runcorn, T. H.

R. I. Woodward, R. T. Murray, C. F. Phelan, R. E. P. D. Oliveira, T. H. Runcorn, E. J. R. Kelleher, S. Li, E. C. D. Oliveira, G. J. M. Fechine, G. Eda, and C. J. S. D. Matos, “Characterization of the second- and third-order nonlinear optical susceptibilities of monolayer MoS2 using multiphoton microscopy,” 2D Mater. 4, 011006 (2016).
[Crossref]

Schedin, F.

K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim, “Two-dimensional atomic crystals,” Proc. Natl. Acad. Sci. USA 102, 10451–10453 (2005).
[Crossref]

Scully, M. O.

Z. He, D. V. Voronine, A. M. Sinyukov, Z. N. Liege, B. Birmingham, A. V. Sokolov, Z. Zhang, and M. O. Scully, “Tip-enhanced Raman scattering on bulk MoS2 substrate,” IEEE J. Sel. Top. Quantum Electron. 23, 113–118 (2017).
[Crossref]

Shan, J.

K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, “Atomically thin MoS2: a new direct-gap semiconductor,” Phys. Rev. Lett. 105, 136805 (2010).
[Crossref]

Silvain, J. F.

D. Li, W. Xiong, L. Jiang, Z. Xiao, H. R. Golgir, M. Wang, X. Huang, Y. Zhou, Z. Lin, J. Song, S. Ducharme, L. Jiang, J. F. Silvain, and Y. Lu, “Multimodal nonlinear optical imaging of MoS2 and MoS2-based van der Waals heterostructures,” ACS Nano 10, 3766–3775 (2016).
[Crossref]

Sinyukov, A. M.

Z. He, D. V. Voronine, A. M. Sinyukov, Z. N. Liege, B. Birmingham, A. V. Sokolov, Z. Zhang, and M. O. Scully, “Tip-enhanced Raman scattering on bulk MoS2 substrate,” IEEE J. Sel. Top. Quantum Electron. 23, 113–118 (2017).
[Crossref]

Soh, D. B. S.

D. B. S. Soh, C. Rogers, D. J. Gray, E. Chatterjee, and H. Mabuchi, “Optical nonlinearities of excitons in monolayer MoS2,” Phys. Rev. B 97, 165111 (2018).
[Crossref]

Sokolov, A. V.

Z. He, D. V. Voronine, A. M. Sinyukov, Z. N. Liege, B. Birmingham, A. V. Sokolov, Z. Zhang, and M. O. Scully, “Tip-enhanced Raman scattering on bulk MoS2 substrate,” IEEE J. Sel. Top. Quantum Electron. 23, 113–118 (2017).
[Crossref]

Song, J.

D. Li, W. Xiong, L. Jiang, Z. Xiao, H. R. Golgir, M. Wang, X. Huang, Y. Zhou, Z. Lin, J. Song, S. Ducharme, L. Jiang, J. F. Silvain, and Y. Lu, “Multimodal nonlinear optical imaging of MoS2 and MoS2-based van der Waals heterostructures,” ACS Nano 10, 3766–3775 (2016).
[Crossref]

Splendiani, A.

A. Splendiani, L. Sun, Y. Zhang, T. Li, J. Kim, C. Y. Chim, G. Galli, and F. Wang, “Emerging photoluminescence in monolayer MoS2,” Nano Lett. 10, 1271–1275 (2010).
[Crossref]

Strempel, J.

J. Strempel and W. Kiefer, “Polarized and depolarized continuum resonance Raman scattering of molecular iodine: accurate determination of repulsive states,” Can. J. Chem. 69, 1732–1739 (1991).
[Crossref]

Sun, L.

A. Splendiani, L. Sun, Y. Zhang, T. Li, J. Kim, C. Y. Chim, G. Galli, and F. Wang, “Emerging photoluminescence in monolayer MoS2,” Nano Lett. 10, 1271–1275 (2010).
[Crossref]

Tay, B. K.

