Bow-tie nano-antenna assisted generation of extreme ultraviolet radiation

We report on the generation of extreme ultraviolet radiation utilizing the plasmonic field enhancement in arrays of bow-tie gold optical antennae. Furthermore, their suitability to support high-order harmonic generation is examined by means of finite-difference time-domain calculations and experiments. Particular emphasis is paid to the thermal properties, which become significant at the employed peak intensities. A damage threshold depending on the antenna length is predicted and confirmed by our experimental findings. Moreover, the gas density in the vicinity of the antennae is characterized experimentally to determine the number of atoms contributing to the measured radiation, which is almost an order of magnitude larger than previously reported.


Introduction
For radio frequencies and in the microwave regime, antennae are widely used for various applications. In the visible spectral range however, the concept has only recently been introduced [1]. Optical antennae offer a wide range of applications though, spanning from the extreme concentration and manipulation of light [2], nonlinear optics [3,4] to the generation of high-order harmonic radiation [5]. This process is of particular interest because it paves the way for experiments on attosecond time-scales [6], e.g. among other things, new measurements in fundamental physics to study electron dynamics in molecules [7]. Moreover, it enables the extension of the frequency comb technique [8] in high-precision spectroscopy to the extreme ultraviolet (EUV) regime [9]. This extension is challenging though, due to the low conversion efficiency of the high-order harmonic generation (HHG)-process in combination with the pulse energies available from few-cycle femtosecond oscillators. In order to mitigate these issues external enhancement cavities have been developed and investigated extensively [10][11][12][13].
By employing a plasmonic resonance in optical nano-antennae, an compelling alternative approach for HHG directly from a laser oscillator has been proposed by Kim et al [5]. Theoretical investigations of the scheme have revealed many interesting phenomena like evenorder harmonics [14,15], which are triggered by the occurring steep near-field gradients. Based on a different antenna geometry even the generation of attosecond pulses [16] is predicted. Experimentally however, the scheme is challenging to implement and atomic line emission (ALE) alone instead of HHG has been reported in a similar experimental setup [17]. Recently Park et al [18] have published new results and provided experimental details to clarify the origin of the observed EUV radiation. As pointed out by Raschke [19] further experiments are necessary to resolve this open question, though.
Here, we present a detailed analysis of bow-tie optical antennae with respect to their suitability to support HHG. Particular attention is paid to the thermal properties, which become significant at the peak intensities necessary for HHG. By means of a theoretical model and finite-difference time-domain (FDTD) calculations, we are able to explain the experimental findings, giving rise for future improvements. Moreover, the number of atoms contributing to the measured EUV spectrum is determined experimentally to get a better insight into the involved processes. For theoretical considerations of the generated spectra we refer to the respective literature looking into different aspects of HHG driven by plasmonic fields [20][21][22][23][24][25][26][27][28].  Figure 1 depicts the experimental set-up, which is analogous to the one used in previous experiments on low order harmonic generation with gold nano-rods as optical antennae [29]. A Ti:sapphire oscillator (Venteon, Pulse one) delivers pulses with a pulse duration of <10 fs and a pulse energy of up to 5 nJ centred at 820 nm. The pulses are negatively chirped by several bounces on dispersive mirrors to compensate for dispersion added later, i.e. a vacuum window, an achromatic lens and the substrate. The dispersion is fine-tuned via a pair of thin fused silica wedges. Finally, a telescope with a ratio of one to three expands the beam size to enable tight focusing with a variety of achromatic lenses. The lens is mounted on a translation stage to adjust the focal position as indicated by the green arrow, without breaking the vacuum. The focal spot size ranges from 20.6 × 13.8 to 8.2 × 5.6 µm with corresponding peak intensities of 2 × 10 11 -13 × 10 11 W cm −2 , respectively. The sample with the nano antennae is attached to a second translation stage moving in xand y-direction to selectively address different antenna arrays, which appear as squares in the SEM image in figure 1 due to their extremely high packing density. The laser polarization and the antenna axis are aligned parallel to each other. To efficiently detect the generated EUV radiation a confocal monochromator setup (modified McPherson 234/302, 1200 lines mm −1 grating for 110-310 nm, 2400 lines mm −1 grating for 20-110 nm) is used, where the generation volume acts as an entrance slit. The sample is thus mounted in the focal point of the toroidal mirror and the photon collection efficiency is maximized [30,31]. Finally, a photo multiplier (PMT) capable of single photon counting (Hamamatsu H8259-09) is used in combination with a photon counter (Scientific Research SR400) to measure the third harmonic signal behind the exit slit. By flipping a mirror into the harmonic beam and setting the monochromator to the appropriate wavelength, it is possible to easily switch between signal detection for the third harmonic and EUV radiation. The latter Harmonic signal in dependence of illumination time. The signal drops exponentially and stabilizes at a significantly reduced level. After approximately 100 s the sample was slightly translated to illuminate a fresh spot within the antenna array leading to a temporary signal increase. This points to an initial change of the original antenna structure, which is not altered further.

