Simultaneous Enhancement and Preservation of Valley-Polarized Second-Harmonic Generation in Monolayer WS₂ via Mie Resonances

Abstract

Second-harmonic generation (SHG) with rigorous polarization preservation is essential for next-generation optical information processing. Monolayer transition-metal dichalcogenides offer an attractive platform for atomically thin, on-chip light sources owing to their valley-dependent polarization selection rules for SHG. However, their atomic-scale thickness severely limits conversion efficiency. To overcome this challenge, nanophotonic structures capable of simultaneously enhancing signal intensity and maintaining high-purity polarization states are required for practical device applications. Herein, we demonstrate the simultaneous resonant enhancement and high-fidelity preservation of valley-polarized SHG in monolayer WS₂ coupled with Mie-resonant silicon nanospheres. We show that the valley polarization state is spectrally modulated by the Mie modes of silicon nanospheres, achieving circular polarization retention of ∼80% within the enhanced spectral regime. These findings establish a robust strategy for manipulating polarization degrees of freedom in integrated nonlinear valley photonics.

Second-harmonic generation (SHG) is a fundamental mechanism for frequency conversion in nonlinear photonics. , Rigorous preservation of the polarization state in nonlinear frequency conversion is indispensable for a wide range of photonic applications, including maintaining high-fidelity polarization-encoded qubits, , translating polarization-multiplexed signals, , manipulating optical spin angular momentum, , and characterizing ultrafast vectorial optical fields. , To realize these functionalities on integrated photonic platforms, compact and efficient nonlinear light sources are required. However, conventional bulk crystals are constrained by their macroscopic dimensions and stringent phase-matching requirements, rendering them unsuitable for on-chip integration. Therefore, exploring nanoscale materials capable of generating strong and highly polarized SHG is critical for next-generation optoelectronics. Atomically thin transition-metal dichalcogenides (TMDs) have emerged as an ideal platform to address these challenges. , In contrast to their bulk counterparts, monolayer TMDs inherently lack inversion symmetry, resulting in exceptionally large second-order nonlinear susceptibilities. , Importantly, they exhibit unique valley-dependent optical selection rules arising from broken inversion symmetry and strong spin–orbit coupling, , which strictly couple the valley index to circularly polarized light. − Despite this intrinsic polarization purity, the atomic-scale interaction volume severely limits their absolute SHG efficiency, , creating a fundamental bottleneck for practical applications. To utilize these materials for new valleytronic devices, it is essential to enhance the SHG response while preserving valley-dependent polarization information. Plasmonic nanostructures have been widely investigated to overcome this limitation. , However, simple achiral plasmonic structures often scramble valley-dependent polarization information owing to scattering or complex near-field distortions. Chiral plasmonic metasurfaces can control circularly polarized emission, , but ohmic losses and structural chirality complicate the extraction of intrinsic valley information.

Recently, high-refractive-index dielectric nanomaterials have emerged as a compelling alternative. − Dielectric nanoparticles, such as silicon, exhibit negligible ohmic loss while maintaining strong light confinement. When their dimensions are comparable to the wavelength of light, these nanoparticles support Mie resonances, the spectral position of which can be tuned by varying particle size. − A distinctive feature of dielectric nanoparticles is their ability to sustain both electric and magnetic resonance modes. ,− When these electric and magnetic dipole resonances satisfy specific amplitude and phase correlations, the nanoparticle can preserve the helicity of incident circularly polarized light, ,− offering a robust pathway for valley-polarized nonlinear optics. Giant SHG enhancement from monolayer WS₂ has been achieved using dielectric metasurfaces, but preserving the valley polarization through the enhancement process remains challenging.

Herein, we demonstrate the simultaneous enhancement and polarization preservation of SHG from a WS₂ monolayer coupled to Si nanospheres (Si NSs). Linearly polarized SHG measurements reveal a significant enhancement arising from contributions of magnetic dipole (MD) and higher-order resonances. Under circularly polarized excitation, we further show that the degree of circular polarization (DOCP) is spectrally modulated by the resonance modes, achieving a high polarization retention (∼80%) at specific wavelengths. Finally, we elucidate the underlying mechanism responsible for the observed enhancement and polarization preservation through numerical simulations.

