Abstract
The integration of metallic plasmonic nanoantennas with quantum emitters can dramatically enhance coherent harmonic generation, often resulting from the coupling of fundamental plasmonic fields to higherenergy, electronic or excitonic transitions of quantum emitters. The ultrafast optical dynamics of such hybrid plasmon–emitter systems have rarely been explored. Here, we study those dynamics by interferometrically probing nonlinear optical emission from individual porous gold nanosponges infiltrated with zinc oxide (ZnO) emitters. Fewfemtosecond timeresolved photoelectron emission microscopy reveals multiple longlived localized plasmonic hot spot modes, at the surface of the randomly disordered nanosponges, that are resonant in a broad spectral range. The locally enhanced plasmonic nearfield couples to the ZnO excitons, enhancing sumfrequency generation from individual hot spots and boosting resonant excitonic emission. The quantum pathways of the coupling are uncovered from a twodimensional spectrum correlating fundamental plasmonic excitations to nonlinearly driven excitonic emissions. Our results offer new opportunities for enhancing and coherently controlling optical nonlinearities by exploiting nonlinear plasmonquantum emitter coupling.
Introduction
Nonlinear plasmonics of metallic nanoantennas is highly promising for creating subwavelength coherent light^{1} and electron^{2} sources, and for ultrafast alloptical control^{3}. Importantly, the geometry of such nanoantennas can be flexibly designed, allowing to tune their plasmonic modes to be resonant with the fundamental or higher harmonic frequencies of the driving laser^{4} or even to be doubly resonant^{5,6}. The nonlinear efficiency of pure plasmonic nanoantennas, however, is limited by their intrinsically weak optical nonlinearities and the weak penetration of light into the metal. To further enhance nonlinear emission, hybrid metal–semiconductor nanostructures have been fabricated by combining the strong field enhancements of plasmons and the large nonlinear susceptibility of semiconductors^{7,8,9,10,11,12,13,14}. The enhancement of nonlinear emission often results from the coupling of fundamental plasmonic fields to higherenergy, electronic^{7} or excitonic^{9,14,15} transitions of quantum emitters. Although many studies have been performed on various combinations of plasmonic nanoantennas and semiconductors in the frequency domain, considerably less is known about their ultrafast optical dynamics. Accessing such dynamics is not only important to understand the microscopic origin of the coupling and the mechanism of nonlinear signal enhancement, but also necessary for full coherent control of coupled nanosystems^{3}. Such femtosecond dynamics have been probed on pure plasmonic nanostructures and have proven crucial in understanding plasmonic coherence properties^{16,17,18,19}. Furthermore, most studies on the hybrid nanostructures focus on enhancing second or thirdharmonic generation that doubles or triples energetically degenerate photons, respectively. Other nonlinear wavemixing channels, such as sumfrequency (SF) generation, that provide more possibilities and tunabilities to mix different colors of fundamental photons, have been rarely explored.
Here, by using fewcycle driving pulses, we record interferometric timeresolved electron and light emission from bare Au and hybrid Au/ZnO nanosponges. We show that the coupling between plasmonic hot spot fields and excitonic quantum emitters, via SF quantum channels, boosts nonlinear excitonic emission from ZnO. The results are valuable for improving and controlling optical nonlinearity via nonlinear plasmon–quantum emitter coupling^{20}.
Results
Nonlinear light emission from localized plasmonic hot spots
For our studies of nonlinear plasmon–exciton coupling, we take gold nanosponges—porous halfspherical nanoparticles with diameters of several hundreds of nanometers—as a promising plasmonic nanoantenna^{21}. Such nanosponges are perforated with 10–20 nm sized nanopores throughout the entire particle, forming a randomly disordered ligament network (see scanning electron microscopy (SEM) image in Fig. 1a, more SEM images can be found in Supplementary Fig. 1). Their unique structure allows us not only to efficiently couple farfield light to the dipolar mode of the particle, but also to funnel the electromagnetic energy into a series of localized hot spots via multiple coherent scattering of surface plasmons in the disordered structure^{22,23}. Darkfield white light scattering spectra show a broad resonance superimposed with some random spectral modulations, reflecting the excitation of multiple hot spot modes superimposed to the dipole mode of single nanosponges (Supplementary Fig. 3). Since the scattering spectra are largely inhomogeneously broadened, they do not give direct insight into the plasmonic properties of single hot spots. Light scattering from individual hot spots has recently been studied using scanning nearfield optical spectroscopy, which directly shows that these hot spots are highly localized on a 10nm scale^{23}. The narrow spectral line widths suggest long dephasing times T_{2} of ~20 fs of hot spots^{23}. Their high quality factors (up to 40) and large field enhancements make them appealing for plasmon–emitter coupling. Particularly, different types of quantum emitters can be readily infiltrated into the nanopores and thus be placed in the hot spots, without the need for lithography methods. Furthermore, the broad spectral variation of the hot spot resonances offers an opportunity to probe the effect of detuning on the coupling between plasmons and emitters.
To time resolve the surface plasmon fields of the nanosponge, we performed interferometric frequencyresolved autocorrelation (IFRAC) measurements (Fig. 1a)^{24,25,26}. The sample is excited by a pair of broadband, phaselocked 8fs pulses, timedelayed by τ. The pulses are centered at ~880 nm and have a nearly transformlimited time structure E_{L}(t) (Supplementary Fig. 4). The resulting local plasmon field E_{P}(t) generates a secondorder nonlinear field E_{NL}(t, τ) ∝ (E_{P}(t) + E_{P}(t − τ))^{2}. The signal at detection angular frequency ω_{d} is resolved in a spectrometer and recorded as a function of τ, giving an IFRAC trace, \(I_{{\mathrm{IF}}}\left( {\omega _{\mathrm{d}},\tau } \right) = \left {\smallint E_{{\mathrm{NL}}}\left( {t,\tau } \right){\mathrm{e}}^{{\mathrm{i}}\omega _{{\mathrm{d}}t}}\mathrm{dt}} \right^2\). Figure 1b depicts such a trace from a single gold nanosponge, showing broadband nonlinear emission centered at ω_{d} ~ 4.4 fs^{−1} (~430 nm) that is modulated periodically along the delay axis τ. We find a strong and longlived (>25 fs) coherent secondharmonic (SH) signal, superimposed on a weak incoherent twophoton photoluminescence background (Supplementary Figs. 5 and 7)^{25}.
