Since the invention of the laser 50 years ago, scientists have been striving to generate coherent beams at shorter wavelengths. X-rays are unique for imaging since such wavelengths are well matched to nanoscale objects and characteristic inner-shell absorption edges whose position depends on the local element, charge and spin state. Ultrafast x-ray pulses can in principle capture all electron-ion motion relevant for the nanoscale. Fortunately, high harmonic generation (HHG) allows for producing ultrafast coherent beams from the EUV to keV regions of the spectrum in the set up of table top experiment. In the process of HHG atomic electrons acquire energy from the driving laser, which can be subsequently released in the form of high frequency coherent radiation.
One of the grand challenges has been how to generate bright harmonics, particularly at the high photon energies needed for many applications in imaging and spectroscopy. In order to generate bright beams of high harmonic x-rays, the laser and x-ray waves must propagate in phase throughout a medium to ensure that the signals from many atoms add coherently. Major theoretical challenge in theory is that in order to study phase matching properties one needs to augment the microscopic description of HHG (within Schroedinger equation) with a macroscopic one.
Projects studied by our group related to this topic:
1. Mollow sidebands in HHG from molecules
In the intense field regime the intensity of the Mollow sideband harmonics are comparable to the intensity of the main harmonic. Another consequence of the coupling is visible in the HHG phases and ellipticity, where one can see clearly enhanced inner valence contributions. Our simulations for the phases of the harmonic radiation show that the phases of the fractional harmonics are close to the phases of the ‘main’ harmonics. This indicates that the sidebands and odd harmonics can add coherently and for example it can influence the properties of the generated attosecond x-ray pulses and pulse trains. Since it leads to the effective 'broadening' of the harmonics signal it might offer a route to shortening of the attosecond pulse. The time frequency analysis performed by us shows also interesting trajectories interference effect and modification in a form of the suppression of the long trajectories. This path selection mechanism offers another route to influence or even optimize generated attosecond pulses.
2. 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.