The semiconductor Bloch equations provide a very versatile and microscopic approach to compute and analyze optical and electronic properties of semiconductors. Here, we focus on high harmonic generation arising from the driving of crystalline systems with very strong optical and Terahertz pulses. Implementing a proper gauge allows us to solve the semiconductor Bloch equations in the length gauge. The length gauge turns out to be advantageous since it converges for a smaller number of bands than the velocity gauge and, in addition, enables a unique distinction between inter- and intraband contributions. Besides odd harmonics polarized parallel to the incoming field our approach also describes even harmonics which originate from the Berry curvature and are polarized perpendicular to the incident field. Next, we demonstrate that the electron and hole collision/recombination dynamics is mainly responsible for the anisotropy of the interband high harmonic generation. Our findings connect the electron/hole backward scattering to van Hove singularities and the forward scattering with critical lines in the band structure and we show that this dynamics can be controlled by properly designed two-color fields. Furthermore, we consider excitonic effects within a two-band model and show that they can strongly enhance the high harmonic emission intensity for suitably chosen incident pulses. When an odd-order harmonic corresponds to the energy of the 1s exciton this harmonic is several orders of magnitude larger than the emission from non-interacting electrons and holes.
When coherent electromagnetic radiation generated by powerful laser system is tightly focused, pursuing the aim to achieve the highest value of intensity possible, it may be challenging estimating this intensity with a sufficient degree of accuracy. If the energy of a laser pulse, its duration, time profile and focal spot radius are known, evaulation of the maximal intensity is straightforward. However, for high power (sub-petawatt and above) femtosecond laser systems, the inherent uncertainties of these four parameters (except maybe the pulse duration) are rather high, so that different estimation models of the laser intensity in the focus may substantially disagree. Presently, the question of whether or not intensities above 10^21 W/cm2 have ever been achieved remains debatable, although values of this order and above are the main goal of the two Extreme Light Infrastructure (ELI) pillars.
In this context, a reliable method allowing to calibrate ultrahigh laser intensities becomes of even higher demand. Here we discuss the reliability of a method for the measurement of ultrahigh laser intensities, based on the effect of tunneling field ionization of heavy atoms and ions. To this end, we employ the highly nonlinear dependence of tunneling ionization rates on the laser intensity. This nonlinearity leads to the emergence of steep plateaus in the distribution of charge states in the laser focus and in such a way to allowing estimate, with a high degree of certainty, the laser intensity at focus.
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