Global imaging for polarization resolved second harmonic generation of WS2 monolayers

Second-harmonic generation (SHG) is a nonlinear optical effect enhanced by broken crystallin symmetry and is very sensitive to electronic structures. SHG has recently been applied to two-dimensional transition metals dichalcogenides (2D-TMDs). 2D-TMDs have been the focus of much recent research due to their ultrathin scale, high quantum confinement, and energy gap toning ability that results in unique linear or nonlinear optical and electrical properties. WS2 monolayers are well-known 2D TMDs with strong SHG. They have attracted a great deal of interest due to their potential applications in fundamental material characterization and nanophotonic device development. In this study, we grew WS2 monolayers using the chemical vapor deposition (CVD) technique and characterized them with Raman and photoluminescence (PL) spectroscopy. The intense direct excitonic peak A at 630 nm was identified in the PL spectra, while the Raman spectra exhibited the two distinctive modes A1g (at 418 cm−1) and E2g (at 356 cm−1). The monolayers were pumped by an 830 nm circularly polarized and defused pulsed laser to produce the SHG image. global one-shot SH images for different growth shapes were obtained and crystalline domains were identified using polarization-resolved second-harmonic generation imaging (PRSHGI). The defect level was observed to clearly enhance the SHG signal following the increase in broken crystalline centrosymmetric and relaxing the optical selection roles at the valley degree of freedom.


Introduction
The bulk transition metal dichalcogenide (TMD) family has a layered structure with the general chemical formula of MX 2 , whereby M refers to a transition metal and X refers to a dichalcogenide.Each single layer of the TMD family consists of three planes, namely a plane of metallic atoms sandwiched between two planes of chalcogen atoms, creating a top view of a hexagonal lattice structure.This structure involves strong covalent bonds within one layer and weak van der Waals bonds between different layers, resulting in the thinning and exfoliating of the materials to a few layers, thus achieving a monolayer structure [1,2].Monolayers display distinctive properties compared to their bulk version due to strong quantum confinement.They have extraordinary photoluminescence resulting from an indirect-to-direct band gap transition, providing a large range of applications for future nano-optoelectronic devices [1,3,4].
Monolayer materials have a crystalline structure with a binary atomic arrangement that breaks the crystal inversion symmetry.Monolayers, or structures with a few odd-numbered layers, are identified as noncentrosymmetric crystals that support the generation of second-order nonlinear optical emissions.The Second Harmonic Generation (SHG) intensity of such materials has a characteristic six-fold polarization dependence pattern following the crystalline structure of a hexagonal lattice [5][6][7].Centrosymmetric crystals are reconstructed with an even number of layers or bulk materials as a unit cell consisting of two mirrored sublattices, which leads to the disappearance of SHG [8].A large nonlinear response has been identified for numerous monolayer TMDs, providing a new tool to characterize and investigate the structure and properties of materials [9][10][11][12].Furthermore, this nonlinear response can be enhanced and integrated to create advanced quantum and photonic nanodevices [4-6, 13, 14].
Polarization-resolved second harmonic generation imaging (PRSHGI) has become a powerful and fundamental technique for analyzing 2D materials due to its atomic-scale sensitivity, versatility, and simplicity [23].The PRSHGI experimental setup in the literature produces a pixel-by-pixel mapping SH image where the laser beam could raster scan the sample, or the sample could be mounted on a fully motorized scanning stage [24][25][26][27][28][29][30].The sample is pumped with a linearly polarized and highly focused laser beam then the SH signal is analyzed by a linear polarizer rotated to select the SH polarization component parallel to the polarization of the exciting beam [24][25][26][27][28][29][30].In this work, a simple and fast PRSHGI technique is introduced where a global one-shot SH image for WS 2 monolayer is produced.The entire flake on the sample is pumped with a circular polarized and defused laser beam, and then the SH signal is analyzed by a linear polarizer rotated to produce a global SH image with the selected polarization component.The global image of the entire flake acquired for each polarization clearly distinguishes crystalline domains and boundaries.A high SHG signal was detected in the monolayers.

Synthesis of WS 2 sample
For the CVD procedure, 2 mg of WO 3 powder (99.9%,CAS: 12036-22-5, Chemsavers, USA) was distributed in a thin line on a graphite holder and covered by the edge of a clean Si/ SiO 2 substrate (SiO 2 thickness of 400 nm).The graphite sample holder was maintained in the center of a two-inch quartz tube furnace.In addition, 80 mg of sulfur powder (CAS: 7704-34-9, Spectrum Chemicals, USA) placed in a boron nitride boat was positioned 3 cm from the heating zone at the upstream edge of the furnace where temperatures were very low.The furnace was closed and an inert gas (Ar) was released under atmospheric pressure at 100 sccm for 5 min to clean the furnace while it was gradually heated to the desired growth temperature (850 °C).The flow was then reduced to 20 sccm until the end of the growth process.When the furnace reached 850 °C, the sulfur was heated by an external heater to 200 °C for 20 min and was subsequently turned off and cooled down to room temperature.

