Generation of 10 μW relativistic surface high-harmonic radiation at a repetition rate of 10 Hz

Experimental results on relativistic surface HHG at a repetition rate of 10 Hz are presented. Average powers in the 10 μW range are generated in the spectral range of 51 to 26 nm (24–48 eV). The surface harmonic radiation is produced by focusing the second-harmonic of a high-power laser onto a rotating glass surface to moderately relativistic intensities of 3 × 1019 W cm−2. The harmonic emission exhibits a divergence of 26 mrad. Together with absolute photon numbers recorded by a calibrated spectrometer, this allows for the determination of the extreme ultraviolet (XUV) yield. The pulse energies of individual harmonics are reaching up to the μJ level, equivalent to an efficiency of 10−5. The capability of producing stable and intense high-harmonic radiation from relativistic surface plasmas may facilitate experiments on nonlinear ionization or the seeding of free-electron lasers.


Introduction
The generation of high-order harmonics of high-power femtosecond laser pulses is the most prominent way to create extreme ultraviolet (XUV) coherent radiation and, at the same time, the shortest available pulse durations, i.e. attosecond pulses [1]. In the last decade, attosecond pulses produced by high-harmonic generation (HHG) in gases had a considerable impact on the development of experimental techniques in attosecond laser physics [2][3][4]. The efficiency of this HHG process is typically in the order of 10 −6 -10 −5 and has been the topic of a recent review [5]. However, many experimental approaches would benefit from higher photon fluxes or higher XUV pulse energies. Unfortunately, the process of HHG in gases cannot easily be scaled to higher XUV intensities and higher photon energies. Scaling the latter is largely limited by the ionization of the target gas [6], which defines an upper boundary for the intensity of the driving laser pulses. With increasingly powerful lasers, the photon flux can only be increased by using longer focal lengths. Applying this strategy, XUV pulses with energies of 1 µJ [7] up to 10 µJ [8] have been reported at a laser repetition rate of 10 Hz. This corresponds to a maximum average power of 100 µW [8]. An efficiency of HHG in gases of 10 −4 and sub-µJ harmonic pulse energies have been reported using an advanced scheme that combines loose focusing and two-color laser fields [9].
The inherent limitations of HHG in gases do not exist for relativistic surface high-harmonic generation (SHHG) because a fully ionized relativistic plasma is used, i.e. the full potential of the highest achievable laser intensities can be exploited. The laser pulses are focused onto a surface to an amplitude of the normalized vector potential of a 2 0 = (I · λ 2 )/(1.37 × 10 18 W cm −2 ·µm 2 ) 1, such that the surface electrons oscillate at relativistic velocities. Here, λ is the laser wavelength and I its intensity. For oblique incidence and p-polarization, the dominant process of energy transfer to the plasma occurs via the electric field component normal to the target surface. When the laser pulse is reflected at the relativistically oscillating plasma surface, its electromagnetic field is strongly modulated [10]. Accordingly, the reflected spectrum will contain high harmonics of the driving laser field. In the time domain, the harmonics correspond to a train of attosecond pulses. This simplified model of SHHG driven by a 'relativistically oscillating mirror' (ROM) [11] includes most of the essential physics. The spectral characteristics of the harmonic emission were predicted by an extended version of this model [12]. The efficiency of ROM harmonic generation in the ultra-relativistic limit a 0 1 follows the spectral power law η ∼ (ω/ω 0 ) −8/3 , which predicts high efficiencies, e.g. η = 10 −4 for the 30th harmonic. Such efficiencies would enable attosecond XUV sources with pulse energies orders of magnitude higher than the current state-of-the-art. In fact, using 3 ultra-relativistic intensities it has been shown that bright harmonics up to keV photon energies can be generated [13].
Apart from delivering relativistic intensities to the target surface, also a well-defined plasma density gradient is essential for the SHHG process. In order to achieve efficient SHHG with a low divergence, the main pulse needs to interact with a steep plasma density gradient [14]. This can be realized by suppressing those prepulses that are intense enough to ionize the target before the arrival of the main pulse, which typically implies the use of contrast enhancement techniques such as plasma mirrors [15] or nonlinear optical filters, see, e.g. [16,17]. Another practical issue for SHHG is the local destruction of the surface by each laser shot, such that a fresh surface of optical quality has to be provided for the next laser shot. For SHHG at nonrelativistic intensities, a rotating glass target with interferometric stabilization has been used at a repetition rate of 1 kHz [18]. However, relativistic SHHG, having more favorable properties like lower divergence [19] and higher photon energies [20], is harder to realize. As a consequence, previous experiments on ROM harmonic generation were performed in single-shot mode only.
We report on the demonstration of ROM harmonic emission performed at a repetition rate of 10 Hz using a computer-controlled rotating glass surface. A divergence of 26 mrad has been measured for the ROM harmonics emission in good agreement with previous results. The XUV emission was recorded using a calibrated spectrometer [21] thus enabling an absolute determination of the harmonics pulse energy and efficiency. We report on harmonic pulses with µJ energies and efficiencies of 10 −7 -10 −5 leading to an average power of >10 µW for the observed XUV harmonic emission. Surface high-harmonic radiation is thus becoming a competitive source in terms of pulse energy.

