1. Introduction

Enhancement of HHG in gaseous media as a result of atomic and ionic resonances has been the subject of extensive theoretical work over the last ten years [1–5]. The most significant experimental results in this field were, however, reported for HHG in plasma plumes. Weakly-ionized plasmas from some solid targets displayed resonances in the excitation of neutrals at certain harmonic wavelengths [6–8]. These experiments also showed that singly charged ions can enhance the yield of specific harmonics. As a much wider range of solids are available compared with gaseous target materials, HHG studies in plasma plumes dramatically increase the chance of finding an ionic transition, which is resonant with a harmonic wavelength.

Several mechanisms explaining the origin of resonant harmonics in laser-produced plasmas have recently been proposed [9–13]. In [9], it was shown that the influence of atomic autoionizing states on the phase matching of HHG in calcium plasma may result in efficient selection of a single harmonic. This was the first report of efficient high-order harmonic selection by autoionizing states. The four-step model, developed in [10], predicts the enhanced generation efficiency for the harmonic resonant with the transition between the ground and the autoionizing state of the ion. In this model, the third (recombination) step of the three-step model of HHG [14,15] is divided into two steps: the capture of a laser-accelerated electron into an autoionizing state of the parent ion, and the relaxation of this state to the ground state accompanied by the emission of a harmonic photon.

It was found by Milošević [12] that the laser intensity dependence of the intensity and phase of the single harmonic generated in the resonant HHG from plasma ablation is different than that of the standard plateau and cutoff high harmonics. The resonant harmonic intensity increases continuously (i.e., without rapid oscillations) with the increase of the laser intensity, while the resonant harmonic phase is almost constant. Such unusual for HHG behaviour of the harmonic phase requires a detailed experimental investigation. Namely, the harmonic phase dependence is important for synchronization of high-order harmonics. The importance of the results [12] was highlighted by the recent reconstruction of a train of attosecond pulses produced through HHG in an ablation plasma [16]; the group of odd harmonics responsible for the pulse train encompassed a resonant harmonic. In order to understand HHG in the presence of such a resonance, a time-frequency analysis was performed in [13]. Consistent with the predictions of the four-step model [10], it was found that the resonance gives rise to a single harmonic in the HHG spectrum.

Resonant enhancements in HHG from metal and semiconductor targets ablated by picosecond pulses [17,18] have been previously studied using a single pump pulse at λ ≈800 nm. However, when HHG is driven by a two-color pump scheme, emission spectra can display both odd and even harmonics, increasing the chance of a spectral overlap with an ionic resonance. Another promising route towards locating additional resonances is to tune the harmonic wavelength. This could be achieved by various methods: tuning the fundamental wavelength of laser pulse [7,19]; chirping the laser radiation [20–23]; altering the laser intensity to control the ionization rate of the nonlinear medium [24–27]; and adaptive pulse-shaping [28,29].

Previous studies of resonance-induced and two-color pump-induced enhancement of harmonics in laser plasmas were demonstrated using relatively low (10 Hz) pulse repetition rate laser sources [7,30]. Increasing the pulse repetition rate to 1 kHz considerably increases the average power of high-order harmonics [31], and allows improved statistics in experimental applications of the emission.

An attractive feature of resonant enhancement is that it can increase the conversion efficiency of a specific harmonic by more than an order of magnitude [17]. In this paper, we combine resonant enhancement with two-color pumping at 1 kHz pulse repetition rate to generate strong harmonics in different spectral ranges. This unique source will be ideal for various applications in physics, chemistry and biology, and for advancing nonlinear x-ray optics and attosecond physics.

2. Experimental setup

These experiments were performed using a 1 kHz Ti:sapphire chirped pulse amplification (CPA) laser (Red Dragon, KML Inc.) delivering 2.5 mJ pulses of 40 fs duration at 780 nm. In these experiments a portion (1.5 mJ, 20 ps) of the uncompressed pulse was split from the beam line prior to the laser compressor stage. This pulse was focused to an intensity of I_ps = 5 × 10⁹ W cm⁻² to 3 × 10¹⁰ W cm⁻² on the target using a f = 400 mm lens, as shown in Fig. 1 . The beam spot of the ablation laser was measured to be 0.4 mm at the target surface. The target was moved constantly up and down manually during these experiments.

