With the development of intense femtosecond laser sources it has become possible to study atomic and molecular processes on their own subfemtosecond time scale. Table-top setups are available that generate intense coherent radiation in the extreme ultraviolet and soft-X-ray regime which have various applications in strong-field physics and attoscience. More recently, the emphasis is moving from the generation of linearly polarized pulses using a linearly polarized driving field to the generation of more complicated elliptically polarized polychromatic ultrashort pulses. The transverse electromagnetic field oscillates in a plane perpendicular to its propagation direction. Therefore, the two dimensions of field polarization plane are available for manipulation and tailoring of these ultrashort pulses. We present a field that allows such a tailoring, the so-called bicircular field. This field is the superposition of two circularly polarized fields with different frequencies that rotate in the same plane in opposite directions. We present results for two processes in a bicircular field: High-order harmonic generation and above-threshold ionization. For a wide range of laser field intensities, we compare high-order harmonic spectra generated by bicircular fields with the spectra generated by a linearly polarized laser field. We also investigate a possibility of introducing spin into attoscience with spin-polarized electrons produced in high-order above-threshold ionization by a bicircular field.

ABSTRACT Quantum-orbit theory of high-order harmonic generation (HHG) by bicircular laser field is presented. HHG is a strong laser-field-induced process in which the energy absorbed from the laser field is emitted in the form of a high-energy photon. This process can be described using the strong-field approximation and its approximation – the quantum-orbit theory. We develop a classification of quantum orbits for HHG by bicircular field which consists of two coplanar counter-rotating circularly polarized field of frequencies and , where r and s are integers and ω is a fundamental frequency. Analysis of the contributions of particular quantum orbits to high-harmonic intensity enables a better understanding of the HHG process. The cases of the ω– and ω– bicircular fields and of the atoms having the s and the p ground state are analysed in detail. Particular attention is devoted to the influence of the ratio of the intensities and of the bicircular field components. For inert gases having the p ground state the asymmetry in the emission of the left- and right-circularly polarized harmonics can be large. This is explained comparing the partial harmonic intensities for HHG from the ground state having the magnetic quantum number m=+1 and m=−1 and analysing the contributions of particular quantum orbits and the corresponding electron trajectories and velocities. The contribution of the shortest quantum orbit is dominant. It was found that the electron velocity at the ionization time, which still allows the return of the electron to the parent ion, determines the height of the high-energy HHG plateau. For this velocity is large which, in the case of the p ground state, leads to a large helicity asymmetry parameter. On the other hand, for this velocity is small and the intensity of the high-energy plateau harmonics is high.

A review is presented of the rescattering plateau in laser-induced above-threshold ionization and its various features as they were discovered over time. Several theoretical explanations are discussed, from simple momentum conservation to the quantum-mechanical improved strong-field approximation and the inherent quantum orbits or, alternatively, entirely classical methods. Applications of the plateau to the extraction of atomic or molecular potentials and to the characterization of the driving laser pulse are also surveyed.

Ionization of atoms by an intense bicircular laser field is considered, which consists of two coplanar corotating or counterrotating circularly polarized field components with frequencies that are integer multiples of a fundamental frequency. Emphasis is on the effect of a reversal of the helicities of the two field components on the photoelectron spectra. The velocity maps of the liberated electrons are calculated using the direct strong-field approximation (SFA) and its improved version (ISFA), which takes into account rescattering off the parent ion. Under the SFA all symmetries of the driving field are preserved in the velocity map while the ISFA violates certain reflection symmetries. This allows one to assess the significance of rescattering in actual data obtained from an experiment or a numerical simulation.

Channel-closing effects, such as threshold anomalies and resonantlike intensity-dependent enhancements in strong-field ionization by a bicircular laser field are analyzed. A bicircular field consists of two coplanar corotating or counter-rotating circularly polarized fields having different frequencies. For the total detachment rate of a negative ion by a bicircular field we observe threshold anomalies and explain them using the Wigner threshold law and energy and angular momentum conservation. For the corotating bicircular case, these effects are negligible, while for the counter-rotating case they are pronounced and their position depends on the magnetic quantum number of the initial state. For high-order above-threshold ionization of rare-gas atoms by a counter-rotating bicircular laser field we observe very pronounced intensity-dependent enhancements. We find all four types of threshold anomalies known from collision theory. Contrary to the case of linear polarization, channel-closing effects for a bicircular field are visible also in the cutoff region of the electron energy spectrum, which is explained using quantum-orbit theory.

