UW4A.41.pdf
International Conference on Ultrafast Phenomena © OSA 2016
Isolated circularly polarized attosecond pulses driven by few-cycle and multi-cycle non-collinear laser beams Carlos Hernández-García1,2, Charles Durfee1,3, Daniel D. Hickstein1, Tenio Popmintchev1, Amanda Meier3, Íñigo J. Sola2, Margaret Murnane1,4, Henry Kapteyn1,4, Agnieszka Jaron-Becker1,4, and Andreas Becker1,4 2
1 JILA, University of Colorado at Boulder, Boulder, CO 80309-0440 USA Grupo de Investigación en Aplicaciones del Láser y Fotónica, University of Salamanca, E-37008, Salamanca, Spain 3 Department of Physics, Colorado School of Mines, Golden, CO 80401, USA 4 Department of Physics, University of Colorado at Boulder, Boulder, CO 80309-0440 USA
[email protected]
Abstract: We propose two schemes for generating pure circularly polarized isolated attosecond pulses by crossing two non-collinear counter-rotating circularly polarized pulses. Isolation of a single attosecond pulse can be achieved either using few-cycle or multi-cycle drivers. OCIS codes: (190.7110) Ultrafast nonlinear optics, (270.6620) Strong-field processes, (320.7120) Ultrafast phenomena, (340.7480) X-rays, soft x-rays, extreme ultraviolet (EUV).
1. Introduction High-order harmonic generation (HHG) is the only source of tabletop coherent beams extending from the EUV to the soft X-ray regime, which emerges either as attosecond pulse-trains or isolated bursts. In a semiclassical picture: an atom undergoes tunnel ionization in an intense linearly polarized laser field, is then accelerated, and is finally driven back to its parent ion, releasing the kinetic energy acquired form the field in the form of EUV/X-ray radiation upon recollision. However, if driven by a circularly polarized field, the electronic wavepacket does not recollide with the parent ion. Fortunately, as proposed theoretically [1] and recently demonstrated experimentally,[2-6] when HHG is driven by two-color counter-rotating circularly polarized lasers, in both collinear and non-collinear geometries, it is possible to generate circularly polarized HHG. Moreover, phase matching of circular HHG is robust [2-6]. Recently, two different schemes have been used to experimentally generate circularly polarized harmonics by combining driving fields with different polarization. First by driving HHG by two-color, collinear, counter-rotating circularly polarized pulses [2-5], bright circular HHG is possible to photon energies of 160 eV, with bright distinct HHG peaks ideal for spectroscopy and imaging. Second, non-collinear circularly polarized HHG has been recently demonstrated using a non-collinear mixing of counter-rotating circularly polarized laser beams of the same color (for instance, 800 nm) [6]. On the other hand, although techniques to produce isolated attosecond pulses with elliptical polarization have been proposed using the two-color collinear technique [7, 8], to the best of our knowledge, so far there does not exist a practical proposal for a tabletop laboratory source of isolated circularly polarized attosecond pulses. In this work we propose two schemes for the generation of isolated attosecond pulses of pure circular polarization that utilize the non-collinear approach for generating circularly polarized high-order harmonics using few-cycle and multi-cycle drivers [9].
Fig. 1: (a) Scheme of non-collinear circularly polarized HHG: 800 nm R circular and 800 nm L circular crossed beams are focused into a gas jet, producing L and R circular harmonic beams. (b) Isolated circularly polarized attosecond pulse produced by NCP-HHG, using few-cycle (3 fs) laser pulses. Light blue lines show the projections into x and y components, and green lines shows integration over time.
