These authors contributed equally to this work. These authors contributed
equally to this work. [1,7]Holger Lange [1,2]Francesca Calegari
[3,4,8,9]Matthias F. Kling 1]The Hamburg Centre for Ultrafast Imaging, Luruper
Chaussee 149, 22761 Hamburg, Germany 2]Center for Free-Electron Laser Science
CFEL, Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg,
Germany 3]Max Planck Institute of Quantum Optics, Hans-Kopfermann-Str. 1,
85478 Garching, Germany 4]Physics Department, Ludwig-Maximilians-Universität
Munich, Am Coulombwall 1, 85748 Garching, Germany 5]Attosecond Science
Laboratory, Physics and Astronomy Department, King-Saud University, P.O. Box
2455, Riyadh 11451, Saudi Arabia 6]Institute of Quantum Optics, Leibniz
Universität Hannover, Welfengarten 1, 30167 Hannover, Germany 7]Institute of
Physics and Astronomy, Universität Potsdam, Karl-Liebknecht-Str. 24, 14476
Potsdam, Germany 8]Stanford PULSE Institute, SLAC National Accelerator
Laboratory, 2575 Sand Hill Rd, Menlo Park, CA 94025, USA 9]Applied Physics
Department, Stanford University, 348 Via Pueblo, Stanford, CA 94305, USA

# Far-field Petahertz Sampling of Plasmonic Fields

Kai-Fu Wong<EMAIL_ADDRESS>Weiwei Li<EMAIL_ADDRESS>Zilong Wang<EMAIL_ADDRESS>Vincent Wanie
<EMAIL_ADDRESS>Erik Månsson<EMAIL_ADDRESS>Dominik Hoeing
<EMAIL_ADDRESS>Johannes Blöchl<EMAIL_ADDRESS>muenchen.de Thomas Nubbemeyer<EMAIL_ADDRESS>Abdallah M. Azzeer<EMAIL_ADDRESS>Andrea Trabattoni
<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>[  [  [  [  [  [  [  [  [

###### Abstract

The collective response of metal nanostructures to optical excitation leads to
localized plasmon generation with nanoscale field confinement driving
applications in e.g. quantum optics, optoelectronics, and nanophotonics, where
a bottleneck is the ultrafast loss of coherence by different damping channels.
The present understanding is built-up on indirect measurements dictated by the
extreme timescales involved. Here, we introduce a straightforward field
sampling method that allows to measure the plasmonic field of arbitrary
nanostructures in the most relevant petahertz regime. We compare experimental
data for colloidal nanoparticles to finite-difference-time-domain
calculations, which show that the dephasing of the plasmonic excitation can be
resolved with sub-cycle resolution. Furthermore, we observe a substantial
reshaping of the spectral phase of the few-cycle pulse induced by this
collective excitation and we demonstrate ad-hoc pulse shaping by tailoring the
plasmonic sample. The results pave the way towards both a fundamental
understanding of ultrafast energy transformation in nanosystems and practical
applications of nanostructures in extreme scale spatio-temporal control of
light.

###### keywords:

plasmonics, plasmon dynamics, gold nanoparticles, petahertz field sampling

## Introduction

In metallic nanoparticles (NPs) the light electric field can drive the
conduction band electrons into a collective oscillation on the nanoscale,
referred to as localized surface plasmon (LSP) maier_plasmonics_2007 .
Coupling of light to a LSP resonance leads to the local enhancement of the
electromagnetic field and to the confinement of the light-matter interaction
on the nanoscale, therefore enabling a manifold of applications including
surface enhanced spectroscopy schlucker_surface-enhanced_2014 , enhanced
luminescence fusella_plasmonic_2020 , strong-field driven nanoscale currents
dombi_strong-field_2020 , enhanced nonlinear optical effects NaturePhoton6 ,
and strong-coupling quantum optics mueller_deep_2020 ;
bogdanov_overcoming_2019 . However, a direct characterization method for the
electric fields emerging from the resonantly excited nanostructure is still
lacking.
Subsequent to its coherent driving by the light field, Landau damping,
electron–electron, electron–phonon, and electron–surface scattering result in
an ultrafast (about 10 fs) plasmon decay with the energy transferred to
highly-excited, nonequilibrium carriers wang_high-q_2021 ; li_correlation_2020
; santiago_efficiency_2020 ; besteiro_fast_2019 ; boriskina_losses_2017 ;
dominik . These hot carriers can contribute to chemical transformations on the
NP surface, intensely studied in the field of heterogeneous catalysis
zhang_surface-plasmon-driven_2018 . The details of the plasmon decay channels,
however, have only been deduced from theory and dependencies on material
parameters and e.g. excitation conditions have not yet been experimentally
confirmed in a direct manner avalos-ovando_temporal_2020 ; anderson ; zentgraf
. For this reason, experiments enabling a more direct access to the plasmon
decay of different NP systems are of strong interest.
Field sampling of plasmonic nanoantennas has been recently achieved with
electro-optical sampling, limiting the approach, however, to the terahertz
domain bib31 . The vast majority of plasmonic nanostructures discussed in the
literature exhibits resonances in the visible spectral region, strongly
motivating the extension to the petahertz (PHz) domain. As a first example
heading in this direction, plasmonic nanoantennas have been utilized as near-
field sensors to enhance the sensitivity for the reconstruction of the
incident light electric field ($E$-field) bib5 . What is still lacking despite
its high relevance, is the realization of PHz plasmonic field sampling.
Here, based on recent advances in methodology Herbst_2022  we demonstrate PHz
far-field sampling of plasmonic responses of colloidal NPs utilizing the
tunneling ionization with a perturbation for the time-domain observation of
the electric field (TIPTOE) technique bib4 . We compare the experimental data
to results from finite-difference time-domain (FDTD) calculations showing that
the temporal build-up and decay of the plasmon field can be resolved.
Furthermore, we demonstrate extreme scale control of the transmitted fields
with the NPs. With our approach we are not only sensitive to the electric
field in the time domain, but also directly sensitive to the phase response,
which is directly imprinted in the phase of the sampled field. This in turn
allows for the specific design of the plasmonic material to optimize the
light-matter interaction for aforementioned applications. In our case we
demonstrate the ability to shape the dispersion of ultrafast light pulses, by
changes of the geometry of our NPs. Our results provide a simple way of
sampling plasmon fields of arbitrary nanostructures on the PHz scale and show
important practical applications in the control of light fields.