Figure a presents a schematic of the resonator structure integrated with monolayer WS₂ and the corresponding SHG process. Si NSs were deposited on a mechanically exfoliated WS₂ monolayer. The left panel of Figure b shows an optical image of monolayer WS₂ decorated with 200 nm Si NSs. To clearly distinguish the optical response of WS₂ coupled to the nanospheres, the monolayer WS₂ was selectively removed by etching, except for the region directly beneath each Si NS. The center panel of Figure b displays an optical micrograph of the etched sample, while the right panel shows the corresponding photoluminescence (PL) mapping at 630 nm. In the PL map, emission is observed exclusively at the positions of the Si NSs. A comparison of the optical images before and after etching confirms that the WS₂ in the regions not covered by the Si NSs was completely removed.

1.

(a) Schematics of the resonator structure integrated with monolayer WS₂ and the SHG process. (b) Optical image and 630 nm PL mapping of the WS₂/Si NS after etching. (c) Calculated radiative rate enhancement factor of Si NSs with diameters of 200 nm (top) and 241 nm (bottom). (d) Fundamental wavelength dependence of the SHG intensity for Si NSs with diameters of 200 nm (top) and 241 nm (bottom). (e) SHG enhancement factor calculated from panel (d) for 200 nm (blue) and 241 nm (red) Si NSs.

Figure c shows the calculated radiative rate enhancement factor (Γ/Γ₀) for an in-plane dipole positioned 3 nm from the surface of Si NSs with diameters of 200 nm (top) and 241 nm (bottom), where Γ and Γ₀ denote the radiative rates with and without the Si NS, respectively. The 200 nm NS exhibits a MD resonance at ∼780 nm, while the 241 nm NS supports a magnetic quadrupole (MQ) resonance at ∼690 nm. This coupling is experimentally corroborated by the PL spectra shown in Figure S2, where additional peaks appear at 750 and 690 nm for the 200 and 241 nm Si NSs, respectively. This close agreement between the calculated resonant modes and the experimentally observed PL peaks confirms efficient coupling between the WS₂ monolayers and the Si NSs.

SHG measurements were performed as a function of the fundamental wavelength under linearly polarized excitation. Figure d shows the wavelength dependence of SHG intensity for samples incorporating 200 nm (top) and 241 nm (bottom) Si NSs, respectively. The black curves represent the SHG intensity from bare WS₂ monolayers, while the blue and red curves correspond to WS₂ monolayers coupled to Si NSs. The bottom axis denotes the wavelength of the excitation laser, and the top axis indicates the corresponding wavelength of the emitted SHG light. The SHG intensity is normalized by the effective excitation area. For a bare WS₂ monolayer, the effective area is defined by the Gaussian beam spot, with an effective diameter of 700 nm, considering the laser spot size of 1 μm and the quadratic power dependence of the SHG process. The diameter of the WS₂ beneath the Si NS is estimated to be approximately 0.9 relative to that of the Si NS based on the reported ion angular distribution of 5–9° from the surface normal. In the present analysis, we use the Si NS diameter as the effective sample diameter, which yields a conservative estimate of the enhancement factor. As shown in Figure d, the SHG intensity from bare WS₂ monolayers (black curve) exhibits a considerably broad peak around 880 nm, corresponding to the C-exciton resonance of WS₂. For the sample with 200 nm Si NSs (blue curve), a strong and broad peak appears around 850 nm. Furthermore, in the bottom panel of Figure d, the sample incorporating 241 nm Si NSs (red curve) exhibits a prominent enhancement (several tens of times) around 920 nm. This increase indicates SHG from monolayer WS₂ is strongly enhanced by coupling to the Si NS.

To confirm the origin of the observed signal, we examined its dependence on excitation power and polarization (Figure S4). The signal intensity exhibits a quadratic dependence on excitation power, confirming the second-order nonlinear nature of the SHG process. Furthermore, the polarization-resolved polar plots exhibit a distinct 6-fold rotational symmetry, consistent with the crystal symmetry of monolayer WS₂. , Combined with the absence of any detectable SHG signal from bare Si NSs (Figure S5), these results conclusively demonstrate that the observed signal originates from resonantly enhanced SHG in monolayer WS₂, rather than from luminescence or SHG generated by the Si NSs themselves.

