Nonlinear interference and electron dynamics: Probing photoelectron momentum distributions in strong-field ionization

Nonlinear interference in the interaction of intense laser pulses with atoms profoundly affects the photoelectron momentum distribution (PMD). We theoretically show that the interference pattern in the PMD arises from the interaction of electrons with the fundamental frequencies concealed within the pulse. Nonlinear interference also imprints distinctive features on the ionization spectrum, providing valuable information about electron dynamics and phase relationships within the laser pulse. Additionally, the augmentation of optical cycles induces a distinct confinement in the PMD.

Figure 1

Schematic representation of strong-field ionization. The left panel illustrates the momentum distribution of a photoelectron emitted from an atom (A) ionized by a strong laser pulse, with the colored lines indicating the frequencies within the pulse imprinted on the momentum distribution along the propagation direction. The right panel displays the momentum distribution of photoelectrons in the laser polarization direction. In both scenarios, the laser pulse is characterized by the vector potential $\mathbf{A}\left(t\right)$, depicted as the solid black line.

Figure 2

Vector potential $\mathbf{A}\left(t\right)$ of a circularly polarized laser pulse as function of time (left panels) and frequency $\left[\mathcal{F}\right(\mathbf{A}\left)\right]\left(\omega \right)$ (right panel). This potential is shown for pulses with two (blue), four (orange) and eight (green) optical cycles, a carrier-envelope phase ${\varphi }_{\mathrm{cep}}=0$, and wavelength $\lambda =800$ nm of the incident laser light. The ordinate in the right panel shows the absolute amplitude of the vector potential at a peak intensity of $5\times {10}^{14}$ W/${\mathrm{cm}}^2$, and the amplitude provides insight into its contributions to the PMD in strong-field ionization measurements.

Figure 3

ATI energy spectra and PMD for a ${sin}^2$ driving laser laser pulses with two (left column), four (middle column), and eight optical cycles (right column). The ATI energy spectra (upper row) are shown as functions of ${\epsilon }_p$(units of $\omega$) and for $p_z=0$, whereas the PMD are displayed in the $p_x-p_z$ plane for the carrier-envelope phases ${\varphi }_{\mathrm{cep}}=0$ (middle row) and ${\varphi }_{\mathrm{cep}}=\pi /2$ (lower row), respectively. All distributions are shown for a laser with wavelength $\lambda =800$ nm and peak intensity $I=5\times {10}^{14}$ W/${\mathrm{cm}}^2$ as well as for an argon target with ionization potential $I_p=15.7596$ eV.

Figure 4

Temporal evolution of the Volkov phase (3) at $p=0.5$ a.u., including the full contribution (top row) and contributions from individual terms (bottom row), as derived from the analytical solution of the time-dependent Schrödinger equation (TDSE). $S_v{\left(\tau \right)}_k$ are the four terms in Eq. (3) representing the four components and only the real components of $S_v{\left(\tau \right)}_k$ and $S_v\left(\tau \right)$ are shown. Each panel sequence (from left to right) represents varying cycle counts (two, four, and eight), corresponding to a wavelength of 800 nm and an intensity of $5\times 10{}^{14}\mathrm{W}/{\mathrm{cm}}^2$. $\beta$ and ${\theta }_p$ are set to 0 and $\pi /2$, respectively. The profile of the vector potential is shown in arbitrary units (middle row).

Figure 5

Temporal evolution of a Volkov phase for an eight-cycle pulse. The left panel shows the composite effect of the temporal evolution of the Volkov phase within the laser pulse, while the right panel focuses on the contribution from the primary two terms. The laser parameters are the same as those in Fig. 4, except for the parameter $p$, which is set to 0.1 a.u.

Figure 6

Full width at half maximum (FWHM) of the prominent ring with the highest intensity in the momentum distribution within the propagation plane. The lines in the figure demonstrate a trend: at higher optical cycles, the FWHM progressively decreases for increasing intensity and vice versa for wavelength. (Left) The wavelength remains consistent at 600 nm. (Right) The intensity remains consistent at $1\times 10{}^{14}\mathrm{W}/{\mathrm{cm}}^2$.