Multi-Color Sculpted Light Waves for HHG Control

Final Report Summary - MUSCULAR (Multi-Color Sculpted Light Waves for HHG Control)

FIGURES SEE ATTACHMENT

Project context and objectives

Femtosecond laser pulses can be focused to such intensities that the electric field of the light tears on the electrons in atoms with equally strong force as the atomic nuclei. One can thus tear away an electron and steer it on trajectories around its parent ion. This is the process at the heart of “strong-field physics”. Of particular interest are trajectories that lead the electron to recollide with its parent ion, entailing a rescattering of the quantum wavepacket representing the accelerated electron. This can be exploited, e.g. to image the ion with sub-atomic spatial resolution and create attosecond (10-18 s) pulses of light (VUV to x-rays) via the process of high harmonic generation (HHG). The electron acceleration and recollision occurs on a time-scale shorter than the driving laser optical cycle – which for the typically used near-infrared lasers is of the order of 1 fs (10-15 s). Strong-field phenomena thus naturally give access to time-scales on which electrons move within atoms, molecules or other forms of matter. These quantum dynamics are fundamental to physical, chemical and even biological processes. Their time-resolved observation and control is one of the prime goals of modern science.

A great deal of control over strong-field phenomena can be achieved via the driving laser waveform which steers the aforementioned electron trajectories. Figure 1 shows some basic examples of laser pulses with different shaped carrier waves. Shaping the waveform of light requires the generation and control of an extremely broad coherent spectrum. For the last about 20 years, this has been achieved by coherently superposing a femtosecond laser pulse with one of its optical harmonics. While this has lead to a great many successes, the possibilities for waveform shaping remained limited, since the frequencies of the additional color-components are not tunable and their generation efficiency plummets rapidly with harmonic order (which is why this method has been limited to 2 color combinations of a fundamental with its second or third harmonic).

The key idea for the waveform (Fourier-)synthesizer we have developed in the course of the MUSCULAR-project is to generate not only frequency-up-converted color-components by optical harmonic generation (as commonly done before) but also frequency-down-converted components by optical parametric amplification (OPA). These down-converted components are generated with high efficiency and tunable frequencies in the IR range, but phase-locking them to the fundamental is more challenging. While the up-converted optical harmonic wave is generated with a fixed delay with respect to the fundamental wave, in our down-conversion method, the delay depends on the exact position of the fundamental wave under its pulse envelope, the so-called “carrier envelope phase” (CEP). We thus have to actively lock the CEP in order to obtain a stable delay between the two color components’ waves, which is a prerequisite for the generation of stable multi-color waveforms.
In order to demonstrate the capability of our “light wave synthesizer”, we apply it to optimize the electron quantum trajectories in the HHG process. Sinusoidal driver waves are not quite optimal for this, since they launch a as many non-recolliding trajectories as useful recolliding ones and the energy transfer from the light wave to the accelerated electron is less efficient than it could be. The most efficient energy transfer is achieved by a waveform, dubbed “the perfect wave for HHG”, which had been derived earlier in a theoretical study by the group of J. Marangos (Imperial College London), with whom we collaborate. It is an example for a waveform that substantially from a sinusoidal shape and requires more than two frequency components to be realized. We set out to realize the first experimental proof-of-concept for this idea with 3-color waveforms.

Main Science & Technology results

To this end, we have boosted by one order of magnitude the pulse energy of a commercial Yb-based laser (“Pharos” by Light Conversion) and added active CEP-locking to the laser amplifier chain. Different amplification approaches have been tried and the successful one consists of adding additional stretching to the pulses before seeding a home-built Yb,Na:CaF2 regenerative amplifier stage. We now achieve ≈ 6 mJ pulse energy at 1 kHz in < 200 fs pulses, with and r.m.s. CEP jitter of 950 mrad. We have thus succeeded in introducing CEP-locking—the key to waveform control—to Yb-based laser amplifier technology, which is of high interest because of its suitability for direct pumping with low-cost high-power laser diodes and average-power-upscaling thanks to the low heat -load on the laser crystals.

This 1-μm laser pumps a white-light seeded OPA, generating fully phase-locked down-converted color components at 1.5-μm and 3-μm wavelength. These 3 colors components, spanning 2 octaves, form the base of the synthesizer, schematically shown in Fig. 2. Optical harmonic generation stages are easily added to create more color components. In the challenging OPA development, we succeeded generating sufficient power in the new color components, while conserving high spatial quality of the OPA-output (wavefront distortions obviously wash out phase locking) and limiting nonlinear phase-jitter. For “gentle” amplification, the OPA design has evolved to a three-stage amplifier, producing 1.5-μm-pulses with 0.4-mJ@1kHz and correspondingly 3-μm-pulses with 0.2-mJ@1kHz. The multi-color waveform, with a power-level amply sufficient to drive high harmonic generation, is finally created by combination of the components in an interferometer with sub-cycle stability. At the end of the project, we had not yet used the 3-μm-component in our HHG experiments. Instead, we include the second harmonic of the 1-μm-component. All custom optics required to add the 3 µm component have been designed and ordered, and first experiments will be made in the following months.
In order to study high harmonic generation driven by our shaped waveforms, a dedicated beamline has been constructed—including design and implementation of vacuum chambers, pumping system, and the XUV spectrometer. We typically measured the dependence of the generated XUV spectra on the two relative timings of our three wave components (examples of such measurements are shown in Fig. 3), observing strong modulations which demonstrate that we do generate powerful and reasonably stable waveforms. The remaining timing jitter will be improved in planned future developments, e.g. an active stabilization of the multi-color interferometer.

