1. Introduction

When metal nanostructures are illuminated by light, collective electron oscillations called surface plasmons can be excited, possisbly leading to enhanced fields in regions much smaller than the diffraction limit of light. Large field enhancement can be obtained by exciting surface plasmons resonantly. The resonances depend on the shape and size of the nanostructures [1]. By designing the structures appropriately, the enhancement can thus be optimized. The nanostructures, functioning as optical antennas, have many possible applications such as high-resolution microscopy and spectroscopy, photo-voltaics or light emission tailoring [2]. One efficient nanostructure for high field enhancement is the commonly used bowtie-shaped antenna [3–5], which consists of two triangular prisms separated by a small gap.

Optical antennas are commonly fabricated using electron beam lithography and focused ion beam (FIB) with gallium ions [6] because of the flexibility in pattern design possible with these techniques. Due to its direct write capabilities we concentrate on FIB. FIB is based on sputtering of material via ions. The sputtering efficiency depends on crystal directions and facets [7, 8] which on polycrystalline metal films lead to a certain random shape variation of the produced structures [9, 10]. The smallest achievable feature size is typically around 10 nm [8, 11], so shape variations of this order can be expected. While new developments have improved on these issues, such as helium FIB [12] and FIB on monocrystalline metal films [9], gallium FIB on evaporated films is still a common approach for top-down fabrication of optical antennas. It is therefore important to investigate how the antenna optical properties are affected by the exact antenna shape [13] in comparison to other parameters which can be more easily controlled, such as the overall size.

A prominent feature of the bowtie geometry is the support of multiple surface plasmon modes, facilitating field enhancement across a large bandwidth [14]. This broadband field enhancement can be used to tailor the temporal evolution of electromagnetic fields induced by femtosecond laser pulses at the nanoscale. These ultrafast near-field dynamics have applications such as coherent control [15], harmonic generation [16], and electron acceleration [17,18]. However, these applications are sensitive to the detailed ultrafast near-field dynamics in each nanoantenna. Information about the near-field dynamics of plasmonic nanostructures can for example be obtained by using femtosecond laser pulses combined with interferometric frequency resolved optical gating [19], second harmonic generation microscopy [20] and near-field scanning optical microscopy [21]. As these techniques study one structure at the time, they cannot, however, probe the near-field dynamics of many individual antennas simultaneously. A simultaneous recording is preferred when the responses of different antennas are to be compared, especially in the presence of few-cycle laser pulses which may fluctuate.

In this work, we use photoemission electron microscopy (PEEM) together with few-cycle laser pulses centered around 800 nm to simultaneously probe the few-cycle near-field dynamics of individual gold bowtie nanoantennas fabricated by FIB. For metals illuminated with infrared light, photoemission occurs via the absorption of multiple photons. The probability of such a process is typically low, but local field enhancement at the sample can strongly promote the multiphoton photoemission [22]. This makes PEEM suitable for direct sub wavelength imaging of plasmon-enhanced fields in metallic nanoparticles [23]. In interferometric PEEM an interferometer is used to split the laser pulse into two pulses delayed with respect to each other. The total near-field, and thus the photoemission, is affected by the time delay. Scanning the delay between the pulses allows for recording nonlinear autocorrelation traces of the near-field induced by a single pulse. Interferometric PEEM thus provides information about the near field dynamics. The technique has previously been used to study plasmon dynamics in rough silver films [24], nanoblocks [25] and in one single bowtie nanoantennna [26]. Recently, we have combined interferometric PEEM with few-cycle laser pulses to study the few-cycle near-field dynamics induced on single nanoparticles [27].

Using 6 fs pulses, which is close to only two cycles of the driving field, the collective electron oscillations are driven only for a very short time after which the motion continues unperturbed by the laser field. This means that the measured photoemission signal to a large extent depends on the interference between the driven oscillation and the free oscillation, and not mainly by interference between two driven oscillations as would be the case for longer pulses. The measurement is therefore sensitive to the intrinsic dynamics of the antennas, which is of major interest for the above mentioned applications. While infrared interferometric measurements are now pushing towards the few fs level, it is conceivable that PEEM in the future could allow nanoscale imaging of plasmons even in the attosecond regime [28, 29].

