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

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

Introduction X-ray absorption spectroscopy is a very powerful technique for the probing of the local chemical environment of molecules and to explore ultrafast inner shell charge dynamics in molecular systems. Ecutofff = Ip+3.17Up Up~λ2 3-step model 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)

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. The optimal time delay between two replica is τ=1.29T, resulting laser amplitude of the synthesized field is equal to one of the two input pulse replica. Both fields have same CEP (ϕ) , and wedges are used to control CEP. 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)

Results The TDSE is solved in order to calculate the harmonic spectra while employing double pulse nonhomogeneous driving laser field. Then the cutoff is extended up to 12.5Up that is greater than 1 keV. The harmonic spectrum obtained in helium for β=0.002. 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)

Results (cont.) Photon energies as a function of the laser cycles for different β parameter. The spatial nonhomogeneity of the laser field strongly modified some of the high energetic trajectories. This modification forces these trajectories that do not recombine in the case of β=0 to finally recombine when the inhomogeneity is present leading to cutoff extension greater than 1keV. 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)

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 β and get noticeably different only for really high values of β. *PRL 110, 053001 (2013)

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 12.5Up cutoff 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)

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)

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