1. Introduction

Frequency conversion processes significantly extend the spectral region accessible by lasers. This holds in particular true for short wavelengths towards the regime of vacuum-ultraviolet (VUV) or even extreme-ultraviolet (XUV) radiation. Such short wavelengths find a large number of applications, e.g. in spectroscopy, microscopy, lithography or the generation of ultra-short radiation pulses in the sub-femtosecond domain. Typically, highly nonlinear interactions of gaseous atomic media with intense ultra-short laser pulses are applied to generate XUV radiation. However, the efficiency of harmonic generation in low density gaseous media is rather small, rarely exceeding the regime of 10⁻⁸ to 10⁻⁴.

Excitation of atomic resonances exhibits a simple way to enhance conversion efficiencies. The basic idea is straightforward: The driving laser is tuned to an atomic resonance (usually a multi-photon resonance, e.g. with n photons from the driving laser involved). The resonance enhances the nonlinear susceptibility χ⁽ⁿ⁾ of order n. If permitted by selection rules, this supports generation of the n-th harmonics of the driving laser or frequency mixing processes with m additional photons from the same laser field, e.g. generating harmonics of order (n + m). Such resonantly-enhanced frequency conversion is well known from low-order frequency conversion processes, driven by lasers of moderate intensities. As a simple example, we note resonantly-enhanced four-wave mixing in atomic gases. Here, a first laser pulse drives a two-photon transition, which serves to resonantly enhance a sum or difference frequency mixing process with a second laser pulse. However, it is not obvious, that resonance-enhancement also works for (higher) harmonic generation, driven by high-intensity ultra-short laser pulses. The strong electric field of the laser significantly perturbs the level structure of the medium and may destroy any resonance effect in conversion processes.

From this simple consideration it becomes clear, that resonantly-enhanced harmonic generation with ultra-short pulses may be efficient, if the driving radiation field is on one hand sufficiently strong to drive (higher) harmonic generation – and on the other hand the field is still not too strong to destroy the resonance structure of the medium. In the terminology of high intensity laser-matter interactions and photoionization, we require operation in the regime of “multi-photon ionization” rather than “tunneling ionization” [1,2]. This choice provides appropriate conditions to observe pronounced resonance effect. The restriction towards not too strong laser intensities still enables a large range of applications – and the possibility to exploit resonances for efficient harmonic generation. We note, that proper investigation and application of resonance effects also requires tunable lasers and moderate frequency bandwidth (i.e. not too short pulse durations) to properly address isolated atomic resonances.

In recent years there already have been some (but still quite few) experimental investigations of resonance enhancements in harmonic generation via bound atomic states. As early examples, we note the work by L’Huillier et al. [3] and Toma et al. [4]. The authors observed enhancement of particular harmonics for specific laser intensities, e.g. an increase in the yield of the n-th harmonic by exciting a dynamically shifted n-photon resonance. We also note work by Barkauskas et al. [5], aiming at the development of a sophisticated laser system to provide intense, rather long laser pulses (duration 300 ps) with small frequency bandwidth and spectral tunability in the near infrared. In an application of the laser system for high harmonic generation, the authors found enhancement of harmonics for appropriate choice of the driving laser wavelength. The authors suggest, that phase matching effects or multi-photon resonances may lead to these enhancements. However, no definite explanation was given. Finally we mention a sequence of experiments by Ganeev et al. on pronounced enhancement of single harmonics in laser-driven plasmas (for a summary of these experiments see ref [6].). The authors explain the enhancement by dynamically-shifted ionic resonances close to specific harmonics. However, in most of the above experiments resonance effects were scarcely investigated systematically nor fully understood in detail. Moreover, in most cases only single harmonics were enhanced, while excitation of n-photon resonances should also affect harmonics with order larger than n [7–10].

