Spatial variations in femtosecond field dynamics within a plasmonic

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Spatial variations in femtosecond field dynamics within a plasmonic nanoresonator mode Matthias Hensen, Bernhard Huber, Daniel Friedrich, Enno Krauss, Sebastian Pres, Philipp Grimm, Daniel Fersch, Julian Lüttig, Victor Lisinetskii, Bert Hecht, and Tobias Brixner Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.9b01672 • Publication Date (Web): 10 Jun 2019 Downloaded from http://pubs.acs.org on June 11, 2019

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Spatial variations in femtosecond field dynamics within a plasmonic nanoresonator mode Matthias Hensen1,#, Bernhard Huber1,#, Daniel Friedrich2, Enno Krauss2, Sebastian Pres1, Philipp Grimm2, Daniel Fersch1, Julian Lüttig1, Victor Lisinetskii1, Bert Hecht2,*, and Tobias Brixner1,3,** 1

Institut für Physikalische und Theoretische Chemie, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany

2

NanoOptics & Biophotonics Group, Experimental Physics 5, University of Würzburg, Am Hubland, 97074 Würzburg, Germany

3

Center for Nanosystems Chemistry (CNC), Universität Würzburg, Theodor-Boveri-Weg, 97074 Würzburg, Germany

KEYWORDS: plasmonics, cavity, quasinormal modes, time-resolved PEEM

ABSTRACT: Plasmonic resonators can be designed to support spectrally well-separated discrete modes. The associated characteristic spatial patterns of intense electromagnetic hot-spots can be exploited to enhance light–matter interaction. Here, we study the local field dynamics of individual hot-spots within a nanoslit resonator by detecting characteristic changes of the photoelectron emission signal on a scale of ~12 nm using time-resolved photoemission electron microscopy (TR-

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PEEM) and by excitation with the output from a 20 fs, 1 MHz noncollinear optical parametric amplifier (NOPA). Surprisingly, we detect apparent spatial variations of the Q-factor and resonance frequency that are commonly considered to be global properties for a single mode. By using the concept of quasinormal modes we explain these local differences by crosstalk of adjacent resonator modes. Our findings are important in view of time-domain studies of plasmon-mediated strong light–matter coupling at ambient conditions.

TEXT: The design of plasmonic nanoresonators exhibiting resonance frequencies that range throughout the optical regime found great attention in the last two decades1. Plasmonic nanoresonators squeeze light into deep sub-wavelength mode volumes and thereby enable, e.g., strong coupling of single plasmons and excitons2,3, and are therefore promising candidates to bring quantumoptics-based devices to scales compatible with microelectronics. However, plasmon resonances are rather short-lived due to decoherence and (non)radiative damping processes, leading to broad resonance linewidths and hence low resonator quality factors. As a consequence, individual modes tend to overlap spectrally and interfere with each other so that, e.g., the common textbook definition of the spontaneous emission rate of a quantum emitter inside a cavity, in terms of the so-called Purcell factor, needs to be treated with caution4–6 (see also the review and perspective in Ref. 7 and Ref. 8, respectively). The solutions of such open systems are typically discussed within the framework of quasinormal modes9 (QNMs), described by a spatial field distribution and a corresponding complex eigenenergy. This concept has found wide application in the field of photonic and plasmonic resonators7,8 since a decomposition of the system’s response into QNMs provides deeper physical insight, intuitive design, and optimization of optical devices.


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Due to the localized nature of plasmonic resonances, there often exists also a spatial overlap of QNMs of different mode number. The resulting near-field dynamics of a plasmonic nanoresonator can be imaged by high-resolution microscopy techniques like, e.g., time-resolved photoemission electron microscopy (TR-PEEM). For example, Faggiani and co-workers showed10 that the local field dynamics at opposed ends of a 600 nm long rice-shaped Ag nanoparticle, measured by Mårsell and co-workers11, is, beside retardation effects, caused by the simultaneous excitation of two spectrally separated, but spatially interfering, QNMs as a consequence of the broadband laser spectrum. In general, most experiments involving plasmonic resonances, ranging from optical luminescence measurements12,13 to TR-PEEM14–18, may be modelled using damped, and sometimes coupled, harmonic oscillators which exhibit a uniquely defined resonance frequency and Q-factor across the entire resonator structure. In contrast to these established and successful global-parameter descriptions, we here report on the experimental observation of apparently spatially non-uniform Q-factor and spatially nonuniform resonance frequency within a plasmonic nanoslit resonator. To this end, we investigate 100-nm-separated hot-spots, presumably the maxima of a single eigenmode, by combining 20 fs optical laser pulses and TR-PEEM. A similar nanoslit resonator was recently used to establish strong coupling between single excitons and single plasmons at room temperature3. A non-uniform Q-factor and resonance frequency are detected although the laser spectrum is tuned to excite a specific resonance of the nanoslit. We explain this observation by a non-negligible influence of adjacent resonator modes on the local response function covered by the laser spectrum although the adjacent spectral resonance features appear to be well separated with respect to the laser bandwidth. We support our conclusion by modelling the spatially resolved response function, which was retrieved from finite-difference time-domain (FDTD) simulations (FDTD Solutions,