In order to investigate the effect of the size and precise shape on the near-field dynamics of individual antennas, we designed arrays containing a large number of bowtie antennas with different sizes. With one interferometer arm blocked, the location of the field enhancement on the nanostructure, the order of the photoemission process involved and the polarization dependence were first studied. Using two pulses with a variable delay nonlinear autocorrelation traces for differently sized and shaped antennas were then recorded, thereby probing the plasmon dynamics in these structures. The results were interpreted with the help of Finite-difference time-domain (FDTD) simulations.

We find that the few-cycle near-field dynamics depend on the size of the antenna. However, we also find surprisingly large differences in the dynamics between antennas of similar size. With simulations we show that these differences can be explained by slight variations in exact lateral shape of the antennas, resulting from the fabrication process. This is, to our knowledge, the first study that addresses the effect of size and exact shape on the few-cycle dynamics of optical antennas. The methods are described in Section 2 and the results in Section 3. We finish with some conclusions in Section 4.

2. Method

2.1. Experimental setup

The experiments were performed using a commercial PEEM instrument (FOCUS IS-PEEM). As a light source we used a broadband oscillator (VENTEON Pulse One), delivering 6 fs pulses, centered at 800 nm (photon energy 1.55 eV), at a repetition rate of 80 MHz and with a pulse energy of 1 nJ. The spectral width, at −10 dB, covers 622–1010 nm. The laser light was incident in a grazing geometry with an angle of 65 degrees to the sample normal. A mercury lamp was used to image the gold antennas on the substrate through a linear photoemission process in the PEEM setup and therefore aided with positioning of the sample.

The experimental setup is presented schematically in Fig. 1. Unless specified differently, we oriented the antennas such that the electric field is fully parallel to the inter-particle, long, antenna axis and thereby used s-polarized light. Both the inter-particle axis and the light polarization was then directed along the y-axis [see coordinate system in Figs. 1 and 2(a)]. In this configuration we reduce retardation effects, which could cause the excitation of dark plasmon modes with vanishing dipole moments [30, 31] and make the experiments more complex to interpret. The laser power was controlled using a broadband half-wave plate and a polarizer (Pol), thus keeping all other parameters unaffected. The power was set so that the PEEM detector was not saturated and it was measured using a photodetector. The polarization of the light on the sample was controlled by placing the half-wave plate after the polarizer and rotating it. For the time delay measurements, the delay between the pulses was controlled using a compact interferometer, including a piezo-controlled delay stage, where the two interferometer arms were separated by a beam splitter (BS) coated so that the dispersion was the same in both arms. A flip mirror allowed for the pulses to be sent off for characterization using the d-scan technique [32]. In order to compensate for all the material in the setup double chirped mirrors (DCM) were used and the dispersion was fine tuned with a pair of glass wedges to obtain the shortest possible pulse duration on the sample. The spot size on the sample was approximately 50µm×100µm.

 

Fig. 1 A schematic of the experimental setup, including a spectrum of the oscillator output shown as spectral power density as a function of wavelength.

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2.2. Nanostructure fabrication

Antenna dimensions for an optimal field enhancement with 10 fs-pulses centered at 800 nm were calculated in [16]. Our basic antennas were fabricated in-house with a similar design, shown in Figs. 2(a) and 2(b). 25 nm of gold was evaporated onto a sapphire substrate. The bowties were milled using a FIB (FEI NanoLab 600), with a current of 1 pA and a voltage of 30 kV. The obtained antenna dimensions were found to resemble the ideal dimensions more closely if the milling was performed in two steps. First a frame sized 340 nm × 800 nm was milled, leaving an inner area untouched. Then the actual bowtie was milled in that area. The antennas were put into two rows of 12 antennas each. Antennas of different sizes were obtained by scaling the scanning patterns, both the actual bowtie and the frame around it, by the size scale factors s [Figs. 2(a) and 2(b)], where s = 0.5, 0.75, 1, 1.25, and 1.5. For each size a different area dose was used, (1.8, 2.5, 1.8, 2.6, and 2.8)×10¹⁶ ions/cm² for the frames and (1.2, 1.1, 1.3, 1.6, and 1.4) ×10¹⁶ ions/cm² for the antennas. The distance between adjacent bowties was 2 µm. 24 antennas of the same size (120 antennas in total) were fabricated, giving an array sized 18 µm×22 µm. A part of a scanning electron microscopy (SEM) image of the array is presented in Fig. 2(c). A high resolution SEM image of an s = 1-antenna is given in Fig. 2(d). To investigate the dependence of the photoemission yield from the antennas on incident light polarization, we produced antennas with orthogonal orientation with respect to each other.