H. Li, Q. Zhang, C. C. R. Yap, B. K. Tay, T. H. T. Edwin, A. Olivier, and D. Baillargeat, “From bulk to monolayer MoS2: evolution of Raman scattering,” Adv. Funct. Mater. 22, 1385–1390 (2012).
[Crossref]

Teer, D. G.

N. M. Renevier, N. Lobiondo, V. C. Fox, D. G. Teer, and J. Hampshire, “Performance of MoS2/metal composite coatings used for dry machining and other industrial applications,” Surf. Coat. Technol. 123, 84–91 (2000).
[Crossref]

Tian, Z.-Q.

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

Voronine, D. V.

Z. He, D. V. Voronine, A. M. Sinyukov, Z. N. Liege, B. Birmingham, A. V. Sokolov, Z. Zhang, and M. O. Scully, “Tip-enhanced Raman scattering on bulk MoS2 substrate,” IEEE J. Sel. Top. Quantum Electron. 23, 113–118 (2017).
[Crossref]

Wada, A.

C. Hirose, H. Ishida, K. Iwatsu, N. Watanabe, J. Kubota, A. Wada, and K. Domen, “In situ SFG spectroscopy of film growth. I. General formulation and the analysis of the signal observed during the deposition of formic acid on Pt(110)-(1×2) surface,” J. Chem. Phys. 108, 5948–5956 (1998).
[Crossref]

Wang, F.

A. Splendiani, L. Sun, Y. Zhang, T. Li, J. Kim, C. Y. Chim, G. Galli, and F. Wang, “Emerging photoluminescence in monolayer MoS2,” Nano Lett. 10, 1271–1275 (2010).
[Crossref]

Wang, J.

Y. Li, N. Dong, S. Zhang, X. Zhang, Y. Feng, K. Wang, L. Zhang, and J. Wang, “Giant two-photon absorption in monolayer MoS2,” Laser Photon. Rev. 9, 427–434 (2015).
[Crossref]

F. Zahid, L. Liu, Y. Zhu, J. Wang, and H. Guo, “A generic tight-binding model for monolayer, bilayer and bulk MoS2,” AIP Adv. 3, 052111 (2013).
[Crossref]

Wang, K.

Y. Li, N. Dong, S. Zhang, X. Zhang, Y. Feng, K. Wang, L. Zhang, and J. Wang, “Giant two-photon absorption in monolayer MoS2,” Laser Photon. Rev. 9, 427–434 (2015).
[Crossref]

Wang, M.

D. Li, W. Xiong, L. Jiang, Z. Xiao, H. R. Golgir, M. Wang, X. Huang, Y. Zhou, Z. Lin, J. Song, S. Ducharme, L. Jiang, J. F. Silvain, and Y. Lu, “Multimodal nonlinear optical imaging of MoS2 and MoS2-based van der Waals heterostructures,” ACS Nano 10, 3766–3775 (2016).
[Crossref]

Wang, R.

R. Wang, H. C. Chien, J. Kumar, N. Kumar, H. Y. Chiu, and H. Zhao, “Third-harmonic generation in ultrathin films of MoS2,” ACS Appl. Mater. Interface 6, 314–318 (2014).
[Crossref]

Wang, Z.

Z. Wang, Z. Dong, Y. Gu, Y. H. Chang, L. Zhang, L. J. Li, W. Zhao, G. Eda, W. Zhang, G. Grinblat, S. A. Maier, J. K. Yang, C. W. Qiu, and A. T. Wee, “Giant photoluminescence enhancement in tungsten-diselenide-gold plasmonic hybrid structures,” Nat. Commun. 7, 11283 (2016).
[Crossref]

Watanabe, N.

C. Hirose, H. Ishida, K. Iwatsu, N. Watanabe, J. Kubota, A. Wada, and K. Domen, “In situ SFG spectroscopy of film growth. I. General formulation and the analysis of the signal observed during the deposition of formic acid on Pt(110)-(1×2) surface,” J. Chem. Phys. 108, 5948–5956 (1998).
[Crossref]

Wee, A. T.