Figure 1: Experimental approach. a Sketch of the field sampling setup. The
incident laser pulse is split into a fundamental and a signal pulse in an
interferometer. The signal pulse interacts with the sample. Both pulses are
recombined with variable delay and focused between two electrodes, where the
TIPTOE measurement takes place. b TEM image of the employed AuNS with scale
bar corresponding to 100 nm. c TEM image of the AuNRs with scale bar
corresponding to 200 nm. d Absorption spectra of the investigated NPs (AuNS:
red curve, AuNRs: orange curve) together with the incident light spectrum. BC:
beam combiner, PM: parabolic mirror.

## Results

Few-cycle pulses with a pulse duration of 4.5 fs, central wavelength of 780
nm, and a repetition rate of 10 kHz were sent into the experimental setup
shown in Fig. 1a. The incident light was split interferometrically into a
fundamental and a signal beam. The signal beam was propagating through the
plasmonic sample before being recombined with the fundamental beam for field
sampling. The intensity ratio between signal and fundamental beams was chosen
to be roughly 1:1000, to remain in the perturbative regime for the TIPTOE
technique bib4 . The peak intensities for the excitations were chosen to be
under $10^{10}~{}\mathrm{\frac{W}{cm^{2}}}$ to avoid damage of the sample, and
to ensure that the interaction between the few-cycle signal pulse and the
sample is in the linear regime (see Supplementary Notes 3-5). As samples we
employed gold nanospheres (AuNS) with 20 nm in diameter, and gold nanorods
(AuNR) with dimensions of 80 nm $\times$ 26 nm (aspect ratio of 3.1),
respectively. Transmission electron microscopy (TEM) images of each sample are
shown in Fig. 1b-c. From the TEM images we also obtained the size
distributions of the colloidal samples (see Supplementary Note 1). For AuNS,
the plasmon resonance only marginally overlaps with the broad bandwidth of the
few-cycle near-infrared (NIR) pulse (non-resonant case), while the
longitudinal surface plasmon resonance of AuNRs lies right within the NIR
spectrum (resonant case); cf. Fig. 1d. The samples were deposited onto a fused
silica substrate. A replica silica substrate was used as a reference. The
dispersive contribution from the 1 mm thick fused silica substrate for the
deposited NPs was carefully compensated with chirped mirrors. Observed changes
should therefore only arise from the plasmon field itself. Fig. 2 displays the
results obtained from the TIPTOE measurements for both the non-resonant and
resonant cases in the time domain. As expected for a non-resonant sample, the
TIPTOE measurement performed for AuNS shown in Fig. 2a exhibits a very similar
$E$-field as the reference field with a small attenuation that can be
attributed to intraband transitions in gold. This also results in almost
identical spectral amplitudes and spectral phases between sample and bare
substrate as shown in Fig. 2c and e, respectively. Note that the non-resonant
case serves as a benchmark in our field sampling approach. In the case of
AuNRs, a strong reduction in the amplitude of the $E$-field is observed as
expected by the resonant absorption (Fig. 2d). More interestingly, the sampled
$E$-field in the time-domain (Fig. 2b) exhibits deviations from the reference:
starting from the peak of the pulse envelope we can observe a significant
distortion of the optical cycles with oscillations extending in the tail of
the few-cycle pulse. These distortions result in a drastic change of the
spectral phase as well as shown in Fig. 2e, which exhibits a crossing with the
reference phase at the peak of the plasmon resonance around 810 nm. The phase
shift due to the resonance is a well known effect and has been reported in
previous studies bib5 ; Capasso .

Figure 2: Optical field sampling measurements. a TIPTOE trace for the non-
resonant AuNS. b TIPTOE traces for the resonant AuNRs. In both cases, the blue
line depicts the TIPTOE trace of the reference (plain substrate). c and d
display the corresponding transmission spectra obtained via Fourier transform
from the measurements in a and b, respectively. The dashed blue curve displays
the reference few-cycle spectrum. The shaded grey areas display the absorbance
spectrum of the corresponding NPs. e Spectral phases for each case. The dashed
blue line displays the reference, red the non-resonant and orange the resonant
spectral phase, respectively. The black arrow indicates the crossing between
the phases of the resonant and reference case.

The experimental observations were compared to FDTD calculations implemented
using Lumerical 2022 R1 software (ANSYS, Inc) alsayed2023giant . As input
parameters we used the particle dimensions, the dielectric constants of the
materials and the sampled incident $E$-field. To account for the inhomogenous
broadening of the plasmon resonance, we calculated the interaction between the
experimental few-cycle field with five particles of different sizes,
considering the determined size distribution from TEM analysis as weighting
factor. The calculation results are summarized in Fig. 3.

