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Abstract
Separation of the high average power driving laser beam from the generated XUV to soft-X-ray radiation poses great challenges in collinear HHG setups due to the losses and the limited power handling capabilities of the typically used separating optics. This paper demonstrates the potential of driving HHG with annular beams, which allow for a straightforward and power scalable separation via a simple pinhole, resulting in a measured driving laser suppression of 5⋅10−3. The approach is characterized by an enormous flexibility as it can be applied to a broad range of input parameters and generated photon energies. Phase matching aspects are analyzed in detail and an HHG conversion efficiency that is only 27% lower than using a Gaussian beam under identical conditions is demonstrated, revealing the viability of the annular beam approach for high flux coherent short-wavelength sources and high average power driving lasers.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
High harmonic generation (HHG) is a well-established method for the generation of coherent ultrashort light pulses in the extreme ultraviolet (XUV) and soft X-ray spectral range, using a table-top setup [1]. Numerous applications already benefit from the unique laser like properties to investigate physical mechanisms on the atomic length (nm) [2] and time (as-fs) scale [3,4]. Especially coincidence experiments (where only a single event can take place per pulse [5]), excitations of highly-charged ion beams with low particle densities [6] or non-destructive imaging experiments (where a high photon flux is desired for high resolution [2,7,8]) need high repetition rate, as well as a high XUV photon flux. The very inefficient HHG process, with conversion efficiencies dropping from 10−5 at photon energies below 30 eV [9] to 10−9 when going into the water window [10], demands for high average power driving lasers. Such lasers easily damage samples, mirrors and other sensitive devices used in the XUV. Avoiding this, while still keeping a high XUV flux for good statistics and fast acquisition, calls for very good separation methods to suppress the driving laser while keeping losses small for the low average power XUV beam.
To solve this issue, there is a great variety of approaches, like thin metal filters [11], microchannel plates [12], diffraction gratings [13], grazing incidence plates [14], and non collinear schemes [15–17], that have been proposed and implemented. However, each of these approaches has specific limitations.
The most commonly used one is the separation with a few hundred nanometers thick metal foils. Filtering with such foils is a standard technique for most HHG driven experiments, it is very easy to align and works very well for low average powers and nearly all important spectral regions can be reached [18]. Up to date, the use of thin metal filters is the only separation method to suppress the driving laser almost completely, making it an indispensable tool for most experiments. However, the damage threshold of such filters is low, and they will break due to thermal heating, when exposed to higher average powers [19]. Depending on the properties of the employed material such damage can already occur at the sub-Watt level, e.g. for Zirconium filters, which are used in the spectral range between 90 eV and 160 eV. Therefore, other high average power suitable separation methods have to be used additionally to protect the thin foils.
Microchannel plates, with small holes with a diameter similar to the driving wavelength (which are hence suppressing and diffracting the driving laser while the XUV light stays mainly unaffected) have been demonstrated to have a high transmission over a large energy range [12]. Although such plates have a high intensity damage threshold, their small structure is prone to heat induced damage when using high average power driving lasers.
Instead of transmission optics, reflection optics at grazing incidence (that, due to the larger irradiated area, can be exposed to higher pulse energies) can also be used for separation. Diffraction gratings [13] can be designed for any wavelength range. However, besides the low XUV throughput, the separated beam has a high spatial and temporal chirp, which is detrimental for many applications.
This disadvantage can be eliminated by the use of grazing incidence plates (GIPs) that are antireflective (AR) coated for the driving laser and have a high refractive index top layer for high XUV reflectivity [14]. The design of such plates can be tailored to the driving laser used for HHG. Especially for few-cycle pulses that are needed for high XUV photon energies and isolated attosecond pulses, the design of the AR layer is challenging, while the XUV reflectivity drops to almost zero at high photon energies above 250 eV [18]. Shallower incidence angles could in principle improve the reflectivity, however hinder efficient AR coatings at the same time and put very high demand on the surface quality of the coated substrate over large areas. Thus, efficient separation of soft X-rays from the generating driving laser by GIPs will not be possible.