Figure e shows the enhancement factor derived from the data in Figure d. The blue and red curves correspond to samples incorporating 200 and 241 nm Si NSs, respectively. For the 200 nm sample, a broad enhancement of approximately 5-fold is observed around the fundamental wavelength of 850 nm (corresponding to an SHG wavelength of 425 nm). By contrast, the 241 nm sample exhibits a prominent enhancement peak at a fundamental wavelength of 920 nm (corresponding to an SHG wavelength of 460 nm), reaching a maximum enhancement factor of over 40. As shown in Figure c, theoretical calculations of the radiative rate enhancement factor for the 200 nm Si NS indicate the presence of higher-order MD and electric dipole (ED) resonances in the SHG wavelength range, which couple to the emitted SHG signal. The fundamental excitation at 850 nm lies on the long-wavelength side of the MD resonance (which peaks around 780 nm) and is far from resonance, resulting in a weak enhancement of the fundamental field. For the 241 nm sample, the SHG emission couples to the higher-order MQ and electric quadrupole (EQ) resonances, while the fundamental excitation of 920 nm is strongly coupled to the MD resonance at 920 nm. Because the SHG intensity scales quadratically with the fundamental field, this resonant enhancement of the fundamental wave by the MD mode results in the remarkable SHG enhancement observed in the 241 nm sample.

To quantitatively evaluate these results, we calculated the SHG enhancement factor using a realistic numerical model. Figure a shows the model structure of a Si NS positioned on monolayer WS₂. The SHG enhancement process was considered in two steps: enhancement of the excitation field at the fundamental wavelength and enhancement of the emitted SHG signal. In a simplified picture, the total SHG enhancement factor is given by the product of these two contributions. The excitation was modeled as a linearly polarized plane wave incident on the monolayer WS₂ through the Si NS. The resulting SHG emission was modeled as radiation from an in-plane ED source located within the monolayer WS₂ beneath the Si NS. The theoretical SHG intensity was obtained by integrating the calculated far-field radiation pattern over the solid angle corresponding to a numerical aperture (NA) of 0.8.

2.

(a) Schematic illustration of the model structures used for calculating excitation and emission enhancement factors. (b, c) Calculated enhancement factor for Si NSs with diameters of 200 nm (b) and 241 nm (c).

Figure b and c show the calculated enhancement spectra for the monolayer WS₂ coupled to 200 and 241 nm Si NSs, respectively. For the 200 nm sample, the calculation predicts a broad enhancement peak centered at ∼870 nm, with an enhancement factor of 5. By contrast, for the 241 nm sample, a prominent enhancement peak is predicted at 930 nm, with an enhancement factor of approximately 16. These theoretical results, obtained by treating the monolayer WS₂ as the SHG source, are in good agreement with the experimental findings shown in Figure e, particularly in terms of the order of magnitude of the enhancement. This consistency between theory and experiment indicates that the SHG enhancement from WS₂ arises from the contribution of MD and higher-order resonant modes. A slight systematic discrepancy is noted in the peak wavelengths. Specifically, the simulated enhancement peaks for the 200 and 241 nm samples, located at 870 and 930 nm, respectively, are slightly red-shifted compared to their corresponding experimental peaks at 850 and 920 nm. This discrepancy might be attributed to the dependence of the enhancement on the lateral size of the WS₂ region beneath the nanospheres (see Figure S9).

We next performed circularly polarized SHG measurement at room temperature. Figure a shows the dependence of the SHG intensity from a bare WS₂ monolayer on the fundamental wavelength, excited with circularly polarized light (σ^–). The red and blue lines represent the SHG signal from the copolarized (σ^–) and cross-polarized (σ⁺) components, respectively. The signal from the cross-polarized component is significantly stronger than that from the copolarized component. This observation is consistent with previous studies, as monolayer TMDs exhibit a valley-dependent selection rule for SHG, which leads to SHG emission with helicity opposite to that of the circularly polarized excitation laser. ,

3.

(a) Fundamental wavelength dependence of the circular polarization-resolved SHG intensity from a bare WS₂ monolayer. The red and blue lines represent the copolarized (σ^–) and cross-polarized (σ⁺) components, respectively. Inset: Schematic of the valley-selective SHG process. (b) Same measurement as in (a) for the monolayer WS₂ with 200 nm Si NSs. (c) SHG enhancement factor of the cross-polarized component, calculated from panels (a) and (b). (d) DOCP for samples with (red) and without (black) Si NSs.