Experimental set-up
is detected with an electron multiplier (Photonis 4751G) in combination with a pre amplifier (Minicircuits ZFL 500LN+) instead of the PMT.
The pulse duration of the incident laser pulses was measured with an interferometric autocorrelator (Venteon, Pulse four IAC) as well as a SPIDER setup (Venteon, Pulse four SPIDER) at the position of the sample to check the dispersion control and verify the expected pulse duration of < 10 fs.
The bow-tie shaped gold nano-antennae are manufactured with focused ion beam (FIB) milling on sapphire substrates with a thin chromium layer underneath to serve as an adhesion layer. The antennae have a length from 140 nm up to 200 nm with an opening angle of 30 • and a thickness of 50 nm and a nominal gap size of 20 nm. The arrays have a quadratic shape with an edge length of 10 µm as can be seen in the SEM image inset in figure 1. A detailed SEM picture of the antennae prior to illumination with the laser beam is shown in figure 3(a).
To observe EUV radiation gas is fed onto the sample through a homebuilt glass nozzle with a diameter of 50 µm. The gas nozzle is mounted on a x yz-stage to optimally align the gas jet onto the laser focus. Furthermore, a mass flow controller (MKS 647C controller) is used to ensure a constant gas pressure at the sample during the experiments. Details concerning the gas distribution behind the nozzle are discussed in section 5. With the gas flow turned on the background pressure is at around 1 × 10 −4 and 1 × 10 −6 mbar without gas flow, respectively.
We use the plasmonic enhanced third harmonic from the nano-antennae to optimize the focal position as well as the alignment of the antenna array relative to the laser focus.

Experimental results
Similar to our previous experiments with rod-type optical antennae [29] we observe a rapid destruction of the samples, which has recently also been reported by Park et al [18,32]. With xenon gas flow turned on, we measure the highest photon numbers at 118 nm, which is thus used to further characterize the antennae. Figure 2 shows the measured radiation at 118 nm as a function of the illumination time. We observe an exponential decrease of the generated radiation, which saturates at about 10% of its initial value and increases again after translating the sample to illuminate a fresh spot within the antenna array (after approximately 100 s). Thus the original antenna design is presumably first changed due to thermal reshaping and then remains in a different shape without further changes [33]. Despite the substantial decrease, the remaining Figure 3. (a), (b) Bow-tie antennae before and after illumination (with a peak intensity of 2 × 10 11 and 6 × 10 11 W cm −2 ) with varying antenna arm lengths and different achromatic lenses used to focus the laser beam. Only above an intensity threshold antenna destruction is observed (c). Additionally the destruction strongly depends on the antenna arm length since 140 nm long antennae (with a peak intensity of 13 × 10 11 W cm −2 ) are widely damaged (c), whereas only a few 200 nm long antennae (with a peak intensity of 13 × 10 11 W cm −2 ) are changed (d).
enhancement of the nano-antennae is still sufficient to support the generation of radiation at 118 nm. To assess the reshaping process, SEM images are taken before and after laser pulse illumination, which are discussed below. The decrease of the harmonic signal is caused by melting of the nano-antennae as depicted in the SEM images in figure 3. Figure 3(a) shows the antennae prior to laser illumination with clearly identifiable bow-tie optical antennae separated by a gap. At a peak intensity of approximately 6 × 10 11 W cm −2 no antenna damage is observed as shown in figure 3(b). For the highest available peak intensity however, antenna damage is found depending on the antenna length as depicted in figures 3(c) and (d). At an antenna length of 140 nm regular antenna damage due to melting is found, whereas only occasional damage is present for longer antennae with a length of 200 nm. The melting leads to a significantly increased gap size and hence a reduced electric field enhancement. Consequently, the nonlinear signal is also reduced as plotted in figure 2.