Another way to separate the fundamental and the XUV radiation is to use non-collinear schemes [15–17], where two identical pulses interfere in the interaction region under a small angle to the optical axis, while the XUV pulse is emitted on the optical axis [17]. By just placing a pinhole afterwards, the driving laser can be easily blocked. A stable temporal overlap (on an interferometric scale) of the two pulses is an issue here, which potentially translates into HHG signal and pointing fluctuations. An easy way to overcome this problem is to use an annularly shaped driving beam, which is focused onto the gas target. Note that this method can be interpreted as a rotational symmetric non-collinear scheme with an infinite number of beams. While the driving beam is annularly shaped, the generated XUV beam is Gaussian-like and propagates in the inner cone of the driving laser with low divergence (see Fig. 1). Therefore, a simple pinhole can be used to separate the driving laser and the generated XUV light.
Fig. 1 Experimental setup. The drilled mirror could be exchanged with a plane mirror (not shown here) for Gaussian beam operation (GIPs: grazing incidence plates).
Since no reflection or transmission optics are used, this scheme offers another advantage compared to conventional separation methods. The bandwidth of the XUV light can be arbitrary broad and all photon energies can be used e.g. for multi-color experiments or for the generation of shortest attosecond pulses [3,4]. It is important to note, that especially for higher photon energies, the divergence of the XUV light scales favorably for the separation with a pinhole. Furthermore, this method is independent of the choice of the driving laser, regarding average power, central wavelength as well as the bandwidth (arbitrary pulse length) of the driving laser. The concept of this separation method has been already demonstrated in 1994 [20]. Indeed, experiments are using annular beams for HHG with the purpose to drive pump-probe or attosecond experiments [21–25]. However, quantitative investigations of the phase matching conditions and the potential conversion efficiency penalty in this configuration have not been reported so far.
Within this paper we quantitatively analyze, for the first time, the conversion efficiency of HHG with an annular beam compared to a Gaussian beam. In particular, phase matching aspects are highlighted. In addition, a setup for an efficient separation of the driving laser is presented and characterized.
2. Experimental setup
For the experiment (shown in Fig. 1) a femtosecond laser system (Active Fiber Systems GmbH) was used, delivering pulses at a central wavelength of 515 nm at an average power of 5.4 W at 50 kHz repetition rate and a pulse length of 235 fs (pulse energy of 108 µJ). The beam is enlarged to a diameter of 10 mm (1/e2). Then, either a standard plane mirror (for Gaussian beam operation) or a drilled mirror (with a 2 mm hole to shape the annular beam, resulting in 7% less energy compared to the Gaussian beam) is used. Afterwards, HHG is realized by focusing the laser with a f = 150 mm lens into a gas jet. Reduction of the ambient gas pressure by two orders of magnitude is obtained by placing a 2 mm diameter gas catch roughly 500 µm from the nozzle orifice using a xyz-translation stage.
3. Separation of XUV and driving laser beam
Separation of the generated XUV radiation and the fundamental laser is done by either using GIPs (with an antireflective coating for 515 nm) or with a separation pinhole. At the end, the XUV radiation is analyzed using a flat field spectrometer with gold coated 1200 lines/mm variable line spacing flat-field grating and a CCD camera. A 2 µm thick aluminum filter is used to suppress the residual green light and for the suppression of the generated XUV light, to avoid saturation of the XUV CCD camera.
The separation pinhole needs to be placed exactly at the plane, where the surface of the drilled mirror is imaged with the focusing lens. Otherwise, diffraction will lead to an intensity spot [26] in middle of the beam profile which reduces the suppression of the driving laser. The lineout in Fig. 2 nicely shows, that placing the pinhole at this position leads to a very efficient suppression of the driving laser. Without a gas jet a suppression of the driving laser of 10−5 has been achieved. With the unavoidable presence of the gas jet this attenuation drops to a still very good value of 5⋅10−3. That suppression results only in a few Watts of average power, even if a 1 kW average power driving laser is used. Enabling an efficient separation in combination with a suitable metal filter. The drop of the suppression is mainly due to the ionization of the target gas and consequently a distortion of the spatial phase of the driving laser, thus leading to diffraction of the driving laser into the inner cone.
