We address high-order harmonic generation with linearly polarized bichromatic fields, concentrating on a modulation in the harmonic yield as a function of the relative phase between the two field components, and on an offset phase shift of this modulation for neighboring cutoff harmonics. These effects have been recently observed in experiments where the relative phase between the two driving fields was controlled. Using the

High-harmonic generation and high-order above-threshold ionization spectra calculated in the strong-field approximation are analyzed in terms of the complex space-time orbits that result from a saddle point analysis of the underlying integrals. For elliptical polarization, the plateaus of the spectra of high-harmonic generation and high-order above-threshold ionization each turn into a staircase of very similar appearance. Each step of the stair can be traced to a particular pair of orbits which are almost identical in both cases.

We consider the use of strong static fields to control two related atomic processes: laser-assisted x-ray-atom scattering (XAS) and high-harmonic generation (HHG). We first analyze the laser field intensity dependence of the differential cross section (DCS) plateau structures for the laser-assisted XAS process in the presence of a static electric field as a function of the number of photons exchanged with the laser field. Besides the recently discovered (Milosevic, D.B. and Starace, A.F., 1998, Phys. Rev. Lett., 81, 5097) extended plateau for absorbed photons, which indicates a substantial increase of the scattered x-ray energies, a new plateau, having many orders of magnitude larger DCS, appears for higher laser field intensities. We show furthermore a connection between this process and HHG. We also consider control of HHG with static electric and magnetic fields which are parallel to the laser polarization. The B field can considerably increase the harmonic emission rate (Milosevic, D.B. and Starace, A.F., 1999, Phys. Rev. Lett., 82, 2653). The rate of a chosen harmonic is maximal whenever an integer multiple of the cyclotron period of the electron's motion perpendicular to the magnetic field is equal to the return time to the nucleus of the laser-field-generated electron wave packet in the intermediate state. While the B field has only a modest effect on the plateau cutoff positions, the static electric field can introduce additional plateaus and cutoffs. A properly chosen combination of static E and B fields can increase both the emission rate and the maximum harmonic order. The locations and magnitudes of the plateaus, both for XAS and HHG, are explained using the classical three-step model.

The dependence on laser intensity of recently discovered plateau structures in laser-assisted x-ray‐atom scattering, both with and without a static electric field present, is analyzed. Using the ‘‘three-step’’ model and the strong-field approximation we demonstrate a connection between laser-assisted, x-ray‐atom scattering and high-order harmonic generation: For high laser-field intensities without a static field present, both processes have plateaus whose energies extend to the cutoff value 3.17Up , where Up is the ponderomotive potential energy. For x-ray‐atom scattering in the presence of a static electric field we show that at high laser-field intensities two plateaus appear: One is our recently predicted high-energy plateau for the same process @Phys. Rev. Lett. 81, 5097 ~1998!#, while the other, low-energy plateau, has a differential cross section six orders of magnitude larger. The energy positions and relative magnitudes of these new plateaus are explained using semiclassical arguments. @S1050-2947~99!07211-X#

We consider the scattering of 50 eV x-rays by hydrogen atoms in the presence of a bichromatic, linearly polarized laser field with frequencies and r, where r = 2,3, = 1.17 eV, and with relative phase between the bichromatic laser field components. Numerical results for the differential cross-section (DCS) as a function of the number n, where n is the energy exchanged with the laser field, are presented. For either a monochromatic laser field or a bichromatic laser field with the frequencies and 3, the integer n can only be even, while for a bichromatic laser field with the frequencies and 2, the integer n can have any value. For small values of |n| we find pronounced maxima in the DCS. For larger |n| we find plateaus which are different for negative and positive values of n. For lower values of the laser field intensity the plateau for negative values of n is much more extended and greater in magnitude than that for positive values of n. The height of either plateau is also higher for the bichromatic laser field than for either monochromatic field. In the (, 2) case we find the symmetry DCS(+) = DCS(). We show that the relative phase influences the DCS so that phase control of the x-ray-atom scattering process is possible. For some values of the energy of the outgoing x-ray photons can be increased. Finally, a quasi-classical explanation of the results is presented.

