Atto- and Zeptosecond Pulses Generation

Recently we have studied the following projects within this topic.

1. Collinear and non-collinear generation of EUV high harmonics with circular polarization
We theoretically model microscopic and macroscopic response for  experiment performed in M. Murnane and H. Kapteyn group @JILA, where two counter‐rotating circularly polarized femtosecond laser pulses are focused into a noble‐gas (Ar or Ne), to produce both left and right circularly polarized beams of EUV light via HHG. Each harmonic emerges at a different angle (well separated from the driving laser beams), allowing for example the spectroscopy to be performed on a sample without a spectrometer. The phenomena can be understood within the photon model, noticing that the divergence of each harmonic follows the simple vector addition of the wave‐vectors for each absorbed photon. Alternative picture is that the two circularly polarized beams add up to yield an electric field that exhibits linear polarization that rotates as a function of the transverse position across the laser focus, producing a “rotating polarization grating”  resulting in circular polarization in the far field. Numerical simulations performed by us support the experimental results, and provide insight into several additional capabilities of this method, which have not yet been demonstrated experimentally. For example in the simulations we study the process for the maximum gas target pressures higher than currently attainable  in experiment. The results predict that combination of 400nm+400nm driving fields at a 64 mrad crossing angle will produce harmonics that are completely angularly separated. This separation allows for spectroscopic experiments without using a spectrometer to disperse the harmonics, a distinct advantage considering the high expense, low efficiency, and temporal dispersion of gratings in the EUV and soft X‐ray regions.

2. Efficient soft X-ray high harmonic generation in multiply-ionized plasmas in the ultraviolet regime
In the HHG process the emission from each atom is highest for ultraviolet driving laser pulses. However, the phase matching conditions favor longer wavelength mid-infrared driving lasers. We have perfomed calculations for HHG driven by ultraviolet laser plses. Results show that one can generate bright beams in the soft X-ray region of the spectrum, up to photon energies of 280 eV. Surprisingly, the high linear and nonlinear refractive indices of both neutral atoms and ions enable effective phase matching - even in a multiply-ionized plasma. We predict that the X-ray pulses emerge as  100 attosecond pulse trains with low temporal chirp.

3. Optimizing isolated broadband attosecond pulse generation via time-gated phase and group velocity matching
Recently we have performed theoretical analysis of the time-gated phase matching mechanism in HHG in order to identify optimal conditions for the isolation of attosecond pulses for both few-cycle and multi-cycle driving lasers. Results of our high harmonic generation and three-dimensional propagation simulations show that broadband isolated pulses spanning from the EUV well into the soft X-ray region of the spectrum can be generated for driver wavelengths ranging from the near-infrared to the mid-infrared and likely even longer wavelengths. Group velocity matching plays crucial role for generating bright, isolated, attosecond pulses using long wavelength multi-cycle pulses. Finally, we showed that this technique is robust against carrier-envelope phase and peak intensity variations.

4. Group Velocity Matching in High-order Harmonic Generation
We studied theoretically the effects related to group velocity matching (GVM) between the driving laser pulse and the harmonics. We introduced a semiclassical definition for the associated 'walk-off length', different from that used to describe GVM in perturbative harmonic generation. We performed numerical quantum simulations to corroborate the validity of this new definition and study the effect of GVM on the generated attosecond pulses. We showed that Group Velocity Matching (GVM), not only reduces the efficiency of the HHG radiation, but has two novel effects: the contribution from the so-called "short quantum paths" is favored, and attosecond pulses emitted around the peak of the driving field are selected. We presented the scaling of the walk-off length in HHG with driving laser wavelength and pulse duration, showing that the harmonic emission from longer wavelengths and shorter laser pulses is more sensitive to GVM.

5. Control of attosecond pulse and XUV high-order harmonic generation with spatially-chirped laser pulses
One of the interesting recent developments has been the use of spatially-chirped pulses to drive HHG. In the so-called "lighthouse effect" the laser beam is focused to create a transverse spatial chirp and variation of the local frequency across the focal spot leads to the high-energy photons emission in different directions in the HHG process, which enables  the attosecond pulses separation in the far field. We propose using different scheme, namely a pulse with angular spatial chirp a the focal plane. We have performed calculations boths singla atom and within macroscopic description for this sub-topic and results showed that both in temporal and spectral domains, the resolution can be controlled by adjusting the spatial chirp imprinted to the fundamental beam. We proposed a technique to improve the control over the spectral and temporal scales in high-order harmonic generation by using angularly, spatially chirped laser pulses. In contrast to the so called 'lighthouse effect', which exploits transverse chirp at the focal plane to separate attosecond pulses, we propose the use of a pulse with angular spatial chirp at the focal plane where the wavefronts are parallel to each other. This technique could lead to dramatic improvements in spectral and temporal resolution in ultrafast absorption experiments.

6. Isolated attosecond x-ray pulse beyond water window
We performed analysis of  high harmonic generation from atoms including 3D propagation within discrete dipole approximation and show that the production of bright isolated x-ray attosecond pulses from midinfrared laser high-order harmonic generation is scalable to photon energies well beyond the water window. Counter intuitively, efficient and broad bandwidth isolated attosecond pulse generation in this regime requires long multi-cycle driving pulses instead of few-cycle, to avoid group velocity walk-off at the high-pressures used.

7. Multiple rescatterings in HHG from atoms and molecules
We have shown previously that the multiple rescatterings for atoms can be used to obtain zeptosecond waveforms. Recently we studied the control over the HHG yielded for our system by adding a VUV pulse to interrogate the traditional HHG process in the following way.  The target atom, prepared in its ground state, is exposed to an intense infrared (IR) driving laser field. The intensity of this field is tuned to be insufficient for depletion of population from the ground state. An isolated ultrashort VUV light pulse is introduced at a controlled delay time with respect to the IR field, transferring population into excited states that can be depleted by the driving laser. Consequently the transferred population rapidly transitions into the continuum and is propagated in the laser field until recombination with the parent ion results in emission of high order harmonic radiation. In this framework, the time of ionization is gated by the application of the VUV field, so that the time of ionization becomes an accessible and controllable quantity. Within this framework we established the connection between multiple rescatterings and properties of the attosecond pulse/pulse train and show how time gating can control properties and achieve generation of single attosecond pulse. In addition we proposed experimental detection of multiple rescatterings. Recently we have also confirmed the presence of similar multiple rescattering events in the HHG from polyatomic molecules. Our past calculations showed that interferences between the direct and multiple rescattering paths allowed for generation of the zeptosecond waveforms x-ray pulses. Currently we study if generated spectrum for molecules is similarly modified and for example if the interferences due to multiple rescatterings offer a route to generation of elliptically/circularly polarized zeptosecond waveform x-ray pulses.  Furthermore we have found that in the case of molecules interferences between the direct (short and long) and multiple rescatterings trajectories visualized in the time frequency analysis vary for different molecules. We currently study if the interference effects between the direct and multiple rescattering paths can be used for imaging of the molecular system and how they influence the properties of the generated attosecond x-ray pulse.