Circularly Polarized Laser Field Research Articles

Low-frequency–high-intensity limit of the Keldysh-Faisal-Reiss theory

When a frequency of the circularly polarized laser field approaches zero the above threshold ionization rate should approach the well-known static-field limit of tunneling ionization. In the high-intensity limit of the laser field the Keldysh-Faisal-Reiss (KFR) theory is expected to be valid. For the ground state of a hydrogen atom we study various forms of the KFR theory when both conditions: $\ensuremath{\omega}⪡1\phantom{\rule{0.3em}{0ex}}\mathrm{a}.\mathrm{u}.$ and $\ensuremath{\gamma}⪡1\phantom{\rule{0.3em}{0ex}}(\ensuremath{\omega}$ is the frequency and $\ensuremath{\gamma}$ the Keldysh parameter) are satisfied. For the circularly polarized laser field ionization rate in the Keldysh theory [which utilizes the length gauge $(\stackrel{P\vec}{d}∙\stackrel{P\vec}{E})$ form of the matrix element] is calculated analytically. We show numerically that if the WKB Coulomb correction in the final state of the ionized electron is included, the Keldysh theory gives the correct result in the tunneling domain. In the barrier-suppression regime the Keldysh theory without this correction gives ionization rates close to the exact static-field results. The Reiss theory [which utilizes the velocity gauge $(\stackrel{P\vec}{p}∙\stackrel{P\vec}{A})$ form of the matrix element] leads to too small ionization rates in the limit $\ensuremath{\omega}\ensuremath{\rightarrow}0$, $\ensuremath{\gamma}\ensuremath{\rightarrow}0$.

Strong-field ionization of molecules in circularly polarized few-cycle pulses

We have numerically investigated ionization of molecules exposed to circularly polarized (CP) intense few-cycle pulses (FCPs) by solving the three-dimensional time-dependent Schroedinger equation. The resulting photoelectron spectra exhibit an interesting ''plateau'' feature that does not appear for atoms exposed to circularly-polarized laser fields. The origin comes from the intense CP field ionizing a portion of the electron wave packet about one nuclear center and driving it through the other. Moreover, the angular distribution of photoelectrons gives an indication of the carrier-envelope phase of the applied FCP, which implies that steering of photoelectrons in space can be achieved by controlling the FCP phase.

Photodetachment of F-by a few-cycle circularly polarized laser field

We report on calculations of the above threshold detachment of F(-) by a few-cycle circularly polarized laser field, discussing the effects of both the carrier-envelope relative phase and the number of the cycle contained in a pulse on the angular distribution of ejected photoelectron. The results are analyzed in terms of a two-step semiclassical model: after the electrons are detached through tunnelling their motion is determined by the electric field pulse according to the classical dynamics laws. Anisotropies in the angular distributions of the electrons ejected on the plane perpendicular to the laser propagation direction are found that depend on the number of cycle of the laser pulse.

Experimental Study of Photodetachment in a Strong Laser Field of Circular Polarization

Negative fluorine ions are exposed to a circularly polarized infrared laser pulse with a peak intensity on the order of 2.6 x 10(13) W/cm(2). A fundamental difference, as compared to the case of linearly polarized field, is found in the absence of any structure in the photoelectron spectrum that can be associated with the quantum interference effect. This observation is in accord with our recent predictions [S. Beiser, Phys. Rev. A 70, 011402 (2004)10.1103/Phys. Rev. A.70. 011402]. The experiment reveals that the length gauge is appropriate for the description of the field interaction in the frame of the strong field approximation.

Spin asymmetry in an intense-field ionization process.

A relativistic analysis of the rate of spin flips in ionization of an ensemble of Dirac H atoms subjected to intense circularly polarized laser fields is made. A remarkable intensity-dependent asymmetry between the spin up and spin down electron currents is found. It is nonzero even when the retardation effect, hence the magnetic component of the field, as well as the spin-orbit interaction responsible for the well-known Fano effect, is negligible. Transformation properties of the amplitudes show that the sign of asymmetry can be controlled by changing the helicity of the laser photons from outside.

Photodetachment in a strong circularly polarized laser field

The saddle-point analysis of the transition amplitude shows that the quantum interference effect does not occur in the direct process of photodetachment by a circularly polarized laser field. This fact is interpreted in terms of classical electron trajectories. Comparison between the length and velocity gauges is performed by simulating spectra of photoelectrons produced in a focus of a laser pulse. A substantial discrepancy is found in the kinetic energy distribution of photoelectrons. At low energies, only the predictions in the length gauge are consistent with the Wigner threshold law.

