Beyond Carbon K -Edge Harmonic Emission Using a Spatial and Temporal Synthesized Laser Field *

1. Beyond Carbon K-Edge Harmonic Emission Using a Spatial and TemporalSynthesized Laser Field* Muhammed Sayrac Phys-689 Modern Atomic Physics Spring-2016 *PRL 110, 053001 (2013)

2. Motivation • Numerical simulations of HHG in helium using a temporally synthesized and spatially nonhomogeneous strong laser field. • The goal of this study is to extend the cutoff harmonic far beyond the usual semi classical limit by using temporal and spatial laser field. • This laser field has been proven capable of generating coherent extreme ultraviolet photons beyond the carbon K edge (284eV, 4.37nm), an energy region of high interest as it can be used to initiate inner-shell dynamics by using 800nm pulses with synthesis fields. • The new approach we propose involves combining the two techniques to controllably shape the final laser field both in time and in space. *PRL 110, 053001 (2013) https://books.google.com/books?id=clAANTKBStcC&pg=PA2&lpg=PA2&dq=carbon+absorption+edge+in+wavelength&source=bl&ots=M4h8ZyKaX8&sig=wShy-6x9vturc_L26jC9_Hzf47c&hl=en&sa=X&ved=0ahUKEwjlhKDdiLzMAhUM6CYKHbMEBHUQ6AEIODAE#v=onepage&q=carbon%20absorption%20edge%20in%20wavelength&f=false

3. Introduction Ecutofff= Ip+3.17Up • X-ray absorption spectroscopy is a very powerful technique for the probing of the local chemical environment of moleculesand to explore ultrafast inner shell charge dynamics in molecular systems. 3-step model Up~λ2 • One way to extend HHG cutoff is use longer wavelength as it is well known that the HHG cutoff scales as λ2. • The generation efficiency of the harmonic photons decreases with increasing laser wavelength according to a λ-5.5 power law. *PRL 110, 053001 (2013), Nature Photonics 5, 640–641 (2011)

4. Method Two 4-cycle pulses at 800nm are delayed in time for performing the temporal synthesis. For the simulation total number of cycle (N)=4 and ϕ=0 are considered. The potential between the atom and the laser pulse is modified in order to treat the spatially nonhomogeneous fields. where Vl is the laser atom interaction, E is the laser field, the β is the strength of the nonhomogeneity. This parameters are adjusted in such a way that the laser ionized electron feels only a linear variation of the laser field when in the continuum. *PRL 110, 053001 (2013)

5. Results • The TDSE is solved in order to calculate the harmonic spectra while employing double pulse nonhomogeneous driving laser field. The harmonic spectrum obtained in helium for β=0.002. Then the cutoff is extended up to 12.5Up that is greater than 1 keV. • The decrease beyond 650eV can be explained that two trajectories contribute to the harmonic yield, inducing structures in the corresponding harmonic spectrum. • Toward the cutoff energy the excursion time of these trajectories increases, resulting in a harmonic yield drop due to the spreading of the electronic wave packet. *PRL 110, 053001 (2013)

6. Results (cont.) • The direct effect is that the amount of recombination event decreases as β increases. • For β=0.002 the short and long trajectories recombine almost simultaneously, meaning the laser field forces to electron ionized at different times to recombine around the same time. *PRL 110, 053001 (2013)

7. Results (cont.) • ti: 1.25-2.25 long trajectories correspond tr>2.5 optical cycle, and short trajectories are for the tr<2.5 optical cycle. • The long trajectories are modified both by the spatial nonhomogeneity and the temporal double-pulse configuration. • In the homogeneous case (β=0) with ionization times ti around 1.25 and 1.75 optical cycles merge into unique trajectories. • The trajectory with ti~1.75 now has its ionization times greater than half an optical cycle that get smaller while β increases. As a result, the time spent by the electron excursion in the continuum increases. • The electric field strength at the ionization time for short trajectories being greater than for long trajectories, and considering that the ionization rate is a nonlinear function of this electric field, long trajectories are then less efficient than the short ones. • Also short trajectories are almost independent of βand get noticeably different only for really high values of β. *PRL 110, 053001 (2013)

8. Results (cont.) The time-frequency analysis of the calculated dipole (from the 3D-TDSE) corresponding to the case of a nonhomogeneous laser field using a wavelet analysis. β=0.002 • The brown lines are the calculated classical re-scattering energies. • The classical calculations confirms that the mechanism of the generation of this 12.5Upcutoff extension exhibiting a nice continuum • This is the consequence of trajectory selection and consequences of employing the combination of temporally and spatially synthesized laser field. *PRL 110, 053001 (2013)

9. Conclusion • Two identical few cycle pulses delayed in time together with a weak spatial nonhomogeneity are used for extending HHG cutoff. • The main effect of this two identical pulses on the HHG is a considerable extension of the cutoff energy up to 12.5Up. • Trajectories are highly selected while using a laser field that consist of a combination of the double pulse temporal synthesis and the spatial nonhomogeneity. • This approach provides the generation of a coherent attosecond light source at energies beyond the carbon K edge directly from an 800 nm laser system. *PRL 110, 053001 (2013)

10. Thank you