It has previously been shown^{24} that the time structure of the field that is driving the nonlinear emission can be retrieved from a Fourier transform of the IFRAC signal along τ, giving a new delay frequency ω_{τ}. This Fourier transform shows five distinct bands, a zerothorder (DC) band around ω_{τ} = 0, two fundamental (FM) bands around ω_{τ} = ±ω_{d}/2 and two secondorder bands around ω_{τ} = ±ω_{d} (Supplementary Fig. 8)^{24,25}. Both DC and FM bands contain the desired information about the time profile of E_{P}(t) (ref. ^{24}). Figure 1c shows the DC band of the IFRAC trace in Fig. 1b. It appears to be clearly asymmetric and stretched along the ω_{d} axis. This is surprising since the SH emission from a single mode would result in a symmetric, Lorentzian line shape of the DC band with the same, homogeneously broadened linewidth of 4/T_{2} along both ω_{d} and ω_{τ} axes (Supplementary Figs. 8 and 9). Even in the case of an inhomogeneous ensemble of coherently interfering nonlinear emitters, the DC band should also be symmetric, with a width given by the inhomogeneous linewidth (Supplementary Fig. 10)^{27}. This is in contrast to the distinct asymmetry of the DC band seen in Fig. 1c. To explain this observation, we consider that the SH polarization from plasmonic hot spots in disordered metallic nanostructures is usually generated from an Angstrom thin sheet of nonlinear dipole emitters, orientated perpendicularly to the complexshaped and highly curved metal surface^{28,29}. In such a case, one expects that SH emissions from neighboring hot spots do not interfere and that the total SH intensity is given as the incoherent sum of the SH intensities of each hot spot, \(I_{{\mathrm{IF}}}^\prime \left( {\omega _{\mathrm{d}},\tau } \right) = \mathop {\sum }\nolimits_j I_{{\mathrm{IF}},j}\left( {\omega _{\mathrm{d}},\tau } \right)\), with j being the hot spot index^{29,30}.
When considering this in the modeling of the IFRAC traces, we can reasonably well account for the asymmetric DC band (Fig. 1d), assuming an inhomogeneously broadened distribution of several hot spot modes (nonlinear emitters) with comparatively long T_{2} times of ~16 fs (see simulated IFRAC and more details in Supplementary Fig. 13). The T_{2} time is obtained by fitting the DC band signal at a given ω_{d} to a homogeneously broadened line shape model (Fig. 1c, details in Supplementary Fig. 11). The deduced T_{2} times are close to those deduced using nearfield linear scattering spectroscopy of individual hot spots^{23}.
To confirm this observation, we recorded SH spectra at a fixed τ ~ 75 fs for different polarization angles of the linearly polarized incident light (Fig. 1e, completed data in Supplementary Fig. 5). The SH emission shows a rich dependence on polarization angle, with very broad and multipeaked spectra. The polar plot of the SH intensity is indicative of a multipolar emission character (Fig. 1f), as expected for the emission from multiple randomly orientated localized plasmonic hot spots at the surface of a single nanosponge. The dipolar mode of the nanosponges can couple efficiently to the farfield light because of their submicron size that matches to the incident wavelength. The dipolar mode then couples to and excites localized hot spot modes. The linear and nonlinear fields from the hot spots can then couple back to the dipolar mode and radiate into the far field. Since the hot spot fields are much stronger than that of the dipole mode, the nonlinear emission is mainly governed by the hot spots.
Photoelectron emission from individual plasmonic hot spots
The IFRAC measurements suggest that the nonlinear emission stems from multiple localized hot spots on the surface of the nanosponges, but are unable to resolve emission from a single hot spot. For this, we employed interferometric timeresolved photoemission electron microscopy (trPEEM)^{31,32,33,34,35,36}. Similar to IFRAC, the sample is excited by a pair of fewcycle pulses, centered at ~800 nm. Photoemitted electrons are detected, providing sub100 nm spatial resolution to isolate individual hot spots. Figure 2a shows a SEM image of the gold nanosponge used in this experiment. The trPEEM images measured at different τ are depicted in Fig. 2b, from which three individual hot spots are well resolved. Supplementary Videos 1 and 2 show τ dependent photoelectron emission from the nanosponge in Fig. 2a and other nanosponges. We note that the PEEM image at τ = 0 does not allow us to clearly isolate the individual hot spots, because of the overlapping emission from the delocalized dipole mode. Electron emission from this shortlived dipole mode can only be observed for short time delays, whereas for long time delays only the localized hot spot modes survive. Interferometric autocorrelation (IAC) traces of the number of detected electrons recorded at each of those hot spots are shown in Fig. 2c, displaying longlived coherent oscillations, persisting well beyond the time resolution of the experiment of 5–6 fs (ref. ^{32}). The pronounced fringe contrast is consistent with a high order (n = 2.5−3) nonlinear photoemission process. The distinctly different oscillation periods are a clear signature of photoemission from single hot spots with different resonance frequencies^{33}. The IAC traces are reasonably well modeled by assuming nonlinear photoemission from a homogenously broadened hot spot emitter with a T_{2} time of ~13 fs, superimposed by the weak and shortlived field associated with the excitation of the delocalized dipole mode of the entire nanosponge^{22}. The fitted T_{2} times of hot spots are close to those deduced from IFRAC. The trPEEM results thus directly confirm that each hot spot acts as an independent emitter that can be selectively excited by tuning the interpulse delay.
