Enhanced SHG from microscale MoS₂ by a single Au@SiO_x nanoantenna

SHG from monolayer MoS₂ in the presence of a single Au@SiO_x nanoantenna was measured with a laser-scanning multiphoton microscope (A1R-MP; Nikon Instruments Europe, Amsterdam, NLD) coupled to a wavelength tunable, 100 fs Ti:Sapphire laser (MaiTai Deep See; Spectra-Physics, Santa Clara, CA, USA). Figure 2 shows detected spectra arising from 810 to 1000 nm ω excitation of a CVD-synthesized, ~4 × 10⁵ nm²-area MoS₂ monolayer in the absence (gray) and presence (red) of one 150 nm Au@SiO_x nanoantenna at its center. Scattered photons were collected by a 60×, 1.27 NA water-immersion objective and delivered to a photomultiplier tube (PMT) array at 2.5 nm wavelength binning. Corresponding SEM and SHG micrographs are shown above; arrows correlate each SHG micrograph with its associated spectra. Inset confirms second-order nonlinear behavior with a 1.8 power-dependence for the heterostructure. It is noted SHG remains finite at pump wavelengths less than 810 nm and greater than 1000 nm, but acquisition conditions were optimized for this spectral range.

Figure 2.

Scattered SHG (per unit area) spectra from a MoS₂ monolayer, ~4 × 10⁵ nm² area, at 810–1000 nm excitation (10 nm step) in the absence (gray) and presence (red) of a single Au@SiO_x nanoantenna (15 nm Au shell; 120 nm SiO_x core). The inset shows 1.77- and 1.80-power dependence between SH and pump intensities taken at 880 nm excitation, confirming a second-order nonlinear process for the heterostructure and MoS₂ control, respectively. SEM and SHG micrographs at each excitation wavelength are shown (top) with arrows to corresponding spectra.

Integrated SHG intensity from the ~4 × 10⁵ nm² MoS₂ area was enhanced 17–84% across the spectrum in the presence of a single 150 nm Au@SiO_x nanoantenna, ostensibly due to the surface plasmon-augmented local field. This was despite the relatively small ~5–10% MoS₂ surface area shadowed by the nanoantenna, estimated from SEM. At conditions evaluated, ~90–95% of the MoS₂ monolayer did not experience local field augmentation by the nanoantenna. Previous reports of plasmon-enhanced SHG citing order-of-magnitude improvements in SHG signal at the LSPR consider (i) a nonlinear medium doped isotropically with nanoantennas or a lithographed nanoantenna lattice or (ii) local, point-wise SHG data. Highest MoS₂ SHG enhancements by the single nanoantenna here were observed off-resonance, away from its LSPR. In contrast, maximal MoS₂ SHG enhancement by Au@SiO_x nanoantenna dimers was near their LSPR (discussed in forthcoming sections). It is hypothesized that off-LSPR occurrence of the maximal SHG enhancement was in part due to plasmonic losses, which consequently caused different laser excitation conditions for TMD at each pump wavelength. Putative dampening of laser energy by plasmonic activity on nanoantenna could arise from: in-plane scattering away from TMD and/or transduction into Landau-damped hot electrons injected into TMD (approximately 11–38% of LSPR dephasing),^[Reference Yu, Ji, Zu, Du, Kang, Li, Zhou, Shi and Fang^4, Reference Forcherio, Dunklin, Backes, Vaynzof, Benamara and Roper^5] for example. Such plasmonic losses alter how the pump laser couples with the MoS₂, but are neglected for simplicity in Eq. (1) and will be discussed in more detail in forthcoming sections. SHG from MoS₂ and Au@SiO_x nanoantenna controls are discussed in the proceeding section to provide context for enhanced SHG from the heterostructures.

MoS₂ and Au@SiO_x nanoantenna control experiments

Mean SHG intensity measured from ten distinct MoS₂ monolayers exhibited a frequency-dependence corresponding with the expanded density of states along the C exciton transitions.^[Reference Klots, Newaz, Wang, Prasai, Krzyzanowska, Caudel, Ghimire, Yan, Ivanov, Velizhanin, Burger, Mandrus, Tolk, Pantelides and Bolotin^20] The C transition is associated with the van Hove singularity of MoS₂. Malard et al. also measured an association of SHG in this spectral range to the direct C exciton transition near the Γ point at approximately 2.8 eV (450 nm).^[Reference Malard, Alencar, Barboza, Mak and de Paula^7] Figure 3(a) shows the frequency-dependence of SHG from 810 to 1000 nm ω excitation averaged from ten crystals (black squares). Superimposed are DDA-calculated bulk-like $\left[ {\chi _{2\omega} ^{(2)}} \right]^2$ spectra [black dashed line; proportional to SHG via Eq. (1)] and measured linear differential reflectance spectra (blue solid line) of the MoS₂, revealing the C transition. The C transition concomitantly acts as a loss (via absorption of SH signal) and as a SHG gain (via χ ⁽²⁾ resonance).^[Reference Malard, Alencar, Barboza, Mak and de Paula^7] SHG intensity did not decrease over time, indicating no photodamage. Power dependence of SHG exhibited typical quadratic behavior.

