Photoelectron holography in strong-field tunneling ionization by a spatially inhomogeneous field

Photoelectron holography in strong-field tunneling ionization is an efficient way to probe the structures and the ultrafast dynamics information of atoms and molecules. Manipulating the process of photoelectron holography is important for its application. Here, we study theoretically strong-field photoelectron holography in the spatially inhomogeneous field by solving the time-dependent Schrödinger equation. Our results show that the returning energy of the rescattering electron is greatly enhanced in the spatially inhomogeneous field, and the holographic interference pattern can be separated from other types of interference in the photoelectron momentum distribution. Moreover, our results show that the time window of tunneling ionization wherein the electron could be driven back to induce holography is broadened in the inhomogeneous field. These properties are beneficial for the application of photoelectron holography in probing the atomic and molecular structures and dynamics. The origin for these properties is analyzed with the classical trajectory model.

Figure 1

(a), (b) The PEMDs (logarithmic scale) for strong-field tunneling ionization of a hydrogen atom ($I_p=0.5$ a.u.) in an 1600-nm single-color laser field with intensity $I=1\times {10}^{14}\text{W}/{\text{cm}}^2$. The top row shows the results of the spatially homogeneous field ($\varepsilon =0$) obtained by solving the TDSE. The middle and bottom rows correspond to the results of the spatially inhomogeneous field ($\varepsilon =0.003$) obtained by (c), (d) the TDSE and (e), (f) the classical model, respectively. The left and right columns represent the results of (a), (c), (e) $\varphi =0$ and (b), (d), (f) $\varphi =\pi$ of the laser field, respectively.

Figure 2

(a) The electric field of the laser pulse at the origin. The middle and bottom rows are the PEMDs for strong-field tunneling ionization of a hydrogen atom. The middle row corresponds to the electron tunneled out within (b) $1.5–2$ T [the dashed blue curve in panel (a)] and (c) $2–2.5$ T [the dotted red curve in panel (a)], respectively, which is calculated by the classical model. (d), (e) The same as in panels (b) and (c) but calculated by the TDSE. The laser parameters are the same as in Fig. 1 and $\varphi =0$.

Figure 3

The classical momentum evolution of the electrons tunneled out within $1.5–2$ T (the thin light blue curves) and $2–2.5$ T (the thick dark red curves), for the case of spatial (a) homogeneity and (b) inhomogeneity. The dashed green curves are the laser field at the origin. Its parameters are same as Fig. 1 and $\varphi =0$.

Figure 4

(a), (b) Enlarged views of the interference patterns on the left and right parts of the PEMD in Fig. 1, respectively. (c), (d) Enlarged views of the interference patterns on the left and right in parts of the PEMD of Fig. 1, respectively.

Figure 5

Classical electron final kinetic energies as a function of the ionization (blue dots) and rescattering (red diamonds) times in the (a) homogeneous and (b) inhomogeneous fields, respectively. The shaded parts represent the ionization time window of the rescattering electrons which can be retrieved. The middle row shows the travel time between ionization and scattering as a function of the final momentum for the spatial (c) homogeneity and (d) inhomogeneity, respectively. (e), (f) The same as panels (a) and (b), respectively, but for the rescattering energies. The dashed green curves are the laser field at the origin. The laser parameters are same as in Fig. 1 and $\varphi =0$.

Figure 6

The evolution of (a) the classical trajectory and (c) the classical energy of the electron which has the high rescattering energy and final energy, and this electron is released at about 1.6 T. (b) The strength enhancement evolution of the electric field the electron feels, where $E_o$ is the electric field at the origin. The vertical solid black lines indicate the time when the electron return back to the parent ion. The solid green curves are the laser field at the origin. The laser parameters are the same as in Fig. 1.

Figure 7

The PEMDs for strong-field tunneling ionization of a hydrogen atom for (a) $\varepsilon =0$ (homogeneous field), (b) $\varepsilon =0.001$, (c) $\varepsilon =0.002$, and (d) $\varepsilon =0.003$. The laser parameters are the same as in Fig. 1.

Figure 8

The PEMDs for strong-field tunneling ionization of a hydrogen atom in the inhomogeneous field ($\varepsilon =0.003$). The laser parameters are same as Fig. 1 but for (a) $\varphi =0$, (b) $0.4\pi$, (c) $0.8\pi$, (d) $\pi$, (e) $1.4\pi$, and (f) $1.8\pi$.