Experimental setup
The experiment was carried out at Friedrich Schiller University Jena using the Ti:sapphire laser system 'JETI-40', which provides 30 fs pulses with an energy of 0.7 J at a 10 Hz repetition rate. Figure 1 displays the experimental setup. For reasons of contrast enhancement the laser pulses are frequency doubled using a 0.7 mm thick potassium dihydrogen phosphate (KDP) crystal. As SHHG requires horizontal polarization [10] and since type-I phase matching is used for secondharmonic generation (SHG), the polarization of the fundamental laser pulse is first rotated to vertical orientation using a half-wave plate. In order to optimize the horizontal alignment of the polarization and the pulse energy of the second harmonic, the angles of the wave plate and the KDP crystal are fine-tuned. To this end the polarization of the generated 400 nm pulses is adjusted to horizontal orientation by aligning the crystal axis and then SHG is optimized in terms of conversion efficiency by fine-tuning the fundamental's polarization using the half-wave plate.
Two multilayer mirrors, which are highly reflective for 400 nm and anti-reflective for 800 nm, are used in order to suppress the fundamental (800 nm) pulse intensity by more than a factor of 10 5 . The 400 nm pulses are focused onto a fused silica target (<1 nm root mean square (RMS) roughness) at 45 • angle of incidence in p-polarization by an f/2 off-axis aluminum parabola. By imaging the focus of the frequency doubled pulses using a microscope objective (see figure 1(b)), it is found that 29% of the entire pulse energy of up to 100 mJ is contained in the focal area of 3.6 µm 2 (enclosed by the contour line of the full-width at half maximum (FWHM)). Based on the analysis in [22], where the preservation of the pulse duration for transform limited pulses in thin crystals has been shown, the pulse duration of the second harmonic is estimated to be equal to the pulse duration of the fundamental. This results in a peak intensity on the glass target of ≈2.7×10 19 W cm −2 (a 0 ≈ 1.8). The fused silica target is rotated and translated by a remote-controlled motorized mount in order to provide a fresh surface for each laser shot. The distance of the glass surface from the focus is adjusted using a micrometer screw. It is maintained within a range of 10 µm as the target rotates. An additional vertical motion of the target is used to exploit the entire target area. In the present setup, the respective tilt in vertical direction cannot be adjusted and has to be compensated by moving the whole target rotation stage in the beam direction.
The nonlinearity of the SHG process results in an enhancement of the original laser pulse contrast. Using the measured dependence of SHG conversion efficiency on pulse energy, the pulse contrast at 400 nm can be computed as shown in figure 2. At 10 ps before the arrival of the main pulse, a reduction of the relative prepulse intensity to 10 −10 is achieved, which has to be compared to the initial relative prepulse intensity level of 10 −6 . The overall pulse contrast, consisting of the contrast of the 400 nm pulses and the residual intensity of the fundamental, is comparable to the contrast available for a recent experiment on relativistic SHHG using a single-pass plasma mirror [15,23]. One result of that experiment has been the confirmation that a pulse contrast of such quality is a prerequisite for stable surface HHG [14].
The harmonic emission is measured in the specular direction using two different spectrometer setups. A flat-field grating spectrometer is used to determine the divergence of the harmonic beam (figure 3). In this configuration, the incident XUV radiation is dispersed using a 1200 lines mm −1 grating [24] and detected by an XUV camera (back-thinned  Andor DO940N). In the horizontal plane, the XUV emission is recorded with an acceptance angle of 12 mrad. Therefore, the divergence can only be estimated based on the fraction of the harmonic beam that is collected by the spectrometer's aperture [19]. A larger angular range of ∼50 mrad is measured by scanning the harmonic beam over the aperture. This is realized by translating the focusing parabola and thus tilting and translating the centroid beam with respect to the optical axis of the spectrometer. The angular distributions of the 12th to 15th harmonics show a uniform divergence of ∼26 mrad (figure 3), which is a consequence of the spatial denting of the plasma surface due to the ponderomotive force [25].
In a second spectrometer setup, an XUV spectrometer ( figure 1(c)), which was previously calibrated with respect to the incident photon flux [21], was used. Two 0.2 µm aluminum foils located at the entrance aperture of the spectrometer block the intense visible radiation. The transmitted XUV emission [26] is imaged by a nickel-coated toroidal mirror onto the CCD camera. A transmission grating consisting of freestanding gold bars with 1000 lines mm −1 is used to disperse the XUV radiation. The harmonics' energy is determined by taking into account the filter transmission, the absolute sensitivity of the spectrometer [21] and the fraction of the surface harmonics that enters the spectrometer aperture.