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Lumerical Inc.), using QNMs and thereby demonstrate that, in contrast to Refs.

10

and

11

, a

superposition of all QNMs with a mode number smaller than the mode covered by the laser spectrum is necessary to explain the spatially resolved response function and hence the outcome of our experiment.

Figure 1. Time-resolved photoemission electron microscopy (TR-PEEM) for monitoring the nearfield dynamics within a single nanoslit resonator. (a) Geometry of the plasmonic nanoslit on a SiO2 substrate: height of the single-crystalline Au microplate h = 32 nm, slit width w, which is typically 18 nm, and the varied slit length L. The intense near-field hot-spots inside the nanoslit, sketched in red, are investigated by imaging the associated nonlinear photoelectron emission (nonlinear order N ≈ 3.4). Characteristic changes of the photoelectron emission signal are resolved on a scale of x ≈ 12 nm, according to a 16%–84% criterion (see Supplementary Information) (b) Homogeneous laser excitation of the nanoslit and its surroundings is guaranteed by a rather large focus size of ~270 µm and the normal-incidence geometry. Note that the laser polarization is perpendicular to the nanoslits. The single-crystalline Au microplate is deposited on an Au hole mask which ensures electric conductance. (c) Sketch of the experimental setup, including the NOPA laser source, a prism compressor for dispersion control, an actively phase-stabilized Mach– Zehnder interferometer to generate laser pulse sequences and to control the pulse delay T, and an aberration-corrected photoemission electron microscope (AC-PEEM) for imaging the emitted electrons. (d) The length-dependent resonance frequencies of the fabricated nanoslit are


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characterized by gold luminescence (top) and then compared to scattering spectra of finitedifference time-domain simulations (bottom). Here, the excitation source is a continuous-wave diode laser ( = 532 nm) and the incident polarization is oriented perpendicular to the slit.

Nanoslit resonators (Figure 1a) exhibiting a Fabry–Pérot-like resonance spectrum20 were fabricated on a 32 nm thick, chemically synthesized, single-crystalline Au microplate19 by focused ion-beam (FIB) milling. The single-crystalline character improves the FIB fabrication quality which is usually limited by the size of evaporated Au grains, and reduces scattering of surface plasmons at structural defects20. Quite recently, such atomically flat microplates allowed for the observation of sub-femtosecond dynamics of orbital angular momentum in nanoplasmonic vortices21 and facilitated plasmon-mediated strong coupling of single nanoantennas over more than one micrometer distance22. For FIB fabrication and TR-PEEM experiments the microplates were positioned on an Au hole mask such that a large part of the microplate is located on a flat glass substrate (Figure 1b). In comparison to conductive oxide substrates that are widely used in electron spectroscopy, this new approach allows for writing structures on a low-refractive-index material which reduces the impact on surface plasmon properties while at the same time maintaining the required sample conductance. As an excitation source we used a fiber-laser-pumped (Amplitude, Tangerine, 35 W pump power) home-built two-branch noncollinear optical parametric amplifier (NOPA) which allows for generating sub-20 fs laser pulses with a gapless-tunable carrier wavelength from 215 nm to 970 nm at 1 MHz repetition rate (Figure 1c). In the present experiment, we set the central wavelength to ~715 nm and compressed laser pulses with a prism compressor. Associated laser pulse diagnostics were performed directly in front of the PEEM, quantitating a 20 fs pulse duration (see Supplementary Information). The laser pulses were focused into the PEEM (customized ACLEEM, Elmitec Elektronenmikroskopie GmbH) under normal-incidence geometry so that the