Z. Wang, Z. Dong, Y. Gu, Y. H. Chang, L. Zhang, L. J. Li, W. Zhao, G. Eda, W. Zhang, G. Grinblat, S. A. Maier, J. K. Yang, C. W. Qiu, and A. T. Wee, “Giant photoluminescence enhancement in tungsten-diselenide-gold plasmonic hybrid structures,” Nat. Commun. 7, 11283 (2016).
[Crossref]

Whitwick, M. B.

B. Radisavljevic, M. B. Whitwick, and A. Kis, “Integrated circuits and logic operations based on single-layer MoS2,” ACS Nano 5, 9934–9938 (2011).
[Crossref]

Woodward, R. I.

R. I. Woodward, R. T. Murray, C. F. Phelan, R. E. P. D. Oliveira, T. H. Runcorn, E. J. R. Kelleher, S. Li, E. C. D. Oliveira, G. J. M. Fechine, G. Eda, and C. J. S. D. Matos, “Characterization of the second- and third-order nonlinear optical susceptibilities of monolayer MoS2 using multiphoton microscopy,” 2D Mater. 4, 011006 (2016).
[Crossref]

Wu, D.-Y.

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

Wysmolek, A.

K. Gołasa, M. Grzeszczyk, R. Bożek, P. Leszczyński, A. Wysmołek, M. Potemski, and A. Babiński, “Resonant Raman scattering in MoS2—from bulk to monolayer,” Solid State Commun. 197, 53–56 (2014).
[Crossref]

Xiao, Z.

D. Li, W. Xiong, L. Jiang, Z. Xiao, H. R. Golgir, M. Wang, X. Huang, Y. Zhou, Z. Lin, J. Song, S. Ducharme, L. Jiang, J. F. Silvain, and Y. Lu, “Multimodal nonlinear optical imaging of MoS2 and MoS2-based van der Waals heterostructures,” ACS Nano 10, 3766–3775 (2016).
[Crossref]

Xiong, W.

D. Li, W. Xiong, L. Jiang, Z. Xiao, H. R. Golgir, M. Wang, X. Huang, Y. Zhou, Z. Lin, J. Song, S. Ducharme, L. Jiang, J. F. Silvain, and Y. Lu, “Multimodal nonlinear optical imaging of MoS2 and MoS2-based van der Waals heterostructures,” ACS Nano 10, 3766–3775 (2016).
[Crossref]

Yang, J. K.

Z. Wang, Z. Dong, Y. Gu, Y. H. Chang, L. Zhang, L. J. Li, W. Zhao, G. Eda, W. Zhang, G. Grinblat, S. A. Maier, J. K. Yang, C. W. Qiu, and A. T. Wee, “Giant photoluminescence enhancement in tungsten-diselenide-gold plasmonic hybrid structures,” Nat. Commun. 7, 11283 (2016).
[Crossref]

Yap, C. C. R.

H. Li, Q. Zhang, C. C. R. Yap, B. K. Tay, T. H. T. Edwin, A. Olivier, and D. Baillargeat, “From bulk to monolayer MoS2: evolution of Raman scattering,” Adv. Funct. Mater. 22, 1385–1390 (2012).
[Crossref]

Ye, Y.

X. Yin, Z. Ye, D. A. Chenet, Y. Ye, K. O’Brien, J. C. Hone, and X. Zhang, “Edge nonlinear optics on a MoS2 atomic monolayer,” Science 344, 488–490 (2014).
[Crossref]

Ye, Z.

X. Yin, Z. Ye, D. A. Chenet, Y. Ye, K. O’Brien, J. C. Hone, and X. Zhang, “Edge nonlinear optics on a MoS2 atomic monolayer,” Science 344, 488–490 (2014).
[Crossref]

Yi, J.

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

Yin, X.

X. Yin, Z. Ye, D. A. Chenet, Y. Ye, K. O’Brien, J. C. Hone, and X. Zhang, “Edge nonlinear optics on a MoS2 atomic monolayer,” Science 344, 488–490 (2014).
[Crossref]

Yoffe, A. D.

R. A. Bromley, R. B. Murray, and A. D. Yoffe, “The band structures of some transition metal dichalcogenides. III. Group VIA: trigonal prism materials,” J. Phys. C 5, 759–778 (1972).
[Crossref]

Zahid, F.

