Strong Field Physics with Mid-infrared Lasers

Transcription

1 Journal of Modern Optics Vol. 00, No. 00, DD Month 200x, 1 8 Strong Field Physics with Mid-infrared Lasers K. D. Schultz 1, C. I. Blaga 2, R. Chirla 1, P. Colosimo 2, J. Cryan 1, A. M. March 2, C. Roedig 1, E. Sistrunk 1, J. Tate 1, J. Wheeler 1, P. Agostini 1, L. F. DiMauro 1 1 The Ohio State University, Department of Physics, 191 W. Woodruff Ave., Columbus OH, 43210, USA 2 SUNY Stony Brook, Department of Physics and Astronomy, Stony Brook NY, , USA (v1.0 released April 2006) The generation of short, intense, mid-infrared laser pulses allows for the exploration of atom-laser interactions deep in the tunneling regime as well as providing the ability to explore scaled interactions. In this paper we present recent experimental and theoretical results for this largely unexplored parameter space. 1 Introduction In the last decade or so, multi-kilohertz, chirped-pulse amplified (CPA) lasers have revolutionized our understanding of an isolated atom interacting with an intense electromagnetic field. Such discoveries as above-threshold ionization (ATI) [1], high-harmonic generation (HHG) [2, 3], multiple ionization [4], and attosecond pulse generation [6, 7] have benefited from such lasers. Concurrent with these experimental advances, there has been a great deal of progress theoretically [8 10]. From these advances it was found that the physics underlying these discoveries reveals simple scaling laws such that the laser-atom interaction scales with wavelength and intensity. Until recently, suitable lasers for such studies have been Titanium-Sapphire (Ti:S) operating at a central wavelength near 0.8 µm and Nd:YAG, YLF, and glass lasers operating near 1.0 µm. A quasi-classical model describing how a single electron bound to an atom responds to an intense laser field is the rescattering or three-step model [11, 12] and has been found to give good agreement with both experimental and theoretical findings. In this model, the electron is promoted to the continuum via tunneling ionization, which places the electron far from the ionic core with little or no initial kinetic energy. The electron then propagates under the combined influence of the ion potential and the strong laser field where it escapes or recollides with the parent ion approximately one half of an optical period later. While in the laser field the electron can gain from the field a maximum energy of 3.17U p, where U p is the ponderomotive energy, or the cycle-averaged kinetic energy of a free electron. The dynamics and energy of the electron are determined by the phase of the field at the time of ionization. Upon returning to the ion the electron can be recaptured leading to HHG, rescatter elastically off the core and gain up to 10U p of energy, or it can liberate additional electrons through inelastic scattering. When experiment and theory have been carefully compared for helium [13], the rescattering picture has been shown to quantitatively capture the important physics. The condition for this semi-classical description to be applicable is that the interaction energy be strong enough that the tunneling or quasi-static approximation be valid. Keldysh s theory of ionization is a useful framework for determining by what processes ionization takes place [14]. According to this theory the ratio of the time it takes for the electron to tunnel through the barrier to the optical period of the light field parametrizes the interaction. If the field changes directions before the electron has a chance to tunnel through the barrier, then ionization, if it occurs, takes place via multi-photon ionization (MPI). Otherwise the electron can escape over or tunnel through the potential barrier. This so-called Keldysh parameter can be written as γ = I p /2U p, where I p is the ionization Corresponding author. schultz.283@osu.edu Journal of Modern Optics ISSN print/issn online c 200x Taylor & Francis DOI: / YYxxxxxxxx