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sample was excited with a constant phase across the illuminated area. In order to guarantee a spatially homogeneous excitation of the sample, the spot size exhibited an e-2-intensity diameter of approximately 270 µm (Figure 1b). Emitted photoelectrons were imaged with an aberrationcorrected PEEM which provides an ultimate imaging resolution of < 3 nm. To observe the highest possible resolution of the PEEM device experimentally, sample objects showing a perfectly stepshaped amplitude contrast would be required23. Hence, in general, it is not possible to observe the maximum device resolution with an arbitrary sample. Here on this sample, we determine characteristic changes of the photoemission signal across a minimum length scale of 12 nm (see Supplementary Info). The highest electron yield was obtained by setting the laser polarization perpendicular to the nanoslits, since this geometry gives the best overlap with the plate-capacitorlike electric field distribution of the resonant modes. The double-pulse sequences used in twopulse correlation experiments, i.e., TR-PEEM, were generated by sending the NOPA output through a phase-stabilized Mach–Zehnder interferometer24, which exhibits an interpulse time jitter of about 70 as. First, in order to characterize the resonant behavior of the fabricated nanoslits, we performed Au luminescence experiments25 in which the fluorescence intensity is enhanced by plasmon resonances. Figure 1d (top) exemplarily shows the background-corrected fluorescence spectra of three nanoslits with different length L upon illumination with a pulsed 532 nm laser beam (7 ps pulse length, GE-100, Time-Bandwidth Products AG). A resonance peak near  = 750 nm is present in all three spectra, and there is also an indication of a resonance peak near  = 640 nm. The resonance peaks at smaller and longer wavelengths are attributed to modes of different order since both of them shift to longer wavelengths with increasing L. This behavior is expected for Fabry–Pérot-like resonators25 and is hence also seen in the scattering cross sections retrieved from


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FDTD simulations (Figure 1d, bottom), in which the resonantly scattered light of a plane-wave source is collected by a transmission monitor surrounding the modelled nanoslit resonator. Moreover, the resonance positions of the experiment agree well with the simulation-based expectations suggesting that our fabrication process is deterministic and reliable. The systematic red-shift of the experimental curves with respect to the simulated ones is explained by a slightly longer slit length in the experiment. Additionally, deviations in slit width w and the overall shape can lead to deviations from the expected resonance position.

Figure 2. Photoelectron emission patterns of nanoslits with increasing length L as indicated upon broadband laser pulse excitation. (a) Scanning electron microscopy image of the nanoslit array and coordinate system used in the discussion. (b) Normalized equidistant contour plot of the recorded photoelectron emission. The integration time of the image was ten seconds. Note that the yield of the two rightmost slits was multiplied by a factor of eight to increase visibility. The difference in yield likely originates from carbon deposition during SEM investigations. (c) Normalized contour plot of the modelled photoelectron emission patterns using the data of finite-difference timedomain (FDTD) simulations for various slits of indicated length L and width w = 18 nm. Modelling involves temporal integration of |Eloc(t)|2N at each position of a line monitor (red-dashed line in zoom window) along the nanoslit, where Eloc(t) is the calculated local field and N is the nonlinear photoelectron emission order, and by convoluting the outcome with a 2D Gaussian (25 nm e-2width) to mimic emission spots. The line monitor is positioned close to the flake–vacuum interface with respect to z direction.


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Before discussing time-resolved experiments, we present results of static PEEM experiments on nanoslits with varying length L by using the 20 fs laser pulses and comparing the hot-spot-induced photoelectron emission patterns to those simulated with FDTD near-field data. A scanning electron microscopy image of five nanoslits with a width w of about 18 nm and varying length L is shown in Figure 2a. The separation of the nanoslits of 500 nm is a compromise between choosing small fields of view in PEEM mode in order to increase spatial resolution, and precluding near-field coupling between adjacent nanoslits. Moreover, the distance between the slits is small enough to prevent the launching of undesired surface plasmons by grating coupling since the associated wave-vector phase matching at the gold–vacuum interface would require a slit distance of about 678 nm for light with a wavelength of  = 700 nm under normal-incidence geometry26. The PEEM yield of the nanoslits is shown as a contour plot in Figure 2b. While the three smallest nanoslits reveal mainly a single emission hot-spot, there are three and two hot-spots for the nanoslits with L = 296 nm and L = 316 nm, respectively. For these two slits the PEEM yield is magnified by a factor of eight in Figure 2b to match the signal level to that of the three leftmost slits. We ascribe the different observed yield strengths to local surface modifications introduced during SEM imaging, i.e., carbon deposition which is known to cause a change of surface properties, e.g., the work function of gold.27 Also note that the photoemission pattern in Figure 2b shows a slight (~10°) rotation with respect to the nominal slit orientation detected with SEM. Imperfect adjustments of the magnetic lenses in the PEEM can lead to similar distortions, but also a near-by edge of the sample holder aperture resulting in a surface potential deformation is a conceivable origin of this observation. In order to compare the experimental results to theory, we simulated the photoelectron emission by using the FDTD near-field data, R(y,), two nanometers away from the right edge, along the