 

Fig. 2 The nanoantennas. Figures (a) and (b) show the design parameters used in the fabrication process. A SEM image of part of the antenna array with size scale factors s = 0.5 − 1.5 is shown in (c) and a SEM image of a single antenna (s = 1) is shown in (d). Figures (e) and (f) show PEEM images of an antenna scaled with s = 1.25. The image obtained using the mercury lamp only is shown in (e), whereas the image in (f) was obtained using both the mercury lamp and the laser. The polarization of the electric field E is shown. For better visualization, an outline of the antenna is drawn (white dashed lines) and the images in (e) and (f) are divided by the maximum pixel value of the image in (e), which makes the image in (f) saturated.

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During fabrication, the nanostructure edges were inevitably rounded as compared to the design. The reproducibility of the antennas was also limited in the gap region, as found in [10], and the actual gap size varied. To quantify the fabrication induced variations we concentrated on the s = 1-antennas. From SEM images, the lengths of the prisms were obtained, where the length is defined as the height of the triangle [the dimension having the length 195 nm in Fig. 2(b)]. Distorted bowties or bowties with obviously connected prisms were discarded, resulting in 2×21 considered prisms. Their average length was found to be 189 nm and the standard deviation 14 nm.

2.3. Data treatment

From each PEEM image the background was subtracted. The background was defined as either an image taken without light source (for the laser power dependence) or the mean signal from an area without antennas (all other measurements). The photoemission signal was integrated over the central region of each antenna. This sum is referred to as ”PEEM signal”. To remove noise, only the antennas with signal above a certain level were considered. In the near-field autocorrelation measurements, the peak positions in terms of delay were obtained by extracting the center of mass of each peak, where each peak ranges from the relevant local minimum to the next.

2.4. Simulations

FDTD simulations were performed using the commercial software FDTD Solutions (Lumerical) [33]. The bowtie antennas were modelled either as ideal coupled gold prisms with perfect geometry, or as realistic objects whose shapes reproduce the fabrication output. In the latter case, the antennas were obtained by extruding the lateral (x-y plane) antenna profiles obtained from SEM images. The bowtie antennas were modelled as single objects lying on a sapphire substrate. The dielectric functions of gold and sapphire were fitted to tabulated data [34, 35]. The bowtie antennas were meshed with a mesh size of 1 nm. We used a conventional staircase mesh with a mesh override region surrounding the bowtie antennas. The excitation sources used were total field-scattered field plane wave sources. Perfectly Matched Layer boundaries were applied along the edges of the simulation space.

Absorption cross sections were computed at normal incidence by calculating the net power flow from a broadband excitation source into the antennas for a polarization along the inter-particle antenna axis. The steady state electric field distributions at constant frequency were recorded on a plane located 2 nm above the objects.

For comparison with PEEM experiments, we performed modelling in a grazing incidence geometry by calculating the electric field induced by a Gaussian pulsed excitation on the top surface, close to the tip of one of the prims. The pulsed excitation (5 fs duration) was set to have the same bandwidth as the experimental laser pulses. As most of the electrons in the experiment are assumed to leave due to the electric field component normal to the surface (z-component), this component was considered. Autocorrelation traces were then simulated, assuming a perturbative 3 photon process, as [27]: $S\left(\tau \right)={\displaystyle {\int }_{-\infty }^{\infty }{\left|E_z\left(t\right)+E_z\left(t+\tau \right)\right|}^{6}dt}$, where S is the photoemission signal for a given time delay τ and E_z(t) the component of the electric field normal to the object as a function of time.

3. Results

PEEM images of the antennas are exemplified in Figs. 2(e) and 2(f). Figure 2(e) shows an image where the mercury lamp was used as the only light source. The gold regions can be clearly discerned from the sapphire region, with a higher photoemission signal from the gold. Illuminating the sample with also the laser light, polarized as shown, Fig. 2(f), results in an additional high photoemission signal from the center of the antennas. The polarization of the electric field E is shown in the figure. For our laser spectral range, 3 to 4 photons are expected to be needed for an electron to overcome the gold work function of ∼5.3 eV [36]. The nonlinear photoemission process in combination with a high field concentration around the gap [3–5] explains the strong photoemission signal from the center of the antennas.