Figure 3: FDTD calculation for the resonant case. a Simulated $E$-field with
the plasmonic contribution (orange) and the input pulse as experimental data
(blue). b Retrieved spectrum (blue) and spectral phase (orange) from the FDTD
calculation, displaying the transmitted $E$-field after propagation through
the plasmonic sample. As a reference the field without sample interaction is
depicted in dashed lines as well. The shaded gray area displays the absorption
spectrum of the sample, in which five different sized AuNRs embedded on a
fused silica matrix are used for the calculations. Insets: simulation geometry
of AuNRs, with five different size dimensions considering the colloidal size
distribution of the AuNRs.

The obtained traces for the plasmonic interaction agree with the experimental
traces (Fig. 3a). At 5 fs the discontinuity of the $E$-field is indicated and
the delayed oscillation can be observed until 12 fs. The agreement persists
for the spectral phases. As in the experiment, the spectral phase between
reference and plasmonic system exhibits a visible phase crossing at the
central resonance around 750 nm in this case, cf. Fig. 3b (indicated by the
arrow).
To resolve the onset of the plasmonic excitation from the time-resolved
measurements, we subtracted the TIPTOE traces between the sample and
reference. In this way, we isolate the contribution of the plasmon from the
driving few-cycle field in the far-field domain. The results are reported in
Fig. 4.

Figure 4: Sampling of plasmon fields. a Differential field contributions for
the non-resonant AuNS with the experimental data as solid line and the FDTD
data as dashed line. b Differential field contributions for the resonant
AuNRs.

For the non-resonant case, the differential signal is almost negligible. For
the resonant case, a clear build-up of an additional field component can be
resolved, with a subsequent decay with a lifetime in the order of 10 fs, after
which the differential field approaches the baseline. Treating the calculated
data the same way, we observe a qualitative agreement with the experiment. The
plasmon drive is well reproduced by the simulations, while we experimentally
observe a faster decay, which could be attributed to inhomogeneous broadening
due to plasmon coupling and increased damping at elevated temperatures
brown_nonradiative_2016 . The visible ultrafast decay can be attributed to the
ultrafast dephasing time of the plasmon, which conversely to previous
measurements bib5  can now be retrieved from far-field measurements (cf.
Supplementary Note 7). The pulse interaction with the plasmon is also
reflected in the optical dispersion. Applying a polynomial fit to extract the
group delay dispersion (GDD) yields different values for the plasmonic
interaction compared to the reference sample. A positive GDD enhancement of
approximately 8.03 fs2 compared to the original phase value was observed after
propagation through the resonant AuNRs sample. The enhancement was consistent
with differently chirped pulses (see Supplementary Notes 2). Interestingly, we
observe that the residual spectral phase, representing the plasmonic
contribution, displays a positive parabolic shape close to the peak of the
plasmon resonance. In contrast, the non-resonant AuNS induce no significant
change of the dispersion. To further explore this effect, we performed
measurements with samples displaying different plasmon resonances by altering
the aspect ratio (AR) of the AuNRs. As samples we used AuNRs with dimensions
of 71 nm $\times$ 26 nm and 78 nm $\times$ 19 nm corresponding to an AR of 2.7
and 4.1 respectively. As the AR for AuNRs changes, the longitudinal plasmon
resonance shifts in frequency. We observe that the spectral phase of the few-
cycle pulse is altered correspondingly; cf. Fig. 5.

Figure 5: Comparison of the propagating pulse spectral properties for AuNRs
with resonances shifted relative to the AuNRs discussed before. a Blue-shifted
AuNRs. b Red-shifted AuNRs. The absorption position of the plasmonic
resonances are hinted as shaded grey area.The residual spectral phase
contribution with its extracted GDD value is depicted as the gray line in each
case. Exemplary TEM images of the AuNR samples with corresponding scale bars
of 200 nm each are shown as insets.

As the plasmon absorption shifts relative to the previous resonant case, we
also observe a shift of the positive parabolic contribution. In particular,
for the plasmon resonance overlapping with the blue part of the spectrum, the
minimum of the parabola shifts towards the blue, and correspondingly the
remaining spectral phase exhibits a slightly negative parabolic shape that
results in a negative GDD. In contrast, for the plasmon resonance overlapping
with the red part of the spectrum, the minimum of the parabola shifts towards
the red and results in an increase of the positive GDD. Tailoring of the
plasmonic resonance is straightforward by changing the properties of the NP
such as shape, size or environment and thus allows the realization of ad-hoc
pulse shaping. Moreover, the ability to tailor plasmon resonances with a broad
bandwidth facilitates the possibility to manipulate the spectral properties of
broadband few-optical-cycle pulses. This concept was already anticipated in a
theoretical study proposing the use of plasmonic NPs as metasurfaces to
engineer ultrashort pulses bib6  and it has been experimentally demonstrated
with 45 fs long pulses geromel . In this context, our approach demonstrates
the feasibility of shaping broadband few-cycle pulses using broad plasmon
resonances.