Experimental results
We recorded SHHG spectra for every laser pulse at a repetition rate of 10 Hz. 250 subsequent spectra taken over a period of 25 s are displayed in figure 4(a). Each line represents a single spectrum reaching from the 8th up to 15th harmonic of the 400 nm driver laser field. It should be noted that harmonics with frequencies lower than the plasma frequency can also be produced by the nonrelativistic mechanism of coherent wake emission (CWE) [27]. For the fused silica targets used, the maximum plasma frequency is approximately situated at the 10th harmonic and constitutes the cutoff frequency for CWE harmonics [28]. Consequently, higher harmonic orders must be produced by the ROM process. The fact that there is no significant change in divergence or efficiency around the 10th harmonic order suggests that the ROM is the dominant process for all the harmonics observed at our conditions. Nevertheless, the CWE mechanism might contribute to the 8th and 9th harmonic orders as we also recorded these orders at nonrelativistic intensities. In fact, the efficiency of 10 −5 (table 1) conforms to the discussion given in [27].
The spectral energy distribution averaged over all 250 spectra consists of harmonic lines and a broad XUV background signal as shown in figure 4(b). It is worth mentioning that the double-peak structure in the harmonic spectra is evidence of a spectral modulation owing to the generation of unequally spaced attosecond pulses [23]. This effect arises from the superposition of the ROM process and a temporal denting of the plasma surface due to the radiation pressure at relativistic intensities.
We have calculated the stability of ROM harmonic generation based on the data set of 250 spectra. A relative deviation of ∼30% for the SHHG intensity and <10% for the background Table 1. An analysis of the 250 spectra presented in figure 4 reveals pulse energies of µJ for individual harmonic lines thus yielding an efficiency of 10 −5 and an average power of the order of 10 µW. The analysis of a ROM spectrum from single shot operation under optimized conditions shows a difference of half an order of magnitude. 10 Hz average Optimized single shot Monitoring and positioning the target surface in a closed loop will lead to a substantial increase in stability. The determination of SHHG efficiency requires subtraction of the background XUV spectrum. We measure a total XUV background yield of 0.4 µJ in the spectral range covered by the spectrometer. Integration of individual harmonics of the background-free spectra yields harmonic energies up to microjoules. A detailed list is given in table 1. It should be noted that for the computation of the efficiencies only that fraction of energy of the driving 400 nm pulse is taken into account that is focused to a normalized vector potential of a 0 1 and thus can be considered to be relevant for the ROM mechanism 6 . For the measured focal intensity distribution shown in figure 1(b), 39 mJ of the frequency doubled pulse energy fulfills this condition. The energies for the harmonics in the spectral range of 24 -48 eV result in a total average power of 12.3 µW for the observed ROM harmonic emission. The efficiencies at our conditions are of the order of 10 −5 -10 −7 . Selected laser shots from single shot operation, however, produce considerably higher pulse energies and efficiencies, cf figure 4(b) and table 1. An obvious conclusion is that there exists a significant potential for further optimization. Nevertheless, it has to be admitted that the efficiency of ROM harmonics under the present conditions falls behind expectations created by theoretical results valid in the ultra-relativistic limit. Apparently, the ROM is only at the onset of being driven efficiently to the relativistic regime.

Conclusion
In conclusion, we demonstrate the first consecutively measured relativistic surface HHG at a repetition rate of 10 Hz. This establishes a compact source of high-intensity XUV pulses from relativistic laser plasma interaction with a repetition rate that is suitable, e.g., for experiments on nonlinear photoionization. The ROM harmonic source has been characterized with respect to the beam divergence, XUV pulse energy and efficiency. At the moderately relativistic intensities used in this experiment, the ROM harmonic emission is at the brink of being capable of competing with HHG from gaseous media in terms of efficiency. There is, however, quite some potential for improvements. In the presented setup the plasma scale length is estimated by the SHG pulse contrast. In order to control and optimize the scale length with respect to harmonic energy, prepulses and different contrast enhancement techniques could be applied. Furthermore, the focal spot could be significantly improved using adaptive optics or a KDP crystal with a higher optical quality. The latter is also capable of increasing the conversion efficiency and energy of the SHG pulses.