Figure 3.

SHG control experiments. (a) Normalized SHG intensity (integrated over SH bandwidth) versus central SH wavelength averaged from ten distinct MoS₂ monolayers (black squares). Superimposed are bulk-like $\left[ {\chi _{2\omega} ^{(2)}} \right]^2$ magnitude calculated DDA (black dashed line) and measured differential reflectance spectra (blue line) for MoS₂ monolayers. (b) Mean 2ω emission intensity (per unit area) for five distinct Au@SiO_x nanoantennas (15 nm Au shell; 120 nm SiO_x core). The top panel shows 2ω images of the five individual Au@SiO_x nanoantennas according to summed, maximum 2ω luminescence from 400 to 480 nm detected within a 5 µm z-scan using 820 nm excitation. Error in each graph reflects the maximum and minimum from the mean.

Measured SHG profile for undecorated MoS₂ monolayers aligned closely with DDA-simulated bulk-like $\chi _{2\omega} ^{(2)} $ (black dashed line), which was based on Miller's rule using linear MoS₂ susceptibility, χ ⁽¹⁾, as detailed in the Supplementary Material. The measured C exciton transition (blue line) occurred 15 nm blue-shifted from the 450 nm SHG maximum, consistent with measurements by Malard et al.^[Reference Malard, Alencar, Barboza, Mak and de Paula^7] Density functional theory (DFT) calculations and a Bethe-Salpeter exciton model of χ ⁽²⁾ for MoS₂ corroborate the measured SHG trends.^[Reference Clark, Senthilkumar, Le, Weerawarne, Shim, Jang, Shim, Cho, Sim, Seong, Rhim, Freeman, Chung and Kim^6, Reference Wang and Guo^21, Reference Trolle, Seifert and Pedersen^22] This is illustrated in Fig. S7. An approximate 7 nm offset between SHG maximum and simulated bulk-like $\left[ {\chi _{2\omega} ^{(2)}} \right]^2$ was attributable to the water environment of the immersion-objective used here versus the air environment^[Reference Mao, Chen, Liu, Zhang and Xie^23] of the MoS₂ sample used to obtain linear dielectric data by Mukherjee et al.^[Reference Mukherjee, Tseng, Gunlycke, Kumar, Eda and Simsek^24] from which $\chi _{2\omega} ^{(2)} $ was derived via DDA. Polarization-resolved SHG from the MoS₂ to elucidate depolarization or crystal axis orientation was not measured herein but has been well-characterized elsewhere.^[Reference Clark, Senthilkumar, Le, Weerawarne, Shim, Jang, Shim, Cho, Sim, Seong, Rhim, Freeman, Chung and Kim^6, Reference Malard, Alencar, Barboza, Mak and de Paula^7]

Isolated Au@SiO_x nanoantennas atop SiO_x exhibited broadband 2ω luminescence when excited across the ω wavelength range of 810–1000 nm, whereas SHG was observed from MoS₂. This was attributable to interband relaxation of d-orbital electrons in the Au^[Reference Palomba, Danckwerts and Novotny^25] rather than SHG originating from the nanoantenna. Figure 3(b) shows the mean detected intensity in the 2ω spectrum from five Au@SiO_x nanoantennas; intensity magnitude was negligible compared with that of MoS₂ SHG in Fig. 2. The centrosymmetric fcc structure of Au and amorphous SiO_x prohibited SHG beyond minute surface contributions, where crystalline symmetry is inherently broken. Luminescence decreased as ω was detuned from the 817 nm dipole LSPR, consistent with the LSPR profile in Fig. 1(d) and other reports.^[Reference Grinblat, Rahmani, Cortes, Caldarola, Comedi, Maier and Bragas^15] Broadband luminescence has been widely noted for high-fluence laser excitation of metal nanoantennas.^[Reference Palomba, Danckwerts and Novotny^25] Multiphoton identification of single Au@SiO_x nanoantennas, corroborated independently with SEM, was facilitated by a secondary method of multiphoton image acquisition where maximal detected 400–480 nm luminescence from 820 nm excitation across a 5 µm z-scan was translated into a 2D projection [see top of Fig. 3(b) and Fig. S5].