## Conclusion

We demonstrated the PHz sampling of resonant plasmon fields from gold
nanostructures in the far-field. The implementation of the TIPTOE technique
allowed direct access to the plasmon fields at visible wavelengths, which are
the most relevant in nanoplasmonics. The plasmon dephasing dynamics was
resolved on a subcycle scale. This will allow to benchmark theoretical
descriptions and address the different channels contributing to the ultrafast
dephasing. The free space integration of the samples enables investigating
details of the plasmon dephasing of arbitrary plasmonic nanostructures. For
example coherence in strongly coupled hybrid systems can be addressed directly
saez-blazquez_can_2023 ; li_correlation_2020 . Furthermore, we demonstrated
that the broadband plasmon resonance of nanostructures can alter the optical
properties of few-cycle pulses. Additionally, the field sampling allows for
direct extraction of the spectral phase without applying any reconstruction
algorithms. With careful design of such plasmonic nanostructures their usage
for shaping of ultrashort laser pulses becomes in principle feasible.

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## Methods

Sample preparation. Monocrystalline NPs with uniform size distribution were
synthesized via established wet-chemistry approaches namely the seed-mediated
growth-approach. The detailed protocol for the synthesis of AuNS is stated in
ref. Xia ; schulz_optimizing . The protocol for AuNRs is stated in ref.
schulz_effective_2016 . To prepare the NPs for the optical experiment, in a
first step the hexadecyltrimethylammonium chloride
(CTAC)/hexadecyltrimethylammonium bromide (CTAB) stabilized particles in
aqueous solution were transferred to an organic solution (toluene), in which
the particles are stabilized by thiol-terminated polystyrene (PSSH) with a
molar weight of 25k $\mathrm{\frac{g}{mol}}$. The reaction was carried out in
1 mL of tetrahydrofuran (THF), where the solution was stirred for three
minutes in a glass vial. By shaking the vial after the reaction a thick
product stuck at the side of the vial, with the remaining supernatant on the
bottom, which was removed. The remained product in the vial was treated under
nitrogen atmosphere to dry the sample and was then redispersed with toluene.
After three washing steps via centrifugation (10k g, 20 minutes each washing
step) with toluene in which 0.1 M PSSH was dispersed, the 25 µL of the
particle solution were spin-coated onto the plasma cleaned silica substrate
(EKSMA Optics) at low spin speeds (100 rpms) until the organic solution
evaporated completely. Materials: CTAB and CTAC were purchased from Sigma-
Aldrich (USA), thiol-terminated PSSH was purchased from Polymer Source
(Canada), THF ($>$99.5%) was purchased from VWR Chemicals (USA) and toluene
($>$99.8%) was purchased from Thermo Fisher Scientific (USA).
Characterization of samples. For the as-synthesized particles, the
characterization was carried out via UV/Vis-absorption spectroscopy and
transmission electron microscopy (TEM). Absorption spectra were recorded using
a Varian Cary 50 spectrometer. For TEM analysis a droplet of AuNS or AuNP
solution was deposited on amorphous carbon-coated copper grids. The grids were
dried in air over night to remove residual solvent. TEM images were obtained
using a Joel JEM-1011 transmission electron microscope operating at 100 kV The
particles displayed a narrow size distribution, which was determined based on
the width of the plasmon absorption and the TEM data. The deposited NPs were
characterized by UV/Vis-absorption spectroscopy. For the NPs on the substrate
a slight red-shift and broadening can be observed, one possible source
originating from plasmon coupling. This would most likely lead to a faster
damping of the plasmon oscillation. Further effects which play a role for the
broadening could be changes of the environment. Nonetheless, the assumption
that the observed plasmon response mainly displays the properties of the
individual particles is valid, as the shift is not too pronounced.

## Data and materials availability

All data needed to evaluate the conclusions in the paper are present in the
paper or the supplementary materials.

## Acknowledgements

We acknowledge fruitful discussions with Nirit Dudovich and Ferenc Krausz.
This work was supported by the German Research Foundation (DFG) via the
Cluster of Excellence ”Advanced Imaging of Matter” (EXC 2056, 390715994). H.L.
acknowledges funding by the DFG via project 432266622. M.F.K. is grateful for
partial support by the Max Planck Society via the Max Planck Fellow program.
J.B. acknowledges support by the Max Planck School of Photonics. M.F.K.’s work
at SLAC is supported by the U.S. Department of Energy, Office of Science,
Basic Energy Sciences under DE-AC02-76SF00515, and FWP SC0063. Z.W.
acknowledges support from the Alexander von Humboldt Foundation. A.M.A. is
grateful for support by the Researchers Supporting Project RSP-2021/152, King
Saud University, Riyadh, Saudi Arabia.

## Author contributions

M.F.K. and F.C. conceived the research project and designed the experiment
with H.L.; D.H. and H.L. developed the samples. K.F.W. and W.L. performed the
experiments under guidance of Z.W.. A.M.A. was involved in the original design
of the field sampling setup. W.L. and Z.W. performed the FDTD simulations.
J.B. and T.N. supported the laser and experimental operations. V.W., E.M. and
A.T. were involved in the analysis of the experimental data and assisted the
preliminary characterization of the samples. K.F.W., and W.L. wrote the
initial draft of the manuscript, on which all co-authors commented.

## Competing interests

None declared.

Supplementary Material on

’Far-field Petahertz Sampling of Plasmonic Fields’

by Kai-Fu Wong, Weiwei Li et al.

## Supplementary Note 1: Determination of nanoparticle average size and aspect
ratio

For the determination of the average AuNP dimensions, TEM images were
analyzed. For the AuNS, the diameter is used as main quantity, while the
aspect ratio (AR, length per width) serves as quantity for the
characterization of the AuNRs. The determined distributions are displayed in
Fig. S1.

