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Keywords:

  • plasmonics;
  • high-harmonic generation;
  • laser oscillator;
  • bow-tie antennae

Abstract

  1. Top of page
  2. Abstract
  3. 1 Introduction and motivation
  4. 2 Experimental idea
  5. 3 High-order harmonic generation
  6. 4 Plasmonics in intense laser fields
  7. 5 Experiments
  8. 6 Conclusion and outlook
  9. References

High-order harmonic generation in xenon with oscillator repetition rates is studied. The necessary intensity is reached via plasmonic field enhancement at nanostructured arrays of bow-tie gold antennae. The theoretical analysis focuses on the thermal properties and the damage threshold of the bow-tie antennae. On the experimental side the number of contributing atoms is determined and optimized. Extreme ultraviolet radiation is successfully observed with photon fluxes almost an order of magnitude larger than previously reported.

1 Introduction and motivation

  1. Top of page
  2. Abstract
  3. 1 Introduction and motivation
  4. 2 Experimental idea
  5. 3 High-order harmonic generation
  6. 4 Plasmonics in intense laser fields
  7. 5 Experiments
  8. 6 Conclusion and outlook
  9. References

Although plasmons are known for a long time [24], the field has rapidly developed throughout the last decade and a broad range of applications has emerged particularly for extreme light concentration [52]. For instance, nano-particles can be used to locally heat biological tissue, which has already found applications in novel methods of cancer therapy [14]. There, nano-particles are used to specifically destroy cancer cells without affecting the surrounding cells as in conventional approaches. Additionally, plasmons and nano-antennae in particular are a tool in non-linear optics facilitating, for example, enhanced second harmonic generation [10]. Recent theoretical calculations even suggest the generation of isolated attosecond pulses, employing the nano-plasmonic field enhancement in ellipsoidal antennae [57]. Moreover, numerical simulations reveal the feasibility of attosecond plasmonic streaking [56].

This bridges the gap to a different rapidly growing field – namely high-order harmonic generation (HHG) in noble gases. The process was first observed roughly twenty years ago [11, 33] and has ever since provided a coherent light source in the extreme ultraviolet spectral range. Due to the shorter wavelength, the pulse durations achieved have been pushed from the femtosecond into the attosecond regime [41]. Today, light pulses as short as 67 as can be generated [25] and a whole new field of physics has been opened up [23]. This unprecedented temporal resolution enables, among other things, new measurements in fundamental physics to study electron dynamics in atoms, molecules and solid state materials.

In parallel to these developments, high-precision spectroscopy was revolutionized by the frequency comb technique, which is now commonly used [62]. However, its extension to the ultraviolet regime is challenging due to the low conversion efficiency of the HHG-process. To circumvent this issue and to increase the harmonic photon flux, external enhancement cavities have been developed and investigated extensively [13, 17, 37, 68]. One intriguing application of a frequency comb in the vacuum-ultraviolet range is the possibility of performing direct frequency comb spectroscopy [32, 66, 69] in this spectral range.

Recently, the first frequency comb measurement on helium in the extreme ultraviolet regime has been reported with an improved accuracy of nearly one order of magnitude. Thus, new tests of quantum electrodynamics as well as upper bounds on the drift of fundamental constants are envisaged [18]. Furthermore, some of the lowest nuclear transitions are also located in this spectral range. For instance, Th-229 has a resonance at 7.8 eV [3], which could be probed with the fifth harmonic of a Ti:sapphire laser [42]. A successful measurement would be the first spectroscopy of a nuclear transition with a laser system.

In summary, there is tremendous interest among physicists to establish a frequency comb in the ultraviolet regime. By employing a plasmonic resonance in optical nano-antennae, a new approach for HHG directly from a laser oscillator is envisaged [19]. A successful implementation of this novel scheme would furthermore bridge the gap between two different fields of physics: plasmonics with typically low pulse energies and structure dimensions in the nanometre regime on one hand and high-field physics with peak intensities in excess of 1014 W cm−2 on the other.

Within this review nano-antennae are analysed both theoretically and experimentally with respect to their applicability for high-order harmonic generation. Numerical simulations provide a tool to determine crucial antenna parameters for HHG. Here, particular emphasis is put on the thermal properties of the antennae to assess possible damage processes which are likely to occur for high incident intensities. Finally, the antennae are optimised to facilitate a maximised field enhancement without being thermally destroyed. The obtained results are experimentally verified and measurements on nano-antenna-assisted HHG are performed. During the experiments, great care has been taken to fully understand all experimental parameters and rigorously characterise the used components.