In the following, we present systematic investigations of resonantly-enhanced harmonic generation, involving observations of dynamic (Stark) shifts, and simultaneous enhancement of several harmonics with order higher than the resonantly-driven multi-photon transition. To address single atomic resonances, in our experiments we apply intense pulses with quite short pulse duration in the regime of 1 ps, sufficient spectral resolution (small bandwidth) well below 1 nm, as well as center wavelength in the visible regime. The latter permits us to proceed already with lower-order frequency conversion processes quickly towards the XUV.

2. Coupling scheme and experimental setup

Figure 1 shows the coupling scheme and relevant energy levels in a jet of Argon atoms. We tune intense, picosecond laser pulses in the vicinity of the five-photon resonance 3p^{6 1}S₀ → 4s’ [1/2]₁ at 95400 cm⁻¹, corresponding to a fundamental laser wavelength of 524 nm. In the experiment we observe resonantly-enhanced fifth harmonic generation of the driving laser radiation as well as harmonics of higher order (indicated by dashed arrows in the figure).

 

Fig. 1 Coupling scheme in Argon atoms with relevant energy levels. The short designation (5p/5p’) indicates the manifold of closely spaced states 5p’ [3/2]₂, 5p [1/2]₀, 5p [3/2]₂ and 5p [5/2]₂. Full arrows depict the driving laser at 524 nm, dashed arrows indicate the 5th, 7th and 9th harmonics, as investigated in the experiment.

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The experimental setup is as follows (see Fig. 2 ): A titanium:sapphire oscillator (MIRA 900P, Coherent), pumped by a frequency doubled, continuous-wave Nd:YAG laser (VERDI V18, Coherent), generates laser pulses with a pulse duration of 1.2 ps (full width at half-maximum, FWHM). The pulse train synchronously pumps an optical parametric oscillator (OPO) with intracavity frequency doubling (OPO automatic, APE GmbH). The setup provides tunable (ps) radiation pulses in the visible regime, with linear polarization, pulse duration of approximately 1.4 ps (FWHM), and spectral bandwidth close to the Fourier transform limit. The average output power of the OPO is 100 - 200 mW, corresponding to pulse energies around 2 nJ, at a repetition rate of 76 MHz.

 

Fig. 2 Schematic representation of the experimental setup with some details of the home-made, four stage (S1-S4) dye amplifier chain. (BS: beam sampler, VBS: variable beam splitter, CL: cylindrical lens, PM: power meter).

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The picosecond pulse train propagates into a home-made four-stage dye amplifier chain (see Fig. 2), pumped by the third-harmonic frequency of a pulsed, injection-seeded Nd:YAG laser (Pro 230-20, QuantaRay). The pump laser provides pulse energies of approximately 350 mJ at 355 nm, with pulse duration of 8 ns at a repetition rate of 20 Hz. The dye amplifier chain essentially consists of two transversally and two longitudinally pumped dye amplifier stages. For the experiments discussed below, we operated the first and second stage of the dye amplifier with Coumarin 540, solved in a mixture of dioxane and ethylene glycol. In the third and fourth stage we used Coumarin 504, solved in methanol. The four-stage dye amplifier chain permits amplification of tunable, visible picoseconds pulses with output pulse energies up to 2 mJ. The duration of the amplified pulses is (1.45 ± 0.25) ps (FWHM) with a bandwidth close to the Fourier-transform limit (as determined by measurements in a home-made setup for frequency-resolved optical gating (FROG)). In the experiment, we focus the laser beam by an achromatic doublet (focal length f = 150 mm) into a pulsed gas jet of Argon atoms. The diameter of the picosecond laser beam in the interaction region is approximately (18 ± 4) μm (FWHM). This yields intensities up to 100 TW/cm² (peak intensity, assuming a spatial Gaussian and a temporal sech² intensity envelope).

The harmonics, generated in the gas jet propagate into an evacuated monochromator (VM502, Acton Research, maximal resolution Δλ = 0.1 nm). The monochromator separates the harmonics and directs them onto an electron multiplier tube (EMT R595, Hamamatsu) for detection. In parallel to acquisition of harmonic spectra, we carefully monitor the laser pulse energy and the spatial beam profile to guarantee stable conditions in the interaction volume.