Figure S1: a Size distribution of the employed AuNS. b Aspect ratio
distribution of the employed AuNRs. The black curve represents the normal
distribution.

From the obtained size distribution a mean diameter of 19.63 nm with a
standard deviation of 0.54 nm for the AuNS is obtained. For the AuNRs a mean
aspect ratio of 3.16 with a standard deviation of 0.35 is obtained. Both
results are in good agreement with the values expected from the synthesis
parameters of 20 nm and 3.08 respectively.

## Supplementary Note 2: Extraction and validation of group delay dispersion

To validate the GDD values obtained from our experiments, we performed
additional TIPTOE measurements by chirping the compressed few-cycle pulses
using materials with defined GDD values. In our case we inserted a 1 mm thick
fused silica substrate into the pathway of the signal pulse before the
plasmonic interaction takes place. The results for the measurements performed
in the main text while using chirped pulses are shown in Fig. S2:

Figure S2: TIPTOE traces measured for the a non-resonant and b resonant case
in the time domain using chirped pulses with a known induced GDD. c Spectral
phase of each measurement. The black arrow indicates the region of the
crossing between reference and resonant spectral phase.

Fig. S2 displays a clear broadening in the time- as well as in the frequency
domain. Most notably the spectral phase displays a strong positive parabolic
shape, indicating a positive chirp. Applying a polynominal fit to the spectral
phase yields the GDD value, which for the reference is determined to be 41.72
fs2 whereas the literature value for the GDD at 780 nm is 37.8 fs2, which
agrees well with our experimental observations. Thus, we can also assume that
the deviations induced by the resonance are real, which is again confirmed by
the chirped measurements, as the non-resonant case displays similar values
compared to our reference as in the non-chirped case, while the resonant case
shows a significant higher value compared to the reference.

## Supplementary Note 3: Experimental setup and linear-response calibration

To obtain the few-cycle pulses required for performing the TIPTOE measurement,
the output of a $10\text{\,}\mathrm{kHz}$ Ti:sapphire chirped pulse
amplification (CPA) system was sent through an Argon filled hollow-core fiber,
generating white light with a broad spectrum ranging from
$500\text{\,}\mathrm{nm}$ to $950\text{\,}\mathrm{nm}$. The white light pulses
were then compressed down to $4.56\text{\,}\mathrm{fs}$ using chirped mirrors,
and the compressed few-cycle pulses were sent into the setup for performing
the TIPTOE measurements.

Figure S3: Detailed schematic of the experimental setup.

A sketch of the complete experimental setup is shown in Fig. S3. The few-cycle
laser pulse is split into two pathways, i.e. the strong pump beam and the weak
signal beam. While the pump pulses were sent to a delay stage, the signal
pulses interacted with the sample exciting the plasmon resonance. A wedge-pair
(WPF) was used to finely compress the fundamental pulses which induce tunnel
ionization serving as a subcycle gate for the field sampling, while another
wedge-pair (WPS1) was employed to finely compress the signal pulses that
interact with the gold NPs. The extra dispersive contribution from the
$1\text{\,}\mathrm{mm}$ thick fused silica substrate was carefully compensated
with two pairs of chirped mirrors (CMs) in combination with an additional
wedge-pair (WPS2). Thus, observed changes should only arise from the plasmonic
field itself. Moreover, an intermediate focus was formed in the probe beam
path using a pair of parabolic mirrors, where an optical chopper operating at
$5\text{\,}\mathrm{kHz}$ was applied, enabling the lock-in detection of the
modulated ionization yield in the form of current. Both beams were recombined
and focused in between a pair of electrodes with a fixed bias of
$40\text{\,}\mathrm{V}$ in ambient environment. The transmitted probe light
field which interacted with the sample can be sampled while scanning the delay
stage and changing the time delay between the fundamental pulses and the
signal pulses.

Figure S4: Setup linear-response calibration: the spectral magnitudes were
integrated and plotted against the $E$-field strength incident in-between the
electrodes. A linear response can be identified by the slope of 0.96 in the
log-log plot. The black arrow indicates the used $E$-field strength in our
experiment.

A scan of the signal $E$-field strength was done during a series of test
measurements on the fused silica reference. The measured temporal traces under
different $E$-field strengths incident in-between the electrodes were Fourier-
transformed into the frequency domain, and the obtained spectral magnitudes
were integrated in the concerned wavelength range. As can be seen in Fig. S4,
by plotting the integration against the signal $E$-field strengths, a linear
response can be identified throughout the whole measured range by a linear
slope in the log-log plot. This observation confirms that the setup shows a
linear response to the incident signal $E$-field in a wide range, and the used
signal $E$-field, as marked by the black arrow in Fig. S4, is also weak enough
to avoid inducing any unexpected influence on the measurements.

## Supplementary Note 4: Linear plasmonic response determination

To ensure that the signal pulses are weak enough to only excite linear
plasmonic response from the gold nanoparticles, a determination of the linear
plasmonic response was conducted. This was done by performing the TIPTOE
measurements using the resonant (AuNRs) sample with varying signal power. A
Fourier transformation was applied to the measured temporal traces to obtain
the corresponding spectral information in frequency domain. Similar to the
process in Appendix B, in order to determine the linear response regime of the
sample, the spectral magnitude profiles under different signal intensities
were integrated and plotted as shown in Fig. S5. In the linear regime the
integration should in principle increase linearly with increasing signal
$E$-field strength.