SHG from nanoantennas has been shown to increase with the degree of non-centrosymmetry in antenna geometry. For example, Walsh et al. enhanced SHG 40 ×  from Au nanocylinder arrays by plasmon-phonon transduction at various laser intensities to introduce morphological disorder into the otherwise centrosymmetric cylinders.^[Reference Walsh and Dal Negro^26] Augmentation of surface SHG by plasmon-enhanced local electric fields is an alternative mechanism that has been studied.^[Reference McMahon, Ferrara, Bowie, Lopez and Haglund^27] The Au@SiO_x nanoantennas studied herein had centrosymmetric core-shell morphology that resulted in negligible SHG with no appreciable surface contribution.

Enhanced SHG from MoS₂ by Au@SiO_x nanoantenna dimers

SHG intensity from MoS₂ monolayers was enhanced in presence of Au@SiO_x nanoantenna dimers, ostensibly due to augmentation of the local electric field governed by the inter-nanoantenna gap within the dimer. Figure 4 shows the measured SHG intensity enhancement factors, X, by a Au@SiO_x nanoantenna dimer with 280 nm (blue) or 170 nm (black) gap, relative to two comparably sized MoS₂ controls. Corresponding SEM micrographs are inset. Overall SHG gain was low. Likewise, Metzger et al. cited difficulty in clearly resolving THG gain from an indium tin oxide nanoparticle placed within a resonating plasmonic Au nanodimer.^[Reference Metzger, Hentschel, Schumacher, Lippitz, Ye, Murray, Knabe, Buse and Giessen^17] Linear extinction spectra calculated by DDA for each nanoantenna dimer suspended in water (due to water immersion objective) are superimposed onto the measured X values. Trend and relative magnitudes of the measured X values were consistent with their respective nanoantenna dimer extinction spectra. Field strength between nanoantenna dimer elements increases exponentially as gap size narrows due to capacitive coupling.^[Reference Kadkhodazadeh, De Lasson, Beleggia, Kneipp, Wagner and Kneipp^28] Power-dependence of SHG was measured to be 1.87 and 1.82 for 280 and 170 nm gap dimers, respectively. Error bars reflect maximum and minimum from the mean due to minute variation in the size of MoS₂ controls.

Figure 4.

Measured SHG enhancement factor, X, for MoS₂ monolayers, each ~4 × 10⁵ nm² in area, by nanoantenna dimers composed of 150 nm Au@SiO_x (15 nm Au shell; 120 nm SiO_x core) separated by 170 nm (black) and 280 nm (blue). Error reflects the maximum and minimum from the mean enhancement over two nearby, comparably-sized MoS₂ controls. One dimer was measured for each gap distance. Superimposed are DDA-calculated linear extinction spectra (dashed lines) for MoS₂-free Au@SiO_x chains in water with spacing equal to each measured dimer gap, and was scaled to show correlation with their respective X profile. SEM micrographs for each dimeric heterostructure are shown.

Enhancement of SHG from MoS₂ at the Au@SiO_x LSPR was highest for the 170 nm gap dimer, reaching up to 88% (i.e., X = 1.88) at 810 nm. Expanding the gap to 280 nm decreased X to 74%, which is consistent with reduced coupling as the two Au@SiO_x nanoantenna comprising the dimer separate. SHG enhancement by the 280 nm gap dimer decreased as ω was detuned from the LSPR. The decrease coincided DDA-calculations of optical field intensity enhancement factors, i.e., γ ², at the MoS₂ monolayer by the LSPR (see Fig. S13). For the 170 nm gap dimer, however, X increased beyond 860 nm excitation in correspondence with the emergence of a second plasmon resonance near 960 nm arising from the capacitive interaction. The emergence of capacitively-coupled plasmon resonances at energies lower than the single-particle LSPR has also been observed elsewhere.^[Reference Kadkhodazadeh, De Lasson, Beleggia, Kneipp, Wagner and Kneipp^28] DDA simulation of parallel-polarized excitation of single Au@SiO_x nanoantennas arranged in a chain with 170 nm gap confirmed the emergence of such a coupled resonance (see the black dashed line in Fig. 4 and black solid line in Fig. S11). Higher X exhibited by the 170 nm gap dimer in the 800–890 nm range relative to the 280 nm gap dimer appears counter to the absolute, MoS₂-absent extinction magnitudes of the nanoantenna dimers shown in Fig. S11. However, their true optical extinction could differ upon the inclusion of the MoS₂ (prohibitive computationally, detailed later) and the local field around a nanoantenna differs from the field at its interface with a MoS₂ sublayer.