2 Experimental idea

  1. Top of page
  2. Abstract
  3. 1 Introduction and motivation
  4. 2 Experimental idea
  5. 3 High-order harmonic generation
  6. 4 Plasmonics in intense laser fields
  7. 5 Experiments
  8. 6 Conclusion and outlook
  9. References

As described in the previous section there is tremendous interest among physicists to establish a coherent EUV-source by utilising high-order harmonics with repetition rates in the MHz regime. High-order harmonics are routinely generated with amplifier systems allowing for peak intensities in excess of 1014 W cm−2. These systems however, rely on the chirped pulse amplification (CPA) technique, which involves a reduction of the pulse repetition rate in order to achieve the desired peak intensities. This in turn destroys the original mode-comb structure of the driving laser and thus no frequency comb is obtained.

A pronounced enhancement of the near field is observed in the vicinity of optical antennae with enhancement factors in the order of up to 103 [58]. By tightly focussing a few-cycle laser pulse (Fig. 1), peak intensities in the range of 1011 W cm−2 are feasible. Thus by focussing few-cycle laser pulses onto an array of optical antennae peak intensities sufficient for HHG are envisaged. Since the field enhancement is caused by plasmonic resonances in the antennae no reduction of the pulse repetition rate is necessary and hence the mode comb structure is expected to be preserved.

image

Figure 1. Sketch of the experimental idea. Few-cycle laser pulses are tightly focussed onto an array of optical antennae. The plasmonic resonance causes an enhanced near field, facilitating peak intensities in the order of 1013  W cm−2. Thus, extreme ultraviolet (EUV)-photons are generated in the antenna gap region.

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An experiment implementing this approach has first been reported by Kim et al. in 2008 [19]. Despite the intriguing idea, the concept also poses some major challenges: first, the intensity enhancement only occurs in the vicinity of the antennae, i.e. the total volume in which the peak intensity necessary for HHG is present is rather small compared to conventional HHG experiments in gas jets or in enhancement cavities. To overcome this drawback the gas density, i.e. the number of emitters within the enhancement volume has to be maximised to achieve an appreciable amount of harmonic photons. This becomes particularly important, baring the low conversion efficiency of the HHG process in mind. The results from Kim et al. have been challenged during the last years, and meaning and prospects of this approach have been lively debated [55, 53, 46, 43].

In the following a brief introduction into HHG in general is given, followed by an analysis of possible phase-matching effects in the case of HHG in the near field of optical antennae. Section 'Own experiments' focusses on current experimental results and discusses the challenges involved.

3 High-order harmonic generation

  1. Top of page
  2. Abstract
  3. 1 Introduction and motivation
  4. 2 Experimental idea
  5. 3 High-order harmonic generation
  6. 4 Plasmonics in intense laser fields
  7. 5 Experiments
  8. 6 Conclusion and outlook
  9. References

Already shortly after the invention of the laser in 1960 optical harmonic generation has been demonstrated by frequency doubling in a crystal [12]. Since then a large variety of highly nonlinear effects has been observed with increasing available laser power. For the experiments presented within this chapter, particularly HHG in noble gases in presence of optical antennae is of special interest.

For intensities of up to 1013  W cm−2[61] of the incident laser field its interaction with atoms has a perturbative character and is thus described by perturbation theory. For higher intensities however, the interaction becomes strongly non-perturbative and, among other things, HHG is possible [22, 50]. Figure 2 shows a sketch of a typical harmonic spectrum generated in a gaseous medium, with the maxima occurring at odd integer multiples of the fundamental laser frequency. Within region I the intensity of low-order harmonics decreases rapidly with increasing order [38] and is thus referred to as the perturbative regime. In the plateau region II on the other hand, the harmonic intensity stays relatively constant over many harmonic orders [33, 11]. This observation of a plateau in the harmonic spectrum is not explained by perturbation theory. The end of the plateau is marked by the cutoff in region III, where the harmonic intensity again decreases rapidly with harmonic order.

image

Figure 2. Sketch of a typical spectrum of high-order harmonics generated in a gaseous medium. The labelled areas are the perturbative region I, the plateau region II and the cutoff region III.

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In general, microscopic and macroscopic aspects have to be considered separately in HHG. The former is intuitively described by a semi-classical model introduced in Sec. 'Semi-classical model' and originates from the non-linear response of the atoms to the strong laser field. Macroscopic effects on the other hand, are caused by the coherent superposition of the fields emitted by all the atoms in the generating volume and are explained in Sec. 'Geometric phase'.