F. Zahid, L. Liu, Y. Zhu, J. Wang, and H. Guo, “A generic tight-binding model for monolayer, bilayer and bulk MoS2,” AIP Adv. 3, 052111 (2013).
[Crossref]

Zhang, J.

X. Ling, W. Fang, Y. H. Lee, P. T. Araujo, X. Zhang, J. F. Rodriguez-Nieva, Y. Lin, J. Zhang, J. Kong, and M. S. Dresselhaus, “Raman enhancement effect on two-dimensional layered materials: graphene, h-BN and MoS2,” Nano Lett. 14, 3033–3040 (2014).
[Crossref]

Zhang, L.

Z. Wang, Z. Dong, Y. Gu, Y. H. Chang, L. Zhang, L. J. Li, W. Zhao, G. Eda, W. Zhang, G. Grinblat, S. A. Maier, J. K. Yang, C. W. Qiu, and A. T. Wee, “Giant photoluminescence enhancement in tungsten-diselenide-gold plasmonic hybrid structures,” Nat. Commun. 7, 11283 (2016).
[Crossref]

Y. Li, N. Dong, S. Zhang, X. Zhang, Y. Feng, K. Wang, L. Zhang, and J. Wang, “Giant two-photon absorption in monolayer MoS2,” Laser Photon. Rev. 9, 427–434 (2015).
[Crossref]

Zhang, Q.

H. Li, Q. Zhang, C. C. R. Yap, B. K. Tay, T. H. T. Edwin, A. Olivier, and D. Baillargeat, “From bulk to monolayer MoS2: evolution of Raman scattering,” Adv. Funct. Mater. 22, 1385–1390 (2012).
[Crossref]

Zhang, S.

Y. Li, N. Dong, S. Zhang, X. Zhang, Y. Feng, K. Wang, L. Zhang, and J. Wang, “Giant two-photon absorption in monolayer MoS2,” Laser Photon. Rev. 9, 427–434 (2015).
[Crossref]

Zhang, W.

Z. Wang, Z. Dong, Y. Gu, Y. H. Chang, L. Zhang, L. J. Li, W. Zhao, G. Eda, W. Zhang, G. Grinblat, S. A. Maier, J. K. Yang, C. W. Qiu, and A. T. Wee, “Giant photoluminescence enhancement in tungsten-diselenide-gold plasmonic hybrid structures,” Nat. Commun. 7, 11283 (2016).
[Crossref]

Zhang, X.

Y. Li, N. Dong, S. Zhang, X. Zhang, Y. Feng, K. Wang, L. Zhang, and J. Wang, “Giant two-photon absorption in monolayer MoS2,” Laser Photon. Rev. 9, 427–434 (2015).
[Crossref]

X. Ling, W. Fang, Y. H. Lee, P. T. Araujo, X. Zhang, J. F. Rodriguez-Nieva, Y. Lin, J. Zhang, J. Kong, and M. S. Dresselhaus, “Raman enhancement effect on two-dimensional layered materials: graphene, h-BN and MoS2,” Nano Lett. 14, 3033–3040 (2014).
[Crossref]

X. Yin, Z. Ye, D. A. Chenet, Y. Ye, K. O’Brien, J. C. Hone, and X. Zhang, “Edge nonlinear optics on a MoS2 atomic monolayer,” Science 344, 488–490 (2014).
[Crossref]

Zhang, Y.

A. Splendiani, L. Sun, Y. Zhang, T. Li, J. Kim, C. Y. Chim, G. Galli, and F. Wang, “Emerging photoluminescence in monolayer MoS2,” Nano Lett. 10, 1271–1275 (2010).
[Crossref]

Zhang, Z.

Z. He, D. V. Voronine, A. M. Sinyukov, Z. N. Liege, B. Birmingham, A. V. Sokolov, Z. Zhang, and M. O. Scully, “Tip-enhanced Raman scattering on bulk MoS2 substrate,” IEEE J. Sel. Top. Quantum Electron. 23, 113–118 (2017).
[Crossref]

Zhao, H.