Characterizations of the monolayer WS 2 sample
The sample was first characterized by an optical microscope with a homogenous white light halogen lamp.Optical contrast was used to distinguish between the growth of the multiple layers and the monolayer.Raman spectroscopy was used to identify the material and confirm the monolayer nature.Raman spectra were collected using a confocal microscope system (WITec, Alpha SNOM, Germany) with a 50-× objective microscope and a 0.85 numerical aperture at room temperature (532 nm laser wavelength, 1800 grooves/mm gratings, and 800 nm laser spot diameter).PL spectra were collected using the same confocal microscope system at 0.1 mW and 150 grooves/mm gratings.

Second harmonic generation (SHG) experiment
PRSHGI was performed using a circularly polarized excitation beam produced by a tunable pulsed Ti-Sapphire laser oscillator (Spectra-Physics Tsunami, USA) operating at a rep rate of 80 MHz with 2 ps pulses.The wavelength was tuned to 830.4 nm.To utilize the low-light imaging capabilities of the liquid nitrogen-cooled CCD (PyLon, Teledyne Princeton Instrument, USA), the SHG images were acquired using a single-stage 0.75 m spectrometer (TriVista 777, Teledyne Princeton Instrument, USA) in 'imaging' mode and a 0°grating acting as an effective mirror.The entrance slit of the spectrometer was fully opened to 3 mm.A simple configuration of the experiment is shown in figure 1.Two short pass filters were placed in front of the spectrometer, each with 98% transmission at 415 nm and greater than Optical Density (OD) 5 suppression at 830 nm.The filters were used in series to block the laser excitation and pass the SHG light.A 20× microscope objective was used to collect SHG signals in addition to a 200 mm imaging lens positioned in front of the spectrometer resulting in a CCD image with each pixel approximately 1 μm in size.A linear polarizer was placed just before the microscope objective and aligned 0°vertically with the spectrometer slit.Furthermore, a 50 mm convex lens was placed in the laser path to defocus the beam at the sample.The defocusing lens was chosen such that the FWHM of the excitation spot covered the entire flake under study.Under this configuration, a global image of the entire flake was acquired with bright and dark areas related to each polarization setting.The defocused circularly polarized excitation beam exits the entire flake area producing all the possible SHG signals and each SHG polarization component is detected by rotating the analyzer (linear polarizer placed just before the microscope objective) (figure 1).

Material structure
The sample was initially examined by a high-magnification optical microscope under white light illumination to identify the growth of the multiple layers and the monolayer.Using a Si substrate coated with 400 nm-thick SiO 2 allowed the differentiation between the monolayer and multi-layer materials via color contrast due to the effect of thin film interference.Pink denotes a substrate while materials are observed in different shades of purple and blue [31,32].The monolayer (1 L) structure exhibits a degree of purple (figures 2(a), (b)).Light blue corresponds to two, three, or a few layers (FLs), and the darker the blue, the greater the number of layers [31] (figures 2(a), (b)).Shiny regions correspond to the bulk material structure due to the reflection of light rather than the thin film interference.The CVD growth of the materials results in large areas of monolayer flakes as individual or connected triangles and polygons that expand to flower-like shapes (figures 2(a), (b)).To further understand the growth of the multi-layers and monolayers, we examine the PL spectra.WS 2 monolayers generally exhibit two direct excitonic peaks, A (1.97 eV, 630 nm) and B (2.4 eV, 517 nm) [2,32,33].These two peaks are a result of the direct recombination of electrons at the conduction band and the holes at the spin-orbit split valance band [2,32,33].The PL spectra exhibit peak A but not B for 532 nm excitation.Figures 2(c) reveals the expected A excitonic peak at 1.97 eV (630 nm).The extremely high intensity and small width of peak A indicate a monolayer structure due to the direct transition of this exciton.The intensity then dramatically drops as the number of layers increases to two or more, corresponding to an indirect transition [1,32,33].The material and number of layers are further confirmed by evaluating the Raman spectra.The monolayer exhibits the expected Raman modes, namely, the low-intensity A 1g mode at 418 cm −1 and high-intensity overlapped 2LA(M) (351 cm −1 ) and E 2g (356 cm −1 ) modes [34,35].The typical separation of 62 cm −1 between A 1g and E 2g is another indication of a monolayer structure (figure 2(d)).E 2g is slightly red-shifted with the increasing number of layers, while A 1g is blue-shifted.This results in a slight increase in the separation between the two modes for the multi-layer structure, and more importantly, the intensity ratio (2LA(M)+E 2g )/A 1g is greatly enhanced for 1 L [34,35] (figure 2(d)).Additional modes observed in figure 2(d) are related to the second-order Raman peaks [2LA(M)] of the materials (at 297 and 327 cm −1 ) [34,35].
The CVD-grown materials are of high quality, with several differences in their properties according to the growth location.For example, the growth edge and boundary between different growth domains exhibit distinct defect and strain levels that can be identified by the PL and Raman intensities.The flower-like shape growth of the material (figures 3(a), (b)) clearly exhibits different connected growth domains (polycrystalline materials).