3.1 Semi-classical model

The semi-classical model explains the response of a single atom to the incident strong laser field [5]. Both the laser field and the electron motion in the field are described classically, whereas the atom's electronic states are considered quantum mechanically. The generation process is then decomposed into three steps depicted in Fig. 3, where subfigure (a) shows the atomic potential without an external laser field.

image

Figure 3. Semi-classical model of high-order harmonic generation. Subfigure (a) shows the atomic potential without an external laser field. In (b) the laser field has lowered the Coulomb barrier and electrons tunnel out from the core. These electrons are accelerated within the field (c) and can recombine with the parent ion (d), resulting in an emission of an XUV photon.

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3.1.1 Ionisation

In the strong field the atomic potential is deformed significantly leading to a lowered Coulomb barrier. Thus, the electron can tunnel out from the core with increased probability and tunnel ionisation becomes the dominating ionisation process as depicted in Fig. 3(b). In general, the tunnelling probability is high, when the electric field is at its maximum and minimal, when the electric field has a zero-crossing. Furthermore, the electron velocity inline image after the ionisation is assumed to be zero and the electron is located at the nucleus' position.

3.1.2 Acceleration

The freed electron undergoes oscillations in the electric field E, while the Coulomb force from the nucleus can typically be neglected. The mean kinetic energy acquired by a free electron oscillating in the laser field is given by inline image

  • display math(1)

where e denotes the electron charge, me the electron mass and ω the laser frequency. inline image is also known as the ponderomotive potential. When the laser field switches its sign, the electron travels in reverse direction and can thus return to its origin as shown in Fig. 3(c).

3.1.3 Recombination

Some of these returning electrons interact with their parent ion and lead to a radiative recombination depicted in Fig. 3(d). This light emission occurs at odd harmonics of the fundamental laser frequency due to inversion symmetry. According to classical mechanics, the maximum kinetic energy acquired by the electron is inline image. In combination with the atom's binding energy inline image, the maximum photon energy, i.e. the cutoff energy, is therefore given by

  • display math(2)

Empirical values for the maximum kinetic energy range from 3.0 inline image to 3.2 inline image [22, 28, 50].

The assumptions made by the semi-classical model have been justified by full quantum mechanical treatments, where a strong field approximation (SFA) to solve the time-dependent Schrödinger equation (TDSE) has been employed [26]. Moreover, numerical simulations of the semi-classical model are qualitatively in good agreement with results from the full quantum mechanical description of HHG by the TDSE [27, 5].

3.2 Macroscopic effects/phase-matching

In order to observe efficient HHG the fields emitted by all atoms in the generating volume have to be coherently superimposed, i.e. the phase difference between the fundamental wave and the qth harmonic wave has to be minimised. In case of HHG, different phases contribute.

3.2.1 Geometric phase

For HHG the fundamental laser beam is tightly focussed to reach the necessary peak intensities. The resulting change in wavefront curvature leads to a spatially dependent phase in comparison with a plane wave. This phase is typically referred to as the geometric phase and given by

  • display math(3)

where the first term represents the Gouy-phase on the propagation axis and the second term the radial distribution resulting from the wavefront curvature with the propagation coordinate z, the radial coordinate r, the confocal parameter b, the wavefront curvature R and the fundamental wavelength λ. The wave vector inline image describes the focussed laser beam and the wavefront's locus. It reads

  • display math(4)

with inline image.

3.2.2 Atomic phase

Another major phase contribution results from the electrons released during step 1 in the HHG process. While in the continuum, the electrons accumulate quantum phase, leading to a phase lag with respect to the generating laser field. It is usually referred to as the atomic phase and is obtained from the time-dependent dipole moment. Both the dipole strength as well as the phase depend on the intensity I. Within certain intensity ranges the latter is to a first order given by

  • display math(5)

Here, α is a coefficient depending on the quantum path [2], which is determined from quantum mechanical calculations [26]. Figure 4 shows the dipole strength and the atomic phase for the seventh harmonic in xenon for intensities of up to 2 × 1014  W cm−2. In the plateau regime, i.e. for intensities larger than 5 × 1013  W cm−2, the phase fluctuates. This is caused by different quantum paths interfering with each other. For lower intensities only one quantum path contributes, which leads to a smooth phase. The proportionality factors are inline image and inline image respectively. The wave vector describing atomic phase contributions is

  • display math(6)
image

Figure 4. Dipole strength and dipole phase of the seventh harmonic in xenon as a function of intensity. The data is obtained from numerical simulations based on SFA solutions to the TDSE [26]. For intensities higher than 5 × 1013  W cm−2 the seventh harmonic lies in the plateau, leading to phase fluctuations caused by quantum path interference. The dashed lines indicate piecewise linear phase approximations for the plateau and cutoff regime.

