The red and green dotted lines in Figure 1d display the same resonant mode of the PC cavity measured before and after the integration of GaSe, and the black dashed lines are Lorentzian fittings. After the integration, the GaSe layer works as a positive perturbation of the dielectric function around the resonant mode, which shifts the resonant wavelength from 1536.5 to 1551.0 nm. It also weakens the confinement of the resonant mode, lowering the Q factor from ~2000 to ~1750. These variations of the resonant mode are confirmed using three-dimensional finite element simulations (COMSOL Multiphysics) with the refractive index and thickness of the GaSe layer chosen as 2.8 and 7.8 nm35.
To implement the cavity-enhanced SHG measurement, we tune the laser wavelength as 1551 nm to excite the cavity's resonant mode, and the reflected resonant signal is filtered out using a short pass dichroic mirror (Supplementary Information). The frequency conversion signal scattered from the cavity is monitored using a 0.5-m spectrometer mounted with a cooled silicon camera. Figure 2a displays an obtained spectrum, when the pump power is 0.5 mW measured after the objective lens. At the wavelength of 775.5 nm, a strong peak is observed, corresponding to the second harmonic signal of the pump laser. Another weak peak arises as well at 517 nm, equaling to the THG wavelength of the pump laser.
(a) Spectrum of the cavity's scattering signal with a 1551 nm pump laser, which has two signals at 775.5 and 517 nm corresponding to SHG and THG, respectively. (b) Pump power-dependence of the cavity-enhanced SHG with a fitting slope of 2.01, where the pump power is measured after the objective lens. (c) Cavity-enhanced SHG spectrum when the pump wavelength is tuned cross the resonance, where the dashed line is a squared Lorentzian fitting curve of the cavity resonant mode. (d) Spatial mapping of the cavity-enhanced SHG, where the PC boundary is indicated by the dashed line.
Before we transfer the GaSe layer, we examine the harmonic generations from the bare silicon PC cavity as well, which presents the similar THG peak intensity but no SHG peak. As reported in Ref. 31, resonantly enhanced SHG in a bare silicon PC cavity is also possible due to the surface second order nonlinear process. However, this SHG signal is about two orders of magnitude weaker than the cavity-enhanced THG31, which is a possible reason for the failed observation of SHG in our bare PC cavity. Hence, the obtained strong SHG from the GaSe–PC cavity is due to the top GaSe layer. Also, the THGs measured before and after integration of GaSe have no noticeable power variation, indicating the THG in Figure 2a mainly results from the third order nonlinear process in the bulk silicon slab. Comparing SHG and THG of the GaSe-PC cavity, the SHG peak is more than 650 times stronger than the THG peak. From the resonant mode simulation, we calculate the optical power distributions in the GaSe-PC cavity, indicating the power inside the nine-layer GaSe flake is only 1.5% of that in the bulk silicon slab. The remarkably strong SHG signal is in consistent with the ultrahigh second order nonlinear susceptibility of GaSe11, 22, 28.
We also evaluate the pump power dependence of the SHG by varying the laser power, as shown in the log-log plot of Figure 2b. The dashed line indicates a fitting with a slope of 2.01, verifying the quadratic power dependence of the cavity-enhanced SHG. By measuring the cavity reflection of the on-resonance laser, and combining the far-field collection efficiency of the resonant mode (~40%)33, the coupling-in efficiency of the pump laser is estimated as 6%. Therefore, even for a 0.1 mW pump illuminating on the PC cavity, the power coupled into the cavity is < 10 μW, which can still generate a detectable SHG.
For the previously reported SHG in mono-layer or few-layer 2D materials, pulsed lasers are employed to achieve high peak pump power and increase the SHG output signal. In our GaSe-PC cavity, the successful observation of SHG with a CW pump could be attributed to the strong enhancement of the pump power coupled into the cavity. To verify this, we acquire the SHG powers as we tune the pump laser wavelength cross the cavity resonance, as plotted in Figure 2c. As the laser wavelength is away from the resonance, the SHG signal is nearly not detectable due to the weak light-matter interaction. For the on-resonance pump, the laser power coupled into the cavity is enhanced by a factor proportional to Q, and the enhancement over the second order nonlinear process has a factor proportional to Q2 (Refs 25, 29, 31). Hence, the SHG spectrum could be very well described by the squared Lorentzian lineshape, which is used to fit the fundamental resonance shown in Figure 1d.