 

Fig. 1 Experimental setup: HPP, heating pump pulse; FPP, femtosecond probe pulse; M, mirrors; VC, vacuum chamber; T, target; FM, focusing mirror; FFG, flat field grating; MCP, microchannel plate; CCD, charge coupled device.

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The compressed pulse (30 fs, 1 mJ) was focused into the plasma in a direction orthogonal to that of the picosecond pulse using a f = 200 mm mirror. The position of the focus with respect to the plasma plume was chosen to maximize the harmonic signal. The intensity at the focus of the femtosecond pulse was estimated to be I_fs = 5×10¹⁴ W cm⁻². The delay between plasma initiation and femtosecond pulse was varied in the range of 6 – 57 ns using an optical delay line. A flat-field grating (1200 lines/mm, Hitachi) and imaging microchannel plate (Photonis USA, Inc.) with a CCD camera were used to record the high-harmonic spectrum.

To drive HHG using two colors, the second harmonic (2ω) of the fundamental (ω) femtosecond pulse was generated using a 0.5-mm-thick BBO crystal in a type-I phase matching scheme. Group velocity dispersion between the ω and 2ω pulses in nonlinear crystal was compensated for using a calcite plate. The second harmonic conversion efficiency was 4%. HHG was enhanced by the presence of the 2ω field despite the 25:1 energy ratio between the ω and 2ω pulses.

The chirp of the femtosecond laser pulse was tuned by adjusting the separation of the two gratings in the CPA compressor. Only the wavelength at the leading edge of the pulse contributes significantly to HHG because at the intensity used the strong field induced plasma grows increasingly with time, eventually preventing HHG; thus the wavelengths of the high-harmonic comb from a chirped pulse can be controlled through this ionization gating effect [20,21,24,25]. We calibrated the chirp by measuring the spectrum, spectral phase, and pulse duration of the laser pulses as a function of grating separation using SPIDER [32].

3. Results

In this section we present the results of single- and two-color HHG studies using three different target materials: silver, chromium and vanadium. The used targets showed best stability at high pulse repetition rate among other materials, where resonance induced enhancement has previously been observed using the low (10 Hz) pulse repetition sources. The optimum delay between heating and driving pulses was found to be 40 ns for these three targets. Through the chirping technique, we are able to locate resonant enhancements of single odd, and in some cases even, harmonics.

Figures 2a and 2b show harmonic spectra generated in silver plasma in the cases of apertureless and apertured single color pump (780 nm). Harmonics above the 50^th order were routinely generated. Apertureless pump means the single color pump without introduction of aperture in front of input window of vacuum chamber. Apertured pump means that the 7 mm diameter pump beam propagates through the 4 mm aperture before entering the vacuum chamber. Introduction of 4 mm aperture on the path of driving radiation in front of vacuum chamber changed the relative distribution of harmonics from being stronger for lower orders in the case of apertureless beam (Fig. 2a) to stronger higher order harmonics in the case of apertured beam (Fig. 2b) due to the propagation effects changing the phase matching conditions for different groups of harmonics.

 

Fig. 2 Harmonic spectra from Ag plasma in the cases of (a) apertureless and (b) apertured single color pump (780 nm). (c) Tuning of 17^th and 19^th harmonics by changing the distance between the gratings in the compressor stage. Positive and negative values of pulse duration correspond to positively and negatively chirped pulses. Dotted lines show the tuning of 17^th and 19^th harmonics with different chirps. Black lines show the wavelengths of these harmonics at chirp-free conditions. Thick black lines on the left side of bottom graph show the tuning range of 17^th harmonic (2.8 nm).

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Variation of the laser chirp allowed a considerable tuning of harmonic wavelengths (2.8 nm in the case of 17^th harmonic, Fig. 2c), while the relative intensities of harmonics in the plateau region remained approximately the same over a broad range of the driving laser chirps, which led to variation of pulse duration in the range of −97 fs to +110 fs (positive and negative values of pulse duration correspond to positively and negatively chirped pulses). Note that effective tuning of harmonic wavelengths through chirp can be achieved only for broadband pulses, where a pronounced difference in the wavelength components at the leading and trailing parts of the pulse can be produced. The pulses used in our experiments have a bandwidth of ~40 nm FWHM. In the case of variable chirp conditions, the conversion efficiency decreased by a factor 6 in the case of 97 fs negatively chirped pulses compared with 30 fs chirp-free pulses.