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3.2.3 Dispersion effects

Principally, neutral atoms as well as free electrons affect phase-matching for HHG. However, for the case of HHG utilising optical antennae the calculated maximum peak intensities are in the order of 1.3 × 1014  W cm−2 as shown in Fig. 8. For xenon, this leads to less than 10% of ionised atoms and a coherence length of more than 1 mm. Given the typical antenna dimensions, this is already five orders of magnitude larger than the generation volume. Therefore, free electrons are not further considered for phase-matching.

The situation is similar for neutral atoms: with an estimated gas pressure at the sample in the millibar regime the coherence length due to neutral atoms alone is in the order of several millimetres. Thus, this effect is also not considered in the following.

3.2.4 Generalised phase-matching condition

The previously introduced phase contributions, namely the geometric phase in Eq. (4) and the atomic phase in Eq. (6), yield the wave vector of the harmonic beam inline image, which is

  • display math(7)

Its length is then inline image and the phase-mismatch becomes

  • display math(8)

The coherence length inline image, i.e. the length in which radiation interferes constructively [2], is inversely proportional to the phase-mismatch inline image:

  • display math(9)

Areas with a small phase-mismatch therefore have large coherence lengths, indicating a significant contribution to the overall harmonic signal and vice versa [47]. In the following the coherence length is used to assess phase-matching conditions for the case of nano-structure enhanced HHG.

3.3 Phase-matching in the case of optical antennae

To analyse the phase-matching conditions in the case of HHG utilising optical antennae, the effects described in Sec. 'Geometric phase' are examined numerically. Instead of relying on the linear approximation for the atomic phase, results from the quantum mechanical model [26] were used. The necessary parameters are taken from the experiment and are listed in Table 1.

Table 1. Simulation parameters to analyse phase-matching conditions
parametervalue
ionisation potential inline image12.1 eV (xenon)
confocal parameter binline image m
peak intensity I1 × 1014 W cm−2
pulse duration τ7fs
central wavelength λ820 nm

Figure 5 depicts the coherence length of the seventh and ninth harmonic in xenon as a function of propagation distance z and the beam radius r, with the fundamental beam propagating from left to right. White areas indicate a coherence length of at least 1 mm, i.e. five orders of magnitude larger than the thickness of the generation volume of approximately 50 nm. For both harmonics the interplay between the geometric and the atomic phase is clearly visible from the solid lines in the plots. For the seventh harmonic, the focus is particularly pronounced in the centre with coherence lengths in the order of 0.1 mm as shown in Fig. 5a. The same feature is also found for the ninth harmonic in Fig. 5b, but less distinct.

image

Figure 5. Phase-matching map for different harmonic orders as a function of propagation distance and beam radius. The fundamental beam propagates from left to right. The solid curve depicts places of the same coherence length.

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Interestingly, there is an area of good phase-matching directly after the focus for the seventh harmonic, similar to the case of conventional HHG [48], which is followed by an area with a lower coherence length.

Figure 6 gives an overview of the coherence length along the propagation axis for various harmonic orders. On a scale of 10−4 m phase-matching limits the harmonic generation around the beam waist for higher harmonic orders. Bearing the optical antenna dimensions with a thickness of 50 nm in mind, phase-matching is not expected to have a significant influence on HHG utilising optical antennae. This is particularly interesting from a theoretical point of view, since it opens up the opportunity to experimentally study microscopic and macroscopic effects of HHG independently.

image

Figure 6. Overview over phase-matching along the propagation axis for various harmonics on a length scale of 10−4 m. Already for a generation volume with a thickness of 1 inline imagem perfect phase-matching is achieved. Therefore for HHG utilising optical antennae, no phase-matching effects are expected to influence the generation process.

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3.4 Field inhomogeneities

So far, the presented models did not consider the field inhomogeneity introduced by optical antennae and bow tie antennae in particular. Moreover, the presence of metallic structures confines the electrons produced during the HHG process within the gap area. Since the highest electric fields occur close to the antenna surface, one can assume that this effect would especially influence cutoff harmonics. Recently, the semi-classical model as well as the quantum mechanical model based on the SFA were extended to include both the field inhomogeneity and the confinement of the electron movement [15, 4]. Interestingly, both models predict an extension of the observed cutoff and also a generation of even harmonics due to a broken symmetry. For a fundamental wavelength of 800 nm electron confinement effects have a low influence on the harmonic generation; they become apparent for longer wavelengths.