2 2 K.D. Schultz, et al. Figure 1. Experimental parameter space plotted as frequency versus (a) field amplitude and (b) Keldysh Parameter in atomic units. The dashed and dotted lines are for γ = 1 for the hydrogen atom in n = 1 and n = 100, respectively. potential of the atom and U p is the ponderomotive energy. In atomic units, U p = I/4ω 2, where ω and I are the frequency and intensity of the laser light respectively. For the majority of ionization studies to date the dominant experimental parameter has been the intensity. As an experimental knob the intensity leaves much to be desired. It is easy to turn down the intensity to explore the multi-photon regime (until you run out of dynamic range in the experiment), but even with the highest intensities possible from a Terawatt tabletop system a bare atom can only experience a relatively low intensity. Helium has the largest I p of any neutral atom and saturates at an intensity of approximately 1 PW/cm 2. Ions can survive higher intensities and important experiments measuring ionization rates have been done [15], but to measure the electron energies corresponding to a particular charge state would require ion trapping, ion beam measurements, or low duty-cycle coincidence experiments, none of which are without their difficulties. Figure 1 shows a global survey of the experiments that have been done to probe both the MPI and tunneling regimes. Inclusion in the plot required that the experiments either recorded ions and electrons or were state-resolved, thus experiments that only looked at ionization rates of highly ionized atoms are not included. In no way is this plot meant to include all of the experiments that have been done to date, but rather to be representative of what has been done. In Fig. 1(a), electric field amplitude is plotted versus frequency in atomic units. The light used in these experiments ranges from the near-infrared (Ti:S and Nd:YAG, YLF, or glass) to the ultraviolet (excimer lasers); in addition the proposed parameter space for experiments using mid-infrared lasers (MIR) is shown. The field amplitudes vary from 10 3 to 0.2 a.u., but it is important to realize that the upper-limit of these experiments is not limited by the laser technology, but the atoms themselves. The diagonal dashed line in Fig. 1(a) corresponds to γ = 1 for ground-state hydrogen and is meant to be a guide to delineate between MPI and tunneling. The systems surveyed include ground-state hydrogen [16], helium [13,17 21], and the other inert gases [17,22 35]. Between all of these experiments 0.3 < γ < 10, however, only two neutral atoms, helium and neon, access the tunneling regime. Looking at Fig. 1(a) it is seen that by using MIR lasers at intensities below saturation it is possible to get further into the tunneling regime than was possible with previous experiments. Looking at the equations for γ and U p it is found that both scale more strongly with wavelength than intensity. For example, He saturates in a femtosecond, 0.8 µm laser field at 1 PW/cm 2, corresponding to U p 60 ev. U p for 4 µm light at the same intensity is 25 times bigger or 1.5 kev. To obtain these energies at 0.8 µm would require an intensity of 25 PW/cm 2, which no neutral atom could ever experience. Additionally, to get well into the tunneling regime requires γ << 1, therefore for a given wavelength higher intensities are needed. Since the majority of short pulse experiments have taken place at 0.8 µm, only He and Ne can experience intensities high enough to ensure tunneling ionization. Using longer wavelength light will help circumvent these problems. Using the example of helium, it is seen that for 0.8 µm light γ = 0.45, while for 4 µm light γ = So with MIR light it is possible to probe further into the tunneling regime providing more stringent tests for the rescattering model which assumes the quasi-static approximation. Not only is it possible to investigate further into the tunneling regime with He, but at these wavelengths and intensities all the noble gas atoms tunnel ionize. Table 1 summarizes these results for helium and xenon at intensities for which over the barrier ionization (I OTB ) occurs. Further implications for the rescattering model at long wavelengths are those relating to the electron wavepacket as it is propagating in the laser field. Once the wavepacket is released into the continuum, the width of the wavepacket transverse to the propagation is freely spreading and is given by α 2 o + (2T/α o) 2.

3 Strong Field Physics with Long Wavelength Lasers 3 Table 1. Scaled parameters for helium at I OT B=1.5PW/cm 2 and xenon at I OT B=0.09PW/cm 2 He He He Xe Xe 0.8 µm 2 µm 4µm 2µm 4µm γ U p, kev E cutoff, kev λ cutoff, nm electron yield Electron Energy (ev) (a) 1000 h U p electron yield 100 (b) h Electron Energy (ev) Figure 2. Photoelectron spectra for γ = 1.2 ionizing (a) xenon with 70 TW/cm 2 of 0.8 µm light and (b) potassium with 1.2 TW/cm 2 of 3.6 µm light. Where T λ is the propagation time of the electron and α o is the initial width of the wavepacket. It is therefore evident that for longer wavelengths, the electron spends more time in the continuum and therefore experiences more spreading. For processes like inelastic (e,2e) scattering and HHG, where the wavepacket needs to overlap with the core, the wavepacket spread will cause the yield to drop. Furthermore as U p increases at longer wavelengths, the electron velocity increases to the point that relativistic regime is approached and the effect of the B-field of the light on the wavepacket dynamics can no longer be ignored [36], nor can relativistic motion [37]. It is possible to exploit the Keldysh picture further. Since γ depends only on I p and U p, it is conceivable that there are appropriate atoms, intensities, and wavelengths such that their Keldysh parameter is the same. Then according to the Keldysh theory the underlying dynamics will be the same between two different atoms irradiated with different colour light. For example, Xe exposed to 50 TW/cm 2 light at 0.8 µm has the same Keldysh parameter as K atoms exposed to 1 TW/cm 2 light at 3.6 µm. Fig. 2 shows electron spectra for Xe and K. These spectra both have ATI peaks with spacings equal to the appropriate photon energy. Similarly, by choosing the proper conditions it is possible to produce HHG in alkali atoms at long wavelengths [38, 39]. An advantage of using alkali atoms exposed to MIR light is the opportunity to easily prepare excited states, thereby tuning the HHG spectrum [40].