Compton scattering by a bound electron in the presence of a low-frequency electromagnetic field

Recently we derived a formula for Compton scattering of high-energy photons on a bound electron in the presence of a weak low-frequency laser field of circular polarization (Voitkiv et al 2003 J. Phys. B: At. Mol. Opt. Phys. 36 1907). However, numerical calculations were performed in the above study using a simplified expression for the parameter describing the coupling between the ‘high-energy photon+target’ subsystem and the laser field. In this paper we reconsider the field-assisted Compton scattering by using the full expression for the coupling parameter. We show that (i) the fully differential spectra of emitted electrons and scattered high-energy photons can be strongly influenced by the laser field (as was suggested in our earlier study although there may exist substantial deviations from the former predictions); (ii) the energy spectrum of the emitted electrons, integrated over all states of the scattered photons, can be profoundly modified by the field (only small deviations from our earlier predictions have been found); (iii) the energy spectrum of the scattered photons, integrated over all final electron states, turns out to be independent of the field, in contrast to our earlier predictions that this spectrum should be shifted to lower energies if the laser field is present. We also show that, despite the full coupling parameter containing a term which changes sign when one of the polarization vectors of the laser field is inverted, the so-called dichroism effect is absent in the field-assisted Compton scattering accompanied by emission of a high-energy electron.

Zeldovich's regularization method in the theory of quasistationary states

The complex quasienergy, including the level width Γ, is calculated for a loosely bound atomic state in an intense monochromatic laser field of circular polarization. The method proposed by Zeldovich for regularizing divergent integrals that involve the Gamow wave function is employed in this calculation. The convergence of the method is demonstrated, and the conditions of its applicability are indicated.

On the problem of negative ions photodetachment in intense circularly polarized laser field

We present the theoretical calculation of photodetachment rate of loosely bound atomic states in an intense circularly polarized monochromatic laser field. Different calculation methods are used: the perturbation theory with respect to laser field intensity, the semiclassical approximation and the exact numerical solution of transcendental equation for complex quasienergy of an atomic level. In the last case we use the regularization method for divergent integrals with Gamow wave function proposed by Zel'dovich. We present the comparison of semiclassical and exact results and discuss the accuracy of semiclassical approximation in the theory of ionization. Results are applied for the calculation of photodetachment rate for negative ions of hydrogen and alkali metals.

Cyclotron mechanism of electron acceleration in subpicosecond laser plasma

The effect of ultrastrong magnetic fields generated in a relativistic-intensity subpicosecond laser plasma on the acceleration of fast electrons was studied. It is shown that resonance electrons can continuously accumulate energy from the circularly polarized laser field in the presence of a longitudinal magnetic field. For the linear polarization and a transverse magnetic field, energy accumulation has a pulse-periodic character, and the electron trajectories correspond to electron rotation in the Larmor orbit in a quasi-stationary magnetic field, while the energy strongly oscillates. In both cases, electron energy may attain values higher than 100 MeV for intensities of 1020 W/cm2.

High harmonic generation spectra of aligned benzene in circular polarized laser field

We present model calculations of high-order harmonic generation in benzene, aligned in the polarization plane of circular polarized laser field. The resonance states of the system are obtained using complex scaling Floquet approach (i.e., within non-Hermitian quantum mechanics) combined with (t,t′) time propagation method. Our results show that the photo-induced dynamics of the model benzene molecule at the laser wavelength of 800 nm is dominated by a single long-lived resonance state up to the intensity of about 90 TW cm−2. The high-order harmonics emitted by the system obey the selection rules derived in [Phys. Rev. Lett. 80, 3743 (1998)] on the basis of the dynamical symmetry of the system, namely the emitted harmonics possess the frequencies (6±1)ω,(12±1)ω,…, where ω is the incident laser frequency. These symmetry-allowed harmonics are found to be the dominant ones in the spectrum also when the laser polarization deviates from the “ideal” circular one by about 5%. The nonlinear response of the model benzene molecule is found to originate mainly from the field-induced transitions between the bound states, in accordance with the earlier analytical theory. The cut-off position in the calculated high-order harmonic generation spectra depends linearly on the field strength in the studied intensity interval. Our numerical calculations reveal the enhancements of particular high-order harmonics in the plateau region of the spectrum at certain field intensities. We show that these enhancements occur under conditions of avoided crossing of two or several resonance quasi-energies in the complex energy plane.

Two-color stabilization of atomic hydrogen in circularly polarized laser fields

Dynamic stabilization of atomic hydrogen against ionization in high-frequency single- and two-color, circularly polarized laser pulses is observed by numerically solving the three-dimensional, time-dependent Schr\"odinger equation. The single-color case is revisited and numerically determined ionization rates are compared with both, exact and approximate high-frequency Floquet rates. The position of the peaks in the photoelectron spectra can be explained with the help of dressed initial states. In two-color laser fields of opposite circular polarization the stabilized probability density may be shaped in various ways. For laser frequencies $\omega_1$ and $\omega_2=n\omega_1$, $n=2,3,...$ and sufficiently large excursion amplitudes $n+1$ distinct probability density peaks are observed. This may be viewed as the generalization of the well-known ``dichotomy'' in linearly polarized laser fields, i.e, as ``trichotomy,'' ``quatrochotomy,'' ``pentachotomy'' etc. All those observed structures and their ``hula-hoop''-like dynamics can be understood with the help of high-frequency Floquet theory and the two-color Kramers-Henneberger transformation. The shaping of the probability density in the stabilization regime can be realized without additional loss in the survival probability, as compared to the corresponding single-color results.