4 Plasmonics in intense laser fields

  1. Top of page
  2. Abstract
  3. 1 Introduction and motivation
  4. 2 Experimental idea
  5. 3 High-order harmonic generation
  6. 4 Plasmonics in intense laser fields
  7. 5 Experiments
  8. 6 Conclusion and outlook
  9. References

Through numerical simulations and theoretical modeling an optimization of optical nano-antennae for different applications can be achieved. Thus, various techniques like the discrete dipole approximation [8] or finite difference frequency methods [16] or finite difference time domain (FDTD) method [67, 59, 60] have been developed over the last decades. The latter is widely used to simulate optical antennae [6, 58, 7] and other plasmonic devices [63]. Here, the method is also applied to assess the response of nano-antennae to ultrashort laser pulses and is explained in more detail in [44].

The respective calculations are performed with the freely available FDTD code MEEP [36]. Periodic boundary conditions in x- and 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 [45], whereas all other parameters are taken from the experiment.

Two quantities are of major interest: the near-field intensity enhancement inline image and the heat source density inline image. The former is defined by

  • display math(10)

where inline image denotes the incident electric field [51], which is obtained from a reference calculation. The heat source density on the other hand is given by

  • display math(11)

with ω denoting the incident laser frequency, inline image the dielectric function of the antenna material and inline image the local electric field. This quantity determines the temperature distribution within the antennae [1] and is therefore an important parameter at high incident intensities. It is plotted together with the normalised intensity enhancement in Fig. 7 both in the inline image- and the inline image-plane for a bow-tie antenna with 140 nm antenna length. In (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.

image

Figure 7. (a) Overview, (b) side view and (c) top view of one bow-tie antenna. (b) and (c) top: Heat source density of a bow-tie antenna with 140 nm antenna length, 30° opening angle, 20 nm feed gap, 20 nm radius of curvature and an antenna height of 30 nm; (b) and (c) bottom: Corresponding normalised intensity enhancement.

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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 inline image-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 inline image-plane is shown in the lower plot in (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 103 are present in large parts of the gap area along the z-direction.

Figure 7(c) shows the heat source density and the normalised intensity enhancement factor for the same bow-tie antenna as before in the inline image-plane. The former exhibits strongly localised maxima at the interface to the surrounding dielectric, which coincide with those observed in the inline image-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 [6]. On the other hand, the accumulated surface charge leads to the strong field enhancement plotted in the lower image in (c).

The heat source density varies with the antenna length and allows to calculate the temperature increase as well as a damage threshold for each antenna as described in [43]. The respective maximum temperature for antenna lengths between 100 nm to 180 nm for different incident intensities is plotted in the upper diagram in Fig. 8. Antennae in the range of the resonance length of approx. 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 inline image-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 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. [34], which would also hamper the generation of EUV radiation.

image

Figure 8. Maximal antenna temperature for different incident intensities as a function of the antenna length L and temperature optimisation of bow-tie nano-antennae. The given peak intensity includes the incident intensity and the enhancement exhibited by the antennae.

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For high-order harmonic generation, intensities in the order of 1013  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 inline image-plane with an intensity of at least 3 × 1013 W cm−2, is plotted for different antenna lengths in Fig. 8. For every length, thermal damage is avoided by choosing the respective maximum incident intensity. Antennae between 140 nm and 175 nm enable peak intensities higher than 1014 W cm−2 with an enhancement area in the inline image- plane of more than 1500 nm2 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 nm and 175 nm are expected to produce the highest harmonic yield, although being slightly off-resonant but thermally more stable.

5 Experiments

  1. Top of page
  2. Abstract
  3. 1 Introduction and motivation
  4. 2 Experimental idea
  5. 3 High-order harmonic generation
  6. 4 Plasmonics in intense laser fields
  7. 5 Experiments
  8. 6 Conclusion and outlook
  9. References

5.1 Historical overview

In 2008 Kim et al. reported a successful implementation of the experimental idea for the first time. It sparked tremendous excitement about emerging opportunities for a high repetition rate EUV source. This publication was followed by additional experimental data and theoretical considerations about the antenna geometry in 2010 by the same group [21]. In 2011 Park et al. published a novel experimental scheme based on a funnel to increase the plasmon enhanced interaction volume in order to increase the harmonic photon yield [40].

