Optical Properties of TMDs

The optical properties of atomically thin 2D semiconductor TMDs are dominated by confinement effects related to carriers, excitons, and charged excitons that influence and can help to maximize linear and nonlinear interactions, also at room temperature, significantly contributing to the performance of TMDs in photonic devices. The following sessions are devoted to the linear and nonlinear optical properties of these materials.

2.3.2.1 Linear Optical Properties of TMDs

In monolayer TMDs, the direct bandgap increases the emission and absorption efficiency of photons with an energy equal to the bandgap, whereas indirect bandgap materials require additional phonon absorption or emission to compensate for the difference in momentum [82]. The stronger light-matter interaction in monolayer TMDs, therefore facilitates their use in diverse photonic applications.

Mak et al. [83] were the first to experimentally demonstrate the change of the bandgap in MoS2 with varying thicknesses through characterization by photoluminescence, absorption and photoconductivity spectroscopy. For mechanically exfoliated monolayer MoS2, the measured bandgap was of 1.84 eV. Other 2D semiconductor TMDs, such as WS2, WSe2

and MoSe2, with the same prismatic trigonal structure as MoS2, also exhibit direct bandgap for a single atomic layer and indirect bandgap for two layers or more. For MoS2, MoSe2, MoTe2, WS2 and WSe2, the usual direct optical bandgap values for a monolayer are of 1.9 eV, 1.57 eV, 1.08 eV, 1.97 eV, and 1.65 eV, respectively[84].

As previously mentioned, theoretical-experimental differences in the bandgap energy values tend to occur both due to the precision of the adopted computational methods and due to specific experimental conditions. The optical bandgap may vary with the used substrate and other experimental factors such as the quality and level of contamination of the materials. Thus, the choice of substrate and the use of clean and precise techniques for manipulation and synthesis of the 2D TMDs are of key importance so that the studies of its properties are reproducible and conclusive at the nanoscale.

For photonic applications based on linear optical effects, 2D TMDs are especially attractive because, despite the atomic thickness, they present strong electron-photon interaction[3], [85] especially at excitonic resonances[86], [87]. The strong interaction with light can be understood through the nature of the electronic and excitonic states of the material.

Singularities in the density of electronic states of TMDs ensure a strengthening of light-matter interactions, leading to an increase in photon absorption[3]. TMDs absorb more than 15% of the incoming light at the lowest excitonic resonance energy[88] despite their atomically thin character. Considering their thickness of 6 ~ 7 Å, they achieve one order of magnitude larger sunlight absorption than GaAs and Si, for example[89].

Excitonic resonances consist of energetically localized states, which enable the maximization of not only the linear but also the nonlinear optical effects. In the absence of

excitonic effects, the expected absorption for a monolayer MoS2 would be as shown by the blue (theoretical) curve in Figure 7. The experimental absorbance of a mechanically exfoliated MoS2

monolayer, however, presents characteristic and well-defined peaks as shown by the green line in the same figure. Two peaks, one at 1.92 eV and the other at 2.08 eV are associated with the formation of excitons known as A and B, respectively [14], [80]. Luminescence peaks associated with the recombination of these excitons are also observed in the PL spectrum.

Figure 7. Absorption spectrum of mechanically exfoliated monolayer MoS2 at low temperature (solid green line) with two prominent resonances, known as the A and B excitons. The blue dashed line shows the theoretical absorbance in the absence of excitonic effects. Reproduced with permission [14].

Copyright 2016, Springer Nature.

Cadiz et al. [90] also experimentally demonstrated how the strong light-matter interaction in TMDs behaves as a function of the temperature by photoluminescence measurements. The typical spectra for multi-layer TMDs deposited on a SiO2 substrate at room temperature can be observed in Figure 8(A). It is observed that MoS2 has the broadest PL emission at 300K, while WS2 multi-layer exhibit the narrowest emission. Figure 8(B) shows the PL spectra for the same TMDs at cryogenic temperature. While at room temperature the PL spectra of TMDs are determined by a broad peak corresponding to bright exciton transitions, at low temperatures a series of additional spectrally narrow resonances appears. These resonances can be ascribed to excitons trapped in local potential wells, due to the presence of impurities

and/or strain in realistic TMD samples. They vanish at higher temperatures, where the thermal energy is sufficient to overcome the trapping potential [88].

Figure 8. Typical PL spectra for different multilayer TMDs at 300 K (top) and 4 K (bottom) on a SiO2 substrate. Reproduced with permission [90]. Copyright 2017, American Physical Society.

Licensed under CC BY 4.0.