Stabilization dynamics in an intense circularly polarized laser field

We study quantum and classical dynamics of the electron in ionization stabilization of the two-dimensional hydrogen atom irradiated by an intense circularly polarized laser. When the quantum time evolution of the wave packet is stable but the corresponding classical time evolution is diffusive, stabilization can be understood to arise from the effect of quantum localization that suppresses classically chaotic diffusion. When both the quantum and classical time evolutions exhibit a stable behavior, stabilization can be regarded as originating from stable classical orbits generated by nonlinear resonance. We also investigate the effect of the bare Coulomb singularity on ionization stabilization.

The Photoionization of Atomic Hydrogen in an Intense Circularly Polarized Laser Field**The project supported by National Natural Science Foundation of China under Grant No. 10075004

We calculate nonperturbatively the irfluence of a strong circularly polarized laser beam on the hydrogen atom energy levels by making use of the time-independent formalism proposed by one of us. The photoionization cross section of the hydrogen atom irradiated by this laser beam and the angular distribution of photoelectrons are also calculated. From the numerical results we clearly see the intensity dependence of the whole photoionization process,including the intensity dependence of the photoelectron energies.

Dynamicalsymmetries and harmonic generation

We discuss harmonic generation in the case of laserfield-dressed Hamiltonians that are invariant under so-calleddynamical symmetry operations. Examples for such systems aremolecules which exhibit a discrete rotational symmetry of orderN (e.g. benzene with N = 6) interacting with a circularlypolarized laser field and single atoms in a bichromatic field,with the two lasers having circular polarizations. Within ageneral group theory approach we study the harmonics one obtainsfrom the interaction of a laser pulse and a circular molecule.When the system is in a pure field-dressed state the knownselection rule kN±1, k = 1,2,3,... results. However,other lines are observed when recombinations with states of asymmetry different from the initial one become important. Thisis the case for realistic laser pulses (i.e. with a finiteduration), in particular when the fundamental laser frequency(or one of its multiples) is resonant with a transition betweenfield-dressed states. Numerical ab initio simulations,confirming our analytical calculations and illustrating thepower of the group theory approach, are presented.

Harmonic generation in ring-shaped molecules

We study numerically the interaction between an intense circularly polarized laser field and an electron moving in a potential which has a discrete cylindrical symmetry with respect to the laser pulse propagation direction. This setup serves as a simple model, e.g., for benzene and other aromatic compounds. From general symmetry considerations, within a Floquet approach, selection rules for the harmonic generation [O. Alon Phys. Rev. Lett. 80 3743 (1998)] have been derived recently. Instead, the results we present in this paper have been obtained solving the time-dependent Schroedinger equation ab initio for realistic pulse shapes. We find a rich structure which is not always dominated by the laser harmonics.

Threshold effects and dichroism in scattering of an electron in intense laser field on a Coulomb potential

The cross sections for elastic and inelastic scattering of an electron in an intense circularly polarized laser field on a Coulomb potential are obtained within the unitary transformation method for the Schrödinger equation. The behaviour of cross sections is studied near the the threshold caused by opening of the inelastic scattering channel with an emission of one photon. A circular dichroism in cross sections has been revealed near the threshold.

Energy gain of injected electrons subjected to an intense laser field and its magnetic field induced in plasma.

Cyclotron-resonance energy gain of injected electrons subjected to an intense circularly polarized laser field and the magnetic field induced in a low-density plasma is investigated theoretically. By considering the inverse Faraday effect (IFE), where a circularly polarized finite area laser beam induces an axial magnetic field in a plasma, it is found that very interesting energy gains can be obtained by Doppler-shifted cyclotron resonance in this field for the appropriate injection velocity. This same IFE field also acts to confine these electrons radially and, on exiting the plasma adiabatically, it is in this way that the transverse electron energy is converted to axial energy. Two limits to the energy gain are discussed: (i) cyclotron radius of the energetic electrons becoming comparable to the beam, and (ii) axial dephasing.

Ionization Problem for Hydrogen Atom in Intense Circularly Polarized Laser Field Revisited**The project supported by National Natural Science Foundation of China, the National High Technology Committee of Laser, and partly the Science Foundation of China Academy of Engineering Physics

Ionization rate for circular polarization laser field is reformulated in length gauge. The Volkov state or the Coulomb-corrected Volkov one is served at the final wavefunction and would lead to that the ionization rate in length gauge is closer to the experimental data than the corresponding result in velocity gauge. It is also found that the ionization rate as a function of laser intensity has nevertheless the stabilization effect, although in the sense more weakly in length gauge than in velocity gauge, when the field is to be comparable or exceeds to the atomic binding field.

Above Threshold Ionization Spectra of He in a Circularly Polarized Laser Field

A new analytic model for the above threshold ionization spectrum of He in a circularly polarized laser field is proposed. The experimental spectrum obtained by Mohideen et al. can be quite well described by this model. The spectra predicted by our model agree with experiment better than those of Reiss when the spatiotemporal profile of the laser pulse is taken into account and better than those of the Keldysh-Faisal-Reiss theory when the profile is not taken into account. At the same time, we find that the experimental value of the peak laser intensity was overstated by a factor of about 5. This result supports the previous similar claim by Reiss.