UW4A.41.pdf
International Conference on Ultrafast Phenomena © OSA 2016
The technique consists of focusing two crossed counter-rotating pulses into a gas target, as depicted in Fig. 1(a). Though the technique does not depend on the specific wavelength of each pulse, here we consider counter-rotating circularly polarized pulses having the same wavelength and equal amplitude. The superposition of the electric fields of the two non-collinear beams at the focal plane yields a linearly polarized electric field that rotates as a function of the transverse position. Thus, locally at any point in the focus the same single-atom physics as for linearly polarized HHG applies. Consequently, strategies previously established to isolate linearly polarized attosecond pulses, can be adopted to generate isolated circularly polarized HHG pulses in the non-collinear technique. In addition, in the noncollinear geometry each harmonic order emerges at a different angle and harmonic beams with right and left-circular polarization are separated in the far field. As a consequence, the capability of generating isolated attosecond pulses of pure circular polarization comes along with the opportunity of selecting the central energy and helicity of the light field. First, we analyze the generation of isolated circularly polarized attosecond pulses by restricting the driving pulse duration to a single cycle. Second, we show an alternative method, in which a time delay between the driving pulses provides a polarization gating scheme that enables the generation of isolated circularly polarized pulses even when longer driving laser pulses are used. 2. Isolated circularly polarized attosecond pulses driven by few-cycle laser pulses In order to study the generation of high harmonics and attosecond pulses through the non-collinear HHG scheme, we perform numerical simulations including propagation through the electromagnetic field propagator, where the single-atom dipole acceleration is computed using an extension of the strong field approximation [10]. The gas in the interaction region is modeled as an argon gas at a pressure of 5 Torr. Each non-collinear driving beam is assumed to have a Gaussian spatial profile with a beam waist of 80 µm, with a crossing angle of 32 mrad. In Fig. 1(b) we show the circularly polarized HHG pulses obtained after Fourier transform of the harmonic spectrum. The laser pulse envelope is modeled by a sin2 function truncated at the first zeroes, with peak intensity of 8.75x1013 W/cm2 at the focus of each beam, 800 nm in wavelength, and pulse durations of tFWHM=2.9 fs. We observe that the harmonic signal is confined to an isolated pulse of attosecond radiation of circular polarization (with a couple of small side bursts). Thus, as expected due to the superposition of the two beams to a local linearly polarized driving field with a rotating polarization direction as a function of the transverse position, attosecond pulses of circular polarization are generated upon each recombination event. Furthermore, as in the case of linearly polarized harmonics, the reduction of the duration of the driver pulse leads to the isolation of a single burst. 3. Isolated circularly polarized attosecond pulses driven by multi-cycle laser pulses Near single-cycle driver pulses, as those presented in the previous section, are difficult to obtain in the laboratory. To this end, we have also analyzed schemes to obtain isolated circularly polarized attosecond pulses with longer multi-cycle driving pulses. These schemes can be considered as extension of the polarization gating technique, which has been successfully applied in linearly polarized HHG to obtain isolated linearly polarized attosecond pulses [9]. Our approach in the noncollinear geometry consists on applying a time delay (td) between the driving pulses. For two Gaussian pulses of equal duration (1/e2 half-width ), delayed by td, the ellipticity of the resulting pulse changes with time as [9] (1) Thus, by superposing two non-collinear laser pulses at the focal plane, the polarization of the resulting pulse changes from circular to linear and back to circular, thus restricting the spatial region over which polarization is linear [8]. In Fig. 2 we present the attosecond pulses (linear scale) and HHG spectra (logarithmic scale) obtained using this scheme in the non-collinear geometry, where the pulse duration of the driving pulses is tFWHM=5.8 fs (twice as in Fig. 1). The results of the simulations confirm, that as the time delay increases from td= 0 (c) to td =0.75tFWHM (f), the side bursts in the train get suppressed relative to the main center cycle burst and, hence, the number of attosecond pulses within the train reduces towards the selection of an isolated circularly polarized attosecond pulse. On the other hand, in the HHG spectra we observe the two circularly polarized harmonic beams arising from the non-collinear geometry. At the same time, as expected, the cutoff energy and the harmonic yield reduces, as the time delay td is increased. Thus, the isolation of circularly polarized attosecond pulses is indeed possible, even with longer duration driving lasers, though there is a trade-off in conversion efficiency.