4 4 K.D. Schultz, et al. 2 Experimental Apparatus 2.1 Laser Systems Experiments were performed using two separate laser systems. The first has been described elsewhere [38, 39], but recent modifications merit a brief description here. Difference frequency generation (DFG) from Ti:S and Nd:YLF (Yttrium Lithium Fluoride) mode-locked lasers is used to produce 3 4 µm light. The Ti:S produces pulses centered at 815 nm, with a pulse width of 100 fs and 2.6 mj of energy and is synchronized to the Nd:YLF laser which produces 15 ps, 550 µj pulses centered at 1053 nm. The pump (Ti:S) and the signal (Nd:YLF) are mixed in a 5 mm long KTP crystal. Nominally the phase matching is collinear, but in practice the pump and signal are slightly non-collinear to facilitate separation of the idler. For the experiments discussed in this paper the crystal is tuned for 3.6 µm and produces pulses 100 fs long with 160 µj of energy. The second system uses the idler from DFG from a commercial optical parametric amplifier [41]. The pump is an amplified Ti:S laser with 4.5 mj of energy and a pulse width of 50 fs. This signal is generated from superfluorescence in a β-bab 2 O 4 (BBO) crystal pumped with a small amount of the Ti:S beam. The signal is then amplified in this BBO before passing through a second BBO where it is mixed with the majority of the pump beam. This second amplifying stage uses a nominally collinear geometry for phase matching, however, as in the previous laser system a slight detuning away from collinearity is used to facilitate separation of the pump, signal, and idler. The idler is tunable from 1.6 µm to 2.6 µm. For these experiments the idler puts out 600 µj of energy at 2 µm with a pulse width of 50 fs providing peak intensities in excess of 1 PW/cm 2, which is near the saturation intensity of helium. 2.2 Photoelectron Spectrometers Two different time-of-flight (TOF) spectrometers are used in these studies to measure photoelectron spectra, each capable of running at multi-khz rates. The first TOF spectrometer is used for study of the alkali and alkaline atoms as well as the inert gases. It is capable of running in electron or ion collection mode, but not simultaneously. The flight tube is kept grounded for electron spectroscopy so that the electrons are allowed to freely propagate to the multi-channel plate (MCP) detector. For ion collection there are three field plates used in the Wiley McClaren configuration [42] which are tuned to maximize the resolution for the ion under investigation. The flight tube and interaction region have mu-metal shielding to reduce the effects of any stray magnetic fields. The flight tube is 40 cm long and the timing resolution of the electronics is 1 ns, giving an energy resolution of better than 5% at energies below 300 ev. This spectrometer is currently being used to study the rare gases and a precision leak valve is used to backfill the chamber to the correct target density. To minimize space-charge effects and pulse pile-up the pressure is adjusted such that the count rate is approximately 0.5 events/shot or lower. The second spectrometer is a coincidence spectrometer and has been discussed in depth elsewhere [21,35] although in the results presented here it has not been used in coincidence mode. Briefly, the spectrometer is a pulsed-plate dual-sided TOF design which measures the electron energy or ion m/q distribution. The resolution of the electron energy analyzer and mass spectrometer is 5% and 1/300, respectively. Using the spectrometer in coincidence mode allows the determination of the efficiencies of the two detectors [43] and these have been measured to be 30% and 1% for ions and electrons respectively. The background pressure is bar and like the previous spectrometer a precision leak valve is used to control the atomic density to maintain a count rate of 0.5 events/shot or lower. 3 High Harmonic Generation HHG at long wavelengths is an interesting area which is being vigorously pursued by this group [38]. It has been shown experimentally and theoretically that HHG cuts off at photon energies of I p U p, and therefore it should be possible to generate higher energy harmonics with MIR than has been possible to date. To help determine the validity of the scaling of electron energies and consequently harmonic

