Electron-Energy Bunching in Laser-Driven Soft Recollisions

We introduce soft recollisions in laser-matter interaction. They are characterized by the electron missing the ion upon recollision in contrast with the well-known head-on collisions responsible for high-harmonic generation or above-threshold ionization. We demonstrate analytically that soft recollisions can cause a bunching of photoelectron energies through which a series of low-energy peaks emerges in the electron yield along the laser polarization axis. This peak sequence is universal, it does not depend on the binding potential, and is found below an excess energy of one tenth of the ponderomotive energy.

Figure 1

The deflection function $p_z$ for the momentum along the laser axis as a function of the initial vector potential $A^{\prime }=A\sin {\varphi }^{\prime }$ and the initial transversal momentum $p_{\rho }^{\prime }$ shown after (a) one, (b) two, and (c) three laser cycles. Spectra according to Eq. (2) with $w=1$ integrated over the initial parameter range of panels (a)–(c) are shown in the right panel (d). The arrows point to the predicted momenta according to Eq. (7). The laser has a wavelength of $\lambda =2\mu \mathrm{m}$ ($\omega =0.0228\mathrm{a}.\mathrm{u}.$) at an intensity of $I={10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ ($F=0.0534\mathrm{a}.\mathrm{u}.$).

Figure 2

Time-dependent drift momentum $p_z(\varphi )+A\sin (\varphi )$ for three trajectories (left panel) with different initial drift momenta showing the effect of the Coulomb potential after release [a] and the bunching during the soft recollision [c]. Sketch of the rescattering trajectory (right) in a Coulomb potential (orange-shaded area). Full trajectory (upper panel) and details (lower) of the three interactions events: [a] emission at $\varphi \approx 0$, [b] effectless passing at $\varphi \approx 3\pi /2$, and [c] soft recollision at $\varphi \approx 3\pi$.

Figure 3

Deflection function (left) and corresponding photoelectron spectrum with finite resolution (right) for the Gaussian potential Eq. (9) with $s=32\mathrm{a}.\mathrm{u}.$, laser parameter as in Fig. 1. The missing interval in the deflection function represents initial conditions which lead to trapped or chaotic trajectories. The dashed line corresponds to the strong-field drift momentum $p({\varphi }^{\prime })=A\sin {\varphi }^{\prime }$.