Figure S5: Determination of the linear plasmonic response: the spectral
magnitudes were integrated and plotted against the $E$-field strength incident
onto the sample. A linear scaling of 1.08 can be seen in the investigated
region in the log-log plot. The black arrow indicates the used $E$-field
strength in our experiment.

The plot in Fig. S5 reveals no nonlinear behavior for the system in the
measured range of signal $E$-field strengths, where the typically used signal
$E$-field strength was $51.1~{}\mathrm{{MV}\cdot{m^{-1}}}$, as marked by the
black arrow. Based on this observation, the experimental measurement with
AuNRs samples can most likely be assumed to happen in the regime where the
plasmonic response is linear.

## Supplementary Note 5: Laser pulse characterization and sample damage
evaluation

The few-cycle signal pulses used for interaction with the NPs were
characterized using the dispersion-scan (D-scan) technique, and the
reconstructed results are shown in Fig. S6. The spectral intensity (blue) and
phase (orange) are plotted in Fig. S6a, where the spectrum shows a wavelength
range from $500\text{\,}\mathrm{nm}$ to $950\text{\,}\mathrm{nm}$ with an
almost flat phase curve in the region of interest, indicating a good
compression of the pulses. Additionally, the reconstructed spectrum (blue)
exhibits nearly the same profile as that of the measured laser spectrum
(dashed red), which confirms the reliability of the D-scan measurement
results. Fig. S6b shows the reconstructed temporal intensity profile of the
pulse (orange) together with the calculated Fourier Transform limited pulse
(blue). The reconstructed pulse duration (full-width-half-maximum, FWHM) was
measured to be $4.56\text{\,}\mathrm{fs}$ compared to the transform-limited
duration of $3.98\text{\,}\mathrm{fs}$, with a reconstruction error of 0.058%.

Figure S6: Laser pulse characterization: a Reconstructed spectrum and spectral
phase. The spectrum is compared with a spectrum measured with a commerical
spectrometer (dashed red). b Temporal results from D-scan measurement compared
to the calculated transform limited pulse (solid blue). c Signal laser pulse
obtained from the TIPTOE trace measured from the bare substrate.

Furthermore, since the TIPTOE traces in principle provide a replica of the
signal laser field, information regarding the original signal laser pulse can
be obtained from the TIPTOE traces measured from the bare substrate with no
plasmonic contribution, as long as the induced dispersion is carefully
compensated. As shown in Fig. S6c, by taking the square of the amplitude of
the measured $E$-field (orange) and taking the envelope of the positive
intensity trace (blue), a laser pulse profile with a FWHM pulse width of
$4.53\text{\,}\mathrm{fs}$ can be obtained, which is in great consistency to
the results of the D-scan measurement.

The displayed TIPTOE traces are averaged over three consecutive measurements.
To the averaged trace we applied the Savitzky-Golay-filter to filter out
residual noise components. The comparison between non-filtered and filtered
trace can be seen in Fig. S7a. To validate the accuracy of the TIPTOE
measurement the FFT retrieved spectral amplitude is compared to a measured
spectrum of the probe pulse under the same conditions using a commercial
spectrometer, which is shown in Fig. S7b.

Figure S7: a Filtered TIPTOE trace (blue) compared to the raw averaged trace
(orange, dashed) obtained out of three consecutive measurements. b FT of the
experimentally trace, which shows the spectral amplitude (blue) and the
spectral phase (orange). The retrieved spectral amplitude is compared to an
acquired spectrum with a commercial spectrometer (red, dashed)

In Fig. S7b the retrieved spectrum from the TIPTOE compared to the spectrum
obtained with the spectrometer agrees well. Additionally, the retrieved
spectral phase displays a relative flat phase with a small residual negative
GDD.

The damage threshold for the synthesized samples was determined by using
comparable few-cycle pulses ($5.9\text{\,}\mathrm{fs}$) as in the experiment
at a repetition rate of 1 kHz. The range of peak intensities, which was
applied to the samples ranged between $10^{10}~{}\mathrm{\frac{W}{cm^{2}}}$
and $10^{14}~{}\mathrm{\frac{W}{cm^{2}}}$. The damage was mainly determined by
observation of the transmission spectrum to observe significant changes. At
intensities starting from $1.5\cdot 10^{12}~{}\mathrm{\frac{W}{cm^{2}}}$ we
observe strong modulations of the spectrum with fringes in the few-cycle
spectrum. These fringes also appear for the pure substrate, but at higher peak
intensities at $2.5\cdot 10^{12}~{}\mathrm{\frac{W}{cm^{2}}}$. Therefore, the
determined threshold for the synthesized NPs should not exceed a value above
$10^{12}~{}\mathrm{\frac{W}{cm^{2}}}$, as the range from induced damage for
NPs to the fused-silica substrate itself is relatively small. We do not expect
significant changes for a higher repetition rate of 10 kHz as used in the
experiment, as at this frequency rate heat dissipation can still occur after
two consecutive pulses. Literature which also performed damage threshold
measurements on gold NPs with ultrashort laser pulses showed remarkably
similar values on the same magnitude kern_damage_2011 . During our experiments
we operated at intensities which were substantially lower than the determined
threshold, as the highest peak intensity used in the experiment was below
$10^{10}~{}\mathrm{\frac{W}{cm^{2}}}$, which means that we operated at least
two magnitudes lower. This way we also ensure that we are operating in the
linear regime for the interaction between the pulse and the plasmonic sample
as also confirmed by the linear calibration measurements. The modulations at
high intensities compared to transmission spectra below the determined damage
threshold are shown in Fig. S8:

Figure S8: Transmission spectra for different input intensities for the few-
cycle pulse propagating through the sample. The grey shaded area represents
the few-cycle transmission spectrum without any sample inserted.

