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In high-order harmonic generation in low-dense media, the application of two-colored pump has been shown to enhance odd-order harmonics, as well as the generation of strong even harmonics. Here, we apply this approach to compare high-order harmonic generation from laser-produced plasmas and gases using different mechanisms of harmonic emission enhancement. We generate two-color pump (TCP, 806 nm + 403 nm and 1030 nm + 515 nm) using two nonlinear crystals of different thickness (0.2 and 0.4 mm in the case of experiments with plasmas using 806 nm pump; and 0.1 mm and 0.4 mm in the case of experiments with gases and plasmas using 1030 nm pump) to demonstrate the enhancement of odd and even harmonics in laser-produced plasmas and by applying weak second field (403 or 515 nm) at different overlaps of pump pulses. The high-order harmonic generation in two media using TCP pulses is optimized. We demonstrate the wavelength dependence and the prevailing role of the partial overlap between the two orthogonally polarized waves in laser-produced plasmas and gases over large ratios of the second-order and fundamental photons. Our results are supported by the non-perturbative single atom theory and the interference model simulations.

The change in the polarization state of the atomic response due to the appearence of the longitudinal component, which has been predicted in [A. Andreev, S. Stremoukhov, and O. Shoutova, Europhys. Lett. 120, 14003 (2017)], has been studied. The dependence of the vector properties of the atomic current induced in an atom with unit angular momentum in the ground state on the properties of a two-color laser field with orthogonally polarized components has been analyzed. It has been shown that the variation of the delay time between the frequency components of the laser field makes it possible to efficiently control the polarization of the components of the atomic response field. The effect of the mutual orientation of the electric component of the laser field and the angular momentum of the atom on the longitudinal component of the atomic current and on the polarization properties of the generated radiation has been demonstrated.

Within the framework of the non-perturbative light–atom interaction theory, we consider the population dynamics of the ground-state sublevels corresponding to the different values of the orbital quantum number (l) projections and its influence on the high optical harmonics. We study the problem of high optical harmonics generation in two geometries: (1) two linearly polarized fields at frequencies ω and 2ω for different angles of azimuthal projection difference and arbitrary orientation with respect to the angular momentum of the atom direction; (2) two elliptically polarized fields at frequencies ω and 2ω rotating in opposite directions with variable mutual ellipticity. We show that the unequal population dynamics of the levels with different projections of the atom angular momentum (magnetic quantum number) has a significant impact on the value of the ellipticity of the generated radiation.

A theoretical investigation of the generation of high-order harmonics in an ensemble of atoms interacting with femtosecond laser pulses of high intensity is conducted. It is shown that the cut-off frequency of the photoemission spectra is saturated in a laser field of subatomic strength. A model of the effect dispersion has on the radiation of high-order harmonics in extended environments is proposed.

In comparative experiments, it was found that the maximum efficiency of third harmonic generation (THG) in cluster nanoplasma was ∼9x10−5 and was approximately 4 times less effective than the case of THG in gas under similar experimental conditions. This result is consistent with theoretical calculations and show that THG amplitude in a gas is about an order of magnitude higher than in a cluster medium. The discrepancy between the THG efficiency in gas and clusters obtained theoretically and experimentally in discussed.

Excitation of the isomeric nuclear state $^{229\mathrm{m}}\mathrm{Th}$ in the process of thorium atom irradiation by a two-color femtosecond pulse of a Ti:Sa laser at the fundamental wavelength and second harmonic ($\ensuremath{\omega}+2\ensuremath{\omega}$) is analyzed. It is shown that the rate of isomeric state excitation can be enhanced significantly with respect to other nucleus excitation processes in laser plasma or by an external coherent source at the resonance wavelength. This enhancement is due to the process of ``nonlinear laser nuclear excitation,'' which consists in excitation of a nuclear transition by e.m. radiation, generated by an electronic shell of the atom interacting with an intense laser field, with the photon energy coinciding with the nuclear transition energy. The process is based on the following. First, the atomic current associated with the motion of valence electrons in a strong $\ensuremath{\omega}+2\ensuremath{\omega}$ field is a nonlinear function of the field amplitude. Second, the energy of photons at the frequency of the Ti:Sa laser fifth harmonic coincides with the energy of the $^{229\mathrm{m}}\mathrm{Th}$ state. The yield of this harmonic is much higher if the two-color pulse (first and second harmonics of the fundamental) is used. Third, the intensity of the field produced by valence electrons at the atomic nucleus reaches the near-atomic value, which exceeds significantly the field strength associated with any other mechanism of laser plasma emission.