The cavity-enhanced SHG is verified as well using a spatial mapping of the SHG with an on-resonance pump, as shown in Figure 2d. The device is mounted on a 2D piezo-actuated stage with a moving step of 100 nm, and the generated second harmonic signal is measured using a photomultiplier tube (PMT). As the cavity-enhanced SHG is pumped by the evanescent field of the cavity resonant mode, efficient SHG can only be observed when the pump laser couples into the cavity. Therefore, the spatial position of the detected SHG is determined by cavity's coupling-in region. For the modified point-shifted cavity, light could vertically couple into the cavity effectively around the modification region33, which has a dimension about 2.5 × 2 μm2. In the SHG mapping, a similar area with strong signal is observed. Outside the cavity mode-coupling region, the GaSe layer is only pumped by the vertically illuminated laser, which is too weak to yield observed SHG for a CW pump.
Because of the optical losses from various optical components in the microscope setup, as well as the absorption by the silicon substrate, it is difficult to evaluate the absolute SHG power enhanced by the cavity. To evaluate the cavity-enhancement factor, we switch the CW laser into a pulsed laser to pump the GaSe-PC cavity, with pumping wavelength (at 1560 nm) being off-resonance from the cavity mode. In this regime, both the on-resonance CW pump and the off-resonance pulsed pump share the same excitation and collection optical paths, as well as the same location of GaSe layer to maintain the dielectric environment of the SHG emission. For a 2.8 nW SHG measured by the PMT, the required powers for the CW laser and pulsed laser are measured as 2.5 and 1.56 mW (averaged power), respectively. For both the CW and pulsed laser excitations, the SHG process strongly depends on the strength of electric field. With parameters of the pulsed laser, we can calculate the effective electrical field used to generate SHG in GaSe. Combining with the experimental results and the calculations, we can estimate the enhancement factor as 612 (Supplementary Information).
In Figure 3a, we display the simulated electric fields of the resonant mode located at the GaSe layer, decomposed into the two orthogonal components Ex and Ey. Because the odd-symmetry of Ey would generate a far-field pattern splitting into a large oblique angle, the coupling between the cavity mode and a y-polarized far-field is very small. For a light with x-polarization, its far-field coupling with the resonant mode is high due to the vertically directed far-field pattern of Ex. Therefore, when an on-resonance laser focuses on the cavity, only the x-polarized component can couple into the cavity effectively. If the laser polarization is changed by rotating the HWP, the power coupled into the cavity is proportional to sin2(2θ), where θ is the angle between the HWP's fast-axis and the y-axis of the PC cavity. And the cavity-enhanced SHG, which is proportional to the square of the coupled power, should follow a function of sin4(2θ). Considering the cross-polarization of the experimental setup, the vertically scattered SHG after the HWP is then projected onto the output polarization direction, and the finally collected SHG has a function of sin6(2θ), as plotted in Figure 3b. Here, the four peaks have different maximum values. We attribute it to the imperfection of the HWP at the SHG wavelength (the achromatic wavelength range of the HWP is 1200–1600 nm).
(a) Simulated electric fields (Ex and Ey) of the resonant mode and the corresponding nonlinear polarizations (Px and Py) calculated from the nonlinear susceptibility matrix and crystal orientation of GaSe. (b) Polarization-dependence of the cavity-enhanced SHG. The black solid line is a fitting of sin6(2θ), where θ is the angle between the HWP's fast axis and y-axis of the PC cavity. (c) Polarization-dependences of the SHG pumped by the on-resonance CW laser and off-resonance pulsed lasers. The SHG pumped by the off-resonance pulsed laser is fitted by a function of sin26(θ+3°), indicated by the black solid line. (d) Alignment of the GaSe crystal orientation with respect to the axes of the PC cavity.