The introduction of a second-harmonic field increased the conversion efficiency of odd harmonics, in agreement with previous studies in gaseous [33–38] and plasma targets [39]. The conversion efficiency of the harmonics in the long wavelength range of plateau was almost two times stronger in the case of two-color pump compared with the single-color pump. In the case of the silver plasma, we also observed strong even harmonics, at the same intensity as the odd ones (Fig. 3a ), which extended into the cutoff region in some cases, as seen in Fig. 3b. Tight focusing (f = 200 mm) led to much stronger odd harmonics than even harmonics, as seen in Fig. 3c, while the application of the 500 mm local length lens for the focusing of driving radiation in to the plasma increased the intensity of the even harmonics (Fig. 3d). Application of shorter focal length lens increased the intensity of second harmonic field in the plasma area, and at the same time decreased the overlapping of two beams in the plasma area thus decreasing the influence on the overall dynamics of two-color field HHG.

 

Fig. 3 (a) Harmonic spectra from Ag plasma using the two-color pump configuration. (b) Optimization of even harmonics with regard to the odd ones in the cutoff region. (c) Harmonic spectra using 200 mm focal length focusing mirror. (d) Harmonics spectra using the 500 mm focal length lens.

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An interesting feature of the spectrum in Fig. 3a is the enhanced even (20^th) harmonic compared with neighboring even harmonics, although this enhancement (2×) was not as pronounced as those previously reported in studies of single odd harmonics from some plasmas [17]. No spectral line was identified from the NIST tables in this part of the spectrum, but the behavior was similar to resonance enhancements in other metal plasmas. One can note that this ionic line appeared along with harmonic spectra at stronger excitation of silver target.

The resonance-induced growth of a single even harmonic motivated us to search for improvement of harmonic yield in two additional media, chromium and vanadium, which have already displayed enhanced properties using low pulse repetition rate (10 Hz), narrowband (10 nm) laser sources [40,41].

We identified two regimes for HHG in chromium plasma displaying different spectral features. For a weak excitation of the target, a cutoff was observed at 31.2 nm (E = 39.74 eV, 25H). With increased target excitation and increased femtosecond pulse intensity inside the plume by moving the plasma towards the focus of 780 nm radiation, a second plateau appeared with strong 27^th and 29^th harmonics, and the cutoff was extended toward the range of E = 58.81 eV (37^th harmonic). For zero-chirp the 27^th and 29^th harmonics were approximately equal in intensity. Varying the laser chirp changed the relative intensities of these two harmonics, while the intensities of the other harmonics remained approximately the same. As the chirp was varied and the pulse duration vas changed from +114 fs to −92 fs, the intensity of 27^th harmonic considerably increased (15×), while the 29^th harmonic became weaker, as seen in Fig. 4a . This is because the 27^th harmonic (λ = 28.88 nm, E = 42.91 eV for zero-chirp) is shifted towards the ionic resonance. The presence of such a resonance is confirmed by over-exciting the chromium plasma; the ionic line can be seen at the blue side of 27^th harmonic on Fig. 4b.

 

Fig. 4 (a) Harmonic spectra from chromium plasma at different chirps of laser radiation. Positive and negative values of pulse duration correspond to positively and negatively chirped pulses. (b) Harmonic spectrum at over-excited conditions of Cr plasma formation, with ionic lines appearing close to the enhanced 27^th and 29^th harmonics. The arrow shows one of these lines close to the 27^th harmonic.

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The meaning of “weak” excitation stays for intensity of heating pulse on the target surface below 1×10¹⁰ W cm⁻². In that case, chromium plasma emission shows only spectral lines from excited neutrals and singly charged ions. With increase of intensity (≈2×10¹⁰ W cm⁻² - 3×10¹⁰ W cm⁻²), the doubly charged ions appear in the plasma plume, which led to their involvement in harmonic generation. Over-excitation of plasma at these conditions means even stronger heating of target when high concentration of free electrons appearing during laser ablation causes the phase mismatching of HHG.

