Direct Observation of Multiphoton Processes in Laser-Induced Free-Free Transitions

Abstract

Multiphoton processes are detected in the scattering of electrons on argon atoms in the presence of a strong C0 2 -laser field. The observations are in accordance with a recently developed semiclassical model.We present here what we believe to be the first direct observation multiphoton absorptions and emissions by electrons in a strong laser field. Measurements were made in an electron-argonatom scattering experiment in the field of a focused, pulsed C0 2 laser with a peak power of 50 MW. The following multiphoton absorption [Eq.(1)] and emission [Eq.(2)] processes were studied:^"(.E^+Ar + laser -<* e~ {E { +nhv) + Ar +laser;(1) e~(£ t .)+Ar + laser-e~(E { -nhv) +Ar +laser;where E { is the incident electron energy, hv is the energy of a laser photon, and n can be any positive integer. The one-photon (n = l) processes have recently been reported by Andrick and Langhans 1 using a 50-W continuous-wave C0 2 laser as a light source, which after focusing resulted in a flux density of 6x 10 4 W/cm 2 . At this flux density, a first-order perturbation expansion with respect to the laser field is suitable and provides in the soft-photon limit the following simple relation 2 between the one-photon absorption (emission) cross section <2a ff {1) /da and the cross section without laser field do el /dQ: da p { da with T 2 given by 5 =4.86xl0-13 X 4 F£ j [ €# fc^] 2 ,where the laser wavelength X is expressed in units of microns, the flux density F in units of watts per square centimeter, the incoming electron en-ergy E { in eV, and the polarization e is normalized according to ?-?=l such that, for all incoming and outgoing electron momenta p t . and py, the quantity in brackets in always between 0 and 1. In the present experiment, however, flux densities in the order of at least F = 10 9 W/cm 2 have been achieved in the scattering center. At these F values the quantity T 2 in Eq. (4) is about 50, which means that a perturbation expansion with respect to the laser field no longer applies and multiphoton processes are expected to contribute significantly. In the case of a C0 2 laser, however, a semiclassical soft-photon approach 3 " 5 can be applied, which yields the following cross-section formula for a free-free transition with a net absorption (emission) of n laser photonsHere J n (T) is the Bessel function of the first kind and order n, and T is given by Eq. (4). Clearly, if |r|« 1 and w = ±l, Eq. (5) reduces to Eq.(3), which shows the connection between the nonperturbative and the perturbative treatments of the laser field. From J 0 2 (*) + 2SJ" 2 (*) = 1,we note the sum rule (n< 0 correspond to emissions; n> 0 correspond to absorptions of a net number of nhv)

Experimental and theoretical study of free–free electron–helium scattering in a CO2laser field

“…Most work has been performed by Weingartshofer, Wallbank and co-workers at Saint-Francis Xavier University in Canada, using a CO 2 laser and a variety of noble gas targets (see [4][5][6][7][8][9][10][11][12] and references therein). From a theoretical point of view, non-perturbative treatments are generally required, even at quite moderate laser intensities.…”

Ramsey-type phase control of free-electron beams

“…One of the most elementary forms of optical control is the dressing of free-electron states in a periodic field 12,13 , which is observed, for example, in two-colour ionization 14,15 , free-free transitions near atoms 12,16 , and in photoemission from surfaces [17][18][19][20] . Similarly, beams of free electrons can be manipulated by the interaction with optical near-fields 7,[21][22][23][24] .…”

Two-photon bremsstrahlung processes in atoms: Polarization effects and analytic results for the Coulomb potential

“…In addition to spontaneous emission, considerable interest in multiquanta bremsstrahlung processes was stimulated by laser experiments, which made it possible to observe induced multiphoton bremsstrahlung emission and absorption in the optical frequency range. The first measurements of the cross sections of freefree electron transitions in the presence of a high-intensity laser wave were made in [21,22]. Such experiments were subsequently repeated more than once with different atomic targets for different electron beam energies and experimental geometries (see, for example, [23] and review [24]).…”