Enhanced excitonic emission from Au/ZnO hybrid nanosponges
We now make use of this selectivity to study the coupling of individual hot spots to nonlinear quantum emitters, by depositing a thin layer of ZnO onto the nanosponge surface^{37}. The material is chosen because of its large secondorder susceptibility and sharp exciton absorption resonance that is spectrally overlapping with the broad SH emission from the ensemble of plasmonic hot spots. SEM and transmission electron microscopy (TEM) images of such a hybrid Au/ZnO nanosponge (Fig. 3a, more in Supplementary Fig. 2) show that the ZnO material nicely fills the interior of the nanopores and covers the entire gold ligament surface with a 10nm thick layer.
An IFRAC trace of a single hybrid nanosponge is shown in Fig. 3b. A broad emission is observed around ω_{d,P} ~ 4.3 fs^{−1} (~440 nm), very similar to that seen for the bare gold nanosponge in Fig. 1b. We thus assign this band mostly to plasmonic SH emission. Additionally, a distinctly enhanced emission at the exciton frequency of ZnO, ω_{X} ~ 4.8 fs^{−1} (~390 nm)^{25,37,38}, is observed. This band therefore reflects excitonic emission from ZnO and is almost one order of magnitude stronger than the emission from the bare gold nanosponge at the same frequency (Supplementary Figs. 6 and 16). Nonlinear optical spectra taken from many individual ZnOinfiltrated nanosponges confirm this enhancement effect^{37}. Spectrally integrated IAC traces \(\bar I_{{\mathrm{IF}}}\left( \tau \right) = \smallint I_{{\mathrm{IF}}}\left( {\omega _{\mathrm{d}},\tau } \right){\mathrm{d}}\omega _{\mathrm{d}}\) from the plasmonic band between 4.1 and 4.65 fs^{−1} show coherent oscillations persisting for >25 fs (Fig. 3c, bottom), indicating SH emission from longlived plasmonic hot spots. Interestingly, the IAC trace from the excitonic peak (4.65–4.95 fs^{−1}) displays a characteristic beating pattern, reflecting a coherent superposition of at least two modes (Fig. 3c, top). Notably, the IAC trace of the excitonic emission is slightly longerlived (>30 fs) than the nonlinear plasmonic emission, reflecting the coupling to the sharp ZnO exciton resonance, as will be further discussed later. The DC band of the IFRAC trace has a similarly stretched shape as that of the bare gold nanosponge, again a feature of nonlinear emission from multiple hot spots (Supplementary Fig. 12).
Quantum pathways of nonlinear plasmon–exciton coupling
The FM band of the IFRAC trace in Fig. 3b is shown in Fig. 4a, plotting the nonlinear emission intensity as a function of detection (ω_{d}) and excitation frequency (ω_{τ}), which is obtained by Fourier transform along τ. This twodimensional (2D) FM spectrum allows us to visualize the effect of a selective excitation of different hot spots (vertical arrows) on the nonlinear emission (horizontal arrows). In the plasmonic emission range, the signal is distributed along the diagonal line, \(\omega _{\mathrm{d}} = 2\omega _{\uptau}\), with a slope of 2, indicating a SH process. Here, the selective excitation of hot spots with resonant frequencies ω_{P,j} (j is the hot spot index) leads to SH emission at 2ω_{P,j}.
In the excitonic emission range, we observe a comparatively large intensity, about four times stronger than that in the 2DFM spectrum of the bare gold nanosponge (Supplementary Figs. 7 and 16). Surprisingly, the signal splits into two side peaks, symmetrically positioned around the diagonal. Analytical analysis suggests that this split is the characteristic of SF generation, ω_{d} = ω_{1} + ω_{2}, i.e., the nonlinear mixing of different linear fields at ω_{1} and ω_{2} (see a completed analytical formalization in Supplementary Note 7). The horizontal crosssectional spectrum at ω_{X} ~ 4.8 fs^{−1} shows that the excitonic emission is mainly SF generated from fundamental modes at ω_{1} ~ 2.3 fs^{−1} and ω_{2} ~ 2.5 fs^{−1}, whereas SH generation from 2.4 fs^{−1} mode is weaker. This splitting also explains the beating of the IAC trace at ω_{X} in Fig. 3c, reflecting the coherent superposition of those two distinct fundamental modes. The 2DFM spectrum thus nicely correlates fundamental excitation to secondorder emission frequencies (see more detailed discussion and prove in Supplementary Note 7). The resonances and their line shapes in this map provide an opportunity to reveal the quantum pathways of the enhanced excitonic emission, which can either be excited through direct light–exciton coupling or driven by plasmonic near fields via linear or nonlinear plasmon–exciton coupling. We shall examine each of the three quantum pathways.
First, we assume that ZnO excitons are excited only by farfield light. In case of a narrowband laser excitation, efficient excitonic emission can only be achieved via SH generation when tuning the laser to half of the exciton frequency. In the 2DFM spectrum, this pathway will show up as a peak at the diagonal, centered at (ω_{X}/2, ω_{X}), in stark contrast to the experiment. For a broadband, fewcycle laser excitation, excitonic emission can also be triggered by many SF channels, mixing a pair of colors ω_{1} and ω_{2} from the laser spectrum such that ω_{1} + ω_{2} = ω_{X}. Hence, for each pair, we will see two split peaks at (ω_{1}, ω_{X}) and (ω_{2}, ω_{X}) in the 2DFM spectrum. A simulation of such a 2D spectrum using a classical nonlinear oscillator model and the time profile of our laser is shown in Supplementary Fig. 17. We find that the crosssectional spectrum I(ω_{τ}) at ω_{d} = ω_{X} extends over the entire bandwidth of our laser and has a spectral width that is much wider than the experimental data. Farfield laser excitation therefore cannot account for the experiments, in agreement with observing no detectable signal from a pure, 10nm thick ZnO layer under the same experimental conditions.
