contributions (e.g., the static pattern) from the
model allows us to clearly identify the lifetime
phases of the SPP vortex and interpret the obtained experimental results of the dynamic behavior of the plasmonic spin-orbit conversion.
The measurement of the angular velocity of
the vortex rotation (wR) is indeed a direct measure of its integral angular momentum magnitude with the relation OAM per photon =
ħw/wR, where w is the light angular frequency.
Concentrating on the second stage of the vortex evolution, where the vortex is fully evolved
and predominantly only rotating, the series of
suboptical-cycle snapshots in Fig. 1, D to G, clearly
reveals the revolution of the SPP fields capturing the rotation of the fields around the center.
We can clearly measure the dynamic pattern
of 10 lobes encircling the dark center of the
vortex. These lobes correspond to the azimuthal
wavefronts of the vortex and were measured to
exhibit angular velocity of 2p/10 rads per optical cycle corresponding to 10 units of angular
The measurement sequence depicted in Fig. 1,
D to G, is taken starting 58.6 fs after the launching of the SPPs by the pump pulse. This time
delay corresponds to SPPs propagating a distance
of ~17.5 mm away from the perimeter to within the
dynamic region. In the recorded time sequence,
the pump-excited SPPs have already reached the
central region from all locations on the perimeter
and begin to propagate back toward the perimeter. Thus, the central pattern consists of the interference of inward and outward counterpropagating
SPPs, and, therefore, the azimuthal dynamics can
be approximated at this time interval by cos (lq – wt)
without any radial motion, thus corroborating
the observed experimental behavior as a function
of the OAM magnitude l. The complete TR-PEEM
movies, with 100-as (attosecond) time steps, are
presented in the supplementary materials.
To generate truly deep subwavelength vortices,
it is necessary to investigate short-range surface
plasmons at the silicon-gold interface. We there-
fore discuss the dynamical behavior of these
short-range plasmons, which form much more
confined vortices, with typical spatial extent of
tens of nanometers. To achieve this goal, we
fabricated monocrystalline gold flakes electro-
chemically grown on a silicon substrate. The
~20-nm thin flakes support both long- and short-
range SPPs (Fig. 2E), with the latter arising pre-
dominantly from the silicon-gold interface. We
fabricated a double-slit plasmonic vortex–generator
configuration, where the spacing of the concentric
slits is half the long-range SPP wavelength (Fig.
4A). Thus, the long-range SPPs destructively in-
terfere, and effectively are not excited, allowing
the excitation of only the short-range SPPs (fig.
S1). The measured short-range SPPs have a wave-
length of lspp = 180 nm, which is the expected
value considering the presence of a thin native-
oxide layer on the silicon, reducing the effective
refractive index (fig. S1). This results in a fourfold
wavelength shortening compared to the 800-nm
excitation wavelength. The sample was measured
using a different PEEM setup (fig. S2 and sup-
plementary methods) featuring ~15-fs pulses cen-
tered at the same 800-nm wavelength.
Figure 4 depicts the dynamics of a short-
range plasmonic vortex within a plasmonic vor-
tex generator of geometrical order m = 4 with
ri = 1 mm. As in the long-range SPP case, the mea-
sured pattern features static and dynamic regions.
Because of the fourfold reduction of the phase
velocity of the short-range SPPs, compared to the
free-space propagation, the spatial extent of the
static pattern is substantially shorter and com-
prises a static pattern radius of rstatic 600 nm
toward the interior of the lens. The dynamic re-
gion of the vortex field shows four lobes that re-
volve around the center with a velocity of 2p/4
rads per optical cycle. Starting at t0, a given lobe
completes a p/2-rad revolution around the center
of the vortex in 0.665-fs steps, illustrating the
OAM of the short-range SPPs (movie S3).
Our observation and investigation on an ultra-
fast subfemtosecond time scale and nanometer
lateral scale offer progress toward a better under-
standing and manipulation of the angular mo-
mentum degree of freedom of nanoplasmonic
fields. The study reveals the nature of the plas-
monic OAM and vortex formation and elucidate
the process of light spin–to–plasmonic orbit trans-
formation. Furthermore, these observations open
new avenues for designing and directly measuring
exciting applications of OAM in the nanoworld.
Highly localized and surface-confined plasmonic
vortices may become an important investigation
tool for studying 2D materials with material
angular momentum degrees of freedom such
as topological insulators and thin-film magnetic
and magneto-optic materials, as well as spin-
tronic and valleytronic media. Additional appli-
cations may include enantiomer discrimination,
realizations of higher-order qubits for chip-size
quantum information, the rotation of nano-
particles in plasmonic tweezers (33, 38), and
the potential for dark-field nanofluorescent mi-
croscopic imaging. Finally, reducing the size of
the vortex toward dimensions compatible with
molecular wave functions may lead toward
nondipolar transitions in quantum dots and
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This research was supported partially by the Israeli Centers
of Research Excellence “Circle of Light.” D.K. acknowledges
funding from the Irish Research Council and the Marie Curie
Actions ELEVATE fellowship. M.A. and F.-J.M.z.H. acknowledge
funding from Deutsche Forschungsgemeinschaft (DFG) program
SPP1391. F.-J.M.z.H. further acknowledges DFG programs SFB616
and SFB1242. B.F., S.R., and H.G. acknowledge support from
DFG program SPP1391, European Research Council Advanced
Grant “Complexplas,” Baden-Württemberg Stiftung, German-Israeli
Foundation (GIF), and Bundesministerium für Bildung,
Wissenschaft, Forschung und Technologie. We acknowledge
help with sample fabrication by L. Fu and H. Li. We also
acknowledge the technical support by the Nano Structuring
Materials and Methods
Figs. S1 to S3
Movies S1 to S3
7 September 2016; accepted 17 February 2017