As a theoretical support and means to interpret our measurements, a code was developed that solves the fully quantum mechanical Lewenstein model for HHG in the strong-field approximation, applying the stationary-phase approximation for arbitrary laser waveforms. This allows to find a finite number of “quantum trajectories” that dominate the dynamics, and thus yields a very instructive connection of the fully quantum mechanical results to the idea of classical electron trajectories being steered by shaped optical cycles. Simulations made with this code are compared to measured spectrograms in Fig. 3. The qualitative agreement between the measured and simulated spectrograms (calculated for a single atom and a single driver optical cycle) proves that in our experiments, we indeed exert control over the HHG process on the single atom quantum level and a sub-cycle time scale. Closer analysis of the calculated quantum paths in comparison with the experimentally observed spectral modulations allows us to understand in detail the control we exert on the quantum trajectories in HHG and underpin the great potential of our waveforms to enhance HHG.

Figure 4c shows an HHG spectrum generated with a selected optimized three-color waveform. The spectrum clearly extends beyond the 73 eV absorption edge of the Al-filter used. Figures 4a,b show the HHG spectra generated by sinusoidal drivers. Whilst with the full available OPA output at 1.5 μm a fairly high spectral cutoff is achieved, the HHG flux is very low. On the other hand, the laser output at 1.0 μm with the same total pulse energy as the three-color waveform leads to saturated HHG (due to excessive ionzation of the gas medium) with a cutoff below 60 eV, clearly showing the limitations of HHG with single-color near-IR drivers. In comparison, the synthesized optimized waveform generates an HHG spectrum that unites high spectral intensities (> 80 times increase compared to the 1.5 μm-driver) with a cutoff well beyond the saturation limit of the efficient 1.0 μm-driver. The denser harmonic comb spacing, corresponding to the very “long” 10.3 fs-periodicity of our waveforms, leads to even greater enhancement in the integral XUV flux (measured factor > 140 in the 55–65 eV range). According to our simulations for the synthesized waveform, the dominant recollision events indeed occur only once per 10.3 fs, as opposed to once per 2.6 fs in the 1.5 μm case. Consequently, we would expect a several hundred times enhancement in the flux per attosecond burst and thus great implications to future sources of high-energy (isolated) attosecond pulses.

The increase of the parameter space of our waveform synthesizer by adding the 3 μm component to the multi-color interferometer, which had originally been planned as part of the MUSCULAR project, had to be postponed to the months immediately following the end of the project. This is due to technical obstacles (like required repairs of vacuum pumps and the x-ray camera, or lengthy construction works on the laboratory building). Instead, we have made significant progress towards a pump laser upgrade with targeted 15 mJ@1 kHz output energy, which should allow scaling up the total flux of the sculpted waveforms. This will then enable new applications.

Potential impact, dissemination and exploitation of results

While these technical extensions are highly desirable, the experimental proof-of-concept for the “perfect wave” idea has already been achieved. An article reporting both on the development of the three-color waveform synthesizer and its first application to HHG enhancement has been written and submitted during the last semester of the MUSCULAR project and is currently under peer-review (preprint available under http://arxiv.org/abs/1308.5510). The work has already attracted a lot of interest, as, e.g. proven by two recent invitations of the project fellow to present the results on international conferences, as well as four more contributed conference talks. Technical follow-up papers (on the experimental setup, the simulations as well as future technical extensions) will certainly ensue.

Our HHG enhancement results demonstrate a new example of the many possible applications of advanced shaping of optical cycles. Generally, any directly laser-field driven process can be optimized by adequate intra-cycle pulse shaping. The technology we have developed during the MUSCULAR project significantly widens the scope for applications of shaped light waveforms: more color-components, which additionally are freely tunable, give more freedom in sculpting a certain optimal shape, and the scalability of average power and pulse energy will lead to new possibilities to emerge in a broad range of laser-matter interaction regimes. These involve, e.g. Brunel electrons whose field-driven trajectories can lead to THz-emission, plasma heating and HHG on plasma mirrors, or laser particle acceleration.

Final Report Summary - MUSCULAR (Multi-Color Sculpted Light Waves for HHG Control)

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