Coulomb effects in photoionization of H atoms irradiated by intense laser fields

We theoretically study the Coulomb effects on the photoionization processes of the H atom irradiated by the intense laser fields with circular and linear polarizations. For this purpose we represent the final continuum state by the Coulomb-Volkov state. Total ionization rates, photoelectron energy spectra, and angular distribution of photoelectrons are calculated and compared with those obtained using the Volkov state. We find that how much the Coulomb field influences the ionization dynamics depends on the momentum of photoelectrons, among which the photoelectron angular distributions in the linearly polarized laser field represent the most striking difference.

Figure 1

(Color online) Time-independent parts of the CV (solid line), i.e., $u_p^{(-)}\left(\mathbf{r}\right)$, and Volkov (dashed line) states, i.e., $\exp (i\mathbf{p}\bullet \mathbf{r})$, as a function of $\mathbf{r}$. The energy of electron is chosen to be $1.55\mathrm{eV}$ (top row) and $31.1\mathrm{eV}$ (bottom row). The left column is for the real part, and the right column for the imaginary part. We have set $\mathbf{p}\bullet \mathbf{r}=pr$.

Figure 2

(Color online) Time-independent parts of the CV (solid line), i.e., $u_p^{(-)}\left(\mathbf{r}\right)$, and Volkov (dashed line) states, i.e., $\exp (i\mathbf{p}\bullet \mathbf{r})$, as a function of angle between the momentum $\mathbf{p}$ and the position $\mathbf{r}$ for $\mid \mathbf{r}\mid =5a_0$. The energy of electron is chosen to be $1.55\mathrm{eV}$ (top row) and $31.1\mathrm{eV}$ (bottom row). The left column is for the real part and the right column for the imaginary part.

Figure 3

(Color online) The variation of the total ionization rates as a function of laser intensity with linear polarization. The ionization rates in the $E$ gauge are calculated according to the formulas presented in this paper, and the ionization rates in the $A$ gauge are calculated according to the Reiss theory [1] (for the Volkov state) and the formula given by Bauer [15] (for the CV state). The wavelength of the incident laser is $800\mathrm{nm}$.

Figure 4

(Color online) The same as that in Fig. 3, but for a circularly polarized laser field.

Figure 5

(Color online) The photoelectrons energy spectra for linear polarization at the intensities of (a) ${10}^{13}\mathrm{W}∕{\mathrm{cm}}^2$ and (b) ${10}^{15}\mathrm{W}∕{\mathrm{cm}}^2$. The Inset in graph (b) is in a semilogarithmic scale.

Figure 6

(Color online) The photoelectrons energy spectra for circular polarization at the intensities of (a) ${10}^{13}\mathrm{W}∕{\mathrm{cm}}^2$ and (b) ${10}^{15}\mathrm{W}∕{\mathrm{cm}}^2$. The Inset in graph (b) is in a semilogarithmic scale.

Figure 7

(Color online) Polar plots of the PADs, obtained using the CV state, for the (a) first $(l=10)$ and (b) tenth $(l=19)$ peaks in the linearly polarized laser field at the intensity of ${10}^{13}\mathrm{W}∕{\mathrm{cm}}^2$. The plots in (c) and (d) are similar to (a) and (b), respectively, but calculated using the Volkov state.

Figure 8

(Color online) Polar plots of the PADs, obtained using the CV state, for the (a) first $(l=13)$, (b) tenth $(l=22)$, and (c) 20th $(l=32)$ peaks in the linearly polarized laser field at the intensity of ${10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$. The plots in (d), (e), and (f) are similar to (a), (b), and (c), respectively, but calculated using the Volkov state.