Measurement of the Initial Condition of Electrons Ionized by a Linearly Polarized, High-Intensity Laser

We have measured the angular spectrum of electrons born in a linearly polarized, high-intensity laser focus. The spectrum is directly related to the initial conditions of the ionized electrons in the plane perpendicular to the propagation direction. Our measurements for high charge states of neon are in good agreement with predictions of quasistatic tunneling models and limit the initial electron kinetic energy to approximately 0.5% of its average quiver energy. This measurement is important for studies of high-order harmonic generation and direct double ionization. [S0031-9007(96)02268-5] PACS numbers: 32.80.Fb, 32.80.Rm Over the past several years, a simple two-stage model of ionization, referred to as the “quasistatic” or “simpleman’s” model [1‐4], has succeeded in explaining a wide variety of experimental aspects of intense field-atom interactions in the tunneling regime. These include many characteristics of the electron energy spectra [5], direct double ionization in the tunneling regime [6], and the cutoff energy of the high-harmonic plateau [7]. The basic assumption of the model is that ionized electrons can return to collide with the nucleus with an energy that depends on both their initial momentum and the phase within the optical cycle at which they were born. The initial phase, in turn, depends on the ionization model. For classical ionization, or barrier-suppression ionization (BSI) [8], the electrons are born only at the peak of the field and hence have zero initial phase. In ac tunneling models [9,10], the electrons are born over a range in phase within the optical cycle near the peak of the field. After ionization, the trajectory is calculated classically, neglecting the Coulomb force of the residual ions, as it is much weaker than the force due to the laser field [3]. The distributions of electrons as a function of their initial momentum and initial phase determine the rates of several of the abovementioned processes. This Letter reports a measurement of the initial conditions of electrons ionized in the long-pulse tunneling regime. The Keldysh adiabaticity parameter [11] g ; sIpy2Upd 1y2 , 0.1, where Ip is the ionization potential of the atom and Up is the ponderomotive energy [12]. Unlike some previous studies of above-threshold ionization electrons [5,13] in which the effect of the ponderomotive potential was minimized, our intent was for the freed electrons to gain the full energy provided by the field gradient. For electrons born at the peak of the field and with zero initial momentum perpendicular to the propagation direction, the ponderomotive potential leads to an axisymmetric electron distribution in the plane perpendicular to the propagation direction [14]. A small initial momentum perpendicular to the propagation direction or ionization of the electron at an off-peak phase of the optical cycle breaks the symmetry of the ponderomotive potential. We used a high-intensity laser to ionize electrons from neon gas at low density and measured the electron spectra as a function of the forward angle u (relative to k) and the azimuthal angle w (relative to the polarization direction in the plane perpendicular to the propagation direction). We observed a significant asymmetry in the electron number distribution in the plane perpendicular to the direction of propagation, with more electrons detected along the direction of polarization than perpendicular to it. The observed asymmetry is due to the nonzero initial conditions and is consistent with quasistatic tunneling models. Earlier work utilizing the retarding-potential grids attempted to measure the initial drift momentum by calculating the difference between the electron energy spectra parallel and perpendicular to the polarization direction [3,15]. The direction of the initial momentum along the polarization direction implies that the number, as well as the energy, of electrons seen along the polarization direction will be larger than the number seen perpendicular to it. The azimuthal distribution of the number of electrons is a more sensitive measure of the initial conditions than the azimuthal distribution of the energy of the electrons. In addition, at high electron energies, the forward electron momentum [16] complicates the retarding potential method.