Fig. 2 Lineouts of the driving laser beam profiles at the position of the 1 mm pinhole for the annular (blue) and Gaussian beam (red).
Note, that this suppression of the driving laser field is already sufficient for some applications e.g. attosecond streaking experiments, which employ a very intense fundamental field [27].
4. Focusing of annular and Gaussian beams
The focal spots of the used annular and Gaussian beam have been investigated experimentally. Both beams have been focused with a lens of 150 mm focal length. The focal intensity profiles as well as a lineout for the annular beam and the Gaussian beam are shown in Fig. 3. The spatial lineouts are an average over the lineout in x- and y-direction of the focus. The experimental data reveal a focal spot diameter of 15 µm (1/e2) for the Gaussian focus and a slightly smaller focus of 14 µm (1/e2) for the annular focus. Together with the pulse energy loss of 7%, this results in a 6% higher intensity of the annular beam focus. Additionally, the focal shape of the annular beam has been investigated along the z-direction revealing a transversal Gaussian like intensity shape of the annular beam focus of about 2 times the Rayleigh length before and after the focus.
Fig. 3 Lineout (solid lines) and simulation (dashed lines) of the beam profile at the focus (shown on the left). The 3rd picture shows a microscope image of the drilled mirror.
Furthermore, the focal size and shape also have been simulated using a simple simulation tool, calculating the spatial phase and amplitude using the Huygens-Fresnel integral, accounting especially for diffraction effects and optical aberrations. The dashed lines in Fig. 3 show the simulated focal spot size and shape, which match perfectly the measured data. Even tough, a hard aperture is used to generate the annular beam, there are no significant modulations in the spatial phase in the HHG relevant high intensity part in the focus. The difference of the spatial phase of a Gaussian and annular beam in the focus is calculated from the amplitude peak to the 1/e2 diameter of the beam to only 9 mrad.
Notably, the visible imperfections in the drilled hole (see Fig. 3) still allow for a well-defined focal shape of the annular beam.
5. Phase-matching considerations
In the first step the separation pinhole was removed and only the GIPs were used as a separation element. This enables the careful characterization of the HHG efficiency with an annular beam compared to a Gaussian beam.
Efficient HHG is only possible in the phase-matched and absorption-limited regime [28]. The phase mismatch is typically expressed as a wave vector mismatch [29]:
with Δkdispersion denoting the wave vector mismatch due to the dispersion of the neutral gas atoms and the generated plasma, ΔkGouy is the wave vector mismatch due to the Gouy phase gradient, and Δkdipole is the wave vector mismatch induced by the dipole phase. For HHG in the focus or for short trajectories Δkdipole≈0 [29]. The annular beam only has a Gaussian like intensity shape close to the focus and the intensity is too low to generate the desired harmonics one Rayleigh length away from the focus. Therefore, the gas jet is overlapping with the focal position and HHG mainly takes place at the focus. As a result, the wave vector mismatch due to the dipole phase is neglected. In consequence, the dispersion term has to compensate the Gouy phase wave vector mismatch for phase-matched HHG.
First, the wave vector mismatch due to the Gouy phase gradient has been analyzed. Former theoretical [30] and experimental [31] observation show a larger Gouy phase shift (and, therefore, also a larger Gouy phase gradient) of an annular beam compared to a Gaussian beam, which is more severe for larger hole diameters (assuming the same outer diameter). Here, an analysis of the Gouy phase gradient of the driving laser beams with our experimental conditions has been carried out using the same simulation tool which was used to calculate the intensity profiles at the focus. The simulated Gouy phase gradient of the driving laser beams is shown in Fig. 4. The maximum Gouy phase gradient of the annular beam is with −2.96 rad/mm 6% higher than the maximum Gouy phase gradient of the Gaussian beam (−2.78 rad/mm). Even if the gas nozzle is placed one Rayleigh length away from the laser focus, the difference in the Gouy phase gradient is still below 15%.