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inside of the nanoslit (red-dashed line in zoom window of Figure 2c). Since the complex-valued amplitude of the laser pulse EL() is known from laser pulse reconstruction (see Supplementary Information), the local electric field Eloc(y, t) can be calculated via inverse Fourier transformation: E loc ( y , t )  FT 1 R ( y, ) E L ( ) .

(1)

~ The local PEEM yield Yloc ( y ) was then calculated by integrating the N-th power of the local

intensity over time, ~ Yloc ( y ) 



E

loc

( y, t )

2N

dt ,

(2)



in which the nonlinear order N of the photoelectron emission process is equal to 3.4, as retrieved from a series of power-dependent PEEM images (see Supplementary Information). Afterwards, ~ Yloc ( y ) was convoluted with a two-dimensional Gaussian, yielding Yloc ( x, y) , to mimic

photoelectron emission that is blurred by a point-spread function. Yloc ( x, y) is shown in Figure 2c for all five nanoslits and it resembles the measured PEEM yield remarkably well: The three smallest nanoslits exhibit only one emission spot, while the other two slits show the expected pattern of three and two dominant emission spots. The relative amount of photoelectron emission among the hot-spots is also modelled correctly: For both slits the PEEM yield decreases from the Au-terminated end to the open termination. For L = 316 nm one can even observe a small hot-spot in the nanoslit center that is also suggestively seen in the experiment. Deviations of the experimental data occur at the open termination where the emission spots of the two rightmost nanoslits are slightly shifted along the slit towards its interior. This shift is caused by the rounded corners of the FIB-written nanoslits since the field strength, and hence the photoelectron emission, is strongest for a minimum distance of the capacitor-like nanoslit side walls. Note that the three leftmost nanoslits also exhibit an emission spot at the open termination but the photoelectron


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emission at this position is much weaker than indicated by the lowest contour line. This is in accordance with the static PEEM data of Figure 2b. At this point we conclude that the FDTDbased PEEM yield modelling described above is capable of reproducing results from static PEEM experiments and that it should therefore also be applicable to time-resolved investigations. The exact shape of the photoelectron emission patterns will be explained later by the shape of R(y,).

Figure 3. Investigation of local mode dynamics with interferometric TR-PEEM. (a) Timedependent hot-spot photoelectron emission yields for the nanoslit with L = 296 nm, spatially integrated over three representative regions (red, grey, blue) as marked on the left, as a function of laser pulse delay T for experiment (top) and simulation (bottom). The simulation is based on the same response function as Figure 2c. Dashed–dotted lines are inserted to help compare the phase evolution of signals from different emission spots. To increase visibility, pulse overlap data (T < 20 fs) are not shown and the grey and blue curves of the simulation are shifted vertically by 4 and 5.6 units, respectively. Experimental data are shifted by 1.5 and 3 units, respectively. (b) Fast Fourier transform (FFT) of the measured (top) and simulated (bottom) signals at the fundamental (left) and second-harmonic frequency (right) in units of the laser center frequency 0.