R. Wang, H. C. Chien, J. Kumar, N. Kumar, H. Y. Chiu, and H. Zhao, “Third-harmonic generation in ultrathin films of MoS2,” ACS Appl. Mater. Interface 6, 314–318 (2014).
[Crossref]

Zhao, W.

Z. Wang, Z. Dong, Y. Gu, Y. H. Chang, L. Zhang, L. J. Li, W. Zhao, G. Eda, W. Zhang, G. Grinblat, S. A. Maier, J. K. Yang, C. W. Qiu, and A. T. Wee, “Giant photoluminescence enhancement in tungsten-diselenide-gold plasmonic hybrid structures,” Nat. Commun. 7, 11283 (2016).
[Crossref]

Zhou, Y.

D. Li, W. Xiong, L. Jiang, Z. Xiao, H. R. Golgir, M. Wang, X. Huang, Y. Zhou, Z. Lin, J. Song, S. Ducharme, L. Jiang, J. F. Silvain, and Y. Lu, “Multimodal nonlinear optical imaging of MoS2 and MoS2-based van der Waals heterostructures,” ACS Nano 10, 3766–3775 (2016).
[Crossref]

Zhu, Y.

F. Zahid, L. Liu, Y. Zhu, J. Wang, and H. Guo, “A generic tight-binding model for monolayer, bilayer and bulk MoS2,” AIP Adv. 3, 052111 (2013).
[Crossref]

2D Mater. (1)

R. I. Woodward, R. T. Murray, C. F. Phelan, R. E. P. D. Oliveira, T. H. Runcorn, E. J. R. Kelleher, S. Li, E. C. D. Oliveira, G. J. M. Fechine, G. Eda, and C. J. S. D. Matos, “Characterization of the second- and third-order nonlinear optical susceptibilities of monolayer MoS2 using multiphoton microscopy,” 2D Mater. 4, 011006 (2016).
[Crossref]

ACS Appl. Mater. Interface (1)

R. Wang, H. C. Chien, J. Kumar, N. Kumar, H. Y. Chiu, and H. Zhao, “Third-harmonic generation in ultrathin films of MoS2,” ACS Appl. Mater. Interface 6, 314–318 (2014).
[Crossref]

ACS Nano (2)

D. Li, W. Xiong, L. Jiang, Z. Xiao, H. R. Golgir, M. Wang, X. Huang, Y. Zhou, Z. Lin, J. Song, S. Ducharme, L. Jiang, J. F. Silvain, and Y. Lu, “Multimodal nonlinear optical imaging of MoS2 and MoS2-based van der Waals heterostructures,” ACS Nano 10, 3766–3775 (2016).
[Crossref]

B. Radisavljevic, M. B. Whitwick, and A. Kis, “Integrated circuits and logic operations based on single-layer MoS2,” ACS Nano 5, 9934–9938 (2011).
[Crossref]

Adv. Funct. Mater. (1)

H. Li, Q. Zhang, C. C. R. Yap, B. K. Tay, T. H. T. Edwin, A. Olivier, and D. Baillargeat, “From bulk to monolayer MoS2: evolution of Raman scattering,” Adv. Funct. Mater. 22, 1385–1390 (2012).
[Crossref]

AIP Adv. (1)

F. Zahid, L. Liu, Y. Zhu, J. Wang, and H. Guo, “A generic tight-binding model for monolayer, bilayer and bulk MoS2,” AIP Adv. 3, 052111 (2013).
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J. Strempel and W. Kiefer, “Polarized and depolarized continuum resonance Raman scattering of molecular iodine: accurate determination of repulsive states,” Can. J. Chem. 69, 1732–1739 (1991).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

Z. He, D. V. Voronine, A. M. Sinyukov, Z. N. Liege, B. Birmingham, A. V. Sokolov, Z. Zhang, and M. O. Scully, “Tip-enhanced Raman scattering on bulk MoS2 substrate,” IEEE J. Sel. Top. Quantum Electron. 23, 113–118 (2017).
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J. Chem. Phys. (2)