Normalized SHG conversion efficiency analysis

Measured enhancement of MoS₂ SHG in the presence of Au@SiO_x nanoantennas, X, was consistent with augmentation of the local electric field by LSPR excitation, quantified numerically by a factor γ = |E/E_o|_ω. Overall SHG conversion efficiency is proportional to γ ⁴, as in Eq. (1).^[Reference Ishifuji, Mitsuishi and Miyashita^12] An ab initio estimate of overall SHG conversion efficiency, η _2ω, for MoS₂ in the absence of a nanoantenna was calculated to be up to 7.8 × 10⁻⁸ at the 100 GW/cm² irradiation intensity used herein, per Eqs. (2) and (3) (derived in §S8 of the Supplementary Material) under the following assumptions:^[Reference Kumar, Samanta, Devi and Ebrahim-Zadeh^29] (i) interaction length, L = 6.5 Å for monolayer MoS₂, was within the focus depth; (ii) no pump depletion by the MoS₂; (iii) phase coherence; and (iv) bulk-like $\chi _{2\omega} ^{(2)} $ for monolayer MoS₂ calculated from a Miller's rule calculation with DDA (see Supplementary Material):

(2)$$\eta _{2\omega} \equiv \displaystyle{{I_{2\omega}} \over {I_\omega}} = \eta _{{\rm norm}}\; L^2I_\omega $$

(3)$$\eta _{{\rm norm}} \equiv \displaystyle{{2\pi ^2{\left[ {\chi _{2\omega} ^{(2)}} \right]}^2} \over {n_\omega ^2 n_{2\omega} c\epsilon _o\lambda _\omega ^2}} \; $$

Here, the normalized SHG conversion efficiency, η _norm, is introduced to allow direct comparison of SHG performance with other materials or heterostructures by removing dependence on extrinsic parameters I _ω and L.^[Reference Kumar, Samanta, Devi and Ebrahim-Zadeh^29] Absolute determination of η _2ω using measured values of I _2ω and I _ω was precluded by the absence of rigorously characterized signal losses within the microscope (e.g., ω-dependent losses at each lens/mirror, PMT quantum efficiencies, etc.).

Figure 5 shows η _norm for an isolated MoS₂ monolayer (gray line) calculated by Eq. (3) using the DDA-calculated bulk-like χ ⁽²⁾ via Miller's rule, which closely matches the measured intensity profile in Fig. 3. Equation (3) accounts for the wavelength and optical dispersion at the ω and 2ω frequencies, respectively, which advances an interpretation of SHG spectrum profiles beyond only χ ⁽²⁾. The undecorated MoS₂ had a calculated peak η _norm of 0.0159%/W. By comparison, lithium niobate technology performs near 0.0001%/W.

Figure 5.

Normalized SHG conversion efficiency, η _norm, for a MoS₂ monolayer in the absence [gray line; calculated using Eq. (3)] and presence of a (Au@SiO_x)_i nanoantenna, where subscript i is 1 for the monomer (red square) or 2 for the dimers (blue and black squares). Au@SiO_x nanoantennas were a 15 nm Au shell/120 nm SiO_x core particle. “γ ⁴ η _norm” (red line) is the calculated enhancement in η _norm [see Eq. (2)] using DDA-calculated values of γ for nanoantenna monomer-decorated MoS₂ monolayer. “X η _norm” shows measured η _norm for the Au@SiO_x-MoS₂ heterostructures (squares), where X was the measured SHG enhancement factors relative to MoS₂ controls, under the condition that accrued SHG resulted solely from local field augmentation by the nanoantenna (i.e., X = γ ⁴). Note that X η _norm for the 280 nm (blue squares) and 170 nm (black squares) gap dimers are vertically offset by 0.010 and 0.015 units from their absolute magnitudes, respectively, for clarity. The error is the maximum and minimum from the mean from 4 and 2 sample sizes for the monomer and dimer data, respectively.