Secondly, we consider plasmon–exciton coupling. Here, the farfield laser first couples to the delocalized, dipolar plasmon mode of the nanosponge, which resonantly excites different plasmonic hot spots at the nanosponge surface^{22,23}. This strong hot spot field, \(E_{\mathrm{P}}^{(1)}\) generates a secondorder nonlinear polarization at the gold surface, \(P_{{\mathrm{Au}}}^{(2)}\), accounting for the nonlinear emission in the bare gold nanosponge (Fig. 4c, left). In the hybrid nanosponge, this nonlinear plasmonic field can be coherently scattered into the far field by the ZnO inclusion, inducing Rayleigh scattering, i.e., a linear dipole polarization \(P_{{\mathrm{ZnO}}}^{(1)}\) (via secondorder coupling, Ω_{2}, magenta arrows in Fig. 4c). This enhances the amount of light that is scattered into the far field. An estimate based on a simplified coupled dipole model (see details in Methods section and Supplementary Note 8) suggests a maximum intensity enhancement factor of \(\left {\frac{{3\varepsilon (\omega )}}{{\varepsilon \left( \omega \right) + 2}}} \right^2\). The dielectric function of ZnO, ε(ω) = ε_{B} + ε_{X}(ω), is dominated by a strong, almost frequencyindependent background ε_{B} ≈ 4 − 5 and a much weaker resonant exciton contribution with a magnitude \(\left {\varepsilon _{\mathrm{X}}} \right \approx 1\) (ref. ^{39}). Due to this strong background, the onresonant enhancement factor of the scattering intensity at ω_{X} should be only ~10% stronger than the offresonant enhancement factor at ω_{d,P} (Supplementary Note 8). That is, the enhancement is almost frequency independent. This contrasts with the experimentally observed ratio of on and offresonant enhancement factor of >350% (Supplementary Fig. 16). Therefore, the scattering of the nonlinear plasmonic field by a ZnO inclusion alone cannot explain the large resonant enhancement at ω_{X}. Also, a change of the linear optical properties of the hot spot modes, specifically their linewidth and frequency^{11,13}, due to the ZnO inclusion, does not account for this resonant enhancement since it would affect the on and offresonant nonlinear signal in exactly the same way^{13}.
We are led to the third pathway: the linear plasmonic field instead couples to ZnO excitons via firstorder coupling (Ω_{1}, green arrows in Fig. 4c) by driving the exciton nonlinearly. Here, the part of \(E_{\mathrm{P}}^{(1)}\) that is spatially overlapping with the ZnO inclusion can offresonantly drive a secondorder nonlinear polarization from ZnO, \(P_{{\mathrm{ZnO}}}^{(2)}\). Earlier measurements have shown that the SH emission from ZnO thin films is strongly enhanced near the ZnO bandgap with a secondorder susceptibility that is increased by more than a factor of five when approaching the exciton resonance^{40}. Therefore, the nonlinear signal \(P_{{\mathrm{ZnO}}}^{(2)}\) will mostly be centered around ω_{X} (refs. ^{25,38}), showing excitonic enhancement that is consistent with the experiment. We therefore consider this firstorder coupling as the main mechanism for the enhanced excitonic emission. The time structure of \(P_{{\mathrm{ZnO}}}^{(2)}\) will be given by a convolution of \(E_{\mathrm{P}}^{(1)}\) with the resonant excitonic response of ZnO. In comparison to \(P_{{\mathrm{Au}}}^{(2)}\), \(P_{{\mathrm{ZnO}}}^{(2)}\) thus displays a characteristic phase shift by ~π/2 arising from the resonant response of the exciton to the plasmonic driving field (see detailed phase analysis in Supplementary Note 9), and is considerably prolonged in time due to the persistent coherence of the excitonic transition. This is seen in the simulated electric fields for the excitation of a single hot spot at ω_{P} = 2.5 fs^{−1} in Fig. 4d (blue and green curves). In contrast, the linearly scattered field \(P_{{\mathrm{ZnO}}}^{(1)}\) (pink curve in Fig. 4d) is inphase with and shows almost the same dynamics as \(P_{{\mathrm{Au}}}^{(2)}\), resulting from the dominant dielectric background contribution as discussed above. The optical dynamics of the plasmondriven nonlinear excitonic emission therefore depends on both the optical dynamics of the fundamental driving hot spots and the finite dephasing time of the exciton transition, as reflected by the elongated IAC trace of the excitonic emission compared to that of the plasmonic emission in Fig. 3c.
With this, we can now successfully understand the experimental results. To describe the nonlinear emission from the entire hybrid nanosponge, we assume several wellseparated hot spots at its surface with different resonance frequencies (ω_{P,j} = 2.0 − 2.6 fs^{−1}) and dephasing times of ~16 fs. Direct evidence for the existence of these hot spot resonances, their long dephasing times and small spatial localization lengths of ~10 nm is given by scanning nearfield optical spectroscopy^{23} and PEEM (Fig. 2) measurements. Each of these hot spots is driven by the laser field and coupled to neighboring ZnO excitons. We consider all three contributions to the nonlinear emission depicted in Fig. 4c (details of the model in Methods section). The simulated IFRAC trace (Supplementary Fig. 19), 2DFM spectrum (Fig. 4b), and IAC traces (Fig. 3d) can reasonably well account for the experiments, as long as we assume that plasmondriven nonlinear excitonic emission, \(P_{{\mathrm{ZnO}}}^{(2)}\) dominates the emission around ω_{X}. Indeed, as in the experiment, the model predicts a splitting of the 2DFM spectrum near ω_{X} into two excitation peaks around ω_{1} = 2.3 fs^{−1} and ω_{2} = 2.5 fs^{−1}, suggesting that SF generation dominates the nonlinear response in this frequency range.