3. Experimental data and discussion

To spectroscopically identify the relevant multi-photon transition 3p^{6 1}S₀ → 4s’ [1/2]₁ at 95400 cm⁻¹ in Argon, we monitored the intensity of the fifth harmonic frequency when tuning the wavelength of the driving picosecond laser pulse. Figure 3 shows such spectra, obtained for different laser intensities. For rather small intensity of approximately 5 TW/cm², the obtained signal intensity at the fifth harmonic is still quite low. The spectrum shows an isolated peak (i.e. resonantly-enhanced fifth harmonic generation) at a laser wavelength of 525 nm (marked by an arrow in Fig. 3), corresponding to a fifth harmonic wavelength of 105 nm.

 

Fig. 3 Yield of the fifth harmonic vs. driving laser wavelength for different laser intensities. Raw data after averaging 20 laser shots and low pass filtering. For better visibility, the harmonic yields for laser intensities at 5 TW/cm² and 20 TW/cm² are scaled up by factors of 80 and 10, respectively. The arrow in the graph for lowest intensity at 5 TW/cm² indicates the spectral position of the five-photon resonance 3p^{6 1}S₀ → 4s’ [1/2]₁.

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This fits well with the expected transition wavelength at 104.8 nm – in particular taking the resolution of our spectrometer, the laser bandwidth of (0.6 ± 0.1) nm and AC Stark shifts (which we ignored for this “small” intensity) into account. Thus, we can clearly assign the observed feature at 525 nm to the five-photon resonance 3p^{6 1}S₀ → 4s’ [1/2]₁. However, we also observe quite strong fifth harmonic signal in a broad wavelength regime around 510 nm. We attribute this to a resonantly-enhanced difference frequency mixing process via highly excited states. In the photon picture this can be understood as a six-photon transition up from the ground state 3p^{6 1}S₀ to the closely spaced set of four highly excited states 5p’ [3/2]₂, 5p [1/2]₀, 5p [3/2]₂ and 5p [5/2]₂ and down with another photon from the same laser pulse. Also this “six minus one” mixing process yields signal at the fifth harmonic frequency. The spectral positions of the six-photon transitions to states 5p’ [3/2]₂, 5p [1/2]₀, 5p [3/2]₂ and 5p [5/2]₂ are expected at 506 nm, 510.4 nm, 512.0 nm and 512.8 nm. This fits well with the observed broad feature around 510 nm in the spectrum.

When we increase the laser intensity, the signal of the fifth harmonic quickly grows – as expected. Moreover, we also observe systematic shifts in the spectrum. At a laser intensity of (20 ± 9) TW/cm², the five-photon resonance 3p^{6 1}S₀ → 4s’ [1/2]₁ experiences a stronger Stark shift, moves towards shorter wavelengths and shows a line broadening. Moreover, the line seems to be slightly asymmetric now, with a longer tail towards shorter wavelengths. The shift, the line broadening and the asymmetry are all typical for the AC Stark effect. We note, that the Stark shifts are due to off-resonant couplings to all bound and continuum states in Argon, i.e. beyond the simplified two-level picture of states 3p^{6 1}S₀ and 4s’ [1/2]₁ only. As another interesting feature in the spectrum for an intensity of 20 TW/cm², we do not observe the difference-mixing process via six-photon resonances around 510 nm anymore. We also attribute this to an AC Stark effect, which shifts the six-photon transitions to shorter wavelength, i.e. outside the spectral region of observation. We note, that the five-photon resonance is energetically lower than the six-photon resonances. Thus, the Stark shifts should be even stronger for the latter. We could not further investigate the shifts of the six-photon resonances with our laser setup, as the OPO permits output wavelengths longer than 505 nm only. However, this did not matter for our experiment, which deals with the clearly visible five-photon resonance.