Polarization resolved second harmonic generation imaging
Figure 5(a) presents an intense second harmonic signal at λ = 415.2nm produced by the WS 2 monolayer as it is excited by a focused beam 2 λ = 830.4nm pulsed laser with a 2 ps width.This SHG signal exhibits polarization dependence produced by the crystalline symmetry of the materials.The materials are expected to have a six-fold polarization pattern where the SHG intensity changes from a minimum to a maximum for each 30°-angle polarization state rotation (figure 6).As a result, polarization-resolved SHG techniques are used to determine the relative orientation between different crystalline domains on the same monolayer growth.
In this sample, the growth takes a flower shape with petals that have different crystalline orientations obviously defined by their edges.The image produced by the SHG signal is expected to be highly affected by the polarization state.One petal produces the maximum intensity for polarization while another petal exhibits the minimum intensity.Figure 6 presents the images collected using PRSHGI for the flower-like growth at polarization angles ranging from 0°to 110°with 10°steps.The image clearly reveals seven petals with different brightness levels according to the SHG intensity, which is affected by the polarization state.Petal 5 is the brightest at the 0°polarization angle, yet it is not visible at the 30°polarization angle.It exhibits the maximum intensity again at 60°and the minimum intensity at 90°.This trend is observed for each petal, with 30°between each maximum and minimum.Figure 7 depicts the same pattern for number 4, with maximums at 5°, 65°, and 125°, and minimums at 35°, 95°, and 155°.The crystalline growth orientation exhibits 5°differences between petal numbers 4 and 5.  Figure 8 plots the second harmonic intensity as a function of the polarization angle, demonstrating a six-fold pattern for the center and edge of the petal number 5 (totally monolayer in structure).The SH intensity is clearly enhanced at the center compared to the edge, corresponding to an opposite behavior for the PL intensity (reduction at the center compared to the edge) (figures 3(c), (d)).This enhancement of the SHG intensity within the monolayer can be explained by the presence of a defect, which introduces a broken centrosymmetric structure [24].The existence of defects partially enhances the SHG signal and dramatically decreases the PL signal [39].TMD materials not only exhibit the breaking of inversion symmetry, but they also have strong spin-orbit coupling leading to energy degenerate valleys in momentum space in the first Brillouin zone at points called K and K′ [40].K and K′ represent opposite spin states that could be populated by absorbing the right-handed (σ + ) or left-handed (σ − ) circularly polarized light [41].SH emissions follow the nonlinear optical selection roles that cause the circular polarization excitation to populate one valley or the other [42,43].The intervalley scattering at room temperature has a lifetime in the picosecond scale [44,45], therefore the scattering process does not affect SHG.SHG is an instantaneous process faster than the carriers' scattering and accordingly, it is not affected by the population imbalance of the two valleys under circular polarization excitation [42,43].Dasgupta at.all.showed that circular polarization excitation could partially populate both valleys at room temperature for SHG signal in the wavelength range of 400-420 nm [43].This small violation of the nonlinear optical selection roles is explained by the existence of disorders or deformation in the crystal lattice, which tends to weaken the valleydependent selection rule for two-photon excitations way above the band gap [45].Valley population is related to the electronic structure, which is a constant effect across the sample regardless of crystal orientation.As a result, the difference in linear polarization response should be dominated by the structural (crystal) information.The small enhancement of SHG signals at defected areas could also explained through the increased absorption by populating both valleys under the circular polarization excitation for 415 nm SHG signal.