Fig. 4 Simulated Gouy phase gradient for the experimentally observed focal spot sizes. The blue shaded area indicates the beam waist of the focused beam.
Afterwards, the wave vector mismatch due to dispersion of the partially ionized gas has been analyzed. A very important parameter to control the dispersion is the phase matching pressure [29]. Therefore, the phase matching conditions for the HHG have been optimized for both cases separately, by experimentally maximizing the integrated photon flux of the 11th harmonic at 26.6 eV. This was done by iteratively optimizing the target gas density, the position of a gas jet as well as the outer diameter of the beam (by moving a water-cooled pinhole in the divergent beam of the telescope). The optimum phase matching pressure applied to the nozzle, for both cases, is 3.1 bar with argon as a generating gas. While the optimum pulse energies (intensities) are 72 µJ (3.2⋅1014 W/cm2) and 67 µJ (3.4⋅1014 W/cm2) for Gaussian and annular beam, respectively. Note that due to the similar intensity of both beams, the ionization rate has to be similar too, resulting in the same phase matching pressure. Therefore, a similar wave vector mismatch due to the dispersion of the generated plasma is given.
Simulations for the optimal phase matching gas density in the interaction region based on the model presented by Constant et al. [28] reveal a target gas density of 1.8⋅1019 cm−3, and therefore, an absorption length of 16 µm. This results in a distance of the beam to the gas nozzle orifice to be 15 w0 (with w0 being the 1/e2 beam radius) [32]. Consequently, the medium length of >270 µm, defined by the diameter of the nozzle, and a confocal parameter of 686 µm allow for absorption limited HHG (lmed>3 labs) [28].
The resulting experimental spectra covering the 9th and 11th harmonic, generated with a Gaussian and an annular beam are shown in Fig. 5. The spectra are normalized to the peak counts of the 11th harmonic at 26.5 eV generated with a Gaussian beam. Both beams have a similar divergence (6.1 mrad for a Gaussian beam and 6.5 mrad for an annular beam (1/e2), which is due to the difference of the focal spot sizes of the driving laser) and the same spectral shape with a relative linewidth (FWHM) of the 11th harmonic of ΔE/E = 1.8⋅10−3.
Fig. 5 Normalized spectra for the harmonics generated with an annular (blue) and a Gaussian beam (red). The inset shows the spatial lineout of the 11th harmonic at 26.6 eV, while the blue and orange line correspond to annular beam measurements with and without a separation pinhole.
Overall, the pulse length (235 fs) and the repetition rate (50 kHz) are kept constant for both conditions. Additionally, the focal geometry has been shown to be similar. At last, the separate optimization of the phase matching pressure and the driving pulse energy (by shifting the movable pinhole) results in the same phase matching pressure, as well as a spectral and spatial equality of the generated XUV radiation. Therefore, this shows that the phase matching conditions for both beams are similar.
6. Efficiency penalty of the annular beam method
A major difference in the two spectra is found only in the height of the peak counts, which is clearly visible in the in the linearly scaled inset of Fig. 5 (red and blue lineouts). Therefore, the power contained in the 11th harmonic was analyzed by taking the detection and quantum efficiencies of the used CCD camera (supplied by the manufacturer), the diffraction efficiency of the grating, the measured filter transmission, the reflectivity of the GIPs, the reabsorption due to the residual gas in the chamber and spatial cutting of the beam at the grating into account (for detail see [33]).
The power measurement of the 11th harmonic has been done in four sets of 150 measurements per set, while the time between two measurements was 2 s, resulting in an overall measurement time of 20 min per beam. Between each set, the setup was changed from a plane mirror to a drilled mirror and vice versa and the photon flux was maximized as described before. This was done in order to prevent any uncertainties concerning the alignment of the drilled mirror and the position of the gas jet.