We then measured the circularly polarized SHG intensity from the sample incorporating 200 nm Si NSs. Figure b shows the wavelength dependence of the SHG intensity from this sample. As in the bare case, the cross-polarized component (blue) is stronger than the copolarized component (red). Even in the presence of Si NSs, the cross-polarized signal remains dominant, indicating that the selective excitation of valley polarization is preserved.

Figure c shows the enhancement factor for the cross-polarized components, calculated from the data presented in Figure a and b. Evidently, the cross-polarized component is enhanced at ∼840 nm, which is consistent with the results from the linearly polarized measurements. This indicates that the SHG enhancement under circularly polarized excitation arises from resonances, similar to the linearly polarized case. Figure d shows DOCP, defined as (I _σ^– – I _σ⁺ )/(I _σ^– + I _σ⁺ ), for the samples with (red) and without (black) Si NSs. Here, I _σ^– and I _σ⁺ are the SHG intensities of the copolarized (σ^–) and cross-polarized (σ⁺) components, respectively. The bare WS₂ monolayer maintains a nearly constant DOCP value close to −1, confirming that selective excitation of valley polarization is robustly preserved. This stability arises because SHG is a coherent process occurring on a femtosecond time scale, making it immune to the slow, incoherent intervalley scattering processes (picosecond time scale), , that would otherwise degrade the valley-polarized state at room temperature. By contrast, the sample with the Si NS displays a distinct wavelength-dependent DOCP. In the wavelength range of 840–950 nm, DOCP remains high, ranging from −0.6 to −0.8, indicating that the circular polarization is well-preserved in the long-wavelength range. At wavelengths shorter than 840 nm, however, the magnitude of DOCP decreases significantly, dropping to approximately −0.2. These results demonstrate that the integration of Si NSs induces a strong wavelength-dependent modulation of the polarization state.

To investigate the mechanism underlying the DOCP variation, we calculated the enhancement factor and the resulting DOCP. The calculation was performed using the same model as in the linear polarization case (Figure a). In this model, the excitation was assumed to be circularly polarized light, and the SHG emission was treated as radiation from a rotating dipole moment. Figure a shows the calculated enhancement factor for the cross-polarized component. Similar to the linearly polarized measurement, the cross-polarized component is enhanced around 870 nm, showing reasonable agreement with the experimental result. Slight deviations in the peak position and spectral slope, particularly the rising trend at 920 nm in the calculation compared to the drop observed experimentally, might be attributed to the geometric assumptions in the simulation (see Figure S9).

4.

(a) Calculated enhancement factor of the cross-components. (b) Calculated DOCP for Si NSs with a diameter of 200 nm.

Figure b shows the calculated DOCP. The calculation shows that DOCP approaches −1 at longer wavelengths, while its magnitude decreases at shorter wavelengths, consistent with the experimental results. To understand this wavelength dependence of DOCP, we consider the helicity-preserving condition in the scattering process. The circular polarization response of the light scattered from Si NSs is dictated by the balance between their electric and magnetic modes. This correlation is described using the following equation:

$$\mathrm{DOCP}=\frac{2\sum _{l=1}^{\infty }(2l+1)\mathfrak{R}\{a_l{b}_l^{*}\}}{\sum _{l=1}^{\infty }(2l+1)({|a_l|}^2+{|b_l|}^2)}$$ 1

where l represents the multipolar order (l = 1 for dipole, l = 2 for quadrupole), and a _l and b _l are the Mie coefficients corresponding to the electric and magnetic modes, respectively. Helicity-preserving scattering occurs when the phases and amplitudes of the magnetic and electric modes are matched. ,