Despite the initial excitement it proved difficult to reproduce the observations by Kim et al. and only in 2012 Sivis et al. [55] published their results using a similar setup. However, within the data no clear indication of HHG could be found and the authors concluded atomic line emission to be the origin of the measured EUV radiation. Moreover, an estimate of the expected photon yield revealed a strong dependence on the gas density in the vicinity of the optical antennae and a low yield in comparison with conventional HHG sources with kHz repetition rates. These considerations also triggered a comparison of the experimental idea and current experimental results with established high repetition rate EUV sources based on external enhancement cavities [46]. Based on the available experimental data also a considerably reduced harmonic yield in case of nano-antenna assisted EUV generation was concluded.

Recently, additional experiments carried out by Sivis et al. [55] demonstrate a sufficient field enhancement exhibited by the nano antennae to reach intensities necessary for HHG to occur. In experiments carried out with an amplifier system at identical peak intensities as in the respective ones based on nano antennae, HHG in combination with atomic line emission is observed. The authors therefore conclude albeit nano-antennae exhibit a pronounced and sufficiently large field enhancement, that the available interaction volume is too small in comparison with conventional schemes for HHG to occur. Additionally, an increase of the gas density is suggested to enhance the observed nonlinear effects.

In the following our experiments based on nano antennae are presented. Particular emphasis is put on the characterisation of the employed gas jet to determine the gas density within the gap region of the antennae as accurate as possible.

5.2 Own experiments

5.2.1 Experimental set-up

Figure 9 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 [43]. 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 (DCM) 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 focussing 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 inline imagem to inline imagem with corresponding peak intensities of 2 × 1011 W cm−2 to 13 × 1011 W cm−2, respectively. The sample with the nano antennae is attached to a second translation stage moving in x- and y-direction to selectively address different antenna arrays, which appear as squares in the SEM image in Fig. 9 due to their extremely high packing density. The laser polarisation and the antenna axes are aligned parallel to each other. To efficiently detect the generated EUV radiation a confocal monochromator setup (modified McPherson 234/302, 1200 lines/mm grating for 110 nm to 310 nm, 2400 lines/mm grating for 20 nm to 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 grating and the photon collection efficiency is maximised [29, 30]. 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 is detected with an electron multiplier (Photonis 4751G) in combination with a pre amplifier (Minicircuits ZFL 500LN+) instead of the PMT.

image

Figure 9. Experimental set-up. Laser pulses from a Ti:sapphire oscillator are focused by an achromatic lens onto arrays of optical antennae. Low harmonic orders are generated and analysed with different detectors (see text for details).

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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 milling (FIB) 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 inline imagem as can be seen in the SEM image inset in Fig. 9. A detailed SEM picture of the antennae prior to illumination with the laser beam is shown in Fig. 12(a).

Figure 10 shows the resonance spectrum of two antennae with a different arm length as well as the spectrum of the driving laser. Both resonances are covered by the fundamental laser spectrum and can thus be excited upon illumination. Moreover, the setup is robust towards possible differences in the antenna length resulting from the manufacturing process.

image

Figure 10. Resonance spectra of bow-tie antennae with an armlength of 165 nm and 175 nm, respectively. Additionally, the spectrum of the driving laser is plotted (log scale).

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Gas is fed onto the sample through a homebuilt glass nozzle with a diameter of 50 inline imagem. The gas nozzle is mounted on a inline image-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 Sec. 'Conclusion and outlook'. With the gas flow turned on the background pressure is at around inline image mbar and inline image mbar without gas flow, respectively.

We use the plasmonic enhanced third harmonic from the nano-antennae to optimise the focal position as well as the alignment of the antenna array relative to the laser focus.

5.2.2 Experimental results

Similar to our previous experiments with rod-type optical antennae [43] we observe a rapid destruction of the samples, which has recently also been reported by Park et al. [20, 39]. With xenon gas flow turned on, Fig. 11 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 approx. 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 [65]. Despite the substantial decrease, the remaining 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. The decrease of the harmonic signal is caused by melting of the nano-antennae as depicted in the SEM images in Fig. 12. Subfigure (a) shows the antennae prior to laser illumination with clearly identifiable bow-tie optical antennae separated by a gap. At an incident peak intensity of approx. 6 × 1011 W cm−2 no antenna damage is observed as shown in Fig. 12(b). For the highest available peak intensity however, antenna damage is found depending on the antenna length as depicted in (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 Fig. 11.

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Figure 11. Harmonic signal in dependence of illumination time, incident intensity 1 × 1011 W cm−2. After 100s the sample is moved to a fresh spot. The signal drops exponentially and stabilises at a significantly reduced level. This points to an initial change of the original antenna structure, which is not altered further.