J.-S. Park and T. Joo, “Nuclear dynamics in electronic ground and excited states probed by spectrally resolved four wave mixing,” J. Chem. Phys. 116, 10801–10808 (2002).
[Crossref]

C. Hirose, H. Ishida, K. Iwatsu, N. Watanabe, J. Kubota, A. Wada, and K. Domen, “In situ SFG spectroscopy of film growth. I. General formulation and the analysis of the signal observed during the deposition of formic acid on Pt(110)-(1×2) surface,” J. Chem. Phys. 108, 5948–5956 (1998).
[Crossref]

J. Phys. C (2)

A. R. Beal and H. P. Hughes, “Kramers-Kronig analysis of the reflectivity spectra of 2H-MoS2, 2H-MoSe2 and 2H-MoTe2,” J. Phys. C 12, 881–890 (1979).
[Crossref]

R. A. Bromley, R. B. Murray, and A. D. Yoffe, “The band structures of some transition metal dichalcogenides. III. Group VIA: trigonal prism materials,” J. Phys. C 5, 759–778 (1972).
[Crossref]

Laser Photon. Rev. (1)

Y. Li, N. Dong, S. Zhang, X. Zhang, Y. Feng, K. Wang, L. Zhang, and J. Wang, “Giant two-photon absorption in monolayer MoS2,” Laser Photon. Rev. 9, 427–434 (2015).
[Crossref]

Nano Lett. (2)

A. Splendiani, L. Sun, Y. Zhang, T. Li, J. Kim, C. Y. Chim, G. Galli, and F. Wang, “Emerging photoluminescence in monolayer MoS2,” Nano Lett. 10, 1271–1275 (2010).
[Crossref]

X. Ling, W. Fang, Y. H. Lee, P. T. Araujo, X. Zhang, J. F. Rodriguez-Nieva, Y. Lin, J. Zhang, J. Kong, and M. S. Dresselhaus, “Raman enhancement effect on two-dimensional layered materials: graphene, h-BN and MoS2,” Nano Lett. 14, 3033–3040 (2014).
[Crossref]

Nat. Commun. (1)

Z. Wang, Z. Dong, Y. Gu, Y. H. Chang, L. Zhang, L. J. Li, W. Zhao, G. Eda, W. Zhang, G. Grinblat, S. A. Maier, J. K. Yang, C. W. Qiu, and A. T. Wee, “Giant photoluminescence enhancement in tungsten-diselenide-gold plasmonic hybrid structures,” Nat. Commun. 7, 11283 (2016).
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Nat. Nanotechnol. (1)

B. Radisavljevic, A. Radenovic, J. Brivio, V. Giacometti, and A. Kis, “Single-layer MoS2 transistors,” Nat. Nanotechnol. 6, 147–150 (2011).
[Crossref]

Nat. Rev. Mater. (1)

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

Phys. Rev. B (4)

D. B. S. Soh, C. Rogers, D. J. Gray, E. Chatterjee, and H. Mabuchi, “Optical nonlinearities of excitons in monolayer MoS2,” Phys. Rev. B 97, 165111 (2018).
[Crossref]

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K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, “Atomically thin MoS2: a new direct-gap semiconductor,” Phys. Rev. Lett. 105, 136805 (2010).
[Crossref]

Proc. Natl. Acad. Sci. USA (1)

K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim, “Two-dimensional atomic crystals,” Proc. Natl. Acad. Sci. USA 102, 10451–10453 (2005).
[Crossref]

Science (1)

X. Yin, Z. Ye, D. A. Chenet, Y. Ye, K. O’Brien, J. C. Hone, and X. Zhang, “Edge nonlinear optics on a MoS2 atomic monolayer,” Science 344, 488–490 (2014).
[Crossref]

Solid State Commun. (1)

K. Gołasa, M. Grzeszczyk, R. Bożek, P. Leszczyński, A. Wysmołek, M. Potemski, and A. Babiński, “Resonant Raman scattering in MoS2—from bulk to monolayer,” Solid State Commun. 197, 53–56 (2014).
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Figures (11)