We now investigate the dynamics of photoelectron emission hot-spots within a single nanoslit. For this purpose, we performed TR-PEEM experiments on the nanoslit with L = 296 nm that displayed three clearly visible hot-spots. Figure 3a (top) shows the PEEM yields of the Au-


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terminated (upper), the central, and the open-end-terminated (lower) photoelectron emission spots, integrated over spatial regions of interest as indicated in Figure 3a (left), as a function of laser pulse delay . Note that the data of the pulse overlap region, i.e., T < 20 fs, are not shown (see Supplementary Information for full data). All three curves oscillate on the femtosecond timescale. Here, we explicitly point out that these oscillations cannot be interpreted as the local nanoresonator field oscillations after single pulse excitation. Instead, since this is a double-pulse experiment, the signal has to be understood as a nonlinear autocorrelation trace which is based on the superposition of identical, but time-delayed near-fields induced by the first and second laser pulse. The oscillations of the autocorrelation trace carry convoluted information of the laser with the system’s response function, e.g., the resonance frequency, since the local near-field itself is determined by the system’s response function.28 The temporal envelope of the TR-PEEM yield decreases monotonically for all three emission spots until the laser pulses are sufficiently separated in time so that the near-field-induced photoelectron emission of both laser pulses individually adds up to give a constant offset. Although the general time evolution looks similar in all three regions, there is a notable difference: While the yields of the emission spots at both terminations (red and blue curves) oscillate in phase, the yield of the central spot (gray curve) begins to oscillate out of phase with respect to the other two spots for pulse delays of T > 35 fs. More precisely, it oscillates slower, therefore indicating a redshift of the underlying near-field wavelength. This is also visible by looking at the Fourier transformation of the data near the laser frequency 0 and its second harmonic 20 (Figure 3b, top): The central emission spot peaks at a lower frequency than the other two emission spots.


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For comparison, we used the spatially resolved FDTD response function R(y,) of the nanoslit ~ resonator with L = 300 nm from above to calculate the two-pulse correlation signal YTPC ( y, T )

of the local near field Eloc(y,t) via ~ YTPC ( y, T ) 



E

loc

( y, t )  Eloc ( y, t  T )

2N

dt .

(3)



The integrated yield at the three emission spots is shown in Figure 3a (bottom): The delaydependent evolution of the signal reproduces the experiment, i.e., the signal at the central emission spot oscillates with a smaller frequency than the signal at the other two emission spots, which oscillate in phase with each other. This is also seen in the Fourier-transformed data (Figure 3b, bottom) in which the corresponding signal peak of the central emission spot is red-shifted compared to the other two regions. Interestingly, the line width of the peak of the central emission spot is broader than the Fourier peak of the other regions, indicating a faster decay of the near field in the central nanoslit region. Note that this broader line width is also seen in the Fourier transformation of the experimental data (Figure 3b, top). Despite the general agreement of experiment and FDTD modelling, there are slight deviations: For instance, the Fourier peak shapes and positions of the outer emission spots do not fully coincide in the experiment. We assume that these deviations arise from the slightly deviating geometry of the modelled and the fabricated nanostructure. The observation of near-field dynamics with different lifetimes and resonance frequencies at different positions within the same resonant mode is incompatible with the typical attributes of an eigenmode12–17 since it suggests a spatial variation of the Q-factor and resonance frequency of a single mode. To explain this behavior, we now discuss the FDTD-retrieved spatially resolved response function R(y,) that fully determines the near-field dynamics and served well for


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modelling the measured data. A contour plot of |R(y,)|2 as a function of frequency  and the longitudinal slit axis y is shown in Figure 4a, and the spatially integrated curve of this response function is shown in Figure 4b together with the experimental laser spectrum. The spatial mode distribution of the laser-excited resonance at around  = 700 nm features three anti-nodes (i.e., local maxima of the absolute magnitude) along the nanoslit, which explain the three photoelectron emission spots of the L = 296 nm nanoslit in the static PEEM experiments shown in Figure 2b. A closer look at the spectral positions of the anti-nodes reveals an interesting fact: The maximum of the central anti-node is red-shifted by 8 nm with respect to the anti-nodes at the opposed nanoslit terminations. We can therefore explain the detuned near-field oscillations of Figure 3 by the spectral shift of mode anti-nodes. Our conjecture is that this spectral shift is caused by the influence of the adjacent resonator mode around  = 950 nm since the response function |R(y, )|2 exhibits an increased amplitude between the central anti-node of the mode near  = 700 nm and the large, and intense, anti-node near the Au-terminated end of the nanoslit at around  = 950 nm. The spectral slope of the latter resonance then “drags” the central anti-node of the mode at  = 700 nm to longer wavelengths. Similar “bridge-like” structures along the wavelength axis can be observed around  = 650 nm between the mode with three anti-nodes and the subsequent mode at shorter wavelengths.