Discussion
In principle, for a single plasmonic eigenmode, such a splitting is unlikely to occur for a smooth laser spectrum, which would favor SH generation from hot spot fields resonant at ω_{X}/2. This SH channel, however, is not efficiently excited by our laser, which shows a slight dip in the spectrum at ω_{X}/2 ~ 2.4 fs^{−1} (Supplementary Figs. 4 and 20), thus suppressing the coupling of this hot spot field to the ZnO exciton. The spectral structure of our laser therefore results in nonlinear excitonic emission that is offresonantly driven by two different frequency components ω_{1} and ω_{2} of a hot spot field such that ω_{1} + ω_{2} = ω_{X}. As seen in the 2DFM spectra, this new, SF channel is efficient if the hot spot resonance is reasonably close to ω_{X}/2. This SF channel is particularly helpful to enhance the overall yield of nonlinear emission in realistic samples with a large number of hybrid plasmon–exciton antennas, where disorderinduced fluctuations vary the resonance conditions from one antenna to another. In such systems, efficient nonlinear emission can be achieved via SF generation by excitation with ultrashort broadband laser pulses, even if the plasmon resonance is detuned from ω_{X}/2, for which SH generation with narrowband excitation is inefficient.
We note that for more detuned hot spots the coupling to the ZnO excitons is reduced, as seen in Fig. 4a. This arises because the two fields for SF mixing are most likely created by the same hot spot eigenmode, and thus only one of the two fields, ω_{1} ≈ ω_{P}, will be resonantly enhanced (Supplementary Fig. 20). To maximize the efficiency of SF generation, one could use multifrequency antennas with two or more energetically detuned linear plasmonic eigenmodes that are spatially partially overlapping with the same hot spot. Here, more frequency components for SF mixing can be resonantly excited and can coherently interact with the same nonlinear emitter placed in the hot spot. Typical sample geometries of multifrequency plasmonic resonators are twoarm antennas with different arm lengths^{41}, cross antennas with two pairs of nanorods perpendicular to each other^{11,42}, and other tailored sample geometries^{6,43}. These structures support spatially overlapping and thus coherently interacting plasmonic modes that can lead to efficient nonlinear SF coupling to excitons. SF generation thus allows for highly tunable nonlinear plasmon–exciton coupling in a variety of hybrid nanostructures. Our result suggests new SF quantum channels for nonlinear plasmon–exciton coupling. Compared to commonly adopted SH quantum channels, SF generation offers much wider spectral tuneability for the coherent manipulation of the linear and nonlinear fields, opening up new routes for optical control in such a nonlinearly coupled nanosystem. The results also opens up the possibility to explore difference frequency generation \(\left {\omega _1  \omega _2} \right\) of two plasmonic fields for coupling to lowfrequency infrared or terahertz vibrations, for example, for plasmonenhanced stimulated Raman scattering^{44}.
In summary, we have spatially and temporally resolved individual plasmonic hot spot modes at the surface of a gold nanosponge, and studied their nonlinear coupling to ZnO excitons by probing the ultrafast optical dynamics in a hybrid Au/ZnO nanosponge. We demonstrate how fundamental plasmonic fields couple to higherenergy excitons via SF mixing, enhancing coherent excitonic emission. The much prolonged excitonic fields may provide a valuable tool for coherent control via nonlinear plasmon–emitter coupling^{20}. Our results not only allow us to unravel the different microscopic contributions to the nonlinear signal enhancement, but may also prove helpful for the design of a new class of hybrid nanostructures with coupled, phased arrays of plasmonic antennas^{15}, and quantum emitters with strong optical nonlinearities.
Methods
Preparation of nanosponges
Gold nanosponges were synthesized in two steps^{21,45}. First, gold–silver alloy nanoparticles with (sub)micron diameters were fabricated by solidstate dewetting of a bimetallic Au/Ag (8 nm/20 nm thick) thin film on a SiO_{2}/Si substrate. Subsequently, the nanoparticles were dealloyed in which silver was chemically removed in a solution of HNO_{3} (65 wt%), leading to nanoporous structure with 10nm sized channels perforating the entire particle^{22}. To prepare the hybrid nanosponge, a ZnO layer of 10nm thickness was deposited into the nanopores of bare nanosponges using plasmaenhanced atomic layer deposition at 150 °C. The samples were annealed at 500 °C in Ar for 1 h to improve the crystallinity of ZnO. The nanosponges were transferred to indium tin oxide substrate for measurements.
IFRAC microscopy
We used a homebuilt nonlinear microscopy setup^{38} combined with broadband, 8fs pulses from a 80MHz Ti:Sapphire oscillator (Venteon: ultra) centered at ~880 nm. A phaselocked pulse pair is prepared in a dispersionbalanced Mach–Zehnder interferometer with interpulse time delay τ controlled by a piezo scanner (Physik Instrumente P621.1CD PIHera). The laser is focused onto the sample to a diffractionlimited spot size of 1.0 µm through an allreflective Cassegrain objective with a numerical aperture of 0.5, preserving the time structure of the pulses^{46}. The laser power at the focus is ~0.45 mW at τ =0. The pulse in the focus has been characterized by IFRAC measurements on a 15µm thick beta barium borate crystal and a retrieval algorithm was used to retrieve the electric field of the pulse (Supplementary Note 2), showing a nearly transformlimited time structure. A halfwave plate is used to tune the polarization of the incident pulse. The backscattered light is spectrally filtered by a dichroic mirror and then shortpass filtered to remove the linear scattering signal. The nonlinear signal is spectrally dispersed in a monochromator (Princeton Instruments Acton SpectraPro2500i) and detected with a liquid nitrogen cooled CCD camera (Princeton Instruments Spec10).