These results are consistent with other HHG studies in Cr plasma, which also displayed a variation in the 27^th harmonic intensity for different chirps [40]. In those studies, the 27^th harmonic almost disappeared from the harmonic spectra, and a strong 29th harmonic was observed for zero-chirp. The experiments in [40] were performed using 800 nm laser pulses, so the 29^th harmonic was closest to the resonance.

Calculated gf values at photon energies range of 40–60 eV (λ = 20.66 – 31 nm) clearly show a group of transitions from 44.5 to 44.8 eV with very strong oscillator strengths (gf between 1 and 2.2; the gf value is the product of the oscillator strength f of a transition and the statistical weight g of the lower level.) [42]. These transitions are much stronger than those in the range of 40 – 60 nm, and are likely to be responsible for the enhancement of the 27^th and 29^th harmonics we observed in our experiments. Furthermore, strong photoabsorption lines within the 41–42 eV region reported in [42] could decrease the yield of the 25^th harmonic.

Two-color pumping revealed that the resonance ionic line similarly impacts the efficiency of even harmonic generation. Figure 5a shows that even harmonics between the 24^th and 26^th orders (38.15 – 41.33 eV) almost disappeared when chirp-free pulses were used, while the 28^th harmonic (44.50 eV) was much stronger (5×) than the lowest order harmonics and almost equal in intensity to the enhanced odd ones. The efficiency with which some high harmonics were generated was two times greater for two-color pumping than for single-color pumping, as seen in Figs. 5a and 5b in the case of the 15^th to 17^th harmonics. The removal of crystal led to the spectral distribution presented in Fig. 5b, which is similar to Fig. 4b, excluding the stronger 27^th harmonic compared with 29^th one. This was related with better resonance-induced enhancement of 27^th harmonic in the former case.

 

Fig. 5 (a) Two-color pump-induced spectra of harmonics from Cr plasma and (b) the spectra obtained at analogous experimental conditions by removing the SH crystal from the path of 780 nm radiation.

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Finally, we present the results of HHG studies using vanadium plasma. In previous studies, the conversion efficiency in the plateau range of the harmonics of 800 nm radiation was 1.6×10⁻⁷ [41]. Those plasma emission spectra measurements and calculations of the ionization conditions and harmonic cutoffs in the laser-ablation plume showed that the higher harmonics originated from the interaction of the femtosecond laser pulses with doubly charged vanadium ions, which allowed generation of harmonics up to the 71^st order.

In our case, the dynamics of vanadium harmonics variations was the same as in the case of chromium plasma once the chirp and corresponding redistribution of laser spectrum along the pulse caused the tuning of harmonic wavelength. Only low-order harmonics (up to the 23^rd order) were obtained when the V target was weakly excited (I_ps = 6×10⁹ W cm⁻², Fig. 6a ). With a stronger excitation (I_ps = 1×10¹⁰ W cm⁻²), the spectrum extended to higher energies, with the appearance of a “second plateau” beginning with a strong 27^th harmonic, as shown in Fig. 6b. Two-color pumping led to an increase in the harmonic yield (Fig. 6c), accompanied by the appearance of an enhanced (4×) 26^th harmonic (λ = 30 nm, E = 41.33 eV), which is attributed to the influence of a strong ionic transition at this energy. The background that appears in spectra of Fig. 6 is induced by a scattering from some stray light, which appeared from case to case during different alignments of our registration system.

 

Fig. 6 Variations of harmonic spectra at (a) weak excitation of V target (I_ps = 6×10⁹ W cm⁻²), (b) stronger excitation of target (I_ps = 1×10¹⁰ W cm⁻²), and (c) application of two-color pump.

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We have not yet identified the ionic transition responsible for this enhancement. The NIST database contains one relatively strong transition (3p⁶3d - 3p⁵(²P°)3d²(¹G); λ = 31.2 nm) in this spectral region for quadruply ionized vanadium, but it is unlikely that such a high level of ionization was achieved using our laser ablation parameters.

