_{2}Plasmonic Structures for Highly Efficient Second-Order Nonlinear Parametric Processes

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Two-dimensional (2D) layered materials, with large second-order nonlinear susceptibility, are currently growing as an ideal candidate for fulfilling tunable nanoscale coherent light through the second-order nonlinear optical parametric processes. However, the atomic thickness of 2D layered materials leads to poor field confinement and weak light-matter interaction at nanoscale, resulting in low nonlinear conversion efficiency. Here, hybrid three-dimensional (3D) spiral WSe_{2} plasmonic structures are fabricated for highly efficient second harmonic generation (SHG) and sum-frequency generation (SFG) based on the enhanced light-matter interaction in hybrid plasmonic structures. The 3D spiral WSe_{2}, with AA lattice stacking, exhibits efficient SH radiation due to the constructive interference of nonlinear polarization between the neighboring atomic layers. Thus, extremely high external SHG conversion efficiency (about 2.437×10^{−5}) is achieved. Moreover, the ease of phase-matching condition combined with the enhanced light-matter interaction in hybrid plasmonic structure brings about efficient SHG and SFG simultaneously. These results would provide enlightenment for the construction of typical structures for efficient nonlinear processes.

Broadband tunable coherent light sources with small-footprint and low power consumption have attracted great attention because of their potential applications ranging from high-throughput sensing to on-chip photonic communication [

In this work, we demonstrate the construction of hybrid 3D spiral TMDC plasmonic structures for highly efficient second-order nonlinear parametric processes by combining the large second-order nonlinear susceptibility (on the order of 10^{−7} m/V) of 3D spiral TMDC materials with the high subwavelength confinement of electric field of surface plasmonic polaritons (SPP). The 3D spiral TMDC structures, where the basal planes shrink gradually to the top while spiraling up, exhibit efficient SH radiation due to the broken inversion symmetry structure with AA lattice stacking. Meanwhile, the increase of light-matter interaction length due to the increasing atomic layers, along with the highly concentrated local field in hybrid plasmonic structure, leads to the great improved nonlinear optical conversion efficiency (2.437×10^{−5}), which is higher than most other reported metal-related nanostructures. Furthermore, benefitting from the ease of phase-matching condition and enhanced light-matter interaction in hybrid plasmonic structure, the SHG and SFG are realized simultaneously when the hybrid 3D spiral TMDC plasmonic structures were excited by two separated fundamental waves (FWs). We believe that the results demonstrated here would provide guidance for the development of nonlinear optical devices with high conversion efficiency and specific functionalities.

Tungsten diselenide (WSe_{2}) was selected as the model TMDC material for constructing the hybrid 3D spiral TMDC plasmonic structure due to its large second-order nonlinear susceptibility [_{2}, where the basal planes spiral up with gradually decreasing size. Owing to the AA lattice stacking structure (Figure _{2}, the 3D spiral WSe_{2} flakes with the increase of thickness have much longer light-matter interaction length [

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_{2} structure (a) and the corresponding basal planes stacking order (b). (c) AFM image of a WSe_{2} flake. Scale bar: 2 _{2}. Scale bar: 2

The 3D spiral WSe_{2} nanostructures were fabricated with an atmospheric pressure chemical vapor deposition method (Fig. _{2} nanostructure has well-defined 2D plate-like triangle morphology with tetrahedral structure. The magnified AFM image (inset of Figure _{2} flake shrink gradually from the bottom to the top layers with a clear 3D spiral structure, indicating the broken inversion symmetry of WSe_{2} [_{2} nanostructure (Figure _{2} flake and the good alignment of all the layers [_{2} flake has AA stacking configuration of basal planes [

These as-fabricated 3D spiral WSe_{2} structures with broken inversion symmetry provide a promising structure to produce large effective conversion coefficients of second-order nonlinear optical parametric processes. Unfortunately, the thicknesses of these structures are below the diffraction limit (Fig. _{2} structures were transferred onto the top of a smooth silver film with a 10-nanometer magnesium fluoride (MgF_{2}) insulating gap to construct hybrid 3D spiral WSe_{2} plasmonic structures [

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_{2} plasmonic structure where a single WSe_{2} sits on top of the MgF_{2} layer near the Ag film. (b) Spatial resolved spectra collected from the hybrid spiral WSe_{2} structure shown in the inset. Inset: SH image of a single hybrid spiral WSe_{2} structure excited with a CW laser (1064 nm). (c) Measured SHG intensity as a function of FW laser power, which fits to a square dependence. (d) Spectra of SHG and FW from hybrid spiral WSe_{2} plasmonic structure excited with 1064 nm CW laser.

Then, the second-order nonlinear optical response measurements were performed on a home-built far-field micro optical system (Fig. _{2} plasmonic structure. As demonstrated in the inset of Figure _{2} flake under the FW (1064 nm) excitation, indicating the efficient SH radiation. The spatial resolved spectra taken from spiral WSe_{2} (Figure _{2} flake shown in Fig. _{2} crystal, which further confirms the AA stacking mode of WSe_{2} basal planes.