Fig. 1.
Fig. 1. Two pulses (ωp and ωSC) are incident on an MoS2 flake. Two photons of the pump pulse (ωp) and one photon of the supercontinuum pulse (ωSC) interact to produce a fourth (ωFWM).
Fig. 2.
Fig. 2. (a) Atomic force microscope (AFM) image of the MoS2 flake for the region of interest. (b) Cross section of the MoS2 flake along the white line in (a).
Fig. 3.
Fig. 3. Schematic of the multiplex femtosecond coherent anti-Stokes Raman spectroscopy setup. The laser provides 50 fs pulses with an 80 MHz repetition rate. RELP, razor-edge long-pass filter.
Fig. 4.
Fig. 4. (a) Optical microscope image of the MoS2 flake. Two different locations with different thicknesses are investigated (blue, 290 nm; orange, 120 nm). FWM signal obtained from the (b) orange spot and (c) blue spot in (a). The FWM spectra are characterized by a large peak (red) with high variance in the center wavelength due to thin film interference, a more stable peak (blue) centered at approximately 680 nm from the excitonic resonances, and a small peak (green) that represents the coherent anti-Stokes Raman signal of MoS2.
Fig. 5.
Fig. 5. Photoluminescence intensity dependence for (a) pump and (b) supercontinuum pulses on the 290 nm section of the MoS2 flake. The quadratic dependence of the FWM signal on the pump power corresponds to requiring two pump photons for the process, while the linear dependence on the supercontinuum indicates that a single supercontinuum photon is used. Insets show the photoluminescence spectrum as pulse power is modulated. Enlarged insets can be found in Appendix C.
Fig. 6.
Fig. 6. Four-wave mixing spectra of the MoS2 flake with different bandpass filters placed in the supercontinuum pulse path. The numbers indicate the central wavelength of the filters, and the pump pulse is located at wavelength of 806 nm.
Fig. 7.
Fig. 7. (a) Optical microscope image of the MoS2 flake. (b) Four-wave mixing spectra obtained at positions A–C marked in (a). (c) Four-wave mixing spectra obtained at positions D–F marked in (a).
Fig. 8.
Fig. 8. Spectrum obtained at the two locations depicted in Fig. 4(a) by blocking individual pulses. Unblocked spectrum (both pulse trains) is shown in black, supercontinuum only (pump blocked) in blue, and pump only (supercontinuum blocked) in red.
Fig. 9.
Fig. 9. Spectra (solid lines) and fitted peaks (dashed lines) of the MoS2 flake as the power of each pulse is modulated (other pulse’s power held constant). Lorentzian peak fitting was done on each spectrum and the area of the 680 nm peak was calculated.
Fig. 10.
Fig. 10. Measured spectrum of the supercontinuum pulse incident on the (a) blue and (b) orange spots in Fig. 4(a). Spectra were obtained by blocking the pump pulse and removing the short-pass filters that block the incident pulses. A neutral density filter was placed to prevent saturation while maintaining the spectral character.
Fig. 11.
Fig. 11. B excitonic resonance of MoS2 at the blue spot of Fig. 4(a) (thickness of 290 nm). The energy of the B exciton corresponds to a wavelength of approximately 600 nm.

Equations (17)

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ISpectrumIpumpmISCn,
ωFWM=2ωpumpωSC.
dasdz=iγ(aa*+2as)daadz=iγ(as*+2aa),
γ=3η0ωp2ap2χ(3)ε0cn2,
χ(3)=ηαe2τ16πmeh*ωa3,
aa(z)=iγas*z.
aaωp2ωa3ap2as*z,
χ(3)=ηαnce2τL16πmeh*ωa3,
χ(3)=2.04×1019m2V2.
PFWMCountss×Photonscount×energyphoton.
P¯i=18(πln2)32fτW2Ii,
Ii=niϵ0c|εi|22.
P¯i=kni|εi|2,
k=116(πln2)32fτW2ϵ0c=2.522×1019m2·CV·s,
εFWM=i4ωFWM2nFWMcχ(3)|εP|2εSC.
χ(3)=8kcωFWMd1P¯p(P¯FWMP¯SC)12nPnSC12nFWM12.
χ(3)=1.8278×1019m2V2,