5 Strong Field Physics with Long Wavelength Lasers 5 Electron Yield HH Intensity m (a) 0.8 m Scaled Energy (E/U P ) 2.0 m 0.8 m (b) Energy (ev) Figure 3. TDSE calculations of (a) PES of argon exposed to 0.8 µm (dashed) and 2 µm (solid) light at an intensity of 0.16 PW/cm 2. (b) HHG spectra for the same conditions. energies, results obtained from the numerical solutions of the time-dependent Schrödinger equation (TDSE) within the single active electron (SAE) approximation for wavelengths ranging from 0.8 µm to 2.0 µm are presented. The code used is based on the code of H.G. Müller [44] and provides qualitative agreement with the quasi-classical results expected for γ < 1 [45]. For these calculations argon is used as the model atom, since it is a prototypical atom studied in laboratories and a computationally efficient model potential for argon, with spin-orbit coupling neglected, has been developed for TDSE calculations [44]. The atom is subjected to an N-cycle flat-top laser pulse described by the vector potential A(t) = A o ẑ cos ωt, with a half-cycle turn-on and turn-off. The code outputs both angle-resolved photoelectron energy spectra (PES) and the electron dipole moment as a function of time. However, at intensities where there is substantial ionization of the ground state there is also a substantial background obscuring the harmonics due to the non-zero dipole moment at the end of the pulse [46]. The electron acceleration, on the other hand, is always zero at the end of the pulse and is the more physically relevant quantity. The acceleration was calculated using Ehrenfest s theorem, a(t) = Ψ(t) z V (r) + E(t) Ψ(t), where E(t) is the electric field of the laser. This term just adds an oscillation at the fundamental and is suppressed. The HHG spectra presented here were obtained by taking the Fourier transform of the time-dependent acceleration. Figure 3(a) shows the angle integrated PES in scaled energy units for argon exposed to 8-cycle long 0.8 µm and 2.0 µm light at an intensity of 0.16 PW/cm 2. Such light fields correspond to U p of 9.5 ev and 59.7 ev for 0.8 µm and 2.0 µm, respectively. Figure 3(b) shows the HHG spectra for the same laser parameters. The contrast between the two wavelengths is striking in both the PES and HHG spectra. In the PES, a clear break near 2U p as well as a long plateau ending in a sharp cut off at 10U p for the 2.0 µm case is seen. This is what one would expect from the quasi-classical rescattering model. However, there are no such indications in the results at 0.8 µm. Here it is clear that there is a MPI contribution causing a monotonic decline in the yield extending beyond 10U p in contrast to what one expects if the ionization were purely tunneling. The results are just as striking in the HHG spectra. For the 0.8 µm light the photon signal slowly falls off with an indistinct cut off beyond the expected classical cut off of 45 ev. This behaviour is again attributed to MPI. The longer wavelength has a distinct cut off at the expected E max 200 ev. To achieve such an energy in argon with 0.8 µm light requires intensities well beyond argon s saturation intensity More energetic electrons are not the only advantage of working with the inert gases at long wavelengths. Attosecond pulses are created by summing several harmonics together; the more harmonics that are mixed the shorter the pulse that can be obtained if the relative phase between the harmonics is fixed. Unfortunately, an arbitrary number of harmonics cannot be mixed, because differing harmonics originate from electron wave packets that have differing propagation times. This difference in propagation times corresponds to a differing phase between successive harmonics, therefore limiting the number of harmonics to be