Full-field DDA calculations indicated the presence of a single Au@SiO_x nanoantenna as a passive SHG gain element could increase peak η _norm to 0.0239%/W, labeled as γ ⁴η _norm [red line; see Eq. (1) and (S5)–(S7)]. This calculation assumed the nanoantenna (i) did not contribute SHG (confirmed earlier) and (ii) passively enhanced MoS₂ η _norm according to its local plasmonic field factor, γ. In the latter, γ ² incident upon the MoS₂ was calculated by DDA at each ω. Although γ ² “seen” by the MoS₂ from interaction with the nanoantenna followed the LSPR spectral profile in Fig. 1(d), its magnitude remained within ±5% across the 810–1000 nm excitation spectrum, as detailed in Fig. S13.

Plasmonic field-augmentation appeared responsible for the measured SHG enhancements from MoS₂. This was implied by a heuristic comparison in Fig. 5 between MoS₂ η _norm multiplied by (i) DDA-calculated field-enhancement factors by the nanoantenna (γ ⁴η _norm; red line) and (ii) measured SHG enhancement factors (Xη _norm; red squares). The peak measured Xη _norm for the single nanoantenna-MoS₂ heterostructure was 0.0217%/W at 890 nm excitation. Good agreement in magnitude and frequency-dependence is observed at off-resonant wavelengths beyond 880 nm, with an evident dip proximal to the 820 nm LSPR frequency, putatively due to plasmonic losses.

Plasmonic dampening of the pump laser at wavelengths proximal to the 820 nm Au@SiO_x nanoantenna LSPR appeared to diverge measured SHG-enhanced η _norm (i.e., Xη _norm) of the monomeric heterostructure from its DDA-calculated γ ⁴η _norm profile. Good agreement was observed at off-resonant excitation wavelengths. It is hypothesized that plasmonic activity of the nanoantenna dampened the pump laser via plasmon-phonon transduction, plasmonic re-radiation in-plane with the MoS₂ and/or 11–38% plasmonic hot electron injection losses.^[Reference Yu, Ji, Zu, Du, Kang, Li, Zhou, Shi and Fang^4, Reference Forcherio, Dunklin, Backes, Vaynzof, Benamara and Roper^5] For example, frequency-dependent plasmonic re-radiation from a nanoantenna could scatter resonant pump photons away from the MoS₂, thus preventing the production of a SH photon from their annihilation. Plasmonic losses in nanoantenna-TMD heterostructures change the degree to which the pump laser can couple to the TMD, which was not taken into account in Eqs. (1)–(3). Incomplete characterization of these interactions to date precluded quantitation of such pump-TMD coupling effects in presence of plasmonic nanoantennas, but hold interest as future work. At wavelengths beyond 900 nm where plasmonic losses were less appreciable, Xη _norm converged near the calculated γ ⁴η _norm profile with good agreement in magnitude.

Measured SHG enhancement factors for the dimeric nanoantenna-MoS₂ heterostructures gave Xη _norm profiles in Fig. 5 (scaled vertically by 0.010 and 0.015 units for clarity) that were akin to the monomeric heterostructure sans pump losses, despite their distinct capacitively-coupled plasmonic activity. Interestingly, these dimer Xη _norm data closely resemble their raw SHG measurements in a laboratory setting. The 280 nm-gap (170 nm-gap) dimer enhanced peak Xη _norm from 0.0217%/W for the monomer to 0.0222%/W at 840 nm (0.0250%/W at 890 nm). The largest value of overall η _2ω for any measured Au@SiO_x nanoantenna-MoS₂ heterostructure using Eq. (2) was 1.24 × 10⁻⁷ at the I _ω = 100 GW/cm² employed to collect these data.

Quantitation of γ-factors for the dimers to distinguish contributions from multiple single nanoantennas versus inter-nanoantenna coupled interactions (see Fig. S12) was computationally prohibitive to compare with measured X values. DDA computation time scales with the cube of total target dipoles, (N _dipole).^[Reference Bhanu, Islam, Tetard and Khondaker^3] The 15 nm thick Au shell necessitated a 3 nm inter-dipole spacing for solution convergence of optical extinction spectra calculations, giving N _dipole of 65,257 dipoles for one Au@SiO_x nanoantenna in DDA (excluding any substrate). By comparison, a uniform Au sphere with equal volume to the shell@core nanoantennas would have allowed 98 ×  reduced computation time with 14,147 dipoles at a 5 nm spacing. Accurate calculation of near-field enhancement magnitudes necessitates ~1 nm spacings, giving 1,767,063 dipoles that further exacerbate computational expense. A boundary element approach may circumvent these obstacles in future work.