In the actual system, eq is relevant only when the scattering is substantial; the scattering strength itself depends on the excitation wavelength relative to the Mie resonance. For a silicon nanosphere of diameter D and refractive index n, the Mie resonance wavelength scales as n × D, placing the MD resonance at ∼780 nm for the 200 nm sphere (Figure S8). At longer excitation wavelengths well above the MD resonance, the Si NS scatters the field weakly, so the polarization state is predominantly determined by the incident field. In this regime, the contribution of the scattering process is weak, and the total field retains the helicity of the incident wave. At shorter wavelengths approaching the MD resonance, scattering of the incident field becomes stronger, making the scattering process significant and eq relevant; however, the scattering amplitude of the MD resonance far exceeds that of the ED resonance, breaking the helicity-preserving condition described by eq and thus decreasing the DOCP. These behaviors are supported by the experimental and numerical results, which exhibit high DOCP at 840–950 nm and low DOCP at wavelengths shorter than 840 nm. At the boundary of the weak and strong scattering regimes around 840 nm, the MD and ED amplitudes remain comparable as shown in Figure S8, and the simultaneous enhancement and polarization preservation is observed in the experiments. By contrast, for the sample with larger 241 nm Si NSs, the MD resonance (∼910 nm) falls within the measurement range, so that strong scattering across the spectrum decreases circular polarization (Figure S11).

Herein, we demonstrated the simultaneous enhancement and polarization preservation of SHG in monolayer WS₂ using the Mie resonance of Si NSs. By tuning the resonance wavelength through the Si NS diameter, we achieved significant enhancement originating from contributions of MD and higher-order resonances. Importantly, under circularly polarized excitation, we showed that the Si NSs not only enhance signal intensity but also modulate DOCP via mode interference. Numerical simulations corroborate these experimental findings, elucidating the mechanism underlying the helicity-preserving scattering. This study establishes a robust strategy for realizing efficient, valley-polarized nonlinear light sources, advancing the development of integrated valleytronic devices.

Methods

Sample Preparation

Monolayer WS₂ was fabricated on a SiO₂/Si substrate via mechanical exfoliation from bulk single crystals, where the SiO₂ layer had a thickness of 290 nm. WS₂ monolayers were identified using PL and optical contrast measurements. The resonator structure was fabricated by drop-casting the colloidal solution of Si NSs, prepared via thermal disproportionation of SiO, onto the monolayer WS₂ while the substrate was heated to 80 °C. Finally, the monolayer WS₂ in areas not covered by the Si NSs was removed by Ar⁺ etching for 5 min at a flow rate of 40 SCCM. The diameters of the Si NSs were determined using atomic force microscopy (Figure S1).

SHG Measurement

Figure a illustrates the SHG process, where the red and blue arrows represent the fundamental light (laser) and the generated SHG light, respectively. The experiments were performed using a custom-built, angle-resolved SHG system. A pulsed laser, tunable from 800 to 950 nm, was focused onto the sample through an objective lens. The resulting SHG signal was detected in the 400–475 nm wavelength range using a combination of 650 and 500 nm short-pass filters placed in the detection path. For linearly polarized measurements, a half-wave (λ/2) plate was used to rotate the polarization of the incident light, and a polarizer was used to selectively detect the SHG signal component parallel to the polarization of the incident laser. For circularly polarized measurements, a quarter-wave (λ/4) plate was inserted into the beam path before the objective lens. This plate converted the incident linearly polarized light into circularly polarized light before it illuminated the sample. The generated SHG signal then passed back through the same λ/4 plate, converting it back into linearly polarized light. By rotating a half-wave plate placed before a fixed polarizer, the co- and cross-polarized components of the SHG signal were then selectively detected. All measurements were performed at room temperature.

The SHG process driven by circularly polarized light is governed by the conservation of total angular momentum and the 3-fold crystal symmetry of the material:

$$\begin{array}{c}\Delta m\mathrm{\hslash }=\Delta \tau \mathrm{\hslash }+3N\mathrm{\hslash },(N=\mathrm{\pm 1})\end{array}$$ 2

where Δmℏ is the incident spin angular momentum from the photons, Δτℏ is the change in the valley angular momentum, and 3Nℏ is the angular momentum transferred to the crystal lattice. As shown in the inset of Figure a, at the K’ valley, the valley angular momentum τℏ is 0ℏ for the valence band and 1ℏ for the conduction band, resulting in Δτℏ = +1ℏ. According to eq , this process occurs only through the absorption of two σ^– photons, each carrying −1ℏ, followed by the emission of one σ⁺ photon with +1ℏ.