Figure 3(a) shows the photoemission signal summed over a whole array of 144 s = 1-antennas as a function of laser power, in a log-log plot. A slope of 3.4 can be observed, comparable to findings in another PEEM study of gold nanostructures with similar laser excitation conditions [25]. The obtained slope confirms [37] the expected photoemission process requiring three to four laser photons for each emitted electron.

 

Fig. 3 (a) The measured photoemission depending on laser power. Each data point (blue) is the logarithm of the summed signal over an array of s = 1-antennas for a given laser power. The green curve is a linear fit to the data points. (b) Excitation configuration and separate SEM images of two perpendicularly oriented antennas (c) The measured photoemission dependence (individually normalized) on laser polarization angle θ for the two antennas shown in (b).

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The photoemission dependence on light polarization was next characterized. For this, antennas of two different orientations, see SEM images in Fig. 3(b), separated by less than 9 µm, were used. The excitation configuration with the polarization angle θ is illustrated in Fig. 3(b), showing the two polarizations p and s for the electric field E. θ corresponds to the deviation of the polarization from p-polarization. 90° polarization means that the electric field vector is fully in the y-direction (s-polarization). The resulting photoemission signal dependence on θ can be seen in Fig. 3(c). For both antenna orientations, we find that the PEEM intensity is maximum when the light is polarized along the inter-particle axis, consistent with previous measurements [4, 12] showing large field enhancement for such polarization. Both the power and polarization dependence is thus as expected and consistent with previous works.

Before probing the near-field dynamics, we start by estimating which plasmon modes that are excited in the antennas for each size group in our experiment. FDTD-calculations are performed using the design dimensions. Simulated absorption spectra calculated for each set of design parameters at normal incidence are shown in Fig. 4(a). Each spectrum contains multiple resonances, showing that bowtie antennas are multimode antennas [14]. Previous studies have found that there are two competing effects on the resonances when the overall size of an antenna is changed. On one hand, the resonances redshift due to the larger dimensions of the triangle prisms [14]. On the other hand, the resonances blueshift due to the larger gap decreasing the strength of the inter-particle coupling [14, 38]. In our case, the resonances redshift with increasing size, as indicated by the dashed lines, suggesting that the length increase is the most important parameter, as opposed to the gap increase. Figure 4(b) shows the spatial variations of the normal (z) component of the steady state electric field associated with the three resonances A–C of the s = 0.75-antenna. The corresponding multipolar modes are antisymmetric with respect to the gap, and thus have a non-vanishing dipole moment. Depending on the size, we expect a given combination of these or higher order modes to be excited by the laser in the experiments. The modes show localized field enhancements at the central prism tips so an excitation of the modes should result in a high photoemission from this region, in agreement with our experiment [Fig. 2(f)].

 

Fig. 4 FDTD simulations of the optical properties of the bowtie antennas. Figure (a) shows the absorption as a function of excitation wavelength for the five sizes. The supported resonances are indicated by A, B, C, D and E. Depending on the size, different resonances fall within the laser spectral range. The spectra are vertically shifted for clarity, and are together normalized so that the maximum value of all curves (seen for the s = 0.75-antenna) is set to 1. Figure (b) presents spatial variations of the normal component of the steady state electric field associated to the three resonances (A–C) of the s = 0.75-antenna.

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The spatial distribution of the field enhancement in the antenna array is reflected in the PEEM image in Fig. 5(a), obtained with the laser. The image exemplifies the fact that PEEM is an imaging technique, capable of recording the response of several antennas to the same excitation. As the beam spot size is much larger than the antenna array the full array is illuminated. Enhancement is seen to occur for antennas of all sizes and the photoemission spot periodicity follows the periodicity of the array, as observed with SEM. We note large variations in the photoemission intensity for antennas of the same overall, nominal, size, in accordance with [4, 12, 39, 40]. Causes for these variations include minor shape differences (e.g. variations in gap size), differences in grain structure, and different surface modifications on the molecular level, which can all affect the field and/or the photoemission process [4, 12, 39, 40]. Slight differences in field strength are further amplified by the non-linearity of the photoemission signal. Only a few of the largest antennas give a detectable signal, which likely is due to a large gap not enabling a large enough field enhancement for photoemission.

