We report the spark discharge synthesis of aerosol germanium nanoparticles followed by sintering in a tube furnace at different temperatures varying from 25 to 800 °C. The size, structure, chemical composition and optical properties were studied. We have demonstrated a melting mechanism of nanoparticles agglomerates, the growth of the mean primary particle size from 7 to 51 nm and the reduction of the size of agglomerates with a temperature increase. According to transmission electron microscopy (TEM) and Fourier transform infrared (FTIR) data, primary nanoparticles sintered at temperatures from 25 to 475 °C basically have a structure of Ge crystals embedded in a GeOx amorphous matrix, as well as visible photoluminescence (PL) with the maximum at 550 nm. Pure germanium nanoparticles are prepared at temperatures above 625 °C and distinguished by their absence of visible PL. The shape of the experimental UV-vis-NIR extinction spectra significantly depends on the size distribution of the germanium crystals. This fact was confirmed by simulations according to Mie theory for obtained ensembles of germanium nanoparticles.

The theory of photoionization describing the interaction of x-ray free-electron laser (XFEL) pulses and high-harmonic-generated (HHG) radiation is generalized to ultrashort laser pulses, where the concept of the standard ionization probability per unit time in Fermi’s golden rule and in Einstein’s theory breaks down. Numerical calculations carried out in terms of a generalized photoionization probability for the total duration of pulses in the near-threshold regime demonstrate essentially nonlinear behavior, while absolute values may change by orders of magnitude for typical XFEL and HHG pulses. XFEL self-amplified spontaneous emission pulses are analyzed to reveal general features of photoionization for random and regular spikes: the dependences of the nonlinear photoionization probability on carrier frequency and spike duration are very similar, allowing an analytical expectation value approach that is valid even when there is only limited knowledge of random and regular parameters. Numerical simulations carried out for typical parameters demonstrate excellent agreement.

The standard approach to calculate the Thomson scattering probability is reconsidered for the case of ultrashort incident laser pulses (USLPs). We established a new model for the interaction of USLP with plasmas that is based on Fermi's equivalent photon conception to calculate the spectral-angular differential Thomson scattering probability. The simulations demonstrate that the scattering probability for USLP is a non-monotonic function of pulse duration in contrast to the standard long-pulse model showing linear dependence. An analytical approach is developed to study the nonlinear behavior of the scattering probability as a function of pulse duration and other parameters.

On the basis of equations obtained in the framework of second-order quantum-mechanical perturbation theory, the standard approach to the calculation of scattering radiation probability is extended to the case of ultrashort laser pulses. We investigate the mechanism of the appearance of plasmon peaks in the spectrum of the plasma form factor for different parameters of the problem. For the case in which scattering on plasmons dominates over scattering on electron density fluctuations caused by chaotic thermal motion, we derive analytical expressions describing the scattering probability of ultrashort laser pulses on plasmons. Together with this, we obtain a simple expression connecting the frequency of scattered radiation and the energy transmitted from the incident pulse to plasmon, and vice versa. In considering the scattering probability, our emphasis is on the dependence on the pulse duration. We assess in detail the trends of this dependence for various relations between pulse carrier frequency and plasmon energy.

We investigated theoretically the time dependence of ultra-short laser pulse scattering by an atom at the high-frequency limit for the spectral and total probability of the process using new expression which we derived in this paper. We established that the time dependence of spectral scattering is presented by the curve with the maximum for sufficiently large detuning of scattering frequency from the carrier frequency of the pulse, while the total scattering probability is always the monotonically increasing function of time. We also studied the dependence of scattering probability on pulse duration at the long-time limit. It was shown that, at the long-pulse limit, the scattering probability is a linear function of pulse duration, while in the opposite case, it is a function with maximum. The position of this maximum is determined by the detuning of the scattering frequency from the carrier frequency of the pulse.