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Figure 4. Calculated response function. (a) The response function |R(y,)|2 along the nanoslit, i.e., the y coordinate, with L = 300 nm. Note that the data of |R(y,)|2 stems from the slit center, i.e., 8 nm away from the side edges, in order to keep the upcoming FDTD simulations with dipole sources stable. However, the response function is closely related to the one analyzed in Figure 2 and Figure 3, and mainly differs in amplitude. (b) Response function |R|2 integrated along the nanoslit (black solid line). The experimental laser spectrum (gray-shaded area) covers the resonance peak of the mode showing three anti-nodes in the spatially-resolved response function |R(y,)|2.

In order to prove our conjecture, we will now show that the FDTD-based response function R(y,) can be reproduced by a superposition of pure nanoslit eigenmodes with mode number µ, in which µ defines the number of nodes inside the nanoslit. Since the nanoslit modes couple to the far-field, radiation damping is present so that the overall system is considered as an open cavity. Additionally, material damping of surface plasmons in Au increases for increasing resonance frequencies, in particular, due to interband transitions at wavelengths smaller than 600 nm. This leads to a strong decrease of mode amplitudes for resonances with  < 600 nm and therefore only modes with µ = 0 up to µ = 3 are considered in the following.


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The common approach to describe eigenmodes of an open system is to apply the formalism of QNMs9, which are, in electromagnetism, an eigensolution to the homogeneous, and hence sourceindependent, Helmholtz equation with open boundary conditions. While the formalism is well established in numerical electrodynamics7,8,29–31, Faggiani and co-workers only recently applied this concept for the first time to explain the outcome of their TR-PEEM experiments at specific hot-spots10. Here, we will model the complete spatially resolved response function R(y,) according to 3

R ( y, )   A ( )f  ( y )

(4)

 0

with QNMs f  ( y ) that are themselves only a function of space. The frequency dependence of the response function is governed by the Lorentzian-shaped expansion coefficients

A ( ) 

1 , (2 i    2  4 2 2  4 2 2 )

(5)

in which   and   are the resonance frequency and damping parameter, respectively, of the µth QNM. Each fµ(y) is retrieved by using an FDTD simulation in which a dipole is positioned near a corresponding mode hot-spot leading to selective excitation of the associated QNM. An apodization technique is applied to remove the spatial source imprint on the simulation data (see Supporting Information). The spatial mode distributions |fµ(y)|2 up to µ = 3 are shown in Figure 5a. Interestingly, an anti-node of the mode µ always overlaps with two -phase-shifted anti-nodes of the next higher lying mode µ+1. This behavior supports our conjecture that the bridge- and gaplike structures in |R(y,)|2 originate from constructive and destructive interference between different QNMs fµ(y), respectively. The other building block of Equation (4), i.e., the spectral


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response functions 𝐴µ 𝜈 with their defining parameters µ and µ, were retrieved by modelling the spatially integrated response function of Figure 4b with a sum of Lorentzian oscillators (see Supporting Information for details). In a final step, the response function |R(y,)|2 is fitted by a superposition of QNMs according to 2

R fit ( y, ) 

3

2

a A ( )f  ( y)e  

i 

,

(6)

0

in which aµ, the mode amplitude, and φµ, its overall phase, are the only free fit parameters. Their respective values are given in the Supporting Information and |𝐑 fit (y, ν)| is shown as a contour plot in Figure 5b. The bridge-like structures, as well as the shape and relative height of all occurring peaks, are very well reproduced. The exact FDTD data |R(y,)|2 can hence be completely modelled by a superposition of QNMs. The influence of adjacent resonator modes in this superposition can be estimated by looking at the Lorentzian-shaped expansion coefficients 𝑎 𝐴µ 𝜈

in Figure 5c. While the impact of a QNM

at a specific spatial position within the nanoslit is, according to Figure 5a, on the one hand dependent on the spatial position within the nanoslit, the overall amplitude is on the other hand purely scaled by this spectral line-shape function. Interestingly, the oscillator amplitude, and hence the contribution of one mode near the resonance frequency of the other, increases with decreasing mode number µ for all modes different from the directly excited one (see the vicinity around  = 700 nm in Figure 5c). At the excitation wavelength of 715 nm, the amplitude of the fundamental µ = 0 mode, centered at 3 µm, is still at 10% of the maximum amplitude of the µ = 2 mode, which was mainly excited during TR-PEEM experiments. This contribution is so large that it is not possible to reproduce the shape of |R(y,)|2 without this fundamental mode and crucial differences


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occur when it is left out, as it is shown in Supporting Information. Also note that due to the presence of the µ = 0 mode it is unnecessary to include a constant offset in Equation (6) and the entire background signal is determined by this fundamental mode. A noticeable contribution of an offresonant mode has been observed recently in third-harmonic generation at plasmonic nanoantennas32. Here, we disentangle its contribution to the full space- and frequency-resolved linear response function and detect the implications on the ultrafast local near-field dynamics.