We experimentally demonstrate straightforward methodologies for generating high harmonics of arbitrary polarization state. Polarization control is realized by adjusting the intensity ratio of the bicircular driving field or by exploiting chirally dependent Cooper minima transitions. OCIS codes: (140.7240) UV, EUV, and X-ray lasers; (020.2649) Strong field laser physics; (320.7110) Ultrafast nonlinear optics The recent re-discovery of circularly polarized high harmonic generation (CPHHG) has resulted in a renaissance of high-energy, polarization-sculpted attosecond light sources, which are capable of interrogating ultrafast, elementspecific chiral dynamics in condensed matter and molecular systems [1]. In particular, CPHHG driven by bichromatic, counter-rotating laser fields—the bicircular field—has been at the forefront of the attosecond polarization resurgence due to the possibility of controlling the high-harmonic spectral, temporal, and polarization properties afforded via the manipulation of these unique two-color fields [1,2]. Practically, direct control over the spectrotemporal structure of the CPHHG emission process is attractive for generating bright, tailor-made highharmonic beamlets for ultrafast magneto-optical chiral spectroscopies and also isolated attosecond pulses of nearly arbitrary polarization. As such, numerous strategies have been proposed to achieve this level of control by exploiting the helicity-dependent aspects of the microscopic and macroscopic response to the external field [1]. Despite sincere efforts, the complexity of many methodologies has limited active polarization control in CPHHG to just a few experimental demonstrations [2, 3]. In this work, we present two straightforward, yet distinct, methodologies for controlling the spectral distribution of leftand right-circularly polarized (LCP/RCP) harmonics in bicircular-driven CPHHG (Fig. 1A), thus allowing for active manipulation of the polarization of the underlying attosecond pulse trains (APTs). First, we find that the intensity ratio of a commensurate bicircular field—where 2w1=w2—serves as a practical, real-time knob for smoothly varying the ellipticity of the APTs, independent of the CPHHG photon energy and bandwidth (Fig. 1B). Second, we show that a non-commensurate nearand short-wave IR (SWIR) field, combined with an effectively phase-matched geometry, can be utilized to extend the CPHHG cut-off to beyond the Cooper minimum in Ar [4], resulting in the natural production of bright, single-helicity harmonic spectra (and thus circularly polarized APTs) spanning the M absorption edges of several magnetic materials (Fig. 1C). Figure 1. (A) Experimental scheme for bicircular-driven circularly polarized high harmonic generation (CPHHG). (B) Theoretical attosecond pulse trains obtained from highly chiral experimental CPHHG spectra generated in an Ar gas jet. (C) Short-wave-IR-driven CPHHG in a phaseHM2A.4.pdf High-brightness Sources and Light-driven Interactions Congress 2018 (HILAS, MICS, EUVXRAY) © OSA 2018 matched waveguide geometry yields a bright spectrum that extends beyond the Cooper minimum in Ar, which generates a single-helicity spectrum covering prominent magneto-optical absorption edges. In the experiment (Fig. 1A), circularly polarized high harmonics are generated via collinear mixing of the fundamental (w, 790-nm, 45-fs, RCP) of a Ti:sapphire amplifier and either its second harmonic (2w, 395-nm, LCP) or a SWIR field (0.4w, 2000-nm, LCP). The combined fields are then focused onto a supersonic gas jet (w-2w) or coupled into a hollow-core waveguide (w-0.4w). In either geometry, bright, circularly polarized high harmonic spectra are produced, which consist of a series of high-harmonic doublets possessing opposite helicities. The harmonics themselves exhibit a high degree of circularity, as indicated by the suppression of spin-forbidden harmonic orders between the circularly polarized doublets (Fig. 1C and Fig. 2A). For commensurate, w-2w, driven CPHHG in an Ar gas jet, the lower (higher) frequency harmonic in each doublet rotates with the w (2w) field, and these individual harmonics