When we further increase the intensity to (41 ± 18) TW/cm² and (61 ± 26) TW/cm², the shift and line broadening of the five-photon resonance becomes very pronounced. For the strongest intensity at 61 TW/cm² the five-photon resonance shifted by more than 15 nm. If we take the right shoulder of the spectral lines as an indicator for the strength of the shift and the peak of the line at lowest intensity of I = 5 TW/cm² as a reference (see arrow in Fig. 3), we roughly estimate Stark shifts in the range of 0.25 THz per TW/cm² laser intensity.

As already briefly indicated above, our experimental conditions are closer to the multi-photon regime than the tunneling regime. In this case, we can estimate the total Stark shift of level 4s’ [1/2]₁ by adding up contributions from off-resonant couplings to all other states. The relevant expression for the Stark shift of a state |i〉 is [11]: $S=-{\Sigma }_j{\Omega }_{ij}^2/2{\Delta }_{ij}$, with the coupling Rabi frequency Ω_ij between state |i〉 and the manifold of all other states |j〉, as well as the detuning of the laser from the transition frequency ω_ij. We note, that the sum in the expression for the Stark shift is infinite and also includes continuum states. For a first estimation, we calculated the Stark shift of level 4s’ [1/2]₁ by taking off-resonant couplings to the 18 closest states in the 4p, 4p’, 5p, 5p’ manifold into account. The calculation yields the strongest contributions by off-resonant couplings to states 4p’. The latter off-resonant couplings push the level 4s’ [1/2]₁ to higher energy (i.e. shorter wavelength), as also observed in our experiment. The strength of the calculated Stark shift is about an order of magnitude larger than observed in the experiment. We expect this deviation, as in our simplified calculation we ignored contributions from excited states beyond the 5p, 5p’ shells. The higher states (all of them with positive detuning) will reduce the estimated Stark shift. Moreover, we must be careful with interpretations of level shifts in the simple multi-photon picture. At our laser intensities of several 10 TW/cm² we already operate towards the tunneling regime. Nevertheless, our simplified estimations in the multi-photon picture at least confirm the correct direction of the observed Stark shift.”

To investigate resonantly-enhanced harmonic generation, we tune now the laser on and off the Stark-shifted resonances and compare the obtained harmonic spectra. Figure 4 shows harmonic spectra for a laser intensity of 20 TW/cm². In this case, we expect the Stark-shifted five-photon resonance 3p^{6 1}S₀ → 4s’ [1/2]₁ at a wavelength of 522 nm (compare Fig. 3). If we tune the laser to a wavelength of 524 nm (i.e. off the Stark-shifted five-photon resonance), the harmonic spectrum shows a weak 5th harmonic and a very weak 7th harmonic of the driving laser (see Fig. 4(a)). If we tune the laser now on the Stark-shifted five-photon resonance at 522 nm, the intensities of both the 5th and 7th harmonic increase by an order of magnitude due to resonance enhancement (see Fig. 4(b), red line).

 

Fig. 4 Harmonic spectra at different wavelengths of the driving laser, tuned in the vicinity of the Stark-shifted five-photon resonance 3p^{6 1}S₀ → 4s’ [1/2]₁. Raw data after averaging 20 laser shots, but without filtering.

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Thus, the five-photon resonance also enhances generation of a higher harmonic, i.e. with an order larger than the five-photon transition. If we tune the laser further to a shorter wavelength around 510 nm (i.e. again off the five-photon resonance), both the 5th and 7th harmonics decrease significantly (see Fig. 4(c)). However, both harmonics are still slightly stronger than the harmonics, driven with the laser wavelength at 524 nm, i.e. at the other side of the resonance (compare Fig. 4(a)). We attribute this to the long tail of the Stark-shifted resonance towards shorter wavelength (compare Fig. 3). Thus, at a wavelength of 510 nm, we operate still in the tail of the resonance and get some (though weaker) resonance enhancement.