PEEM measurements and fitting
Broadband 6fs laser pulses centered around 800 nm are amplified in an optical parametric chirped pulse amplification laser system at a repetition rate of 200 kHz. They are split into a pulse pair in a dispersionbalanced Mach–Zehnder interferometer and focused onto the gold nanosponge sample in an ultrahigh vacuum chamber, using a lens with a focal length of 20 cm under an angle of 65° to the surface normal (ppolarized)^{32}. The laser pulse energy is attenuated such that only single electrons are emitted from the sample per laser shot. The emitted electrons are collected with the extractor lens of a PEEM (Focus GmbH) and imaged with a spatial resolution of ~50 nm. The time profile of the laser pulses E_{L}(t) is characterized by the dispersion scan and frequencyresolved optical gating techniques close to the vacuum chamber with a replica of the chamber window and the focusing lens in the beam path. The extracted spectral phase from both techniques is very similar and confirms a nearly transformlimited pulse duration of 6.0 fs (fullwidth at halfmaximum of the intensity profile).
To model the IAC traces of the electron emission shown in Fig. 2c, the local electric field at the position of each hot spot E_{S,j}(t) is given as the convolution of the laser pulse and the local response function, which is taken as the sum of a longlived hot spot mode (subscript j being the hot spot index) and a shortlived dipolar mode (subscript dp)^{22},
where ω and T_{2} are the central frequency and dephasing time, respectively, of the plasmonic modes (hot spots or dipole mode). Θ(t) is the Heaviside function. The amplitudes of the hot spot mode and dipole mode are represented as a_{j} and a_{dp}, respectively. The IAC trace of each hot spot is then modeled as
where n_{j} is the order of nonlinearity for photoemission.
In the experiment, we can clearly observe a change of the central wavelength when varying the time delay. At early time delays, both delocalized dipole mode and localized hot spot modes contribute, whereas at later time delays only the hot spot modes survive. Since the PEEM signal depends in a highly nonlinear manner on the local electric field amplitude (I_{PEEM} ∝ E^{6}), both fields must be of very similar amplitude (a_{dp} ≈ a_{j}) to make both contributions significant to the signals at early time delays. For fitting the experimental IAC trace, the amplitude of the dipole mode a_{dp} is kept the same for each simulation of E_{S,j} of the three hot spots in Fig. 2. We find that the amplitudes a_{j} of the hot spots 1–3 are 1.1, 0.84, and 0.83 as large as a_{dp}, respectively.
The fitting gives the following parameters: ω_{P,j} = 2.02, 2.48, 2.37 fs^{−1}, T_{2,j} = 17, 10, 13 fs, and n_{j} = 3, 2.5, 2.7 for hot spots 1–3, respectively. For the dipole mode, ω_{dp} = 2.35 fs^{−1} and T_{2,dp} = 3 fs. Supplementary Figure 21 shows the response functions of the dipole mode and the three hot spot modes, and their convoluted fields with laser in time and frequency domain. We note that the observed order of nonlinearly is slightly lower than estimated from a photon picture needed for the multiphotonemission of electrons from gold. This may be explained by (i) the applied DC bias voltage bending the vacuum level and lowering the work function^{47}, (ii) emission from local surface (adsorbate) states closer to vacuum level, and (iii) emission from a hot, nonequilibrium electron system with an effective electron temperature well above room temperature^{47}.
Model of nonlinear plasmon–exciton coupling
We use a classical nonlinear oscillator model to simulate the secondorder nonlinear emission from the sample by modeling plasmonic hot spots and exciton resonances as Lorentzian oscillators^{48}. We consider three distinct quantum pathways that contribute to the nonlinear emission from hybrid Au/ZnO nanosponges.
The first pathway is the nonlinear plasmonic emission from each of the plasmonic hot spots, which can be excited by an external laser field E_{L}(t),
where the displacement of the induced collective charge oscillations is denoted as x, and −e and m are electron charge and mass, respectively. The resonance frequency of the plasmonic hot spot is ω_{P} and its damping rate γ_{P} = 1/T_{2,P}, with T_{2,P} being the dephasing time of the hot spot. The strength of the secondorder nonlinearity of the hot spot is given as a_{P} which relates to the secondorder nonlinear susceptibility \(\chi_{\mathrm{P}}^{(2)} \propto a_{\mathrm{P}}\). We solve Eq. (3) in two steps using perturbation theory^{48},
Here, superscripts (1) and (2) represent the linear and nonlinear electronic motion, respectively. Equation (4) gives the linear polarization \(P_{{\mathrm{Au}}}^{\left( 1 \right)}(t) \propto x^{\left( 1 \right)}(t)\) and Eq. (5) generates the secondorder surface polarization \(P_{{\mathrm{Au}}}^{\left( 2 \right)}(t) \propto x^{\left( 2 \right)}(t)\). For gold plasmons, the firstorder perturbation is resonant at the frequency of the fundamental plasmon mode (ω_{P} ~ 2.3 fs^{−1}) and the secondorder perturbation is offresonant. This is different from the infiltrated ZnO, for which the polarization is resonantly enhanced at frequencies around the ZnO bandgap (~5.0 fs^{−1}). Therefore, fields emitted from ZnO in the frequency range of the fundamental plasmon mode are comparatively weak and can safely be neglected. Also, the backcoupling of the resonant emission around the ZnO bandgap to the plasmonic hot spots is neglected since it is largely detuned from the plasmon resonance.