At a higher magnification of the SEM images antenna destruction becomes even clearer and additional information is obtained by using different detectors to examine backscattered  figure 4(c) on the other hand not only contain information about the material, but also reveal the sample's topography, which is clearly nonuniform in close proximity to the antennae, although the adjacent substrate material is not altered. Additional information about the chemical compounds in the analysed area is gained by energy-dispersive x-ray spectroscopy, with the respective spectrum plotted in figure 4(a). It only contains measurable peaks for gold, aluminium, oxygen and carbon. The latter is likely caused by handling the sample outside a sealed atmosphere and is low in comparison with the others. Most prominent are the peaks form aluminium and oxygen, which result from sapphire as a substrate material. Since the antennae only comprise a small part of the analysed area, the peaks resulting from gold are also low compared with those from e.g. oxygen. Most importantly no other peaks occur and sample contamination is ruled out as a source for the incongruities in the secondary electron picture. For sapphire optical breakdown with subsequent shape changes has been observed previously at a threshold intensity of 1.4(4) × 10 13 W cm −2 [34]. Based on our simulations described in the following, these intensities are experimentally feasible in the vicinity of the antennae. The incongruities are therefore most likely caused by a damaged substrate material, resulting in a final topography shown in figure 4(c). Moreover, the simulations also reveal a damage threshold depending on the antenna length, which has been found experimentally.

Numerical methods
To simulate the response of the antennae to an ultrashort laser pulse the freely available FDTD code MEEP [35] is employed. Periodic boundary conditions in xand y-direction mimic the antenna array used experimentally and perfectly matched layers in z-direction avoid numerical reflections of the incident field. The parameters to model the dispersive behaviour of gold are taken from [36], whereas all other parameters are taken from the experiment. The temperature distribution within the antennae is given by the heat source density [37] and plotted together with the normalized intensity enhancement in figure 5 both in the x yand the x z-plane for a bow-tie antenna with 140 nm antenna length. In figure 5(b) the substrate is located in the bottom half of both plots and treated as an ideal dielectric with a zero imaginary part of the dielectric function. Thus, the heat source density is also zero and the laser pulse itself does not deposit heat in the substrate. The substrate is therefore only heated via heat conduction and serves as a cooler for the antenna.
In the antenna on the other hand, the non-zero imaginary part of the dielectric function leads to heating of the structure with two prominent maxima in each antenna arm. One occurs at the apex' bottom caused by the strong local electric field there, which also reaches into the antenna material. The other one is located at the top of the antenna at the interface to the surrounding dielectric, i.e. vacuum or air. Its origin becomes clearer after examining the electric field in the x y-plane. Generally, heat deposition within the antenna is strongly non-uniform and mostly concentrated at the antenna half facing towards the gap. In particular, the outer antenna ends are only heated via heat conduction and thus reduce the overall temperature in each antenna arm. Interestingly, a minimum for the heat source density also occurs at the upper apex part, even stretching further into the antenna, although the antenna's bottom part is significantly heated.
The corresponding electric field enhancement in the x z-plane is shown in the lower plot in figure 5(b), which is also non-uniform along the antenna thickness. Two pronounced maxima occur at the antenna's top and bottom side and are caused by the sharp tips in that direction. The top one is particularly strong because the field stretches undisturbed into the dielectric, whereas at the bottom the field distribution is changed due to the additional interface resulting from the substrate. Nonetheless, enhancement factors in the order of 10 3 are present in large parts of the gap area along the z-direction. Figure 5(c) shows the heat source density and the normalized intensity enhancement factor for the same bow-tie antenna as before in the x y-plane. The former exhibits strongly localized maxima at the interface to the surrounding dielectric, which coincide with those observed in the x z-plane and decrease towards the centre line. At both antenna ends no heating occurs, because surface charge is accumulated there, resulting in a decreasing current towards the ends. This is in agreement with previous calculations for currents in bow-tie antennae [38]. On the other hand, the accumulated surface charge leads to the strong field enhancement plotted in the lower image in figure 5(c).
The heat source density varies with the antenna lengths and allows to calculate the temperature increase as well as a damage threshold for each antenna as described in [29].