2.3.2.2 Nonlinear Optical Properties of TMDs

Another optical effect arising from light-matter interactions is second harmonic generation (SHG), the focus of this work, which is characterized by the conversion of incident light with a frequency ω, into 2ω. SHG is the lowest-order frequency conversion nonlinear optical process and plays an important role in frequency conversion devices. Third harmonic generation (THG) and high harmonic generation (HHR) are also important nonlinear optical processes, following the same frequency conversion principle under intense laser light illumination. Several studies have shown that TMDs are extremely promising in terms of efficiency for SHG and other nonlinear processes. In this section we will focus on the literature review of the nonlinear optical properties of TMDs; the theory behind SHG will be presented in the next chapter.

The thickness of TMDs (and other 2D materials) is smaller than the wavelength of the incident light, thus, eliminating the need for phase matching between the pump and the

second-harmonic radiation [91]. Despite the atomic thickness, resonant excitation and other enhancement mechanisms can be used to increase the nonlinear optical effects. Naturally, nonlinear processes also depend on the intrinsic symmetry of the 2D crystals, the strength of the involved oscillators, and as previously mentioned, the excitation wavelength. Thus, TMDs have an advantage over graphene, as they are not centrosymmetric for odd numbers of layers.

That is, TMDs with 1, 3, 5 layers, and so on, present second order nonlinearity.

Indeed, Malard et al. [91] observed efficient second-harmonic generation from odd-layered MoS2 crystals. Figure 9(A) shows the optical image of a sample of mono- and few-layer MoS2, which are more easily distinguishable by the AFM image in the Figure 9(B). Figure 9(C) presents the sample second-harmonic image for the same area in Figure 9(A), showing well-defined regions where the second-harmonic intensity varies, with significant signal only observed for regions with an odd number of layers. Figure 9(D) shows the intensity profile of the SHG image from the left to right along the yellow line shown in Figure 9(D). Li et al. [92]

also observed strong SHG in MoS2 with an odd number of layers.

Figure 9. (a) Optical microscopy image of the MoS2 sample. (b) AFM image of the dashed triangle shown in (a), scale bar is 1 μm. (c) SHG image collected with a pump-laser at 800 nm (1.55 eV).

Brighter colors mean stronger SHG intensity. Scale bar is 5 μm. (d) Intensity profile of the SHG image from the left to right at the yellow line shown in picture (c). Reproduced with permission [91].

Copyright 2013, American Physical Society.

The crystalline orientation of 2D materials can be obtained by analyzing the dependence of the SHG intensity with the pump polarization. Since the nonlinear susceptibility is a tensor dependent on symmetry, a strong dependence of the harmonic intensity with the direction of the incident electric field is obtained[92]. In Figure 10, for example, the crystallographic orientation of a monolayer TMD is indicated by the dark blue arrow (armchair axis) in the optical microscopy image of Figure 10(B). The analysis was obtained by verification of the second-harmonic intensity with incident linearly polarized light as a function of the excitation angle, as shown in Figure 10(A). The SH intensity peaks correspond to the armchair axes of the crystal, with the zig-zag axes at an angle of 30° from the maximum, indicated by the arrows in both Figure 10 (A) and (B). The same characterization can be used and applies to other 2D semiconductor TMDs such as MoS2, WS2 and WSe2.

Figure 10. (A) SHG characterization. Polar plot of the SHG intensity of a single-layer 2D material as a function of the pump linear polarization angle θ. Fitting the angular dependence, the armchair direction (dark blue arrow) of the sample is determined as the highest intensity. The armchair direction

is shifted by 30º from the zigzag direction (light blue arrow). (b) Optical image of the flakes. The axes are indicated as armchair (dark blue arrow) and zigzag (light blue arrow) and were determined by polarization-resolved SHG shown in (A). Reproduced with permission [93]. Copyright 2018, AIP

Publishing LLC. Licensed under CC BY 4.0.

The SHG technique can also be used to probe strain in TMDs [49], [94]. Based on the fact that mechanical strain tends to alter the symmetry of a crystal, even the smallest levels can have a huge impact on the SHG intensity of atomically thin materials. Strain can break the crystal symmetry along different polarization directions and therefore, change the nonlinear susceptibility tensor [49]. Mennel et al. [49] measured SHG for different TMDs and analyzed the mechanical deformation as a function of the polarized SHG intensities. In Figure

11 we can observe the lowest and highest applied strain levels as the purple and yellow plots, respectively. In most samples, the six-fold SHG symmetry is broken even without externally applied strain, attributed to the TMDs exfoliation and transfer processes.

Figure 11. Polarized SHG measurements of different TMDs under varying uniaxial strain. SHG measurements at the lowest and highest applied strain levels, purple and yellow, respectively. Fitted SHG curves at different strain levels. (bottom). Experimental measurements are shown in the top row and theoretical predictions in the bottom row. Reproduced with permission [49]. Copyright 2018, AIP

Publishing LLC. Licensed under CC BY 4.0.