Numerical Simulations

Numerical simulations were performed using the Lumerical FDTD package. A silicon nanosphere supported by a 290 nm-thick silica layer on a semi-infinite silicon substrate was modeled in a three-dimensional finite-difference time-domain simulation. The refractive index of silicon was taken from a previous study, and that of silica was set to 1.46. All simulation boundaries were defined as perfectly matched layers to minimize artificial reflections. A mesh size of 10 nm was applied throughout the simulation domain, with a finer 5 nm mesh used within the Si NS. The calculations were performed in two steps: (i) For the excitation, a circularly polarized wave (1, −i,0) was launched normal to the substrate from the particle side, and the electric fields were obtained at a two-dimensional discrete Fourier transform monitor positioned 3 nm beneath the Si NS. The induced dipole moments, μ _x (2ω) and μ _y (2ω), were calculated based on the driven excitation electric fields as follows:

$$\begin{array}{c}{\mu }_x(2\omega )\propto P_x(2\omega )={\chi }^{(2)}(E_x^2(\omega )-E_y^2(\omega ))\end{array}$$ 3

$$\begin{array}{c}{\mu }_y(2\omega )\propto P_y(2\omega )=-2{\chi }^{(2)}{E}_x(\omega )E_y(\omega )\end{array}$$ 4

The symmetry properties of monolayer WS₂ were taken into account, where P _i (2ω) = ∑ _jk χ _ijk (2ω, ω, ω)E _j (ω)E _k (ω) and χ _xxx = −χ _xyy = −χ _yyx = −χ _yxy = χ⁽²⁾ are the second-order polarization and susceptibility components of WS₂, respectively. (ii) For the emission, the reciprocity theorem was applied for the far-field calculations of the dipole. Plane waves with TE and TM polarizations were introduced from the particle side at incident angles ranging from 0° to 53° matching the NA (0.8) of the objective lens. The electric fields E _y (2ω) and E _x (2ω) were recorded at the same monitor used for excitation. Finally, the two orthogonal electric fields were captured by multiplying the dipole moments as follows:

$$\begin{array}{c}{E}_{\theta }(2\omega )=E_x^{TM}(2\omega ){\mu }_x(2\omega ){+E}_y^{TM}(2\omega )\end{array}{\mu }_y(2\omega )$$ 5

$$\begin{array}{c}{E}_{\phi }(2\omega )=E_x^{TE}(2\omega ){\mu }_x(2\omega )+E_y^{TE}(2\omega ){\mu }_y(2\omega )\end{array}$$ 6

The intensity was integrated over the polar angle θ, determined by the NA of the objective lens, as

$$\begin{array}{c}I(2\omega )={\int }_{\theta =0}^{\theta =53°}I(\theta ,2\omega )\sin (\theta )d\theta \end{array}$$ 7

$$\begin{array}{c}\chi (2\omega )=\frac{{\int }_{\theta =0}^{\theta =53°}\chi (\theta ,2\omega )I(\theta ,2\omega )\sin (\theta )d\theta }{I(2\omega )}\end{array}$$ 8

where

$$\begin{array}{c}I(\theta ,2\omega )={|E_{\theta }(2\omega )|}^2+{|E_{\phi }(2\omega )|}^2\end{array}$$ 9

$$\begin{array}{c}\chi (\theta ,2\omega )=\frac{1}{2}{\sin }^{-1}(\sin (2\alpha )\sin (\delta ))\end{array}$$ 10

where $\alpha ={\tan }^{-1}\left(\left|\frac{E_{\phi }(2\omega )}{E_{\theta }(2\omega )}\right|\right)$ , and δ is the relative phase shift between the two orthogonal electric field components, defined as δ = arg(E _φ(2ω)) – arg(E _θ(2ω)). The DOCP is calculated from the ellipticity χ, DOCP = sin (2χ).

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.nanolett.6c00297.

• AFM data of the Si NSs on WS₂; photoluminescence spectra; Raman spectra; excitation power dependence and polar plot; excitation power dependence of the bare Si NSs; SHG enhancement ratio of different samples; calculated radiative rate enhancement factor of Si NSs; calculated extinction cross section of Si NSs; sample size dependence of the SHG enhancement factor; sample size dependence of the DOCP; loss of circular polarization for the 250 nm sample; and relationship between SHG enhancement and DOCP (PDF)

The authors declare no competing financial interest.