The respective maximum temperature for antenna lengths between 100 and 180 nm for different incident intensities is plotted in the upper diagram in figure 6. Antennas in the range of the resonance length of approximately 110 nm are damaged at lower incident intensities whereas slightly off-resonant antennae withstand higher intensities. These simulation results also agree with our experimental findings, where we have found regular antenna damage for 140 nm long antennae at a given intensity and almost no damage for 200 nm long ones. This is understood by looking at the heat source density in the x y-plane, where almost no heating at all occurs at the outer antenna ends. Therefore one can think of the antenna ends as a passive cooler, which reduces the overall temperature increase for longer and antennae. However, the antennae cannot be made arbitrary long since off-resonant antennae lead to a reduced nonlinear signal as shown by Metzger et al [39], which would also hamper the generation of EUV radiation.
For HHG, intensities in the order of 10 13 W cm −2 are required and the harmonic yield ultimately depends on the peak intensity and the volume in which it is present. Therefore, taking thermal damage into account, not only the maximum enhancement has to be considered, but also the maximally possible incident intensity without damaging the antennae. Both quantities are derived by previously introduced calculations. The intensity in the gap centre including enhancement from the nano-antennae as well as the area in the x y-plane with an intensity of at least 3 × 10 13 W cm −2 , is plotted for different antenna lengths in figure 6. For every length, thermal damage is avoided by choosing the respective maximum incident intensity. Antennas between 140 and 175 nm enable peak intensities higher than 10 14 W cm −2 with an enhancement area in the x y-plane of more than 1500 nm 2 per antenna. Both the peak intensity and the enhancement area are maximal for a 160 nm long antenna. Taking the accuracy of the manufacturing process into account, antennae between 140 and 175 nm are expected to produce the highest harmonic yield, although being slightly off-resonant but thermally more stable.
Here, we do not calculate the actual HHG spectra and focus on experimental aspects of HHG driven by plasmonic fields. However, it should be noted, that this generation scheme potentially offers exciting perspectives to access the single-atom HHG response; this is an ongoing topic of research (see e.g. [15]) and will be the subject of further investigations.

Gas density
As pointed out by Sivis et al [17] the gas density and thus the number of atoms in the gap region of the bow-tie antennae is of major importance to understand the origin of the measured EUV radiation. The gas nozzle employed to feed gas onto the sample is therefore characterized with a velocity-map-imaging spectrometer [40]. For the characterization the gas jet propagates freely into vacuum like in well known HHG experimental setups. This allows to assess the number of contributing atoms as accurately as possible and also enables comparisons with cavity enhanced systems as performed by Raschke [19]. Figure 7 shows the sum of approximately hundred single images to reconstruct the gas density in the x y-plane for two different z-positions. The fringes present in figure 7(b) are caused by a varying overlap of the underlying single images for a constant step size in both dimensions. Nonetheless, the resulting gas jet with its spatial distribution is clearly visible with a nearly circular shape. For larger separations from the nozzle, the gas density drops significantly as expected.
For each z-position the full width at half maximum (FWHM) is determined in xand y-direction, grouped and fitted with a linear function. The intersection of these fit curves then reveals the previously unknown nozzle position. Both the fit curves and the gas density at different z-positions are plotted in figure 7 to illustrate the gas density behind the nozzle. From the fit data a divergence angle of 33 • is obtained. In combination with the mass flow controller the number of atoms at the sample is now accessible. In our experiments typical distances between the sample and the gas nozzle are in the order of 100 µm and the measured mass flow is 0.175 sccm (measured with a MKS 647C controller), which is approximately 1.7 × 10 −5 g s −1 . Hence, the gas density at the sample is in the order of 7.4 × 10 −2 atoms nm −3 . Furthermore, for a 50 nm thick bow-tie antenna with a gap size of 20 nm the conservatively estimated interaction volume is 20 × 50 × 40 nm leading to 2.9 × 10 3 atoms in it. Since roughly 200 antennae are illuminated with the laser pulse, in total 5.9 × 10 5 atoms contribute to the measured signal.
Kim et al [32] on the other hand, report ∼8 × 10 4 gas atoms in the interaction volume, which is almost an order of magnitude lower compared to our experimental conditions.