The results of these measurements are shown in Fig. 6, while the dashed lines show the mean of all values and the shaded area denotes the statistical error of the measurements by means of the standard deviation. Notable is the robustness of the setup, since the mirrors were changed after each set and the optimization was done from the beginning, it shows that the setup was operated reliably at optimized conditions.
The resulting mean average power for the high harmonic generation with a Gaussian beam is (106 ± 6) µW and with an annular beam is (71 ± 3) µW. Corresponding to (67 ± 7) % of the XUV power, when the plane mirror is replaced by the drilled mirror. The conversion efficiencies of the two different methods into the 11th harmonic at 26.6 eV are (2.9 ± 0.2)⋅10−5 and (2.1 ± 0.2)⋅10−5 for a Gaussian beam and an annular beam, respectively. This results in a (27 ± 13) % lower conversion efficiency of HHG when the annular beam method is applied.
A reason for this lower efficiency might be the 13% smaller generation volume of the annular beam driven HHG. Note that this difference is supported by the measurement of the driving pulse diameters, as well as by the different divergence of the XUV beams. Furthermore, the changes of the transversal beam profile of the annular beam during the propagation through the generation medium also contribute to the efficiency penalty.
In case of HHG with an annular beam a simple pinhole can be used to separate the XUV light and the driving laser. For a perfect separation, the divergence of the XUV light needs to be smaller than the divergence of the inner edge of the driving laser. With a divergence of 5.8 mrad of the inner ring and a divergence of 6.5 mrad of the XUV radiation this condition is not fully fulfilled in our particular experiment. Therefore, the used pinhole (diameter of 1 mm) cuts (14 ± 0.1) % of the power of the XUV beam. Nevertheless, we observe a nice XUV beam profile (a cross section is shown as the orange line in the inset of Fig. 4), generating a useful photon flux of (61 ± 10) µW in the interaction region. Compared to applying GIPs, with a measured XUV transmission of (53 ± 4) % and a useful photon flux of (56 ± 7) µW, the presented method still yields a higher useable photon flux.
7. Conclusion and outlook
In summary, it is shown that absorption-limited HHG is possible with an annular beam with similar phase matching conditions as for a Gaussian beam. In this particular case, the resulting conversion efficiency is only (27 ± 13) % lower compared to the case of a Gaussian beam. Furthermore, the spectral and spatial properties of the XUV radiation of HHG with an annular and a Gaussian beam are very similar. In combination with a simple pinhole this method can be used to efficiently separate the generated XUV light from the driving laser beam. For the parameters used in this experiment this separation method yields a higher usable XUV average power of (61 ± 10) µW compared to (56 ± 7) µW using GIPs.
The main advantage of the annular beam approach is its enormous flexibility. It is independent of the driving wavelength and spectral bandwidth, which is especially important for few-cycle pulses that can have an octave-spanning spectrum [34,35], enabling higher conversion efficiencies as well as the generation of isolated attosecond pulses. Furthermore, there is a great power scaling potential of this method up to the multi-kW level which is difficult to be reached by other methods due to heating of the employed separation optics.
The full potential of the presented method will be exploited for harmonics in the soft X-ray regime with much smaller divergence compared to the driving laser. Figure 7 shows the calculated divergence from 20 eV to 300 eV (assuming the same focal spot size of 6 µm for all generated photon energies). This would result in no spatial cutting of the XUV beam at photon energies above 50 eV for the particular experiment presented in this paper. Finally, this method is easily applicable on existing HHG sources with a free focusing geometry, by placing a suitable annular beam shaper before the interaction zone and by putting a pinhole in the plane where the shaper is imaged with the focusing element.
Funding
Federal State of Thuringia (2015 FGR 0094); European Social Fund (ESF); German Ministry of Education and Research (BMBF) (05P15SJFFA).
Acknowledgements
RK acknowledges support from the German Science Foundation DFG, IRTG 2101.
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