We develop theoretically and confirm both numerically and experimentally a comprehensive analytical model which describes the propensity rules in the emission of circularly polarized high harmonics by systems driven by two-color counter-rotating fields, a fundamental and its second harmonic. We identify and confirm the three propensity rules responsible for the contrast between the 3N+1 and 3N+2 harmonic lines in the HHG spectra of noble gas atoms. We demonstrate how these rules depend on the laser parameters and how they can be used in the experiment to shape the polarization properties of the emitted attosecond pulses.

Abstract:The bi-circular scheme for high harmonic generation, which combines two counterrotating circular fields with frequency ratio 2:1, has recently permitted to generate high harmonics with essentially circular polarization, opening the way for ultrafast chiral studies. This scheme produces harmonic lines at 3N + 1 and 3N + 2 multiples of the fundamental driving frequency, while the 3N lines are forbidden owing to the three-fold symmetry of the field. It is generally established that the routinely observed signals at these forbidden harmonic lines come from a slight ellipticity in the driving fields, which breaks the three-fold symmetry. We find that this is neither the only nor it is the dominant mechanism responsible. The forbidden lines can be observed even for perfectly circular, long driving pulses. We show that they encode rich information on the sub-cycle electronic dynamics that occur during the generation process. By varying the time delay and relative intensity between the two drivers, we demonstrate that when the second harmonic either precedes or is more intense than the fundamental field, the dynamical symmetry of the system is broken by electrons trapped in Rydberg orbits (i.e., Freeman resonances), and that the forbidden harmonic lines are a witness of this.

The overdetermination of the mathematical problem underlying ptychography is reduced by a host of experimentally more desirable settings. Furthermore, reconstruction of the sample-induced phase shift is typically limited by uncertainty in the experimental parameters and finite sample thicknesses. Presented is a conjugate gradient descent algorithm, regularized optimization for ptychography (ROP), that recovers the partially known experimental parameters along with the phase shift, improves resolution by incorporating the multislice formalism to treat finite sample thicknesses, and includes regularization in the optimization process, thus achieving reliable results from noisy data with severely reduced and underdetermined information.

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The method inverse dynamical electron scattering (IDES) [1,2] offers a framework to retrieve the electrostatic potential of the object from arbitrary detection geometries in the transmission electron microscope (TEM). This has been illustrated on TEM simulations [1,2] and experimentally on an optical set-up [3]. Although ptychography was already included [2], now a specialized software has been developed: regularized optimization for ptychography (ROP). Contrary to the more conventional Gerchberg-Saxton formalism, ROP retrieves the potential, the electron probe and the probe positions through a derivative-based Polak-Ribiere conjugate gradients optimization, and is capable of regularizing the reconstruction. Furthermore, first results of the practical implementation of structured illumination are presented.By approximating the scattering of the fast electrons in the solid with the multislice algorithm, multiple scattering in the forward direction is taken into account. Furthermore, an arbitrary error function can be defined, and the backpropagation algorithm, combined with the chain rule, enables efficient computation of the derivatives of said function with respect to the object potential, and arbitrary model parameters like amplitude, phase and position of the incoming beam; estimation of the latter parameters is especially important for structured illumination set-ups. The potential can be approximated through Dirac delta functions located at the atom positions and convoluted with a so-called generalized potential accounting for the average atom's width. Adding a regularization term (the sum of absolute values of the reconstructed potential) to the error function prevents overfitting and improves sparsity.Structured illumination was obtained through a diffuser in the condenser plane of the microscope. Its phase modulation was realized through the mean inner potential of a thin film with spatial thickness variation. For production a 200-nm-thick silicon nitride (SiN) membrane over a 200-μm-thick Si substrate was thinned using FEI Helios NanoLab 460F1 focused ion beam milling. A 150-nm-thick Au layer, acting as a diaphragm and reducing charging, was coated on the membrane surrounding the diffuser area. Analogous to [4], the diffuser was designed with a Gerchberg-Saxton algorithm iterating back and forth between real and reciprocal space; each time enforcing the respective constraints: in real space the intensity profile of the beam was set to a cosine of width 2 nm and in reciprocal space the intensity was set to 1 and 0 for angles below and above the Scherzer angle, respectively.In Figure 1. the results from simulated diffraction patterns are shown. The sample is a [001] oriented Si-58