5. Discussion and conclusions

Our two-color HHG studies confirm previously reported spectral features in the vicinity of the 3p - 3d transitions of the Cr II ions [40] and reveal a strong even harmonic generated close to those transitions. The observed enhancement of the 28^th harmonic of the 780 nm pump (corresponding to the 14^th harmonic of 390 nm radiation) is attributed to the influence of these transitions, although it is not as pronounced compared with the 29^th harmonic of 800 nm radiation. The enhancement of the 27^th and 28^th harmonics from vanadium plasma can also be attributed to an overlap with ionic transitions. Although we were unable to identify these ionic transitions, the ionic lines were seen by over-exciting the target.

Calculations of harmonic enhancement for some plasmas, in particular for the chromium ion, can be found in [10,11]. The coincidence of the enhanced harmonics observed in our experiments with the giant 3p - 3d resonance implies the involvement of this transition in the enhancement. The resonant enhancement can also be considered from a macroscopic perspective. At resonance conditions, when the harmonic frequency is close to the atomic transition frequency, the variation in the wave number of a single harmonic could be large, and the influence of dispersion from free-electrons can be compensated by the atomic dispersion for a specific harmonic order [9]. In this case, improvement of the phase matching conditions for single harmonic can be achieved.

The target survived during multiple shots, without considerable modification of the surface. We constantly moved the target up and down, thus returning back to the same ablated area during multiple movements of the target. It follows that, once the ablation area stays at the same spot of target, the target surface became overheated, which can lead to the change of ablation conditions. When we moved the target by heating different spots, previous ablated areas cooled and returned to the initial conditions. This followed with the same HHG conversion efficiency once we return for ablation to the previously ablated spot. The rotation of targets could considerably improve the stability of plasma harmonics.

We would like to emphasize the importance of using high pulse repetition rate lasers for improving the average power of harmonics, which could be additionally enhanced in the presence of resonance effects and two-color field induced enhancement. This is a main motivation of present work and has been demonstrated for the first time.

From the point of view of optical technology where the average power of the XUV radiation may be critical the demonstration at a 1kHz is essential. So not only does the result ratify earlier findings but it paves the way to concrete applications. Some estimations show that, once usual non-resonant conversion efficiency is of order of ~10⁻⁶, with resonance this may be increased by an order of magnitude or higher (~10⁻⁵). So for a mJ class laser we expect at least 10nJ per pulse i.e. average power 10 microwatts of XUV at 1kHz, but only 0.1 microwatt at 10Hz. Present work is a further advancement in this field, which shows considerable improvement of the characteristics of plasma harmonics compared with results presented in [31].

In conclusion, we have studied HHG from laser-produced plasmas using three recently introduced techniques to improve the plasma harmonic yield: resonance-induced and two-color pump-induced enhancement, together with the application of a high repetition rate laser source. Together with an increased HHG output, we observed an enhanced yield of even harmonics compared with odd ones, and resonance-induced enhancement in the intensity of some single even harmonics when the ratio between the 780 and 390 nm pulse energies was 25:1.

Our novel high repetition rate source for resonance- and two-color-induced plasma HHG improved the average power of the emitted XUV radiation by two orders of magnitude compared with previous plasma HHG studies using 10 Hz lasers with equal pulse energy. This improvement will be useful both for investigating the temporal characteristics of the high-harmonics from laser plasma and for studying quantum path interference of long and short electron trajectories, both of which require large numbers of laser shots.

During our experiments, several new resonance-enhanced processes were revealed, mostly due to the modification of electron trajectories in HHG by the presence of a weak second harmonic field. This led to the generation of enhanced odd and even harmonics in different regions of the plateau. In particular, we observed an enhanced 20^th harmonic in silver plasma (2×), 26^th harmonic in vanadium plasma (4×), and 28^th harmonic in chromium plasma (5×). These results support theoretical predictions that the involvement of autoionizing states of atoms and ions will enhance nonlinear optical processes in the vicinity of a resonance [9,10]. Crucially, using broadband (40 nm) pulses for plasma HHG permitted tuning of the spectral position of the harmonic comb over a broad range (2.8 nm in the case of 17^th harmonic), thus allowing us to ensure that a particular harmonic coincided with the resonance wavelength of an autoionizing state.