We demonstrate control of high harmonic generation by a linearly polarized laser field using a uniform static magnetic field parallel to the laser polarization. We predict that particular values of the magnetic field can increase harmonic intensities by orders of magnitude. Classical orbit calculations show that these magnetic-field-induced intensity revivals occur when the return time for laser-driven motion of the electron back to the origin is a multiple of the cyclotron period for motion perpendicular to the laser polarization direction. [S0031-9007(99)08759-1]

We apply the strong-field S-matrix theory to the above-threshold ionization (ATI) in a bichromatic linearly polarized laser field having frequencies and , and the relative phase between the laser field components. The presented theory includes both the Coulomb and rescattering effects. We compute and discuss the electron energy spectra for different angles between the momentum of the ionized electron and the polarization vector of the laser field. We found that the plateau for and for the backward emission of electrons extends up to , where is the ponderomotive energy of the first laser field component (assuming equal intensities of both components). There are no such high-energy electrons for , in contrast to the symmetry , valid in the monochromatic case. In the bichromatic case the ionization rates possess the more general symmetry property . Therefore, for we predict the emission of the high-energy electrons in the forward direction . In a bichromatic field the sidelobe structures are strongly influenced by quantum mechanical interference effects. We also explore the -dependence of the ionization rates for different relative phases , and for those energies which correspond to the classical cutoff law.

We consider harmonic generation by atoms exposed to an intense laser pulse of a few femtoseconds. Our results, obtained by solving numerically the corresponding 3-dimensional time-dependent Schrodinger equation, demonstrate that the harmonic spectra are extremely sensitive to the phase of the laser field. Depend- ing on this phase, the harmonics in the cutoff are resolved or not resolved. The position of the cutoff itself varies with the phase and the so-called “plateau” region exhibits two well-distinct parts: a series of well-defined har- monics followed in the high-frequency region by a series of broad peaks which are not separated any more by twice the laser field frequency. These results are explained in terms of both quantum and classical dynamics. We also show that this phase sensitivity may be exploited in order to probe the phase of the electric field of an ultrashort laser pulse in a single shot experiment. Our discussion about this new method of diagnosis takes into account propagation effects.

We present a generalization of the S-matrix theory of above-threshold ionization (ATI), which includes both the Coulomb and rescattering effects. The Coulomb effects are responsible for a considerable increase of the ionization rates, while the rescattering effects give rise to the appearance of the second plateau of the ATI spectrum. Coulomb effects change the behavior of the rates at the first plateau, but they do not influence the qualitative behavior of the spectrum of the high-energy electrons in the second plateau. Our results are in excellent agreement with recent experiments. We show that the sidelobe positions correspond to the last rounded top before the cutoff of the ATI spectrum for the corresponding angle. Our model is simple, and can be easily generalized to different inert gases.

We calculate the total ionization rate as a function of the kinetic energy of electrons ionized by a bichromatic laser field in an above-threshold ionization process. An improved Keldysh-Faisal-Reiss model, which includes the Coulomb effects of the residual ions on the ionized electron, is used. We compare the results obtained using the length and the velocity gauge. In the case of the bichromatic laser field the phase-dependent effects are observed and a comparison with recent experiments is presented. A classical analysis of the rescattering cut-off laws in a bichromatic laser field is also given.

We consider harmonic generation by atoms exposed to an intense laser pulse of a few femtoseconds. Our results, obtained by solving numerically the corresponding three-dimensional time-dependent Schrodinger equation, demonstrate the strong sensitivity of the harmonic spectra to the phase of the laser. These results are explained in terms of both quantum and classical dynamics. We show that this phase sensitivity may be exploited in order to probe the laser phase for ultrashort pulses. Our discussion about this new method of diagnosis takes into account propagation effects.