UW4A.41.pdf
International Conference on Ultrafast Phenomena © OSA 2016
Fig. 2: Time-gating mechanism for generating an isolated circularly polarized attosecond pulse with multi-cycle driving pulses. Attosecond pulses (left, linear scale) and HHG spectra (right, logarithmic scale) obtained in a non-collinear HHG scheme for a time-delay of (a,b) td=0, (c,d) td =0.5tFWHM, and (e,f) td =0.75tFWHM. Laser parameters are as in Fig. 1(b), except that the driving pulse duration is doubled to 5.8 fs.
4. Conclusions In summary, we have used numerical simulations to propose and analyze two different schemes for generating isolated circularly polarized laser pulses via HHG with non-collinear counter-rotating driver pulses of the same wavelength. A short driving laser pulse duration reduces the number of circularly polarized bursts in the attosecond pulse train towards a single circularly polarized attosecond pulse. We have further shown that a time-delay between the two non-collinear pulses generates an effective polarization gate in the resulting pulse at the focal plane. This provides an alternative route to the generation of isolated circularly polarized attosecond pulses even with longer multi-cycle driving pulses. The isolation of pure circularly polarized attosecond pulses, along with the opportunity to select their central energy and helicity in the non-collinear technique, opens new perspectives to study ultrafast dynamics in chiral systems and magnetic materials. References [1] Long et al., Model calculations of polarization-dependent two-color high-harmonic generation. Phys Rev A 52:2262 (1995). [2] A. Fleischer, O. Kfir, T. Diskin, P. Sidorenko, and O. Cohen. Nature Phot. 8, 543 (2014). [3] O. Kfir, P. Grychtol, E. Turgut, R. Knut, D. Zusin, D. Popmintchev, T. Popmintchev, H. Nembach, J. M. Shaw, A. Fleischer, H. Kapteyn, M. Murnane, and O. Cohen, Nature Phot. 9, 99 (2015). [4] T. Fan, P. Grychtol, R. Knut, C. Hernández-García, D. Hickstein, D. Zusin, C. Gentry, F. J. Dollar, C. A. Mancuso, C. W. Hogle, O. Kfir, D. Legut, K. Carva, J. L. Ellis, K. M. Dorney, C. Chen, O. G. Shpyrko, E. E. Fullerton, O. Cohen, P. M. Oppeneer, D. B. Milosevic, A. Becker, A. A. Jaron-Becker, T. Popmintchev, M. M. Murnane, and H. C. Kapteyn, Proc. Natl. Acad. Sci. USA 112, 14206-14211 (2015). [5] C. Chen, Z. Tao, C. Hernández-García, P. Matyba, A. Carr, R. Knut, O. Kfir, D. Zusin, C. Gentry, P. Grychtol, O. Cohen, L. Plaja, A. Becker, A. Jaron-Becker, H. Kapteyn, and M. Murnane, Sci. Adv. 2, e1501333 (2016). [6] D. D. Hickstein, F. J. Dollar, P. Grychtol, J. L. Ellis, R. Knut, C. Hernández-García, C. Gentry, D. Zusin, J. M. Shaw, T. Fan, K. M. Dorney, A. Becker, A. Jaroń-Becker, H. C. Kapteyn, M. M. Murnane, and Ch. G. Durfee, Nature Phot. 9, 743-750 (2015). [7] D. B. Milosevic, Opt. Lett. 40, 2381 (2015). [8] L. Medisauskas, J. Wragg, H. van der Hart, and M. Yu. Ivanov, Phys. Rev. Lett. 115, 153001 (2015). [9] C. Hernández-García, C. G. Durfee, D. D. Hickstein, T. Popmintchev, A. Meier, M. M. Murnane, H. C. Kapteyn, I. J. Sola, A. Jaron-Becker, and A. Becker, Physical Review A 93, 043855 (2016). [10] C. Hernández-García, J. A. Pérez-Hernández, J. Ramos, E. Conejero Jarque, L. Roso, and L. Plaja, Phys. Rev. A 82, 033432 (2010).