A simple experiment was carried out to estimate the SHG conversion efficiency of the hybrid spiral WSe_{2} plasmonic structure by comparing the intensities of SHG and FW [_{2} plasmonic structure was estimated according to the following equation:^{−5} under the 1064 nm laser excitation, which is larger than most reported nanostructures (Table _{2} (on the order of 10^{−7} m/V).

To look deep into the underlying mechanism of extremely high conversion efficiency of SHG in hybrid 3D spiral WSe_{2} plasmonic structure, we carried out a 3D model to simulate the average intensity of the confined electric field excited by FW in hybrid plasmonic structure (see Materials and Methods). For comparison, the electric field distribution of WSe_{2} on SiO_{2}/Si substrate was also calculated under the same excitation condition, and all the results were shown in Fig. _{2} on the SiO_{2}/Si substrate (Fig. _{2} plasmonic structure shows much more sufficient electric field confinement (Figures _{2} and the gap region between the flake and metal surface. The small mode area of hybrid plasmonic mode with highly confined electric field enhances the light-matter interaction in hybrid 3D spiral WSe_{2} structure, which is favorable for the enhancement of SHG at nanoscale size [_{2}/Si substrate, the reflection enhancement of silver film due to the intrinsic properties of different materials would further strengthen the light-matter interaction in hybrid 3D spiral WSe_{2} structure, which is also beneficial for obtaining efficient SHG [_{2} plasmonic structure, along with the large second-order nonlinear susceptibility of WSe_{2}, brings about the extremely high conversion efficiency of SHG.

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_{2} plasmonic structure. (b, c) The corresponding xy plane (b) and xz plane (c) obtained from the result shown in (a). (d) The magnified image of the region marked with red box shown in (c).

Owing to the extremely high second-order nonlinear optical conversion efficiency, the hybrid 3D spiral WSe_{2} plasmonic structure offers a possibility of achieving SHG and SFG simultaneously. Meanwhile, the subwavelength thickness of 3D spiral WSe_{2} would ease the phase-matching condition for second-order nonlinear parametric processes, which also benefits the achievement of SHG and SFG [_{1} and FW_{2}) excitation, the hybrid 3D spiral WSe_{2} plasmonic structure would produce three discrete coherent signals (SHG_{1} of FW_{1}, SHG_{2} of FW_{2}, and the sum-frequency generation of FW_{1} and FW_{2}), as illustrated in Figure _{2} structure under the excitation of FW_{1} and FW_{2}. Three discrete sharp peaks with centers at 489 nm, 509 nm, and 532 nm were achieved. Except for the SHG_{1} (489 nm) and SHG_{2} (532 nm) generated from the FW_{1} and FW_{2}, respectively, the wavelength centered at 509 nm satisfies the following equation described as_{2} plasmonic structures [

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_{2} plasmonic structure excited with 1064 nm and 980 nm CW laser simultaneously. (c) The spectra collected from the hybrid 3D spiral WSe_{2} plasmonic structure with varied 1064 nm pump power while the 980 nm laser power was fixed. (d) The corresponding signals intensities vary with the increase of the 1064 nm laser power.

Power-dependent measurements were further carried out to explore the relationship between SHG and SFG by fixing the power of 980 nm laser. Figures _{1} remains unchanged while those of SFG and SHG_{2} increase with the increase of 1064 nm laser power. In addition, as we can see from Figure _{2} (532 nm) shows a square dependence of FW_{2} power while that of SFG grows linearly with the increase of FW_{2} power. These results agree well with the mechanism of SHG and SFG, where the intensities of signals varied with the FW power can be expressed as_{2} plasmonic structures.

In summary, highly efficient second-order nonlinear parametric processes were realized in hybrid 3D spiral WSe_{2} plasmonic structures based on the enhanced light-matter interaction through the intense electric field confinement of SPPs. The 3D spiral WSe_{2} with broken inversion symmetry, where the basal planes spiral up from the bottom to the top layers with gradually decreasing size, exhibits large nonvanishing second-order nonlinear susceptibility. The constructive interference of SH fields between the neighboring atomic layers, along with the enhanced light-matter interaction, results in the extremely high SHG conversion efficiency (2.437×10^{−5}). Moreover, SHG and SFG were simultaneously achieved due to the enhanced second-order nonlinear processes and the ease of phase-matching condition in hybrid 3D spiral WSe_{2} plasmonic structures. We believe that the results demonstrated here would provide enlightenment for the construction of typical structures for efficient nonlinear processes.