The process of high harmonic generation (HHG) has a wide area of different applications, in particular, in nanoscale imaging, study the nanoscale energy transport in complex molecules and solids, probe the charge and spin dynamics with the femtosecond time resolution, etc. Here we discuss a possible application of HHG effect related with the study of nuclear transition dynamics. We analyse the efficiency of excitation of the isomeric nuclear state 229mTh by the fifth harmonic of Ti: Sa laser generated in thorium by two-color femtosecond pulse consisting of the fundamental and thensecond harmonic of Ti: Sa laser (ω+2ω). It is shown that the rate of isomeric state excitation can be enhanced significantly with respect to other nucleus excitation processes in laser plasma or by an external coherent source at the resonance wavelength. This enhancement is due to the discussing process of “nonlinear laser nuclear excitation”.

International audience; Recently several techniques demonstrated the production of elliptically polarized high harmonics. One of these techniques consists of the interaction in a noble gas of two-color laser beams having orthogonal linear polarizations. Here we present the theoretical explanation of such a result observed in Lambert et al. [Nat. Commun. 6, 6167 (2015)]. Numerical calculations based on the nonperturbative light-atom interaction theory reproduce well the experimental data. The degree of polarization is analyzed for different harmonic orders and found to be high. With the help of a simplified theoretical model it is shown that the degree of harmonic ellipticity depends mainly on the population of atomic state sublevels with different angular momentum projections.

High optical harmonics generation process in atomic gases interacting with bichromatic laser field in non-collinear scheme is studied with the aim of polarization state of atomic response investigation in dependence on incident field spatial properties. It is shown that the non-dipole transitions (the impact of which increases with laser field intensity) play the crucial role in discussed process.

A theory of the nonlinear optical response of an atom interacting with a superposition of arbitrarily polarized fields is developed. The theory is based on the analytical solution of the boundary-value problem for an electron moving in a spherically symmetric intraatomic field and in the field of an external electromagnetic field. By means of the example of an argon atom interacting with a bichromatic field formed by the first and second harmonics of a Ti:sapphire laser, it is shown that, when an atom interacts with the field of two polarized pulses the polarization directions of which are not collinear, the response spectrum significantly depends on the laser radiation parameters—the duration and intensity of pulses, the time of delay between them, and the angle between the directions of polarization vectors. Generation of THz radiation is shown to be possible in the ionization-free regime due to intraatomic nonlinearity.

A theory of the nonresonant response of a single atom in a state with arbitrary magnitude and direction of the angular momentum of an atomic electron with respect to the polarization vector of the acting electromagnetic field has been developed. It has been shown that the atomic response current has a tensor structure and depends both on the direction of the angular momentum of the atom and on the polarization vector of the external field. The tensor character of the response is due to the effects of the anisotropy of probability density distribution of the atomic electron as compared to the case of the free atom. The selection rules for the axisymmetric problem of the atom in the field have been analyzed. The manifestation of the selection rules in the angular spectra of photoelectrons has been demonstrated. The probability of the ionization of the atom has been analyzed as a function of the amplitude and duration of the pulse. It has been shown that the width of the generation spectrum is a nonlinear function of the field strength and is saturated in the region of nearly atomic fields. Methods for controlling the parameters of the atomic response spectrum have been proposed on the basis of the use of a sequence of laser pulses with various time profiles, carrier frequencies, and polarization states. It has been shown that the generation of terahertz radiation is possible in the preionization regime, where the generation mechanism is attributed to atomic nonlinearity.

