Strong Field Theories beyond Dipole Approximations in Nonrelativistic Regimes

The exact nondipole Volkov solutions to the Schrödinger equation and Pauli equation are found, based on which a strong field theory beyond the dipole approximation is built for describing the nondipole effects in nonrelativistic laser driven electron dynamics. This theory is applied to investigate momentum partition laws for multiphoton and tunneling ionization and explicitly shows that the complex interplay of a laser field and Coulomb action may reverse the expected photoelectron momentum along the laser propagation direction. The magnetic-spin coupling does not bring observable effects on the photoelectron momentum distribution and can be neglected. Compared to the strong field approximation within the dipole approximation, this theory works in a much wider range of laser parameters and lays a solid foundation for describing nonrelativistic electron dynamics in both short wavelength and midinfrared regimes where nondipole effects are unavoidable.

Figure 1

(a) The fitted (a) $\alpha$, (b)$\beta$, and (c) $\gamma$ as a function of the absorbed photon number $N$. The laser intensity is fixed at $10^{14}\mathrm{W}/{\mathrm{cm}}^2$, and the initial electronic state is the hydrogen ground state $(n,l,m)=(1,0,0)$.

Figure 2

(a)$⟨p_z⟩$ and (b)$\mathrm{\Delta }{p}_z$ as a function of the laser intensity. The laser wavelength is 1400 nm and right-handed circularly polarized. (a) and (b) share the same graph legend.

Figure 3

(a) The scaled longitudinal momentum distribution when different screening parameters $\sigma$ are used. (b) $⟨p_z⟩$ as a function of the laser intensity, in which calculations, both the direct and rescattering ionization events are included. (c) $⟨p_z⟩$ as a function of the laser intensity, where only rescattering events are taken into account. (a), (b), and (c) share the same graph legend.