Spectra
In figure 8, exemplary spectra for 200 nm bow-tie antennae are plotted with figure 8(a) covering a broader spectral range in the EUV and figure 8(b) showing a detail scan around 90 nm. For both spectra xenon gas with a backing pressure of 200 mbar was fed onto the sample and the nozzle position has been optimized. Xenon gas is chosen due to its higher harmonic efficiency in comparison with other noble gases. Also the current photon flux does not allow us to switch to argon or helium gas to achieve higher cut-off energies. The nozzle is identical to the one characterized in section 5. Grey background shading indicates the harmonic orders of the driving laser and orange lines represent xenon plasma lines and their relative intensities [41]. Most strikingly, high photon numbers are detected between 100 and 110 nm, which is attributed to multiple plasma lines in this spectral range. A pronounced peak with the highest photon numbers is found at 117 nm, where only four plasma lines can contribute to the total signal. Taking the relative intensities into account and comparing the photon numbers with those at 104 nm a lower signal is expected if plasma radiation alone is its source. Another spectral peak coincides with the spectral position of the ninth harmonic at 91 nm. However, the spectral width is smaller than expected for the harmonic radiation. Figure 8(b) was measured with the grating with a design wavelength from 110 to 310 nm due to alignment purposes. Therefore, no diffraction efficiency is known for the spectral range below 110 nm and the spectrum in figure 8(b) has not been corrected for it. Also note, that the central wavelength is slightly shifted to 810 nm. The dashed green line indicates the noise floor caused by dark counts from the electron multiplier. Interestingly no plasma line contributions for wavelengths larger than 95 nm are found in the spectrum. However, a pronounced peak at 90 nm is present, which does not directly coincide with xenon plasma lines.
Additional spectra were taken under identical conditions as before with 170 nm antennae to maximize the electric field enhancement as pointed out in section 4. The central laser wavelength is 820 nm and figure 9 shows an efficiency corrected spectrum in the range between 50 and 120 nm to check for higher harmonic orders. As before, significant photon numbers are detected around 104 nm, which result from discrete transitions in single-ionized xenon [41]. Surprisingly few photons are measured at 117 nm, though. The highest photon numbers are found at 76 nm, which is close to the spectral position of the eleventh harmonic. Slightly less signal is present at 91 nm, i.e. at the spectral position of the ninth harmonic order. The highest photon numbers occur at 76 nm, which is close to the eleventh harmonic of the driving laser.

Summary and outlook
In summary, we have presented an analysis of important parameters influencing the generation of EUV radiation utilizing the plasmonic field enhancement of bow-tie optical antennae. A damage threshold for the antenna is experimentally found and explained by a simple theoretical model, which facilitates to find thermally stable antennae. Based on the ion imaging technique with a velocity map imaging spectrometer, the gas nozzle employed in the experiments was thoroughly characterized to determine the gas density at the sample as accurately as possible. The spectra obtained with FIB-produced nano-antennae are all in contrast to data reported by Kim et al [5], who reported the observation of harmonic radiation alone without additional lines resulting from plasma radiation in an identical experiment. They are however in agreement with early experiments on HHG with peak intensities of 3 × 10 3 W cm −2 , where contributions from neutral and single-ionized xenon to the spectra have been found [30,42]. These intensities are well within reach in the feed gap of the nano-antennae and ALE as an incoherent process is likely to occur. This is supported by the observed changes to the sapphire substrate, which require peak intensities of at least 1 × 10 13 W cm −2 as outlined in section 3 in order to appear. An insufficient field enhancement from the nano-antennae as a possible source of error is therefore highly unlikely. Moreover, ALE alone has been found in independent experiments on HHG in the presence of optical antennae, which further confirms the measured spectra [17]. Recently Park et al [18] also reported to have found ALE in their EUV spectra.
In order to distinguish between ALE or harmonic generation as a source for the measured EUV radiation additional measurements are necessary. The coherence properties of the bow-tie emitted radiation reveal information on the source of the measured radiation since HHG as a coherent process should exhibit a well defined beam profile. ALE in contrast is an incoherent process and thus no beam profile is expected. Secondly, by switching to a different driving wavelength of e.g. 1064 nm ALE contributions and harmonics of the driving laser would spectrally be well separated and thus enable an unambiguous determination of its source. An increased driving wavelength would be advantageous in even more aspects. The structuring precision requirements are eased due to larger structure sizes, the damage threshold is increased because of a reduced absorption in the gold layer and larger antenna sizes, and finally the HHG cut-off is increased at the expense of conversion efficiency.