The effect of resonantly-enhanced harmonic generation becomes even better visible when more observation channels (i.e. harmonics) appear in the spectrum, e.g. at better signal-to-noise ratio or larger laser intensity. Figure 5 shows harmonic spectra for a laser intensity of 61 TW/cm². In this case, we expect the Stark-shifted five-photon resonance 3p^{6 1}S₀ → 4s’ [1/2]₁ at a wavelength of 510 nm (compare Fig. 3). If we tune the laser to wavelengths of 524 nm and 522 nm (i.e. off the Stark-shifted resonance), besides the 5th harmonic only rather weak 7th and 9th harmonics show up in the spectrum (see Figs. 5(a,b)). If we tune the laser to a wavelength of 510 nm (i.e. onto the Stark-shifted five-photon resonance), we resonantlyenhance 5th, 7th and 9th harmonics (see Fig. 5(c)). The enhancement factor is now between 3 and 10 (depending on which of the harmonics in Fig. 5 we take as reference). As comparison of Figs. 4 and 5 shows, the maximal resonance-enhancement occurs at different wavelengths – obviously depending on the Stark shift (respectively the laser intensity).

 

Fig. 5 Harmonic spectra at different wavelengths of the driving laser, tuned in the vicinity of the Stark-shifted five-photon resonance 3p^{6 1}S₀ → 4s’ [1/2]₁.

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We note, that the harmonic signals for off-resonant excitation with a laser wavelength of 524 nm (see Fig. 5(a)) are slightly stronger compared to the harmonic signals obtained with a laser wavelength of 522 nm (see Fig. 5(b)). This is a bit surprising, as 524 nm is further away from the Stark-shifted resonance at 510 nm. Also the spectroscopic data on resonantly-enhanced fifth harmonic generation (see Fig. 3) provided some similar evidence: At a laser intensity of 61 TW/cm², the yield in the 5th harmonic smoothly decreases from the maximum around 510 nm towards 522 nm. However, for longer wavelengths the 5th harmonic yield seems to slightly increase again. We attribute this to a lower lying five-photon resonance 3p^{6 1}S₀ → 4s [3/2]_1, (see Fig. 1) which is pushed and broadened by Stark shifts from the original position around 533 nm towards the region of 524 nm – and also enhances the harmonic yield.

The experimental data clearly demonstrate the effect of resonant multi-photon excitation to enhance harmonic generation at higher orders than the involved multi-photon transition – provided we take Stark shifts into account and match our laser wavelength to the shifted resonances.

4. Conclusion

We investigated harmonic generation in a dense jet of Argon atoms, driven in the vicinity of the five-photon resonance 3p^{6 1}S₀ → 4s’ [1/2]₁ by intense, tunable picosecond radiation pulses. As a major optical component for the experiment, we implemented a laser setup with a home-made four-stage dye amplifier system to provide picosecond pulses with appropriate specifications. The laser system combines sufficient intensity (i.e. up to 100 TW/cm²) to approach the regime of higher harmonic generation with still fine spectral resolution to address and exploit single atomic resonances.

In a first experiment on resonantly-enhanced fifth harmonic generation, we determined pronounced AC Stark shifts and line broadenings of the five-photon resonance. Moreover, we found evidence for an additional difference frequency mixing process “six minus one photon” via a set of highly excited states in Argon – which also generates radiation at the fifth harmonic of the driving laser. In a second experiment, we investigated the effect of resonant multi-photon excitation on the generation of harmonics (i.e. with higher order than the involved multi-photon transition). When we tuned the laser frequency to the Stark-shifted five-photon resonance, we found a pronounced resonance-enhancement not only of the 5th, but also of the 7th and 9th harmonic. As an important feature of resonance enhancement, the laser wavelength must be matched to the position of the Stark shifted atomic resonance – which depends upon the applied laser intensity. The experimental data clearly demonstrate the effect of resonant multi-photon excitation to enhance harmonic generation. The investigations may serve as another small step to determine appropriate mechanisms for efficient generation of XUV laser pulses.