Crossref journal-article
Springer Science and Business Media LLC
Nature Communications (297)
Abstract

AbstractNonlinear optical processes, such as harmonic generation, are of great interest for various applications, e.g., microscopy, therapy, and frequency conversion. However, high-order harmonic conversion is typically much less efficient than low-order, due to the weak intrinsic response of the higher-order nonlinear processes. Here we report ultra-strong optical nonlinearities in monolayer MoS2 (1L-MoS2): the third harmonic is 30 times stronger than the second, and the fourth is comparable to the second. The third harmonic generation efficiency for 1L-MoS2 is approximately three times higher than that for graphene, which was reported to have a large χ(3). We explain this by calculating the nonlinear response functions of 1L-MoS2 with a continuum-model Hamiltonian and quantum mechanical diagrammatic perturbation theory, highlighting the role of trigonal warping. A similar effect is expected in all other transition-metal dichalcogenides. Our results pave the way for efficient harmonic generation based on layered materials for applications such as microscopy and imaging.

Bibliography

Säynätjoki, A., Karvonen, L., Rostami, H., Autere, A., Mehravar, S., Lombardo, A., Norwood, R. A., Hasan, T., Peyghambarian, N., Lipsanen, H., Kieu, K., Ferrari, A. C., Polini, M., & Sun, Z. (2017). Ultra-strong nonlinear optical processes and trigonal warping in MoS2 layers. Nature Communications, 8(1).

Authors 14
  1. Antti Säynätjoki (first)
  2. Lasse Karvonen (additional)
  3. Habib Rostami (additional)
  4. Anton Autere (additional)
  5. Soroush Mehravar (additional)
  6. Antonio Lombardo (additional)
  7. Robert A. Norwood (additional)
  8. Tawfique Hasan (additional)
  9. Nasser Peyghambarian (additional)
  10. Harri Lipsanen (additional)
  11. Khanh Kieu (additional)
  12. Andrea C. Ferrari (additional)
  13. Marco Polini (additional)
  14. Zhipei Sun (additional)
References 70 Referenced 217
  1. Boyd, R. W. Nonlinear Optics (Academic Press, 2003).
  2. Pavone, F. S. & Campagnola, P. J. Second Harmonic Generation Imaging (Taylor & Francis, 2013).
  3. Saleh, B. E. A. & Teich, M. C. Fundamentals of Photonics (Academic Press, 2003).
  4. Willner, A. E., Khaleghi, S., Chitgarha, M. R. & Yilmaz, O. F. All-optical signal processing. J. Lightwave Technol 32, 660–680 (2014). (10.1109/JLT.2013.2287219) / J. Lightwave Technol by AE Willner (2014)
  5. Zipfel, W. R., Williams, R. M. & Webb, W. W. Nonlinear magic: multiphoton microscopy in the biosciences. Nat. Biotechnol. 21, 1369–1377 (2003). (10.1038/nbt899) / Nat. Biotechnol. by WR Zipfel (2003)
  6. Bhawalkar, J. D., He, G. S. & Prasad, P. N. Nonlinear multiphoton processes in organic and polymeric materials. Rep. Prog. Phys. 59, 1041 (1996). (10.1088/0034-4885/59/9/001) / Rep. Prog. Phys. by JD Bhawalkar (1996)
  7. Tsang, T. Y. F. Optical third-harmonic generation at interfaces. Phys. Rev. A 52, 4116 (1995). (10.1103/PhysRevA.52.4116) / Phys. Rev. A by TYF Tsang (1995)
  8. Karvonen, L. et al. Investigation of second-and third-harmonic generation in few-layer gallium selenide by multiphoton microscopy. Sci. Rep. 5, 10334 (2015). (10.1038/srep10334) / Sci. Rep. by L Karvonen (2015)
  9. Bonaccorso, F., Sun, Z., Hasan, T. & Ferrari, A. C. Graphene photonics and optoelectronics. Nat. Photon 4, 611–622 (2010). (10.1038/nphoton.2010.186) / Nat. Photon by F Bonaccorso (2010)