Specific features of ionization of single atoms by laser fields of a near-atomic strength are investigated. Calculations are performed for silver atoms interacting with femtosecond laser pulses with wavelengths λ = 800 nm (Ti:Sapphire) and λ = 1.064 μm (Nd:YAG). The dependences of the probability of ionization and of the form of the photoelectron energy spectra on the field of laser pulses for various values of their duration are considered. It is shown that the behavior of the probability of ionization in the range of subatomic laser pulse fields is in good agreement with the Keldysh formula. However, when the field strength attains values close to the atomic field strength, the discrepancies in these dependences manifested in a decrease in the ionization rate (ionization stabilization effect) or in its increase (accelerated ionization) are observed. These discrepancies are associated with the dependence of the population dynamics of excited discrete energy levels of the atom on the laser pulse field amplitude.

The dynamics of high-harmonic generation and atom ionization by a strong and superstrong laser field are studied. In contrast to many earlier works, the present theory does not impose limitations on the laser field’s strength. We solve the nonrelativistic problem of a single hydrogen-like atom’s ionization from the ground state by a short laser pulse of subatomic, atomic, and superatomic field strength. Within the framework of the proposed method, we investigated the matrix elements of the ionization transition and revealed its substantially nonlinear dependence on the laser field strength. Both ionization and recombination processes are taken into account. The proposed method enables us to take into account the arbitrary order multiphoton ionization processes.

We present the results of calculations of high-harmonic spectra at different mutual orientations of laser field and atomic angular momentum. The presented results show that the atomic current induced by the external laser field can include the longitudinal component orthogonal to the polarization vector of an incident field. Moreover, it provides an insight into the physics of processes which cause the polarization of generated harmonics. In addition, it hints at the way for the polarization control over high at harmonics.

We present the results of the theoretical study of the high-order harmonic generation (HHG) in atomic gases. It is shown that the photoemission spectra exhibit unusual behavior when the laser field strength approaches near-atomic values. In subatomic field strength the cut-off frequency increases linearly with laser pulse intensity. However, when the field strength approaches near-atomic region firstly cut-off frequency slows down and then saturates. To interpret such kind of photoemission spectrum behavior we have proposed the light-atom interaction theory based on the use of eigenfunctions of boundary value problem for “an atom in the external field” instead of the traditional basis of the “free atom” eigenfunctions.

We present an interpretation of the terahertz (THz) generation in atomic gases interacting with two-color laser fields. Within the presented interpretation the process of the THz generation is associated with purely intra-atomic nonlinearity and the energy of emission is determined by the work (executed by the laser field) on the atomic electron motion in the nonharmonic intra-atomic field. To illustrate the specific features of this generation mechanism we present the results of numerical simulations on an argon atom interaction with a two-color laser field formed by the arbitrary polarized pulses at fundamental frequency and second harmonic of Ti:sapphire laser. The intensity of the laser field has been limited by ${I}_{0}l6.77\ifmmode\times\else\texttimes\fi{}{10}^{12}\frac{W}{{\mathrm{cm}}^{2}}$ (for $\ensuremath{\lambda}=800$ nm) that enables us to model the ionization-free regime of the light-atom interaction. It is demonstrated that the spectrum of the THz emission, integral efficiency of generation, and polarization state of spectral components strongly depend on the angle between the polarization vectors of laser field components. So, the variation of this angle provides the effective method of the THz generation control.

The results of theoretical and experimental study of high-order optical harmonic generation in the ensemble of silver atoms irradiated by intense femtosecond pulses of Ti:Sapphire laser are presented. It is shown that the photoemission spectra exhibit unusual behavior when the laser field strength approaches near-atomic values. In subatomic field strength the cut-off frequency increases linearly with laser pulse intensity. However, when the field strength approaches near-atomic region firstly cut-off frequency slows down and then saturates. To give new interpretation of such kind of photoemission spectrum behavior we have proposed the light-atom interaction theory based on the use of eigenfunctions of boundary value problem for “the atom in an external field” instead of the traditional basis of the “free atom” eigenfunctions. The results of computer simulations clearly demonstrate saturation of the cut-off frequency at near-atomic strength of a laser field. The problem of angular divergence of a harmonic emission is analyzed.