Conclusion
In this paper, a WS 2 monolayer was synthesized using the CVD technique and characterized with PL and Raman spectroscopy.The PL spectra exhibited the intense direct excitonic peak A (630 nm), while the Raman spectra presented the two distinctive modes A 1g (418 cm −1 ) and E 2g (356 cm −1 ).The presence of these features proves the monolayer structure.The normal growth was constructed using the multigrain of different geometrical polygon shapes.A monolayer with a multigrain following a flower-like shape was identified and characterized by PL and Raman scanning images.The images revealed the PL intensities to vary with the location, indicating more defects near the center of the monolayer.The entire monolayer flake was globally imaged using the PRSHGI technique with a circularly polarized excitation beam and analyzed using a rotating linear polarizer.The SHG signals and PRSHGI-global derived images clearly show 60°folds of crystalline symmetry for the material identifying different crystalline domains within the monolayer.Furthermore, the SHG intensity was enhanced for the defective locations due to the increase in broken crystalline centrosymmetric and relaxing of the optical selection roles at the valley degree of freedom.Global PRSHGI can be employed to simply identify the crystalline domains of materials and it can be improved for applications that require the fast and simple determination of crystallographic directions.

Figure 2 .
Figure 2. (a), (b) Optical images for different-shaped growths of WS 2 with 200×-magnification.(c) PL signals at the 1 L and FL locations in the growth.Note that the FL intensity is very low and is thus multiplied by 10 for comparison with the 1 L intensity.(d) Raman signals at the location of 1 L and FLs in the growth.

Figure 3 .
Figure 3. (a) Optical image for the flower-like shape growth of WS 2 with 80×-magnification.(b) Optical image for the flower-like shape growth of WS 2 with 200×-magnification.(c) PL signals at different locations on the monolayer flower growth.(d) PL image of the monolayer flower growth with the brightness level varying with the location.

Figure 4 .
Figure 4. (a) Raman image for the flower-like growth.(b) Raman signals at different locations on the monolayer flower.

Figure 5 .
Figure 5. (a) SHG signal at the center of a petal of the flower-like growth where the PL signals are decreasing.(B) SHG signal near the edge of the same petal of the flower-like growth where the PL signals are increasing.

Figure 6 .
Figure 6.Images of the flower-like growth at different polarization angles collected via the PRSHGI technique.

Figure 8 .
Figure 8. SHG intensity of petal 5 in figure 6 of the flower-like growth at different polarization angles, revealing maximum values at 0°, 60°, and 120°and minimum values at 30°, 90°, and 150°.The intensity of the petal edge is clearly lower than that at the center of the petal.Collected via the PRSHG technique.

Figure 5
Figure8plots the second harmonic intensity as a function of the polarization angle, demonstrating a six-fold pattern for the center and edge of the petal number 5 (totally monolayer in structure).The SH intensity is clearly enhanced at the center compared to the edge, corresponding to an opposite behavior for the PL intensity (reduction at the center compared to the edge) (figures 3(c), (d)).This enhancement of the SHG intensity within the monolayer can be explained by the presence of a defect, which introduces a broken centrosymmetric structure[24].The existence of defects partially enhances the SHG signal and dramatically decreases the PL signal[39].Figure 5 presents the exact SHG signals, again showing the more intense signal at the center (figure 5(a)) compared to near the edge (figure 5(b)).TMD materials not only exhibit the breaking of inversion symmetry, but they also have strong spin-orbit coupling leading to energy degenerate valleys in momentum space in the first Brillouin zone at points called K and K′[40].K and K′ represent opposite spin states that could be populated by absorbing the right-handed (σ + ) or left-handed (σ − ) circularly polarized light[41].SH emissions follow the nonlinear optical selection roles that cause the circular polarization excitation to populate one valley or the other[42,43].The intervalley scattering at room temperature has a lifetime in the picosecond scale[44,45], therefore the scattering process does not affect SHG.SHG is an instantaneous process faster than the carriers' scattering and accordingly, it is not affected by the population imbalance of the two valleys under circular polarization excitation[42,43].Dasgupta at.all.showed that circular polarization excitation could partially populate both valleys at room temperature for SHG signal in the wavelength range of 400-420 nm[43].This small violation of the nonlinear optical selection roles is explained by the existence of disorders or deformation in the crystal lattice, which tends to weaken the valleydependent selection rule for two-photon excitations way above the band gap[45].Valley population is related to the electronic structure, which is a constant effect across the sample regardless of crystal orientation.As a result, the difference in linear polarization response should be dominated by the structural (crystal) information.The small enhancement of SHG signals at defected areas could also explained through the increased absorption by populating both valleys under the circular polarization excitation for 415 nm SHG signal.