The second pathway is the nonlinear excitonic emission from ZnO. ZnO is a direct bandgap semiconductor with a bandgap of ~3.3 eV and a quite complex optical response that has been studied in detail during the past decades. For midbandgap optical excitation, as in the present experiments, the response is usually dominated by excitonically enhanced SH emission showing a pronounced resonant enhancement near the bandgap^{38,40}. Even though more complex responses have been observed for strong optical driving^{49}, we assume that this secondorder nonlinear excitonic emission from ZnO is the dominant contribution to the detected signal in our experiment. It can be excited by (i) the incident farfield laser light E_{L}(t) or (ii) the local linear and nonlinear optical polarization of plasmonic near fields x = x^{(1)} + x^{(2)} of neighboring plasmonic hot spots, with coupling strengths Ω_{1} and Ω_{2}, respectively, defining the relation between plasmonic polarization and the field it creates at the position of the ZnO inclusion. The equation of motion follows
where y^{(1)} and y^{(2)} represent linear and secondorder nonlinear electronic motion of ZnO, and ω_{X} and γ_{X} are resonance frequency, and damping rate of the ZnO exciton, respectively. In contrast to gold plasmons, the linear excitation of ZnO (Eq. (6)) induced by E_{L}(t) and the linear plasmonic field \(\Omega _1x^{\left( 1 \right)}\) is offresonant, but is resonantly enhanced near the bandgap by the nonlinear plasmonic field \(\Omega _2x^{\left( 2 \right)}\) via secondorder coupling, leading to the Rayleigh scattering as will be discussed in detail in the third pathway later. Importantly, however, the nonlinear excitonic oscillation y^{(2)} is mainly induced by the locally enhanced linear plasmonic field \(\Omega_1x^{\left( 1 \right)}\) via firstorder coupling. As discussed in the main text, laser excitation E_{L}(t) cannot explain the experiment and can be excluded (see simulation result in Supplementary Fig. 17), and the effect of \(\Omega_2x^{\left( 2 \right)}\) is completely offresonant (note the square in Eq. (7)). The oscillation y^{(2)} induces a nonlinear excitonic polarization \(P_{{\mathrm{ZnO}}}^{\left( 2 \right)}(t)\) which emits into the far field, interfering with \(P_{{\mathrm{Au}}}^{\left( 2 \right)}(t)\) from the same hot spot. As discussed above, the backcoupling of this field to the plasmonic field can be neglected.
The third pathway is the Rayleigh scattering of nonlinear plasmonic field by ZnO. Here, the electromagnetic fields from the ZnO inclusions can also be emitted by resonantly scattering the local nonlinear plasmonic fields \(\Omega_2 x^{(2)}\) at the position of the ZnO inclusion. Knowing that the plasmonic fields are emitted from localized hot spots with diameters 2r_{P} of ~10 nm (ref. ^{23}), we model each hot spot as a small dipole emitter with nonlinear dipole moment \(p_{{\mathrm{Au}}}^{(2)} = P_{{\mathrm{Au}}}^{(2)}A_{{\mathrm{Au}}}\), where A_{Au} is the surface area of the hot spot. This dipole moment generates a near field at frequency ω of \({\mathbf{E}}\left( {{\mathbf{r}},\omega } \right) = \frac{{\omega ^2}}{{\varepsilon _0{\it{c}}^3}}\mathop {{\mathbf{G}}}\limits^ \leftrightarrow \left( {{\mathbf{r}},\omega } \right){\it{p}}_{{\mathrm{Au}}}^{\left( 2 \right)}(\omega )\), with \(\mathop {{\mathbf{G}}}\limits^ \leftrightarrow\) denoting the nearfield term of the Greens’ propagator. We model the ZnO inclusion as a small, spherical dielectric nanoparticle with radius r_{X}. In quasistatic approximation, the linear polarizability of the ZnO particle is then given as
Here, the frequency dependent dielectric function of ZnO, ε(ω) = ε_{B} + ε_{X}(ω), is dominated by a strong, almost frequencyindependent, realvalued dielectric background ε_{B} ≈ 4 − 5, and a much weaker resonant exciton contribution,
with a magnitude \(\left {\varepsilon _{\mathrm{X}}} \right \approx 1\) (ref. ^{39}). Taking the freespace Greens’ propagator, the maximum local electric field at the center of the ZnO nanoparticle created by the nonlinear plasmonic dipole moment is
with \(\bar r\) being the distance between the center of the nonlinear plasmonic dipole and that of the ZnO nanoparticle. This field is now driving the ZnO oscillator, creating a linear dipole moment
The time profile of the scattered field \(p_{{\mathrm{ZnO}}}^{\left( 1 \right)}(t)\) is obtained by Fourier transform \(p_{{\mathrm{ZnO}}}^{\left( 1 \right)}\left( t \right) = \smallint p_{{\mathrm{ZnO}}}^{\left( 1 \right)}\left( \omega \right)e^{  {\mathrm{i}}\omega t}\mathrm{d}\omega\). This contains two contributions, \(p_{{\mathrm{ZnO}}}^{\left( 1 \right)}\left( t \right) = p_{\mathrm{B}}^{\left( 1 \right)}\left( t \right) + p_{\mathrm{X}}^{\left( 1 \right)}\left( t \right)\), in which the scattered field \(p_{\mathrm{B}}^{\left( 1 \right)}(t)\) by \(\varepsilon _{\mathrm{B}}\) is essentially inphase and has the same time dynamics as that of \(p_{{\mathrm{Au}}}^{\left( 2 \right)}(t)\) because ε_{B} is a realvalued constant. Instead, the field linearly scattered by exciton polarization \(p_{\mathrm{X}}^{\left( 1 \right)}\left( t \right) \propto y^{\left( 1 \right)}(t)\) is ~π/2 phaseshifted with respect to \(p_{{\mathrm{Au}}}^{\left( 2 \right)}(t)\) and with elongated time dynamics given by the linear convolution between \(p_{{\mathrm{Au}}}^{\left( 2 \right)}(t)\) and the response function of the exciton resonance. The total scattered field \(p_{{\mathrm{ZnO}}}^{\left( 1 \right)}(t)\) is, however, dominated by the large ε_{B} with much weaker contribution from ε_{X}(ω). This is seen in the simulated field shown as the pink curve in Fig. 4d, which has almost the same profile as \(p_{{\mathrm{Au}}}^{\left( 2 \right)}(t)\) (blue curve).