6 6 K.D. Schultz, et al. Chirp (as/ev) Wavelength ( m) Figure 4. TDSE calculations of harmonic chirp in argon as a function of wavelength for an intensity of 0.16 PW/cm 2, obtained by determining the slope of τ 1 in Fig. 5. The solid line is the expected λ 1 classical scaling. Kinetic Energy (E/U P ) Kinetic Energy (E/U P ) Time (t/t) Figure 5. TDSE return times as a function of harmonic energy for driving fields of (a) 2 µm and (b) 0.8 µm with an intensity of 0.16 PW/cm 2. The numeric labels refer to the τ n trajectory. The top trace plots the driving electric field. summed to some optimal number [47]. The chirp on the harmonics can be written as, β T/U p 1/Iλ, where T is the propagation time of the electron. Once again the advantage of working at long wavelengths is evident. Not only is it possible to generate higher energy harmonics, but by being able to sum more of them together it is possible to obtain shorter attosecond pulses than was previously possible at 0.8 µm. Figure 4 shows numerical results that confirm the λ 1 scaling of the harmonics. Figure 4 was generated by calculating the return times of given harmonics for the short trajectories. To do this a plot of electron return times as a function of return energy was generated and is shown in Fig. 5. To generate this plot, a portion of the full HHG spectra was selected and inverse Fourier transformed to produce the time dependence of the harmonics. This procedure is done many times to produce the contour plot shown in Fig. 5. There are many interesting features in this plot and many of these are discussed elsewhere [45], but briefly it is seen that at 2 µm the electron makes many returns to the core unlike the electron dynamics at 0.8 µm. The importance of these higher order returns is not clear at the moment and is a subject of interest. The other important result is the classical-like dynamics that the electron has when driven by a MIR pulse. The black lines in Fig. 5 are the expected classical trajectories. In Fig. 5(b) it is obvious that while there is coalescing of the electron around the short classical trajectory, the electron wave-packet rapidly diffuses and the role of higher-order returns is masked. However, the electron dynamics in the 2 µm light show much more classical behavior. Interferences do not occur until much later in the laser pulse, and so higher-order returns become much more evident and strictly follow the expected classical dynamics. It is not clear what the role of these returns has in the generation of attosecond pulses, but is clear that some focusing effect is happening. From these calculations it appears possible to create an attosecond pulse train with pulse widths of 100 as.

7 Strong Field Physics with Long Wavelength Lasers 7 Normalized Electron Yield/100 mev E-3 1E-4 1E-5 1E-6 1E-7 1E-8 (a) 1E Electron Energy (ev) E-3 1E-4 1E-5 1E-6 1E-7 1E-8 1E-9 (b) Electron Energy (U p ) Figure 6. (a) Comparison of xenon PES at different wavelengths and intensities. Black solid line: 80 TW/cm 2 =I sat, 0.8 µm light, γ = 1.2. Gray solid line: 40 TW/cm 2, 2.0 µm light, γ = Dotted line 40 TW/cm 2, 3.6 µm light, γ = (b) Same as above, but plotted vs U p 4 Photoelectron Spectra Figure 6(a) and (b) show preliminary photoelectron spectra of xenon, scaled such that each of the curves has unit area, at wavelengths of 0.8 µm, 2.0 µm, and 3.6 µm in laboratory units and scaled units, respectively. The data taken at the MIR wavelengths are at the same intensity of 40 TW/cm 2 and the spectrum taken at 0.8 µm is at saturation. Figure 6(a) clearly shows that the 3.6 µm light below saturation is producing electrons that are four times more energetic than those produced from 0.8 µm light at saturation. Scaling the electron energy (Fig. 6(b)) clearly shows the dynamics changing from MPI at the shortest wavelength to tunneling ionization at the longest. For the data taken at saturation γ = 1.2 and clear ATI peaks are visible as well as photoelectron energies in excess of 10U p, which are signatures of MPI. At 2.0 µm γ = 0.63 for this intensity. ATI peaks are not visible for the scale used in this plot, but there is faint ATI structure spaced a photon energy apart (0.62 ev). There is also what appears to be a strong 2U p break indicative of tunneling ionization becoming important. Finally, for 40 TW/cm 2, 3.6 µm light interacting with xenon γ = It is expected for this value of the Keldysh parameter that ionization dominantly occurs via tunneling. The data here support such a view. There are no visible ATI peaks, there is a clear 2U p break, and a cut off near 10U p, at these higher energies the spectra are limited by the spectrometer s fixed temporal resolution. It is evident for MIR light that the main mechanism for ionization in xenon appears to be tunneling, even below xenon s saturation intensity. Furthermore, the electron yields in the plateau seem to support the notion that wavepacket spread at longer wavelengths causes rescattering to turn off. 5 Conclusions In summary, we have shown that by using longer wavelength light, it is possible for the experimentalist to delve deeper into the tunneling regime than previously possible. By doing so we are capable of producing more energetic electrons and higher energy photons from HHG. The dynamics of an electron in MIR fields appears to allow for shorter attosecond pulses, enabling experiments to approach the 100 as barrier. We have presented calculations supporting these expectations and preliminary experimental data showing that at these wavelengths, even xenon appears to tunnel ionize and therefore generates much more energetic electrons than has been seen previously.

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