  10. Ferrari, A. C. et al. Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems. Nanoscale 7, 4598–4810 (2015). (10.1039/C4NR01600A) / Nanoscale by AC Ferrari (2015)
  11. Sun, Z., Martinez, A. & Wang, F. Optical modulators with 2D layered materials. Nat. Photon. 10, 227–238 (2016). (10.1038/nphoton.2016.15) / Nat. Photon. by Z Sun (2016)
  12. Mak, K. F., Lee, C., Hone, J., Shan, J. & Heinz, T. F. Atomically thin MoS2: a new direct-gap semiconductor. Phys. Rev. Lett. 105, 136805 (2010). (10.1103/PhysRevLett.105.136805) / Phys. Rev. Lett. by KF Mak (2010)
  13. Eda, G. et al. Photoluminescence from chemically exfoliated MoS2. Nano Lett. 11, 5111–5116 (2011). (10.1021/nl201874w) / Nano Lett. by G Eda (2011)
  14. Li, Y. et al. Probing symmetry properties of few-layer MoS2 and h-BN by optical second-harmonic generation. Nano Lett. 13, 3329–3333 (2013). (10.1021/nl401561r) / Nano Lett. by Y Li (2013)
  15. Kumar, N. et al. Second harmonic microscopy of monolayer MoS2. Phys. Rev. B 87, 161403 (2013). (10.1103/PhysRevB.87.161403) / Phys. Rev. B by N Kumar (2013)
  16. Wang, K. et al. Ultrafast saturable absorption of two-dimensional MoS2 nanosheets. ACS Nano 7, 9260–9267 (2013). (10.1021/nn403886t) / ACS Nano by K Wang (2013)
  17. Malard, L. M., Alencar, T. V., Barboza, A. P. M., Mak, K. F. & de Paula, A. M. Observation of intense second harmonic generation from MoS2 atomic crystals. Phys. Rev. B 87, 201401 (2013). (10.1103/PhysRevB.87.201401) / Phys. Rev. B by LM Malard (2013)
  18. Wang, R. et al. Third-harmonic generation in ultrathin films of MoS2. ACS Appl. Mater. Interfaces 6, 314–318 (2013). (10.1021/am4042542) / ACS Appl. Mater. Interfaces by R Wang (2013)
  19. Trolle, M. L., Seifert, G. & Pedersen, T. G. Theory of excitonic second-harmonic generation in monolayer MoS2. Phys. Rev. B 89, 235410 (2014). (10.1103/PhysRevB.89.235410) / Phys. Rev. B by ML Trolle (2014)
  20. Clark, D. et al. Strong optical nonlinearity of CVD-grown MoS2 monolayer as probed by wavelength-dependent second-harmonic generation. Phys. Rev. B 90, 121409 (2014). (10.1103/PhysRevB.90.121409) / Phys. Rev. B by D Clark (2014)
  21. Seyler, K. L. et al. Electrical control of second-harmonic generation in a WSe2 monolayer transistor. Nat. Nanotechnol 10, 407–411 (2015). (10.1038/nnano.2015.73) / Nat. Nanotechnol by KL Seyler (2015)
  22. Kuc, A., Zibouche, N. & Heine, T. Influence of quantum confinement on the electronic structure of the transition metal sulfide TS2. Phys. Rev. B 83, 245213 (2011). (10.1103/PhysRevB.83.245213) / Phys. Rev. B by A Kuc (2011)
  23. Kadantsev, E. S. & Hawrylak, P. Electronic structure of a single MoS2 monolayer. Solid State Commun 152, 909–913 (2012). (10.1016/j.ssc.2012.02.005) / Solid State Commun by ES Kadantsev (2012)
  24. Wang, Q. H., Kalantar-Zadeh, K., Kis, A., Coleman, J. N. & Strano, M. S. Electronics and optoelectronics of two-dimensional transition metal dichalcogenides. Nat. Nanotechnol 7, 699–712 (2012). (10.1038/nnano.2012.193) / Nat. Nanotechnol by QH Wang (2012)
  25. Shi, H., Pan, H., Zhang, Y.-W. & Yakobson, B. I. Quasiparticle band structures and optical properties of strained monolayer MoS2 and WS2. Phys. Rev. B 87, 155304 (2013). (10.1103/PhysRevB.87.155304) / Phys. Rev. B by H Shi (2013)
