Investigation of Second- and Third-Harmonic Generation in Few-Layer Gallium Selenide by Multiphoton Microscopy

Gallium selenide (GaSe) is a layered semiconductor and a well-known nonlinear optical crystal. The discovery of graphene has created a new vast research field focusing on two-dimensional materials. We report on the nonlinear optical properties of few-layer GaSe using multiphoton microscopy. Both second- and third-harmonic generation from few-layer GaSe flakes were observed. Unexpectedly, even the peak at the wavelength of 390 nm, corresponding to the fourth-harmonic generation or the sum frequency generation from third-harmonic generation and pump light, was detected during the spectral measurements in thin GaSe flakes.

In this paper, we report on employing multiphoton microscopy with a compact 1560 nm femtosecond fiber laser to study the nonlinear optical properties of few-layer GaSe flakes. We observed that the second-and third-order nonlinearities are very sensitive to the number of layers. We also discovered the generated light at the peak wavelength of 390 nm from ~40 nm thick GaSe. To our knowledge, this is the first systematic optical nonlinearity study of few-layer GaSe using the excitation wavelength around 1560 nm of relevance for telecommunication applications.

Results and discussion
Optical microscopy. Figure. 1a presents an optical microscope image of a GaSe flake. The optical contrast corresponds to a different number of layers labeled by Roman numbers I to VII. Surface morphology. The few-layer GaSe flake shown in Fig. 1a was characterized using contact-mode atomic force microscopy to determine the number of layers in the different areas. Since the thickness of single-layer GaSe is known to be ~0.98 nm, 12,14 the flake thickness in nm corresponds roughly to the number of layers. The AFM micrograph from the left edge of the GaSe flake is presented in Fig. 1b. The height of the area V (in Fig. 1a) from the substrate is found to be 13 nm indicating 13 layers. An AFM micrograph from the tip of the flake (Fig. 1c) shows two different areas with a different height. The thinnest area (area I in Fig. 1a) contains 7 layers of GaSe, estimated from the cross-section (9.7-2.6 = 7.1 nm). The additional 2.6 nm on the left side of the SiO 2 substrate comes from an artifact due to the background subtraction process (flattening). From the same cross-section, the thickness of area II corresponds to 9 layers. The thickness differences between the adjacent areas II and III in Fig. 1a was estimated to be 2 nm and the areas III and IV to be 1 nm. Therefore, areas III and IV are 11 and 12 layers thick, respectively. The area VI was estimated to contain 14 layers. The estimated thicknesses are listed in Table 1. The accuracy of the thickness determination is ± 1 layer. Area VII was measured to contain ~40 layers.  Fig. 1a Number of layers Multiphoton imaging. SHG and third-harmonic generation (THG) images of the GaSe flake were recorded simultaneously and are shown in Fig. 2a,2b, respectively. Although the SHG signal was much stronger than the THG signal, the image contrast was scaled in order to visualize most layers in the images. The areas with different number of layers are clearly distinguishable in both SHG and THG images and the signal intensity increases as the number of layers increases. The THG image gives higher contrast between the substrate and the GaSe flakes. The SHG signal is observed to decrease near the edges while the THG signal is constant over the area with the same number of layers. Yin et al. observed strong edge effects for SHG from single-layer MoS 2 . 31 They observed that the edge effect is strongly dependent on the excitation wavelength. It was recently showed that GaSe flakes also display high anisotropy in the optical properties at the crystal edges 18 . In our case, the photon energy of the SHG is below the band-gap of GaSe (~2.1 eV) 32 and the SHG signal decreases significantly near the edges of the flake. Fig. 2c shows an RGB composite SHG-THG micrograph obtained by combining images 2a and 2b. The SHG and THG signals are in the red and green channels of the RGB image, respectively. The areas that simultaneously show a high intensity for both SHG and THG appear yellow in the composite image. The cross-sectional profiles of SHG and THG signals from the dashed line in Fig. 2c are plotted in Fig. 2d. The quenching of the SHG signal near the edges is clearly visible in the profile. The excitation light power dependences of the SHG and THG signals on a logarithmic scale for different layer thicknesses are presented in Fig. 3a,b, respectively. The lines are fits to square (a) and cubic (b) power dependences. The measured SHG and THG signals follow the square and cubic power dependences quite well proving that the signals are SHG and THG. A power dependence measurement was realized by adjusting the laser intensity producing a peak power from 0.3 kW to 1.2 kW. The SHG and THG signals for different layer thicknesses were found to be roughly independent of the excitation peak power. In Fig. 3c, the SHG and THG signals for 1 kW excitation peak power are plotted as a function of the number of GaSe layers. These results show that the SHG signal is proportional to the flake thickness. The highest SHG peak power was about 28 μ W for an excitation peak power of 1 kW. However, the flake . The estimated d eff for different GaSe thicknesses are presented in Table 2. The highest estimated value is 18 pm/V. The second-order nonlinearity coefficient of d 22 = 53 pm/V has been earlier reported for the bulk GaSe at the excitation wavelength of 10 μ m 34 .