In terms of the determined laser induced damage threshold (LIDT) value, it is
ensured that the value is not exceeded for the set of experiments due to the
use of relatively low power and the fact that the sample is placed in a
collimated beam path. The actual laser peak intensity on the sample surface
could be estimated using the following equation (1),

$I_{0}=\sqrt{\frac{16\ln(2)}{\pi^{3}}}\cdot\frac{W}{\tau_{\text{FWHM}}\omega_{0}^{2}}$
(1)

where $W$ is the pulse energy, $\tau_{\text{FWHM}}$ is the pulse duration, and
$\omega_{0}$ is the radius of the beam. With a Gaussian beam diameter of
$5\text{\,}\mathrm{mm}$ on the sample and a pulse duration of
$4.53\text{\,}\mathrm{fs}$, the maximum peak intensity achieved with a pulse
energy of $0.18\text{\,}\mathrm{\SIUnitSymbolMicro J}$ is $3.464\cdot
10^{10}~{}\mathrm{\frac{W}{cm^{2}}}$, which is two magnitudes below the damage
threshold value determined for the AuNPs (and below the estimated value for
the AuNRs as well).

## Supplementary Note 6: Basic concept for data analysis

Taking a bird’s eye view, in the experimental scheme without sample, the
lightwave detector, i.e. the TIPTOE detector, is a linear time-invariant (LTI)
system when it is operated in the linear regime as shown in the dashed box in
Fig. S9. Therefore, the measured electric current $u(t)$ can be modeled as a
temporal convolution of the instrument response function (IRF) of the TIPTOE
detector and the incident light electric field $E_{0}(t)$:

${u}(t)=E_{0}(t)\ast{\textrm{IRF}}(t)\enspace.$ (2)

Figure S9: Simplified model of the field-sampling experimental setup.

The linearity of the detector has been verified in Supplementary Note 3 (cf.
Fig S4). Assuming a flat response of the detector as proven elsewhere bib4 ,
the measured temporal trace from the electric current is directly connected to
the incident electric field as shown below:

$H_{\textrm{IRF}}(\omega)=\textrm{const}\enspace,$ (3)
${\textrm{IRF}}(t)\sim\textrm{const}\ast{\delta}(t)\enspace,$ (4)
${u}(t)=E_{0}(t)\ast{\delta}(t)=E_{0}(t)\enspace.$ (5)

Note that the time and frequency domain signals are connected by the Fourier
transform, where the constant number, i.e. the spectrally flat response, in
frequency domain is a delta function in time domain.

The linear light-matter interaction system, like in our experiment, is also a
LTI system, which can be modeled as shown in Fig. S5. With the sample in beam
path, the entire system can be modelled as two LTI systems put in series. It
has already been demonstrated that measured electric current ${u}(t)$ in the
experiment directly reflects the light electric field reaching the detector,
therefore, we can safely consider the measured results as light electric field
transmitted through the sample, i.e. ${u}(t)\sim E_{\textrm{sample}}(t)$.

Similarly, since it is an LTI system where its linearity has been verified in
Supplementary Note 4, the measured transmitted $E$-field,
$E_{\textrm{sample}}(t)$, is a temporal convolution of the impulse response
function of the sample, ${R}(t)$, and the incident $E$-field $E_{0}(t)$.
Considering very close values between the estimated time scale of plasmonic
response and the pulse duration our incident light, a proper way of extracting
the plasmonic response of the sample would be to perform a deconvolution
process. In the Fourier deconvolution method, one needs to first Fourier
transform $E_{\textrm{sample}}(t)$ and $E_{0}(t)$ in time domain to frequency
domain $\widetilde{E}_{\textrm{sample}}(\omega)$ and
$\widetilde{E}_{0}(\omega)$. The impulse response of the sample in frequency
domain can then be calculated as

$\widetilde{R}(\omega)=\frac{\widetilde{E}_{\textrm{sample}}(\omega)}{\widetilde{E}_{0}(\omega)}\enspace.$
(6)

Finally, the plasmon response in time domain can be obtained by inverse
transforming the $\widetilde{R}(\omega)$, and
$\widetilde{R}(t)={iFFT}[\widetilde{R}(\omega)]$.

Therefore, we note that while the subtraction of time traces between the
transmitted and incident field as shown in the main text may not ultimately
yield the plasmonic response in time domain, it can well serve to expose the
distortion of the $E$-field induced by the plasmon resonance and to magnify
the non-trivial contribution of the plasmonic resonances. A similar analysis
was reported in bib31 .