  26. Zahid, F., Liu, L., Zhu, Y., Wang, J. & Guo, H. A generic tight-binding model for monolayer, bilayer and bulk MoS2. AIP Adv. 3, 052111 (2013). (10.1063/1.4804936) / AIP Adv. by F Zahid (2013)
  27. Kormányos, A. et al. Monolayer MoS2: trigonal warping, the γ valley, and spin-orbit coupling effects. Phys. Rev. B 88, 045416 (2013). (10.1103/PhysRevB.88.045416) / Phys. Rev. B by A Kormányos (2013)
  28. Qiu, D. Y., Felipe, H. & Louie, S. G. Optical spectrum of MoS2: many-body effects and diversity of exciton states. Phys. Rev. Lett. 111, 216805 (2013). (10.1103/PhysRevLett.111.216805) / Phys. Rev. Lett. by DY Qiu (2013)
  29. Gibertini, M., Pellegrino, F. M., Marzari, N. & Polini, M. Spin-resolved optical conductivity of two-dimensional group-VIb transition-metal dichalcogenides. Phys. Rev. B 90, 245411 (2014). (10.1103/PhysRevB.90.245411) / Phys. Rev. B by M Gibertini (2014)
  30. Margulis, V. A., Muryumin, E. E. & Gaiduk, E. A. Optical second-harmonic generation from two-dimensional hexagonal crystals with broken space inversion symmetry. J. Phys. Condens. Matter 25, 195302 (2013). (10.1088/0953-8984/25/19/195302) / J. Phys. Condens. Matter by VA Margulis (2013)
  31. Wu, S. et al. Quantum-enhanced tunable second-order optical nonlinearity in bilayer graphene. Nano Lett. 12, 2032–2036 (2012). (10.1021/nl300084j) / Nano Lett. by S Wu (2012)
  32. Brun, S. J. & Pedersen, T. G. Intense and tunable second-harmonic generation in biased bilayer graphene. Phys. Rev. B 91, 205405 (2015). (10.1103/PhysRevB.91.205405) / Phys. Rev. B by SJ Brun (2015)
  33. Hipolito, F., Pedersen, T. G. & Pereira, V. M. Nonlinear photocurrents in two-dimensional systems based on graphene and boron nitride. Phys. Rev. B 94, 045434 (2016). (10.1103/PhysRevB.94.045434) / Phys. Rev. B by F Hipolito (2016)
  34. Xiao, D., Liu, G.-B., Feng, W., Xu, X. & Yao, W. Coupled spin and valley physics in monolayers of MoX2 and other group-vi dichalcogenides. Phys. Rev. Lett. 108, 196802 (2012). (10.1103/PhysRevLett.108.196802) / Phys. Rev. Lett. by D Xiao (2012)
  35. Rostami, H., Roldán, R., Cappelluti, E., Asgari, R. & Guinea, F. Theory of strain in single-layer transition metal dichalcogenides. Phys. Rev. B 92, 195402 (2015). (10.1103/PhysRevB.92.195402) / Phys. Rev. B by H Rostami (2015)
  36. Rostami, H., Asgari, R. & Guinea, F. Edge modes in zigzag and armchair ribbons of monolayer MoS2. J. Phys. Condens. Matter 28, 495001 (2016). (10.1088/0953-8984/28/49/495001) / J. Phys. Condens. Matter by H Rostami (2016)
  37. Rostami, H., Moghaddam, A. G. & Asgari, R. Effective lattice hamiltonian for monolayer MoS2: tailoring electronic structure with perpendicular electric and magnetic fields. Phys. Rev. B 88, 085440 (2013). (10.1103/PhysRevB.88.085440) / Phys. Rev. B by H Rostami (2013)
  38. Alidoust, N. et al. Observation of monolayer valence band spin-orbit effect and induced quantum well states in MoX2. Nat. Commun 5, 4673 (2014). (10.1038/ncomms5673) / Nat. Commun by N Alidoust (2014)
  39. Rostami, H. & Polini, M. Theory of third-harmonic generation in graphene: a diagrammatic approach. Phys. Rev. B 93, 161411 (2016). (10.1103/PhysRevB.93.161411) / Phys. Rev. B by H Rostami (2016)
  40. Bonaccorso, F. et al. Production and processing of graphene and 2d crystals. Mater. Today 15, 564–589 (2012). (10.1016/S1369-7021(13)70014-2) / Mater. Today by F Bonaccorso (2012)