Area in
The third-order optical nonlinearity coefficient GaSe  Table 2. The χ (3) of graphene is known to be exceptionally high due to the resonant condition for the excitation and THG signals 36 . The absorption of the THG signal (THG photon energy of 2.38 eV is higher than the band-gap of GaSe (~2 eV)) has not been taken into account and therefore, the χ (3) of GaSe could be even higher than estimated.  Spectra of generated light. The spectra of the generated light measured from the three different areas (marked with circles and Roman numbers in Fig. 2c) are presented in Fig. 4. Strong peaks at the wavelengths of ~520 nm and ~780 nm were observed for the flakes with ~40 layers (area VII) and 12 layers (area V). The asymmetric line shape of the peaks is due to the spectrum of the excitation laser (the spectrum of the laser is shown in Methods). This asymmetry is clearly visible for the ~40-layer flake (area VII). The spectra confirm that the signals detected are second and third harmonics. From the area of 9 layers (area II), only the peak around ~520 nm was observed. This is due to the weaker SHG signal in this area and partly due to the reduction of the SHG signal near the edge as noted above (the measurement point is located exactly at the area where the SHG signal starts to decrease). The sensitivity of the spectrometer is also lower than that of the PMT used in multiphoton imaging. However, the measured spectra confirm that generated light consists of the SHG and THG signals and the contribution of the multiphoton excited photoluminescence is minimal. Even the peak at 390 nm can be clearly observed from the ~40-layer GaSe. This peak is exactly at the fourth-harmonic wavelength but it could also be the sum frequency generation from THG and pump light.
Raman microscopy. The Raman spectra of the GaSe samples were also measured for verifying that GaSe does not decompose in the nonlinear microscopy experiments. The relatively high irradiance used during the nonlinear optical microscopy may induce modifications in the GaSe flakes resulting in spectral differences between the bulk and the thin layers. However, a comparison of our Raman spectrum using a 9 layer-flake with the Raman spectrum from a thin GaSe layer (1 nm) adapted from Ref. 12 shows clear similarities with GaSe, see Fig. 5a. Moreover, decomposition of GaSe was ruled out by performing a control experiment on a Se nanowire obtained by chemical decomposition of GaSe. The Raman spectrum obtained from a natural Se crystal is also shown 37 . These data confirm the chemical and structural stability of the GaSe thin layer flakes upon multiphoton microscopy. In thin layers the Raman spectrum is dominated by the band centered around 255 cm -1 . Raman imaging shows that this mode is common all around the flake although its intensity changes with the GaSe thickness as shown in Fig. 5b. The dependence of the Raman spectrum on layer thickness is illustrated in Fig. 5c where the spectra were averaged at different regions indicated by rectangular boxes in Fig. 5b. The spectrum from bulk GaSe is shown in the inset of Fig. 5c. By comparison with few-layer GaSe, we found a drastic difference with its bulk counterpart, which exhibits sharper bands around 213 and 308 cm -1 . The reasons behind such a striking difference are still under investigation.
The band observed around 305 cm -1 cannot be attributed to the A g 1 2 mode of GaSe observed in the bulk at 308 cm -1 . This band clearly corresponds to SiO 2 /Si as shown by the spectrum obtained from the bare substrate. This is in contrast to the conclusion from Late et al. who attributes that band to the A g 1 2 of GaSe and the low-frequency shift when decreasing layer thickness 12 .

Conclusions
In conclusion, the optical nonlinearities of GaSe flakes with different number of layers were investigated using multiphoton microscopy with the excitation wavelength of 1560 nm, relevant for telecommunications. Both second-and third-harmonic generations were observed in few-layer GaSe flakes. The SHG and THG signals showed clear contrast for different numbers of GaSe layers. Second-and third-harmonic generation was confirmed by spectral analysis and also the peak at the wavelength of 390 nm was observed   corresponding to the wavelength of fourth-harmonic generation or the sum frequency generation from THG and pump light. Strong nonlinear characteristics reported here for few-layer flakes demonstrate that GaSe is an intriguing material for all-optical signal processing, even as few atomic layer films. These results contribute to the development of GaSe thin-layer flakes for next generation nonlinear applications satisfying the continuous need for device miniaturization.

Methods
Sample preparation. GaSe flakes were grown by the Bridgman method. Few-layer flakes of GaSe were then obtained by mechanical cleaving from a bulk single crystal and deposited by gently pressing against the oxidized silicon substrate. In order to achieve maximal optical contrast the oxide thickness was 286 nm. Few-layer GaSe flakes were identified using optical microscopy and the number of layers was determined by atomic force microscopy (AFM) in contact mode.
Multiphoton microscope. The nonlinear optical properties of the prepared GaSe flakes were investigated using a unique multiphoton microscope, built in-house, which is shown schematically in Fig. 6. The design of the microscope and the experimental procedure were previously reported 35,38 . The light source in the system is an amplified erbium-doped mode-locked fiber laser operating at a central wavelength of 1560 nm. The spectrum of the laser is shown in the inset in Fig. 6. The maximum average power of the laser is 60 mW with a repetition rate of ~50 MHz and ~150 fs pulse duration at the sample surface. The pulse peak power is estimated to be ~8 kW and the pulse energy is 1.2 nJ. The laser beam is scanned with a 2D galvo mirror system and focused on the sample using a 20x microscope objective. The measured focal spot size is ~1.8 μ m. The backscattered second-and third-harmonic signals generated from each point on the sample are split into two paths using a long-pass dichroic mirror (cut-off at 562 nm) and then detected using photomultiplier tubes (PMT). Narrow band-pass filters are used to select SHG and third-harmonic generated signals at central wavelengths of 780 nm and 520 nm, respectively. The acquisition of the two channels is simultaneous, making the measurement conditions for both channels exactly identical regardless of any perturbations (external vibrations or fluctuations in laser power).