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Figure 12. Bow tie antennae before and after illumination 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 are widely damaged (c), whereas only a few 200 nm long antennae are changed (d).

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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 or secondary electrons in the SEM images in Fig. 13. Due to the backscattered electrons used in (b) the bright areas represent gold, whereas the dark areas correspond to the substrate material. Secondary electrons in (c) on the other hand not only contain information about the material, but also reveal the sample's topography, which is clearly non-uniform 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 (EDS), with the respective spectrum plotted in (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 from 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) × 1013 W cm−2 [64]. Based on our calculations, 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 the final topography shown in Fig. 13(c). Moreover, the simulations also confirm the damage threshold depending on the antenna length.

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Figure 13. SEM analysis of damaged antennae with different detectors and energy-dispersive X-ray spectroscopy. According to spectrum (a) no contamination is present in the analysed area, while from (b) the destroyed antennae are clearly visible. (c) reveals information about the sample's topology and points towards a damaged substrate material.

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5.2.3 Gas density

As pointed out by Sivis et al. [53] 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. Therefore, we characterized the gas nozzle employed to feed gas onto the sample with a velocity-map-imaging spectrometer [9]. For the characterisation 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 [46].

Figure 14 shows the sum of approximately hundred single images to reconstruct the gas density in the inline image-plane for two different z-positions. The fringes present in (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.

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Figure 14. (a) Three dimensional representation of the gas density, recorded from a velocity map imaging setup in spatial imaging modus. The edge of the gas jet is set to the FWHM for each measurement. The dashed lines show a linear fit of the calculated widths from which a divergence angle of 33° is obtained. (b) and (c): Reconstructed gas density behind the nozzle for two different distances. Approximately hundred images are used for the reconstruction at each distance.

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For each z-position the full width at half maximum (FWHM) is determined in x- and 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 Fig. 14 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 inline imagem and the measured mass flow is 0.175 sccm, which is approximately inline image g s−1. Hence, the gas density at the sample is in the order of of 7.4inline image atoms per nm3.

5.2.4 Spectra

In Fig. 15, exemplary spectra for 200 nm bow-tie antennae are plotted with sub-figure (a) covering a broader spectral range in the EUV and sub-figure (b) showing a detailed 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 optimised. The nozzle is identical to the one characterised in Sec. 'Conclusion and outlook'. Grey background shading indicates the harmonic orders of the driving laser and orange lines represent xenon plasma lines and their relative intensities [49]. Most strikingly, high photon numbers are detected between 100 nm 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.

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Figure 15. Measured spectra in xenon with 200 nm bow-tie antennae at a backing pressure of 200 mbar. Grey background shading indicates harmonic orders of the driving laser, whereas orange lines represent xenon plasma lines and their respective relative intensities. (a) Radiation from multiple plasma lines is found around 104 nm. (b) Detailed scan between 80 nm and 110 nm at a central wavelength of 810 nm (spectrum is not efficiency corrected). Contributions from multiple plasma lines around 104 nm do not show up like in (a), which can not be quantified as the grating efficiency for this wavelength range is not known.

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Figure 15(b) was measured with the grating with a design wavelength from 110 nm to 310 nm due to alignment purposes. Therefore, no diffraction efficiency is known for the spectral range below 110 nm and the spectrum in (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 maximise the electric field enhancement as pointed out in Sec. 'Historical overview'. The central laser wavelength is 820 nm and Fig. 16 shows an efficiency corrected spectrum in the range between 50 nm 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-ionised xenon [49]. 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.

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Figure 16. Measured spectra in xenon with 170 nm long bow-tie antennae at a backing pressure of 200 mbar. Again, radiation from multiple plasma lines is found around 104 nm, but surprisingly few photons are detected around 117 nm. The highest photon numbers occur at 76 nm, which is close to the eleventh harmonic of the driving laser.

