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DOI: 10.1039/D0NR01994A
(Paper)
Nanoscale, 2020, Advance Article

Yadong Wang^{ab},
Masood Ghotbi*^{c},
Susobhan Das^{b},
Yunyun Dai^{b},
Shisheng Li^{d},
Xuerong Hu^{be},
Xuetao Gan^{a},
Jianlin Zhao*^{a} and
Zhipei Sun*^{b}
^{a}MOE Key Laboratory of Material Physics and Chemistry under Extraordinary Conditions, and Shaanxi Key Laboratory of Optical Information Technology, School of Physical Science and Technology, Northwestern Polytechnical University, Xi'an 710129, China. E-mail: jlzhao@nwpu.edu.cn
^{b}Department of Electronics and Nanoengineering, Aalto University, Fi-00076 Aalto, Finland. E-mail: zhipei.sun@aalto.fi
^{c}Department of Physics, University of Kurdistan, P.O. Box 66177-15175, Sanandaj, Iran. E-mail: m.ghotbi@uok.ac.ir
^{d}International Center for Young Scientists (ICYS), National Institute for Materials Science (NIMS), Tsukuba, Japan
^{e}Institute of Photonics and Photon Technology, Northwest University, Xi'an 710069, China

Received
10th March 2020
, Accepted 28th May 2020

First published on 28th May 2020

Difference frequency generation has long been employed for numerous applications, such as coherent light generation, sensing and imaging. Here, we demonstrate difference frequency generation down to atomic thickness in monolayer molybdenum disulfide. By mixing femtosecond optical pulses at wavelength of 406 nm with tunable pulses in the spectral range of 1300–1520 nm, we generate tunable pulses across the spectral range of 550–590 nm with frequency conversion efficiency up to ∼2 × 10^{−4}. The second-order nonlinear optical susceptibility of monolayer molybdenum disulfide, χ^{(2)}_{eff}, is calculated as ∼1.8 × 10^{−8} m V^{−1}, comparable to the previous results demonstrated with second harmonic generation. Such a highly efficient down-conversion nonlinear optical process in two-dimensional layered materials may open new ways to their nonlinear optical applications, such as coherent light generation and amplification.

Currently, there are major obstacles in scaling down the nonlinear frequency conversion systems to micro- and nano-scale regimes for various emerging applications, mainly due to the relatively low optical nonlinearity coefficients of the traditional bulk nonlinear optical materials. Introducing the two-dimensional (2D) layered materials with extraordinarily strong nonlinear optical responses for frequency conversions, has created new possibilities for potential on-chip applications.^{6,7} For example, monolayer transition-metal dichalcogenides (TMDs) have been demonstrated with strong second-, third- and high-order nonlinearities.^{8–12}

Among the second-order frequency conversion nonlinear interactions, second harmonic generation (SHG) and sum frequency generation (SFG) are the common processes that generate light with wavelengths shorter than that of input beams (i.e., up-conversion interactions). Because of its simple implementation, by applying only one input light component as the fundamental beam, SHG has been performed widely in different 2D materials including MoS_{2},^{11–16} MoSe_{2},^{17,18} WS_{2},^{19,20} WSe_{2},^{21} and MoTe_{2}.^{22} Similarly, SFG in TMDs has also been reported in recent years.^{23–25}

In contrast to the SHG and SFG processes, DFG is a frequency down-conversion second-order nonlinear interaction, thus extending the application range of nonlinear processes to various fields. The exploration of such a process in nanoscale is highly important,^{26} especially in 2D materials. Thus far, DFG in graphene has been observed in terahertz region.^{27,28} For example, with assistance of graphene plasmon, the photon efficiency of DFG can be as high as 10^{–5} under specific in-plane phase-matching conditions.^{28}

Here, we report the DFG by using monolayer MoS_{2} to produce tunable femtosecond pulses in the visible spectral range of 550–590 nm. Such a nonlinear optical interaction can also be a foundation for other down-conversion interactions, including OPG, OPA, as well as OPO.