  41. Sundaram, R. et al. Electroluminescence in single layer MoS2. Nano Lett. 13, 1416–1421 (2013). (10.1021/nl400516a)
  42. Casiraghi, C. et al. Rayleigh imaging of graphene and graphene layers. Nano Lett. 7, 2711–7 (2007). (10.1021/nl071168m) / Nano Lett. by C Casiraghi (2007)
  43. Zhang, X. et al. Raman spectroscopy of shear and layer breathing modes in multilayer MoS2. Phys. Rev. B 87, 115413 (2013). (10.1103/PhysRevB.87.115413) / Phys. Rev. B by X Zhang (2013)
  44. Säynätjoki, A. et al. Rapid large-area multiphoton microscopy for characterization of graphene. ACS Nano 7, 8441–8446 (2013). (10.1021/nn4042909) / ACS Nano by A Säynätjoki (2013)
  45. Kieu, K., Jones, R. J. & Peyghambarian, N. Generation of few-cycle pulses from an amplified carbon nanotube mode-locked fiber laser system. IEEE Photon. Technol. Lett. 22, 1521–1523 (2010). (10.1109/LPT.2010.2063423) / IEEE Photon. Technol. Lett. by K Kieu (2010)
  46. Kieu, K., Jones, R. J. & Peyghambarian, N. High power femtosecond source near 1 micron based on an all-fiber er-doped mode-locked laser. Opt. Express 18, 21350–21355 (2010). (10.1364/OE.18.021350) / Opt. Express by K Kieu (2010)
  47. Miller, R. C. Optical second harmonic generation in piezoelectric crystals. Appl. Phys. Lett. 5, 17–19 (1964). (10.1063/1.1754022) / Appl. Phys. Lett. by RC Miller (1964)
  48. Chin, A. H., Calderón, O. G. & Kono, J. Extreme midinfrared nonlinear optics in semiconductors. Phys. Rev. Lett. 86, 3292 (2001). (10.1103/PhysRevLett.86.3292) / Phys. Rev. Lett. by AH Chin (2001)
  49. Woodward, R. I. et al. Characterization of the second- and third-order nonlinear optical susceptibilities of monolayer MoS2 using multiphoton microscopy. 2D Mater 4, 011006 (2017). (10.1088/2053-1583/4/1/011006) / 2D Mater by RI Woodward (2017)
  50. Säynätjoki, A. et al. Ultra-strong nonlinear optical processes and trigonal warping in MoS2 layers. Preprint at https://arxiv.org/abs/1608.04101 (2016). (10.1038/s41467-017-00749-4)
  51. Clark, D. et al. Near bandgap second-order nonlinear optical characteristics of MoS2 monolayer transferred on transparent substrates. Appl. Phys. Lett. 107, 131113 (2015). (10.1063/1.4932134) / Appl. Phys. Lett. by D Clark (2015)
  52. Le, C. T. et al. Impact of selenium doping on resonant second harmonic generation in monolayer MoS2. ACS Photon. 4, 38–44 (2017). (10.1021/acsphotonics.6b00530) / ACS Photon. by CT Le (2017)
  53. Liu, H. et al. High-harmonic generation from an atomically thin semiconductor. Nat. Phys 13, 262–265 (2017). (10.1038/nphys3946) / Nat. Phys by H Liu (2017)
  54. Janisch, C. et al. Extraordinary second harmonic generation in tungsten disulfide monolayers. Sci. Rep. 4, 5530 (2014). (10.1038/srep05530)
  55. Le, C. T. et al. Nonlinear optical characteristics of monolayer MoSe2. Ann. Phys 528, 551–559 (2016). (10.1002/andp.201600006) / Ann. Phys by CT Le (2016)
  56. Kumar, N. et al. Third harmonic generation in graphene and few-layer graphite films. Phys. Rev. B 87, 121406 (2013). (10.1103/PhysRevB.87.121406) / Phys. Rev. B by N Kumar (2013)
  57. Hendry, E., Hale, P. J., Moger, J., Savchenko, A. & Mikhailov, S. Coherent nonlinear optical response of graphene. Phys. Rev. Lett. 105, 097401 (2010). (10.1103/PhysRevLett.105.097401) / Phys. Rev. Lett. by E Hendry (2010)
  58. Cheng, J., Vermeulen, N. & Sipe, J. Third order optical nonlinearity of graphene. New J. Phys. 16, 053014 (2014). (10.1088/1367-2630/16/5/053014) / New J. Phys. by J Cheng (2014)