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6 Conclusion and outlook

  1. Top of page
  2. Abstract
  3. 1 Introduction and motivation
  4. 2 Experimental idea
  5. 3 High-order harmonic generation
  6. 4 Plasmonics in intense laser fields
  7. 5 Experiments
  8. 6 Conclusion and outlook
  9. References

In 2012, Sivis et al. stated that nanostructure-enhanced HHG is unfavourable in its conversion efficiency (inline image) compared to conventional HHG in a gasjet (inline image) [53]. Based on their measurements, the ratio between the two generation schemes is given by inline image. The result was controversial to former statements about nano-HHG from Kim et al. in [19]. In reply, Kim et al. [20] claimed to have reached a significantly higher gas density than Sivis et al., leadig to inline image. The reported number of contributing atoms varies between 1 × 103 (Sivis et al.) and 8 × 104 (Kim et al.), respectively. By employing a velocity map imaging spectrometer (see Fig. 14), we have been able to measure the gas density directly behind the nozzle, which is in the order of of 7.4inline image atoms per nm3. For a 50 nm thick bow-tie antenna with a gap size of 20 nm, the conservatively estimated interaction volume is inline image, leading to a total number of 2.9 × 103 atoms per antenna. Since roughly 200 antennae are illuminated with the laser pulse, in total 5.9 × 105 atoms contribute to the measured signal, which is almost an order of magnitude higher than the estimated value from Kim et al. [20].

While we were able to observe radiation at the wavelength of the 7th, 9th, and 11th harmonic order of 820 nm [43] (see Fig. 15, 16), the final proof of coherent harmonics is still open. Such a proof can be the analysis of the spatial emittance properties of the generated radiation and is currently work in progress. After having proven the radiation's origin and further improvements of the source, we believe that Nano-HHG has the potential become an interesting coherent light source. What can be further optimized?

  • The bow-tie shaped structures are well known for high enhancement factors. However for HHG not only a strong enhancement is crucial, but also a large interaction volume. This can be realised e.g. by a higher density of antennae, or suitable new antenna designs, such as patterns of triangles, nanospheres or ellipsoids, or even some 3D structures. The z-dimension of the interaction volume has a quadratic influence on the coherent built-up process [54], and thus thick structures are favourable. Furthermore, if the distances between the hotspots in a planar rectangular array in x- and y-direction are decreased, the emitted radiation will be split up in less diffraction orders [54].
    The enhancement factor itself can be increased by further improving the quality of the structures. Moreover a higher enhancement factor allows for a reduced input intensity, while still achieving the necessary threshold intensity for HHG to occur. This in turn makes thermal destruction processes less likely. Sivis et al. have observed atomic line emission as well (Fig. 16), which is a proof of a sufficiently high intensity in the interaction volume. This indicates that one has to concentrate on reducing thermal effects and increasing coherent build-up, rather than achieving higher intensities. To enlarge the time of interaction, a more sustaining material has to be found, which might be titanium nitride (TiN) [35] or silver [40].
  • Another approach is to change the driving laser to longer wavelengths in order to increase the near-field enhancement, even though this would decrease the density of antennae due to an increased arm length. Major advantages however are a not only a lower diffraction order, but also a decreased relative surface roughness of the nano-antennae and a reduced absorption in gold. Also an increased repetition rate can be beneficial for high-harmonic flux.
  • The harmonic signal scales quadratically with the number of contributing atoms while re-absorption of the harmonics is only a linear process; consequently, it is advantageous to achieve an as high gas density as possible. This has been demonstrated in [40, 39], where HHG by funnel type structures was reported with nonlinear dependence on the backing pressure around 100 mbar. One possible approach to further increase the gas-density is a semi-infinite gas cell, formed by the bow-tie sample and a glass cover slip with one or more holes in it and gas access from the side.

Many advantages of nano HHG such as a high repetition rate, phase-matching, and possibly high fluxes of harmonic radiation with spatial coherence [31] from a very compact source have been elaborated and proposed. What steps would be necessary to develop it into a useful tool with decent photon numbers? Typical values for e.g. the 9th harmonic in a gas jet are around 108 photons per second with a repetition rate of 1kHz. To obtain a comparable photon number with nano-enhanced HHG, the number of contributing atoms has to increase by at least two orders of magnitude. If we compare the flux of the experiments reported here to high repetition rate HHG in enhancement cavities, still about 10 times more contributing atoms to the harmonic signal at the nanostructures would be necessary (inline image [13]). This is not out of reach regarding all above mentioned possible measures.

In conclusion, after all controversial discussion, HHG with nanostructures remains an intriguing and interesting research topic. Our calculations and measurements allowed to formulate guidelines for the next experimental step to finally prove the coherence of the radiation and to increase the photon flux to useful numbers. Many interesting applications such as imaging, sensing, spectroscopy, or processing are in reach with very simple sources.

References

  1. Top of page
  2. Abstract
  3. 1 Introduction and motivation
  4. 2 Experimental idea
  5. 3 High-order harmonic generation
  6. 4 Plasmonics in intense laser fields
  7. 5 Experiments
  8. 6 Conclusion and outlook
  9. References