 

Fig. 5 Experimental results. (a) A PEEM image of the bowtie array. The scale factors below the image describe the size distribution. (b) A recorded near-field autocorrelation trace of the three antennas of different size marked in (a). (c) A finer scan of the delay for the same antennas, with SEM images provided. For better visualization the minimum value is subtracted from each graph before normalization in (b) and (c). (d) The position of the third peak [defined in (b) and (c)] as a function of antenna size. The length of each error bar is twice the standard deviation and the error bars are centered on the mean values (red dots). The points for the individual antennas are shifted slightly to the right of the error bars for easier visualization. (e) The position of the fourth peak as a function of size group. (f) SEM images of three s = 1-antennas exemplifying the minor shape differences resulting from the fabrication. The scale bars in (c) and (f) correspond to 100 nm.

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To investigate the near-field dynamics of the antennas, we measured interferometric near-field autocorrelations by varying the delay between two identical laser pulses. Figures 5(b) and 5(c) show example autocorrelation traces from three differently sized antennas [marked in Fig. 5(a)]. The SEM images of the antennas are shown in the inset in Fig. 5(c). The traces are seen to be in phase at zero delay, but at increasing delays they are more and more out of phase. The s = 0.5-antenna shows the highest frequency in the near-field autocorrelation trace oscillations, followed by the s = 1-antenna. The antenna scaled with s = 1.5 shows the lowest frequency. The same pattern is observed in the finer scan shown in Fig. 5(c). We resolve shifts in the autocorrelation traces already at delays of 2.7 fs (after one oscillation), which is due to the short duration of the laser pulses [27]. The short pulse induces drastically different near-field dynamics for different sizes, due to the excitation of different modes. (See also Fig. 6(b) below for examples of drastical near-field differences for similarly sized antennas.)

 

Fig. 6 Results from simulations. (a) The lateral shapes of three of the s = 1-antennas fed into the simulations. (b) Simulated fields calculated at one of the tips for each of the three antennas. At time t₁ all the fields are in phase. At t₂ all the curves are clearly out of phase with each other. (c) Corresponding near-field autocorrelation traces.

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While it is not possible to exactly reconstruct the time-domain electric field from the interferometric autocorrelation traces, some general features can be identified [24–27]. Most importantly, a closer spacing between the fringes in the traces corresponds to a higher oscillation frequency of the near-field. At delays between −10 fs–10 fs the autocorrelation trace is dominated by interference between the strongest parts of the fields induced by the two laser pulses. Therefore, shifts between the fringes in this region correspond to differences in the oscillation frequency close to the maximum amplitude, which is the dominating part of the field for applications involving nonlinear interactions. Our analysis is therefore focused on this region of small delays. As a measurement of the spacing between the fringes, we, for all antennas, extract the positions of the third and fourth peaks [defined in Figs. 5(b) and 5(c) with the zero delay peak defined as peak zero]. The positions of the third peak as a function of antenna size is presented in Fig. 5(d) and the position of the fourth peak in Fig. 5(e). The measured peaks show a large spread in position within each size group. However, the average position for each peak shifts to longer delays for the larger antennas, corresponding to a larger spacing between the fringes. This is also consistent with the three example antennas shown in Figs. 5(b) and 5(c).

The shifts towards longer delays measured for the larger antennas in Figs. 5(d) and 5(e) suggest a lower oscillation frequency of the enhanced near-field for larger sizes. While such observation is in accordance with the redshift of the plasmon resonances shown in Fig. 4, the expected multimode character of the antennas should lead to a more complicated behavior than a simple redshift of the oscillation frequency as a function of size. This expected combination of multiple plasmon modes makes a quantitative analysis by e.g. fitting a harmonic oscillator model impossible. We therefore focus on the shifts of the positions of peaks 3 and 4 as a simple indication of general differences in the near-field dynamics, and use this to compare the effect of antenna size versus detailed shape. When the antenna size is increased from s = 0.5 to s = 1.5, the average position of the third and fourth peak shifts by 0.5 fs and 1 fs respectively. This can be compared to the variations of the peak positions for antennas with equal size by calculating the standard deviation of the peak position within each size group. The standard deviations of the peak position are 0.1–0.3 fs for the third peak and 0.1–0.7 fs for the fourth peak, with the higher values corresponding to the largest bowties. This means that the variations of the peak positions within a size group are of the same order as the variations due to a change of the antenna dimensions by a factor of 3, as between the s = 0.5- and s = 1.5-antennas. As an example of this inhomogeneity, three s = 1-bowties are discussed. Their SEM images are shown in Fig. 5(f). The bowties have representative lateral shapes. Their small separation from each other of less than 5µm guarantees that they are exposed to identical pulses. Despite their similar overall size and excitation exposure, their autocorrelation traces show distinct differences. The peak 3 positions for the antennas, from the left to the right, are 8.2, 8.1, and 7.9 fs and the peak 4 positions 10.9, 10.7 and 10.5 fs.