Furthermore, literature reports on the observation of SHG in a variety of TMDs such as MoS2 [46], WS2[81], WSe2[82], MoSe2[80][83], ReS2[84] and others. Autere et al. [62], for example, showed strong SHG and THG in semiconductor TMD monolayers. In this case, the authors deposited different TMDs (MoS2, MoSe2, WS2 and WSe2) on the same substrate for a direct comparison between the materials, since the substrate can have critical impact on the measured intensities, as already mentioned. The SHG and THG for the flakes were excited by a 1560 nm mode-locked fiber laser. The nonlinear optical susceptibility χ⁽²⁾ of MoSe2 is found to be approximately two to six times larger than that of the other TMDs analyzed, which is attributed to the resonant enhancement of the SHG in MoSe2. The energy of the A exciton in MoSe2 (∼790 nm) matches closely with the wavelength of the SHG signal (780 nm), causing an SHG ~4 to 40 times larger than that from the other materials. The third-order nonlinear susceptibility χ⁽³⁾ of all four materials was found to be comparable to that of graphene, with the

largest value observed for MoS2. The |χ⁽²⁾| and |χ⁽³⁾| values measured and calculated by the authors are presented on Figure 12 (A) and Figure 12 (B), respectively.

Figure 12. Comparison of experimental and theoretical (A) |χ⁽²⁾| and (B) |χ⁽³⁾| for TMDs at 1560 nm excitation. Reproduced with permission [62]. Copyright 2018, American Physical

Society.

Moreover, the diversity of TMDs, their combination and different excitation wavelength conditions means that bandgap engineering and a wide range of resonances are potentially accessible for nonlinear device implementation and optimization, including those based on SHG, THG and other nonlinear optical phenomena at the telecom wavelengths. Seyler et al. [95] showed a mechanism to electrically control second-order optical nonlinearities in monolayer WSe2. The intensity of second-harmonic generation at the A-exciton resonance was tuned by over an order of magnitude at low temperature and by nearly a factor of four at room temperature through electrostatic gating in a field-effect transistor [95]. Khan et al. [96] showed that the SHG response is highly sensitive to temperature modulation in 2D TMDs, with an effect enhanced by 25.8% in monolayer MoSe2 only by temperature increase, whereas the nonlinear effect is found to be quenched in the case of 3L, 5L, and 7L MoSe2 [96]. In this case, the temperature study is not related to excitonic resonances, but to the different thermal expansion behavior for different layers, leading to variable interband and intraband lattice symmetries triggered by a temperature variation between -120°C and 120°C. Different structures, such as MoS2 nanoscrolls [97], pyramid-like WS2 [98], and heterostructures[99] have also been used to enhance the second-harmonic intensity based on the superposition of the involved fields.

Another promising class of methods to enhance the nonlinear optical effects is the combination of 2D materials with different field enhancement platforms, including

plasmonic nanostructures for localized surface plasmon excitation[100]–[104], hybrid dielectric structures[105], [106], metallic and dielectric metasurfaces governed by bound states in the continuum[107]–[113], photonic crystal nanocavities[114], [115], optical microcavities[116], [117] and waveguides[118].

Although these methods have proven to enhance the SHG fields, complex and time-consuming fabrication processes are required[119]. Plasmonic metal nanostructures, for example, require that the fundamental or the frequency-converted field be overlapped with the resonance spectrum of the nanostructures, thus demanding specific nanofabrication techniques to appropriately tune the plasmon resonance[105]. Also, it is well known that noble metal structures exhibit strong optical loss in the visible band, which greatly influences the nonlinear response[104], [120]. Metasurfaces, in turn, demand structuring with high spatial resolution and often require fabrication by electron-beam lithography, imposing scalability and cost drawbacks to practical manufacturing of nonlinear optical devices. The same applies to photonic crystal nanocavities, which rely on high-definition lithographic methods, which are essential for the design of superior quality resonance structures in which mode coupling is required.

A simpler approach to field-enhancement, however, seems to have been so far ignored. In Chapter 4, we propose and demonstrate the use of substrates presenting an epsilon-near-zero point close to the pump wavelength to increase the nonlinear frequency conversion efficiency in mechanically exfoliated monolayer TMDs [119]. Additionally, waveguides allow for extended interaction length, further promoting the enhancement of the nonlinear optical effects and on-chip applications, to be discussed in Chapter 5.

3 INTRODUCTION TO NONLINEAR OPTICS

The purpose of this chapter is to introduce the basic concepts of nonlinear optics, especially regarding second-harmonic generation, which is described in the case of bulk and sheet nonlinearities.