## Supplementary Note 7: Details of the FDTD simulation

To theoretically determine the influence induced by the plasmonic field on the
incident $E$-field, finite difference time domain (FDTD) simulations were
performed using a commercial software from Lumerical. In the simulation, the
dimensions of the samples with the AuNRs (AuNS as well) including the
dielectric constants were given as the input parameters. The measured
distinction spectra for both resonant and non-resonant cases (see Fig. 2),
showing a broadband plasmonic resonance due to the fact that the prepared
AuNRs and AuNS are not perfectly uniform in size. Therefore, to mimic the
experimental conditions of the broadband plasmonic resonance, five different
sized AuNRs with sizes considering the determined size distributions from the
colloidal samples were modelled in the simulation box. Additionally, AuNS with
sizes of $20\text{\,}\mathrm{nm}$ in diameter were also simulated in the same
condition, serving as the non-resonant reference to the resonant case. The
gold NPs were embedded in a $30\text{\,}\mathrm{nm}$ thick polystyrene layer
coated on a bulk fused silica substrate (Fig. S10a). To accurately model the
fused silica substrate, we assigned a constant refractive index of $n=1.45$.
Optical data for gold were obtained from ref. olmon2012optical . Periodic
boundary conditions were applied in the directions perpendicular to the
substrate surface, while perfectly matched layer (PML) boundaries were
utilized in the parallel direction. The light source used in the simulations
was the incident field obtained from our experiment, which is a linearly
polarized few-cycle pulse of $4.6\text{\,}\mathrm{fs}$ duration centered
around a wavelength of $780\text{\,}\mathrm{nm}$. Time and frequency monitors
are placed $200\text{\,}\mathrm{nm}$ before and after the structure, ensuring
a far-field detection with no influence from the gold NPs.

Figure S10: a FDTD simulation model of AuNRs (green) embedded in polystyrene
layer (cyan) coated on bulk fused silica substrate (gray). b Extinction
spectrum of AuNRs sample obtained from experimental measurement (blue) and
FDTD simulation results (orange).

In the frequency domain, as shown in Fig. S10b, for the resonant case, the
bandwidth of the extinction spectrum can be well reproduced using the above-
mentioned model, indicating that the simulated sample conditions are in good
agreement with our experimentally investigated sample conditions. The time
domain results of AuNRs (resonant case) have been shown and discussed in the
main text, therefore, only the results of AuNS (non-resonant case) are shown
here in Fig. S11. Comparing to the case of AuNRs, the $E$-field interacted
with AuNS does not show any obvious phase shift, and the temporal trace almost
remains the same (Fig. S11a), showing no plasmonic resonance effect from the
sample. By performing a Fourier transform of the temporal traces of the
incident field and the detected field, one can see that both the spectral
amplitude and the spectral phase curves are almost identical (Fig. S11b),
further confirming that the observed plasmonic dephasing and phase crossing
for the resonant case can not be detected in non-resonant AuNS. These results
are quite reliable and consistent to the experimental observations.

Figure S11: FDTD simulation results on non-resonant AuNS. a Temporal traces of
AuNS (red) and bare fused silica substrate (dashed blue) as reference. b
Spectral intensity and phase of AuNS (red solid line, red dots) and bare fused
silica substrate (blue solid line, blue dots) as reference, the light gray
shaded area marks the absorption of the non-resonant sample.

In addition, a comparison between the simulated near- and far-field
differential signal of the AuNRs was conducted. The results are displayed in
Fig. S12.

Figure S12: Simulated differential plasmon fields in the near- (blue) and far-
field (orange) of the resonant AuNRs. The data was treated the same way as for
Fig. 2 of the main text. For comparison, the experimental data is plotted in
dashed orange (cf. Fig. 2).

All data show a qualitative agreement in the first few oscillations after the
driving electric field maximum. As expected the decaying window for the near-
field differential is much longer than for the far-field conditions (cf. main
text).

## Supplementary Note 8: Time-frequency analysis

A time-frequency analysis was conducted by applying a Wigner-Ville
distribution (WVD) function on the measurements, simulations and the
respective differentials. The WVD response of each fields are summarized in
Fig. S13

Figure S13: WVD of the traces shown in the main manuscript. In the left panel
the experimental traces are summarized, whereas the right panel depicts the
FDTD results. S13a and b contain the sampled field with the resonant NPs. S13c
and d contain the sampled field with the reference substrate. The computed
difference of both traces yields the differential signal shown in S13e and f,
which corresponds to the plasmonic response signal in the far-field domain.

An agreement between experimental and simulated traces for the sample response
is qualitatively observable. In the case of the reference a slight positive
chirp of the red component is evident. We also observe prepulses at negative
time delays, which are also indicated in the time traces as shown in the main
manuscript. For the differentials we observe the buildup of the plasmonic
contribution after zero delay and a chirp for both ends of the spectral
frequencies as well.

## Supplementary Note 9: Influence of dielectric medium

To investigate the influence of the dielectric medium, which in this case is
the matrix of polystyrene, in which the particles are embedded, a FDTD
simulation with and without the matrix was conducted to investigate the
plasmon response depending on its environment. To account for the shift of the
plasmon resonance, due to change of the medium, which leads to a change of the
refractive index, we shifted our defined Gaussian pulse, with a pulse duration
of $4.6\text{\,}\mathrm{fs}$, accordingly on the wavelength axis and assume a
negligible residual chirp due to the different dispersion response at
different wavelengths. The results are shown in Fig. S14

Figure S14: FDTD simulations for the interaction of a simple Gaussian beam
with five rods as used in the main manuscript. a depicts the full response
with the sample as used in the initial simulation, including the polystyrene
matrix. b displays the response without the matrix.

The simple simulations display the influence of the dielectric medium on the
plasmon resonance. We observe a strong enhancement of the plasmon resonance
response in the polystyrene medium, whereas the response in vacuum, in which
the particles are only attached to the substrate surface displays a lower
intensity. This effect is also reflected in the spectral phase, as the phase
response for the interaction with the polystyrene medium is much more
pronounced. We are confident that our field sampling technique is sensitive to
these changes in phase, which would prove to be advantageous in the design of
metasurfaces.