Fig. 2(a) shows an illustration of the DFG process in monolayer MoS_{2}, where a pump photon stimulated by a signal photon, generates two photons at different frequencies (the one with same frequency of signal photon is called signal and the other one is called idler). Therefore, this process typically results in the generation of the idler beam at new wavelengths and the amplification of the incident signal beam. The frequencies of newly generated photons follow the law of energy conservation (i.e., ω_{idler}=ω_{pump}−ω_{signal}). The right panel in Fig. 2(a) shows the energy level diagram of DFG.

To perform the DFG interaction, we built an experimental setup as shown in Fig. 2(b). The femtosecond (∼150 fs) pulses from an amplified Ti:sapphire laser system at the wavelength of 812 nm with a repetition rate of 2 kHz is employed as the light source. The output beam is first divided into two beams, one is applied for the generation of pump pulses at 406 nm via frequency doubling in a BiBO crystal and the other for generating the tunable near-infrared pulses (1300 to 1550 nm) by pumping a TOPAS system (Light conversion). The pump and signal beams are combined by a dichroic mirror (DM) and then focused by an objective (40×, NA. 0.75) on the target sample. The full width at half maximum of the pump and signal beam spots is ∼2.5 μm. A delay line is employed in order to synchronize pump and signal pulses. The generated idler is then collected with the same objective lens by a reflection configuration and finally focused into a monochromator followed by a photomultiplier tube (PMT). Colour filters are also used in order to get rid of the residual pump and signal pulses before the monochromator. It should be noted that the repetition rate of our applied laser source (2 kHz) is much lower than the ones (∼tens of MHz) typically applied in the previously reported SHG experiments. While such a low repetition rate will not affect the conversion efficiency, it allows advantages including the reduction of the photon-excited luminescence and the thermal effects.

In order to estimate the effective second-order nonlinear susceptibility χ^{(2)}_{eff}of monolayer MoS_{2}, we simulated the nonlinear optical process in monolayer flake with the coupled-wave equations. Since the thickness of monolayer MoS_{2} (L=∼0.65 nm) is much smaller than the interacting wavelengths and the DFG is generated within only one layer of molecules, no phase matching consideration is needed. By solving the coupled-wave equations, the χ^{(2)}_{eff}in the DFG process can be written as^{2}

(1) |

As shown in Fig. 3(c), the generated idler power at 595 nm can be as high as 120 pW, when the signal power is ∼10.5 μW and pump power is ∼0.9 μW. This corresponds to a second-order nonlinear susceptibility χ^{(2)}_{eff}of ∼1.8 × 10^{−8} m V^{−1}, which is comparable to the reported values for MoS_{2} in earlier works.^{12,14} It should be mentioned that the imperfect temporal and spatial overlaps between the two interacting input pulses in the DFG interaction will notably reduce the interaction efficiency in comparison to the SHG process. In addition, we assume that the substrate introduced doping,^{33} strain,^{18} and interference^{34} effects are to be small in our experiment. In the current condition, the maximum quantum conversion efficiency from the pump to the idler in our DFG process is calculated as ∼2 × 10^{−4}.

We also investigated the relations among polarization directions of the interacting components in the DFG interaction. The structural symmetry group of bulk MoS_{2} is D_{6h} with inversion symmetry which leads to zero second-order nonlinearity. While the structural symmetry group of monolayer MoS_{2} is D_{3h} with broken inversion symmetry and having strong χ^{(2)} supporting highly efficient second-order nonlinear optical responses.^{13,16} In the x′y′z′ crystalline coordinates, the four nonzero elements of χ^{(2)} tensor for monolayer MoS_{2} are −χ^{(2)}_{y′x′x′} = χ^{(2)}_{y′y′y′} = −χ^{(2)}_{x′y′x′} = −χ^{(2)}_{x′x′y′}. In the case of SHG process, the scenario for the polarizations of the interacting beams is simple because of the presence of only one input beam and one output beam as the SHG: the SH radiation components detected in directions parallel and perpendicular to the polarization of the fundamental field are highly dependent on the azimuthal angle.^{13}