can be viewed as being produced by absorption of an additional w (2w) photon from the driving field. The intensity of the RCP (LCP) harmonics in the far-field are directly coupled to the photon density of each color in the two-color driving laser [2]. As such, we can actively control the intensity of either RCP or LCP high-harmonics in the far-field, thus generating highly chiral CPHHG spectra (Fig. 2A). In the time domain, controlling the chirality of the CPHHG process manifests as direct control over the ellipticity of the underlying APTs (Fig. 2B). As the intensity ratio is varied, the x and y components of the bicircular field that correspond to bright CPHHG emission also vary, which imparts ellipticity onto the APT. We confirm the dependence of this attosecond ellipticity on the CPHHG spectral chirality via macroscopic numerical simulations [5] of the upconversion process (Fig 2A, B). Most importantly, this attosecond ellipticity is uncoupled from the polarizations of the driving field, which allows for highly elliptical APTs to be produced without sacrificing the circular polarization of the emitted harmonics [2]. Fig 2. Controlling the ellipticity of APTs in CPHHG. (A) Experimental, w-2w CPHHG spectra in Ar generated at different intensity ratios, I2w/Iw, of the driving field (exact ratios indicated next to spectra). Inset depicts the intensity asymmetry, (IRCP-ILCP)/(IRCP+ILCP), of the CPHHG spectra at different I2w/Iw. (B) Ellipticity of the APTs computed in Ar for experimental intensity ratios. (C) Experimental intensity asymmetries in w-0.4w driven CPHHG as a function of pressure in the hollow-core waveguide. A sharp helicity reversion is observed at the position of the Cooper minimum (~ 50 eV) in Ar. (D) Theoretical simulations confirm the generation of bright, highly chiral CPHHG spectra in the cutoff region. Finally, we show that the generation of highly elliptical APTs can be achieved without manipulation of either the driving laser field or conditions of the generating medium. By driving the CPHHG process with a noncommensurate, w-0.4w field, we generate bright circularly polarized high-harmonics spanning the Cooper minimum in Ar (Fig. 1C). The presence of the Cooper minimum results in a natural suppression of RCP harmonic orders, yielding highly chiral CPHHG spectra in the high energy cut-off region (Fig. 1C and Fig. 2C). Combined with effective phase-matching in the high-pressure waveguide, we generate a single-helicity CPHHG spectrum, which naturally corresponds to circularly polarized APTs [6]. Moreover, this single-helicity region covers many prominent magneto-optical absorption edges, which should allow for spectroscopies of ultrafast magneto-optical phenomenon. In summary, we have shown the spectral chirality, and thus the ellipticity of the APTs, in CPHHG can be actively controlled via two straightforward and simple methodologies. As such, highly elliptical APTs can be readily generated and controlled in real-time, thus greatly extending the applicability of these novel light sources to attosecond spectroscopies of chiral dynamics in a variety of condensed matter and molecular systems. [1] A. D. Bandrauk, J. Guo, K. J. Yuan, “Circularly polarized attosecond pulse generation and applications to ultrafast magnetism,” J. Opt. In Press. https://doi.org/10.1088/2040-8986/aa9673 [2] K. M. Dorney, et al., “Helicity-selective enhancement and polarization control of attosecond high harmonic waveforms driven by bichromatic circularly polarized laser fields,” Phys. Rev. Lett. 119, 063201 (2017). [3] N. Zhavoronkov, M. Ivanov, “Extended ellipticity control for attosecond pulses by high harmonic generation,” Opt. Lett.42, 4720 (2017). [4] D. Baykusheva, et al., “Signatures of Electronic Structure in Bicircular High-Harmonic Spectroscopy,” Phys. Rev. Lett. 119, 203201 (2017). [5] C. Hernández-García, et al., “High-order harmonic propagation in gases within the discrete dipole approximation,” Phys. Rev. A. 82, 033432 (2010). [6] D. B. Milošević. “Low-frequency approximation for high-order harmonic generation by bicircular laser field,” Phys. Rev. A. In Review.