Equation (11) also allows us to estimate the enhancement factor of nonlinear emission near the ZnO bandgap resulting from Rayleigh scattering of \(p_{{\mathrm{Au}}}^{\left( 2 \right)}\) by the ZnO inclusion. Optimally, \(p_{{\mathrm{Au}}}^{\left( 2 \right)}\) and \(p_{{\mathrm{ZnO}}}^{\left( 1 \right)}\) align in parallel, resulting in a total dipole moment \(p_{{\mathrm{tot}}}\left( \omega \right) = p_{{\mathrm{ZnO}}}^{(1)}\left( \omega \right) + p_{{\mathrm{Au}}}^{(2)}\left( \omega \right)\) and an enhancement factor of the emission intensity \(F_{{\mathrm{enh}}}(\omega ) = \left {p_{{\mathrm{tot}}}\left( \omega \right)} \right^2/\left {p_{{\mathrm{Au}}}^{(2)}\left( \omega \right)} \right^2\). To maximize the enhancement, we choose \(\bar r = r_{\mathrm{X}}\), i.e., place \(p_{{\mathrm{Au}}}^{\left( 2 \right)}\) at the surface of the ZnO nanoparticle, and get
The enhancement factor thus simply depends on the dielectric function of ZnO. Using the refractive index \(n(\omega )\) from ref. ^{39} and \(\varepsilon \left( \omega \right) = n(\omega )^2\), the onresonant enhancement factor \(F_{{\mathrm{enh}}}^{{\mathrm{on}}}(\omega = \omega _{\mathrm{X}})\) at exciton frequency is estimated to be ~10% larger than the offresonant enhancement factor \(F_{{\mathrm{enh}}}^{{\mathrm{off}}}(\omega = \omega _{{\mathrm{d}},{\mathrm{P}}})\) at the main plasmonic emission peak \(\omega _{{\mathrm{d}},{\mathrm{P}}}\) ~ 4.3 fs^{−1}, see details in Supplementary Note 8.
In this phenomenological model, the total nonlinear emission from a single hot spot, \(I_{{\mathrm{NL}},j}(\omega )\), in the hybrid nanosponges thus stems from the above discussed three distinct pathways. These are added coherently to give \(E_{{\mathrm{NL}},j}\left( t \right) = a \cdot x^{\left( 2 \right)}\left( t \right) + b \cdot y^{\left( 2 \right)}\left( t \right) + c \cdot y^{\left( 1 \right)}\left( t \right)\) and \(I_{{\mathrm{NL}},j}\left( \omega \right) = \left {\mathop {\smallint }\nolimits E_{{\mathrm{NL}},j}\left( t \right)\mathrm{e}^{{\mathrm{i}}\omega t}\mathrm{d}t} \right^2\). The total emission from an individual hybrid nanosponge is then obtained by incoherently adding up the nonlinear emission from all hot spots, \(I_{{\mathrm{NL}}}^\prime \left( \omega \right) = \mathop {\sum }\nolimits_j I_{{\mathrm{NL}},j}\left( \omega \right)\), as discussed in the main text. The amplitude coefficients \(a\), \(b\), and \(c\) are taken as free scaling parameters to achieve acceptable agreement between simulations and experiments.
Data availability
The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.
Code availability
The MATLAB codes used in this study are available from the corresponding author upon reasonable request.
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Acknowledgements
The authors acknowledge financial support by the Deutsche Forschungsgemeinschaft (SPP1839 ‘Tailored Disorder’, grants LI 580/12, RU 1383/5, SCHA 632/24, and SPP1840 ‘QUTIF’ grant LI 580/13), the Korea Foundation for International Cooperation of Science and Technology (Global Research Laboratory project, K20815000003), the German–Israeli Foundation (GIF grant no. 1256 and 107449.10/2009), the Swedish Research Council, LaserlabEurope EUH2020 654148, and the European Union Horizon 2020 research and innovation program under the Marie SkłodowskaCurie grant agreement 793604 ATTOPIE. J.H.Z. is supported by Alexander von Humboldt Postdoctoral Fellowship and Carl von Ossietzky Young Researchers’ Fellowship from University of Oldenburg. The authors are grateful to Mario Ziegler from IPHT Jena for the help with sample preparation, and Dominik Flock and Dr. Thomas Kups from TU Ilmenau for TEM examination. We thank Moritz Gittinger and Dr. Martin Silies for their help with the measurements of darkfield scattering spectra.
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C.L. initiated and coordinated the study. D.W. and P.S. prepared the samples. J.H.Z. and J.M.Y. performed IFRAC measurements with the help of A.K., and A.C. J.H.Z., J.M.Y., and C.L. analyzed the data, and performed analytical and numerical simulations of the IFRAC. E.R. helped with theoretical modeling. J.V. initiated the trPEEM measurements, set up the experiment, and analyzed the data. J.V. and L.W. performed the trPEEM experiments with the help of S.M. and under supervision of C.L.A, A.L.H., and A.M. J.H.Z. and C.L. cowrote the manuscript. All authors discussed the results and commented on the manuscript.
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Zhong, JH., Vogelsang, J., Yi, JM. et al. Nonlinear plasmonexciton coupling enhances sumfrequency generation from a hybrid metal/semiconductor nanostructure. Nat Commun 11, 1464 (2020). https://doi.org/10.1038/s4146702015232w
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