We present the quantum mechanical theory of the nonlinear atomic response in a strong laser field. The proposed approach provides the self consistent description of the atomic response both in the long (THz) and the short (XUV) wavelength regions. At the subrelativistic intensity of a laser pulse, our approach is valid for the arbitrary ratio between the laser and the intra-atomic field strengths. Instead of the traditional basis of the “free atom” eiegenfunctions, the basis of eiegenfunctions of the boundary value problem for “the atom in an external field” is used to calculate the matrix elements of the quantum mechanical operators. In this case the matrix elements of the generalized momentum operator and the Hamiltonian of the time-dependent Schrodinger equation are directly related with the experimentally measured dipole matrix elements and the energy spectrum of a free atom. The response of the atomic argon in the two-color laser field of arbitrary polarized components has been calculated numerically. The results of computer simulations show that the efficiency of the atomic response depends non-monotonically on the angle between the polarization vectors of the laser pulses. We also show that the most effective mechanism of THz emission in the two-color laser field appears mainly due to the atomic non-linearity, and not to the plasma non-linearities playing the dominant role in the case of the monochromatic laser field. The predictions of our theory coincide with the numerical and experimental results. This fact gives us a reliable base to provide the straightforward explanation of the observed dependencies, and to propose the methods of enhancement of efficiency of the nonlinear transformations both in the long and short wavelength spectral regions.

We present a non-perturbative theory of a single atom interaction with the multicolor laser field. The theory is based on the use of exact mathematical solutions of the boundary value problem for "an atom in the external field", as a result the case of arbitrary orientation of atomic angular momentum and electromagnetic wave polarization vector can be described in the consistent mathematical form. We also present the results of numerical simulations on silver and argon atoms interaction with single-and two-color laser fields formed by fundamental frequency and second harmonic of Ti:Sapphire laser. The results of numerical calculations show that the efficiency of high-order harmonic generation (HHG) depends strongly on the laser field parameters (especially on the orientation of polarization vectors and chirp of the two-color laser field components). We have demonstrated the saturation of the cut-off frequency in the laser fields of near-atomic strength and investigated the impact of the field phase in the case of ultrashort laser pulses.

We present the results of computer simulations on ionization of multilevel atom by femtosecond laser pulse in wide range of its intensity, from low intensities to intensities that overcome atomic one I0 = 3.5⋅1016 W/cm2. The quantitative results are obtained for the case of silver atom ionization by the pulses of Ti : Sapphire (λ = 800 nm) and Nd : YAG (λ = 1.064 μm) lasers. The main goal of our studies was to calculate the probability of ionization as a function of laser field strength as far as the photoelectron energy spectra in dependence on laser pulse parameters and here we present our results. In subatomic region of laser field strength the calculated probability of ionization is in good agreement with Keldysh formula. However, drastic difference between the calculated data and Keldysh formula appeared when the laser field strength approaches to near‐atomic values. The calculated dependencies demonstrate stabilization, drop, and enhancement of ionization probability, which are not observed in the model of atom having only one bound state (Keldysh model). This discrepancy is due to the fact that the rate of transitions between the continuum and discrete spectrum states, i.e. the rate of ionization and recombination processes, depends significantly on their population difference. At the same time, in the absence of resonances between laser photon energy and interlevel energy spacings in atom, the rate of transitions from the ground state to the continuum states and higher‐lying discrete spectrum states depends non‐linearly on the laser field strength. As a result the ionization probability became the non‐monotonic function of field strength.

We present the quantum-mechanical description of the THz amplitude periodical variation appearing due to dispersion effects and affecting the angular spectra of THz emission from extended argon gas interacting with a two-color laser field.

New interpretation of the high order harmonic generation in atomic gases interacting with laser fields is presented. The mechanism is in the temporal evolution of atomic electron density spatial distribution in the external laser field.