Regarding that the DFG interaction is a three-wave interaction: with the pump and signal incident pulses as the input beams and idler as the output, the situation is more complicated and the possible combinations of the relative polarization orientations between each interacting beam and the crystalline axes are increased. In order to check the compatibility of the obtained results with the symmetrical constraints imposed by the D_{3h} symmetry of MoS_{2}, we performed the analytical calculations for determining the dependence of the generated DFG polarization on the polarization orientations of the input (pump and signal) beams. Supposing the crystal surface in the xy plane and the -z as the propagation direction of the input pump and signal beams in the lab frame xyz, we consider β as the angle between the x direction and the crystal armchair direction x′, and also α_{id}, α_{p} and α_{si} as the angles between the idler, pump and signal polarizations, relative to the x direction, respectively. After calculating the components of the generated DFG idler in x′y′z′ (z′ = z) coordinates we will have

(E_{id})_{x′} ∝ − sin(2β + α_{si} + α_{p})
| (2a) |

(E_{id})_{y′} ∝ − cos(2β + α_{si} + α_{p})
| (2b) |

(E_{id})_{x} ∝ − sin(3β + α_{si} + α_{p})
| (3a) |

(E_{id})_{y} ∝ − cos(3β + α_{si} + α_{p})
| (3b) |

(4) |

To investigate the generated idler polarization experimentally, we measured the polarization dependence of the generated DFG pulses on the polarization orientations of two input beams. Both the idler and pump polarization orientations were measured relative to the fixed signal polarization which is supposed to be along the x direction (α_{si}=0). The angular dependence of the idler power for each pump polarization direction was measured by using a linear polarizer before the detector. The results of such measurement at the pump polarization angle of α_{p} = 0° are shown in Fig. 4(a) which also confirms the linear polarization of the generated idler pulse. As shown in Fig. 4(b), the linear polarization angles of the idler for different pump polarization orientations are measured. The polarization angles of the idler light (blue dots) show a good agreement with the calculation (eqn (4), red curve). The results confirm the linear dependence of the polarization orientation of the idler beam on the angle between the polarization of each input beam and the crystalline axis x′ as demonstrated in eqn (4).

The corresponding behaviour of the MoS_{2} monolayers for the DFG at different wavelengths across our available spectral range is also investigated. With the advantage of independence from the limiting phase-matching conditions, in monolayer MoS_{2} the nonlinear interactions can be performed across a broad spectral bandwidth. The wavelength of the DFG idler was tuned from 550 to 590 nm by changing the wavelength of signal from 1520 to 1300 nm with the pump wavelength fixed at 406 nm. The experimental data of the generated idler spectra and the Lorentz fitting curves at each wavelength are shown in Fig. 5. The higher generated idler intensities in the spectral region of 570–590 nm could be attributed to the presence of the resonant excitonic effects in this region.^{35,36}

Performing the DFG process is a confirmation for the possibility of realizing effective optical parametric interactions. In our experiment, the quantum conversion efficiency is about 2 × 10^{−4}, which is much higher than that of the most nonlinear responses in monolayer structures. However, because of the practical difficulties, the demonstration of a more efficient OPA process is still far from the reach. In order to improve the conversion efficiency, the exciton enhancement in single-layer TMDs could be employed as an effective solution in the future explorations.^{21} While the atomic thickness of monolayer TMDs (∼0.65 nm for MoS_{2}) physically limits the light–matter interaction length, 3R-type bulk MoS_{2} with broken inversion symmetry enables strong second-order nonlinear processes, offering a possible method for efficiency improvement.^{16,37} On the other hand, integrating monolayer TMDs and other 2D materials with external cavities (such as photonic-crystal nanocavity, micro-ring resonator, whispering-gallery cavity and metallic plasmonics), or waveguides (including microfibers, on-chip waveguides) is also promising for further improvements,^{6,38} due to the easy and flexible integration advantages of 2D materials. Furthermore, with assistance of the cavities, OPO operation with 2D materials could be achieved.^{39}

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