  59. Hong, S.-Y. et al. Optical third-harmonic generation in graphene. Phys. Rev. X 3, 021014 (2013). / Phys. Rev. X by S-Y Hong (2013)
  60. Neto, A. H. C., Guinea, F., Peres, N. M., Novoselov, K. S. & Geim, A. K. The electronic properties of graphene. Rev. Mod. Phys. 81, 109 (2009). (10.1103/RevModPhys.81.109) / Rev. Mod. Phys. by AHC Neto (2009)
  61. Nair, R. R. et al. Fine structure constant defines visual transparency of graphene. Science 320, 1308–1308 (2008). (10.1126/science.1156965) / Science by RR Nair (2008)
  62. Ramasubramaniam, A. Large excitonic effects in monolayers of molybdenum and tungsten dichalcogenides. Phys. Rev. B 86, 115409 (2012). (10.1103/PhysRevB.86.115409) / Phys. Rev. B by A Ramasubramaniam (2012)
  63. Cheiwchanchamnangij, T. & Lambrecht, W. R. L. Quasiparticle band structure calculation of monolayer, bilayer, and bulk MoS2. Phys. Rev. B 85, 205302 (2012). (10.1103/PhysRevB.85.205302) / Phys. Rev. B by T Cheiwchanchamnangij (2012)
  64. Mak, K. F. et al. Tightly bound trions in monolayer MoS2. Nat. Mater. 12, 207–211 (2013). (10.1038/nmat3505) / Nat. Mater. by KF Mak (2013)
  65. Grüning, M. & Attaccalite, C. Second harmonic generation in h-BN and MoS2 monolayers: role of electron-hole interaction. Phys. Rev. B 89, 081102 (2014). (10.1103/PhysRevB.89.081102) / Phys. Rev. B by M Grüning (2014)
  66. Wang, G. et al. Giant enhancement of the optical second-harmonic emission of WSe2 monolayers by laser excitation at exciton resonances. Phys. Rev. Lett. 114, 097403 (2015). (10.1103/PhysRevLett.114.097403) / Phys. Rev. Lett. by G Wang (2015)
  67. Haug, H. & Koch, S. W. Quantum Theory of the Optical and Electronic Properties of Semiconductors (World Scientific Publishing, 2009). (10.1142/7184)
  68. Zhu, S.-n, Zhu, Y.-y & Ming, N.-b Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice. Science 278, 843–846 (1997). (10.1126/science.278.5339.843) / Science by S-n Zhu (1997)
  69. Butcher, P. N. & Cotter, D. The Elements of Nonlinear Optics (Cambrige University Press, 1990). (10.1017/CBO9781139167994)
  70. Radisavljevic, B., Radenovic, A., Brivio, J., Giacometti, I. V. & Kis, A. Single-layer MoS2 transistors. Nat. Nanotechnol 6, 147–150 (2011). (10.1038/nnano.2010.279) / Nat. Nanotechnol by B Radisavljevic (2011)
Dates
Type When
Created 7 years, 10 months ago (Oct. 6, 2017, 11:13 a.m.)
Deposited 2 years, 8 months ago (Dec. 22, 2022, 4:16 p.m.)
Indexed 1 week ago (Aug. 23, 2025, 1:15 a.m.)
Issued 7 years, 10 months ago (Oct. 12, 2017)
Published 7 years, 10 months ago (Oct. 12, 2017)
Published Online 7 years, 10 months ago (Oct. 12, 2017)
Funders 0

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@article{S_yn_tjoki_2017, title={Ultra-strong nonlinear optical processes and trigonal warping in MoS2 layers}, volume={8}, ISSN={2041-1723}, url={http://dx.doi.org/10.1038/s41467-017-00749-4}, DOI={10.1038/s41467-017-00749-4}, number={1}, journal={Nature Communications}, publisher={Springer Science and Business Media LLC}, author={Säynätjoki, Antti and Karvonen, Lasse and Rostami, Habib and Autere, Anton and Mehravar, Soroush and Lombardo, Antonio and Norwood, Robert A. and Hasan, Tawfique and Peyghambarian, Nasser and Lipsanen, Harri and Kieu, Khanh and Ferrari, Andrea C. and Polini, Marco and Sun, Zhipei}, year={2017}, month=oct }