Figure 5. Modelling the spatially resolved response function R(y,) along the nanoslit by a superposition of quasinormal modes (QNMs). (a) Normalized QNM intensity |fµ(y)|2 along the nanoslit as retrieved by apodization in FDTD simulations using local dipole excitation. An offset of 0, 1, 2, and 3 is introduced for |f4(y)|2, |f3(y)|2, |f2(y)|2, and |f1(y)|2, respectively, to increase visibility. (b) Absolute square of the response function Rfit(y,) which was fitted to the FDTD data of Figure 4a by using Equation (6). (c) Intensity |𝐴µ 𝜈 | of the Lorentzian oscillators for mode numbers µ = 0 – 3.

We hence conclude that the local differences in resonance frequency and Q-factor within a single nanoresonator, as detected in our TR-PEEM experiments, originate not only from constructive and destructive interference of nearest-neighbor QNMs but also from the non-negligible influence of all resonator modes down to the fundamental one, i.e., µ = 0. The influence of plasmonic resonances with low mode number is therefore comparable to that of the low-lying resonances


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associated with the refractive index of materials and it needs to be considered when designing plasmonic resonators for light–emitter interaction. Our findings are in contrast to the wide-spread approach to only consider those modes which are sufficiently covered by the spectrum of the excitation source. As a consequence of the nonnegligible influence of other QNMs, it is not possible to purely excite a single mode of a resonator even when the excitation source is a continuous-wave laser. The significance of other QNM contributions depends on the linewidth of the modes and is therefore most crucial in systems with high loss like plasmonic nanoresonators. From the point of view of quantum optics, the density of states which is experienced by nearby quantum emitters will exhibit a significant contribution from spectrally distant QNMs which act as undesired decay channels. Therefore, the present work emphasizes the importance of dissecting the local response of nanoresonators into the QNM building blocks. As mentioned by Lalanne and co-workers, the density of states, and hence the Purcell factor, is also determined by phase effects of superpositioned QNMs7. Understanding the gradual QNM modification by structural design hence offers the potential to tailor nanoresonators for enhanced light–emitter interaction, and we have demonstrated that the combination of our NOPA and TR-PEEM setup is suitable to investigate the associated local differences within the specific nanoresonators. Beyond that, we aim at observing local dynamics not only of the resonator, but, having resolved sample-dependent characteristic changes of the photoelectron emission signal on a scale of ~12 nm, also of the embedded quantum emitter itself.

ASSOCIATED CONTENT


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Supporting Information. Reconstruction of the electric field of NOPA pulses via FROG technique, measurement of PEEM resolution, measurement of the nonlinear order of photoelectron emission, full data (with pulse-overlap region) of local mode dynamics measured with interferometric TR-PEEM, retrieving QNMs by apodization technique using FDTD simulations, and fitting the FDTDretrieved spatial response function using QNMs.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] **E-mail: [email protected] Orcid Bernhard Huber: 0000-0002-5472-8596 Matthias Hensen: 0000-0002-5578-0118 Tobias Brixner: 0000-0002-6529-704X Bert Hecht: 0000-0002-4883-8676 Sebastian Pres: 0000-0002-8402-4864 Notes The authors declare no competing financial interest. #

These authors contributed equally to this work.


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ACKNOWLEDGMENT T.B. gratefully acknowledges financial support from the European Research Council (ERC Consolidator Grant “MULTISCOPE” – No. 614623).

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(32) Wolf, D.; Schumacher, T.; Lippitz, M. Nat. Commun. 2016, 7, 10361.


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Au flake

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1 2 3 ∆x ≈ 12 nm 4 5 h 6 w 7 8 c9 10 dispersion control 11 12 20 fs 715 nm 13 14 15 16 17 NOPA 18 tunable from 19215 nm to 970 nm 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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