By switching the on-resonance CW laser into the off-resonance pulsed laser (at 1560 nm), we observe another pump polarization-dependent SHG from the GaSe-PC cavity by rotating the HWP, as shown in Figure 3c. A fitting with a function of sin26(θ+3°) is obtained, which is determined by GaSe's D3h symmetry11. This 12-fold variation is not observed in the cavity-enhanced SHG, where the GaSe crystal only interacts with the evanescent field of the cavity mode, and the angle between the crystal orientation and cavity's electrical field vector is fixed no matter how the laser polarization change. The polarization variation of the pump laser only changes the laser power coupled into the cavity, which therefore induces the four-fold variation of SHG following the function of sin6(2θ).
The HWP angle-dependences of GaSe's SHGs pumped by the on-resonance CW laser and off-resonance pulsed laser indicate axes of the PC cavity and GaSe's crystal structure, respectively. We could probe the alignment between GaSe's crystal orientation and axes of the PC cavity by comparing them, as shown in Figure 3c. We conclude the Ga–Se bond is aligned to the y-axis of the PC cavity with an angle of ϕ=6°, as indicated in Figure 3d. With this alignment and the near-fields (Ex and Ey) of the resonant mode in the GaSe layer, we could calculate the nonlinear polarizations Px and Py generated in GaSe according to its nonlinear susceptibility matrix (Supplementary Information), as shown in Figure 3a. The symmetries of the generated Px and Py indicate the y-component of the SHG has a vertical far-field radiation, as well as a high coupling efficiency. Considering the employed cross-polarization setup, the x-polarized pump laser and y-polarized SHG radiation enable the high efficiency generation and collection of SHG.
The low-power CW pumped SHG in 2D materials is also validated in a mono-layer GaSe. Figure 4a shows the AFM image of an integrated mono-layer GaSe-PC cavity, which has a resonant mode at the wavelength of 1548.8 nm and a Q factor of ~1800. By pumping it with a 0.5 mW on-resonance CW laser, we measure the vertically scattered upconversion signal, as displayed in Figure 4b. Two clear peaks are observed at wavelengths of 774.4 and 516.3 nm, which are verified as GaSe's SHG and silicon's THG, respectively. Figure 4c and 4d plot the pump wavelength and polarization dependences of the SHG signal, yielding similar conclusions as those obtained from the nine-layer GaSe-PC cavity. The results also confirm the cavity enhancement effect via resonant mode's near-field. Because the mono-layer GaSe-PC cavity and the nine-layer GaSe-PC cavity have similar Q factors, the cavity-enhanced THGs of the silicon slab from the two devices should be close. Therefore, we could compare the cavity-enhanced SHG powers from the mono- and nine-layer GaSe by calculating the ratios of GaSe's SHG peak to silicon's THG peak of the two devices separately. From the experimental results, the peak ratios from the mono-layer GaSe-PC cavity and nine-layer GaSe-PC cavity are calculated as 8.7 and 650, that is, SHG from the nine-layer GaSe is about 75 times of that from the mono-layer GaSe. The SHG power variation of the two GaSe flakes is closely consistent with SHG's quadratic dependence on the material thickness for a thin film, as demonstrated in Ref. 28. While the absolute SHG power of the mono-layer GaSe is much weaker than that of the nine-layer GaSe, the SHG enhancement factors of the two devices are both around 600, which is determined by the Q factor and mode volume of the cavity mode.
CW pumped SHG from a mono-layer GaSe integrated with a PC cavity. (a) AFM image of the GaSe-PC cavity, indicating GaSe's thickness of ~0.89 nm. (b) Spectrum of the cavity's upconversion signals pumped with a 1548.8 nm CW laser, showing SHG and THG signals. (c) Cavity-enhanced SHG spectrum when the pump wavelength is tuned cross the resonance, where the dashed line is a squared Lorentzian fitting curve of the cavity resonant mode. (d) Polarization-dependence of the cavity-enhanced SHG.