The remarkably large differences in the near-field dynamics of antennas with the same overall size have several possible explanations. These include minor variations in gap size [14, 38], prism length [14], radius of curvature of edges [41] and thickness. Variations in grain structure, variations in gallium deposition [42], and effects from SEM imaging [38], such as carbon contamination, can also affect the optical properties of the individual objects [9, 13].

We investigated if the observed variation in the near-field dynamics for a given size was caused by simple variations in the bowtie geometry, such as differences in gap size and prism length. A possible dependence on the ratio of prism length to gap size was also studied as these two parameters are expected to have the opposite effect on the plasmon resonance frequencies [14, 38]. No simple dependence of peak position on gap size was found for a given size group, neither a dependence on prism length or on the ratio prism length to gap size.

Since no simple shape dependence was found, we implemented the lateral shape of 56 bowties as determined by SEM onto FDTD simulations to elucidate if the measurements could be explained solely by slight variations in the exact detailed shape of the antennas. These simulations confirmed the effect of minor geometrical variations on the near-field dynamics. Three examples of implemented s = 1-antenna shapes are presented in Fig. 6(a). The calculated z-components of the near-field for each of the antennas are presented in Fig. 6(b). As can be seen, there are significant differences in the near-field dynamics despite the same overall size of the antennas. These differences can simply be attributed to the slight variations in exact lateral shape, which considerably affect the optical properties of the antennas. The calculated interferometric autocorrelations of these fields are presented in Fig. 6(c). Clear differences in the autocorrelation traces are observed, reflecting the different field dynamics, Fig. 6(b). For example, the shift to longer delays of the red curve in Fig. 6(c) is due to the slightly lower oscillation frequency during the few strongest cycles of the field. The frequency difference can be observed by simply noting that all the curves are in phase at the time t₁ in Fig. 6(b), while the red curve is out of phase with the blue and green curves at t₂. For some (16) of the antennas, rich dynamics are observed with e.g. beating between multiple excited plasmon modes. This complexity in the temporal field translates to complex autocorrelation exhibiting shoulders and irregular oscillations that prevents us from a meaningful peak position extraction as was done for the experimental data. We did not observe as complex autocorrelation traces in the experiment. We also note slightly larger shifts in peak positions in the simulations for antennas of same overall size as compared to the experiment. These deviations are attributed to the use of a Gaussian pulse in the simulations, while the real pulse shows more complexity. In general, the simulations show that the lateral dimensions have a critical impact on the few-cycle near-field dynamics. This can explain the observed differences in autocorrelation traces for similarly sized bowties. The results are of importance in the fabrication of nanoantenna arrays for enhancement of nonlinear signals, as the effect of the detailed antenna geometry can lead to a large inhomogeneous broadening of the nonlinear response from the whole array.

4. Conclusions

In conclusion, we have studied the few-cycle near-field dynamics of bowtie nanoantennas fabricated by FIB. Variations in the near-field dynamics were measured for differently sized antennas, due to excitations of different or spectrally shifted plasmon modes. However, we also measured surprisingly large and comparable differences in the near-field dynamics for antennas with approximately the same size. Simulations show that slight variations in lateral shape considerably affects the optical properties of the antennas and hence the near-field dynamics. They therefore support the interpretation that the observed differences for similarly sized antennas originate from slight lateral shape variations obtained during fabrication.

The fact that the plasmon dynamics can differ between similar structures shows the necessity of imaging techniques that can study the response of individual nanostructures, such as PEEM. The study is of interest for applications using nanoantennas produced by common fabrication techniques, such as FIB.