The tungsten oxide (WO_{3}, 99.99%) and selenium powders (Se, 99.99%) were purchased from Sigma Aldrich and used without further treatment. An atmospheric pressure chemical vapor deposition (CVD) method (Fig. _{2} nanostructures [_{3} and Se powders. The high nucleation rate at the initial stage was applied to produce a dislocation center with high spiraling-up activity [_{3} powders were loaded in a ceramic boat covered with clean face down SiO_{2}/Si substrate at the center of heating zone 1. Another ceramic boat containing 600 mg Se powders was placed at the high temperature region close to WO_{3} (heating zone 2). To increase the nucleation rate for the increasing possibility of getting spirals, we set the evaporation temperature of Se power at 400°C. Before heating, the tube was vacuum-pumped to evacuate the air and then refilled with mixture of H_{2}/Ar (with 5% H_{2}, the carrier gas) to atmospheric pressure. After that, the center of the heating zone 1 (heating zone 2) was heated to 950°C (400°C) in 30 min and held for 15 min. Then, the furnace was cooled to room temperature naturally. During the growth process, 300 sccm mixture of H_{2}/Ar is continuously supplied as the carrier gas.

The WSe_{2} nanostructures were transferred onto different substrates for the measurements of atomic force microscopy (AFM, Bruker Multimode 8) and aberration-corrected scanning transmission electron microscopy (STEM, JEM-ARM 200F). The optical measurements were carried out on home-built far-field micro optical systems. The schematic demonstration of the experimental setups for optical characterization is shown in Figure _{2} nanosheet through an objective to obtain SH radiation. The excitation laser (FW) was filtered with a 750 nm short-pass filter. The emission from the WSe_{2} nanostructure was collected with the same objective and recorded with a thermal-electrically cooled CCD (Princeton Instruments, ProEm: 1600B). For SHG and SFG measurements, two continuous-wave lasers with wavelength of 1064 nm and 980 nm were employed as the FWs and focused onto a typical WSe_{2} nanosheet through the same objective to achieve SHG and SFG simultaneously. The generated signals were also collected with the same objective and recorded with the thermal-electrically cooled CCD.

The numerical simulations were carried out with the commercial software COMSOL, which can solve three-dimensional Maxwell equations by the finite element method. The frequency domain Wave Optics module was employed. A tetrahedral solid structure was utilized to model WSe_{2} structure with a refractive index (n) of 3.5, sitting on top of 1 _{2} layer (n=1.38). A linearly polarized beam with wavelength of 1064 nm was employed to irradiate from the top of hybrid 3D spiral WSe_{2} plasmonic structure. For hybrid plasmonic structure, the permittivity of Ag is -57.906+0.60878i at wavelength of 1064 nm.

All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors.

The authors declare that there are no conflicts of interest regarding the publication of this article.

Yong Sheng Zhao conceived the original concept. Yong Sheng Zhao and Jiannian Yao supervised the project. Xianqing Lin and Yingying Liu designed the experiments and prepared the materials. Xianqing Lin, Yingying Liu, Kang Wang, and Xiaolong Liu performed the optical measurements. Xianqing Lin, Yingying Liu, Yongli Yan, and Yong Jun Li put forward the theoretical model and contributed to the theoretical calculations. Xianqing Lin, Yingying Liu, and Yong Sheng Zhao analyzed the data and wrote the paper. All authors discussed the results and commented on the manuscript. Xianqing Lin and Yingying Liu contributed equally to this work.

This work was supported financially by the Ministry of Science and Technology of China [Grant Nos. 2017YFA0204502 and 2015CB932404], the National Natural Science Foundation of China [Grant Nos. 21773265, 21533013, and 21790364], and the Youth Innovation Promotion Association CAS

See the attached pdf file for Supplementary Materials, which includes the following: Fig. S1. Schematic illustration of the CVD system for WSe_{2} nanostructures growth. Fig. S2. Height profile of the WSe_{2} nanostructure shown in Figure _{2} plasmonic structure measured under the parallel polarization configuration. Fig. S5. Spectra of SHG and FW obtained from three typical hybrid spiral WSe_{2} plasmonic structures excited with 1064 nm CW laser of varied powers. Fig. S6. Simulated electric field distribution in 3D spiral WSe_{2} on SiO_{2}/Si substrate. Fig. S7. The spectra collected from the hybrid 3D spiral WSe_{2} plasmonic structure with varied 980 nm pump laser power while the 1064 nm laser power was fixed. Table S1. The corresponding mean values and standard error of

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_{2}-based van der waals heterostructures

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_{2}monolayers by laser excitation at exciton resonances

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_{2}monolayer transistor

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_{2}nanosheets

_{2}layered structures for highly efficient edge second-harmonic generation

_{2}crystals on dielectric substrates

_{2}

_{2}spiral pyramid

_{2}by sulfur-assisted chemical vapor deposition

_{2}flakes with low contact resistance grown by chemical vapor deposition

_{2}with broken inversion symmetry

_{2}atomic crystals

_{2}monolayer as probed by wavelength-dependent second-harmonic generation