Strong-field approximation for ionization of a diatomic molecule by a strong laser field. III. High-order above-threshold ionization by an elliptically polarized field

We investigate high-order above-threshold ionization (HATI) of diatomic molecules having different symmetries by an elliptically polarized laser field using the modified molecular strong-field approximation. The yields of high-energy electrons contributing to the plateau region of the photoelectron spectra strongly depend on the employed ellipticity. This is more pronounced if the major axis of the polarization ellipse is parallel or perpendicular to the molecular axis and at the end of the high-energy plateau. For the ${\text{O}}_2$ molecule (characterized by ${\pi }_{\text{g}}$ symmetry) the maximum yield is observed for some value of the ellipticity $\epsilon$ different from zero. On the other hand, in the same circumstances, the ${\text{N}}_2$ molecule $\left({\sigma }_{\text{g}}\right)$ behaves as an atom, i.e., the yield is maximum for $\epsilon =0$. These characteristics of the photoelectron spectra remain valid in a wide region of the molecular orientations and laser peak intensities. The symmetry properties of the molecular HATI spectra are considered in detail: by changing the molecular orientation one or other type of the symmetry emerges or disappears. Presenting differential ionization spectra in the ionized electron energy-emission angle plane we have observed similar interference effects as in the HATI spectra governed by a linearly polarized field.

Figure 1

(Color online) Logarithm of the differential ionization rate of ${\text{O}}_2$ coded in false colors in the $\left(E_{\mathbf{p}},\theta \right)$ plane. The spectra in the upper two panels are for parallel (${\theta }_{\text{L}}=0°$, upper) and perpendicular (${\theta }_{\text{L}}=90°$, lower) orientations of the molecular axis with respect to the direction of the linearly polarized laser field. In the two bottom panels we present the spectra for the same molecule, having the same alignment as in the two upper panels, but now with respect to the semimajor axis of the elliptically polarized field having the ellipticity $\epsilon =0.05$. Laser intensity is $1.2\times {10}^{14}\text{W}/{\text{cm}}^2$ and wavelength is 800 nm.

Figure 2

(Color online) Logarithm of the differential ionization rate of ${\text{N}}_2$, coded in false colors in the $\left(E_{\mathbf{p}},\theta \right)$ plane, for parallel orientation of the molecular axis with respect to the polarization vector of the linearly polarized laser field (uppermost panel), and for the same alignment, but for elliptically polarized field with $\epsilon =0.1$ (second panel). In the remaining three panels, from top to bottom, the partial $T$-matrix contributions $T^{++--}$, $T^{+-}$, and $T^{-+}$, for $\epsilon =0.1$ are shown. Laser intensity and wavelength are the same as in Fig. 1.

Figure 3

(Color online) Differential ionization rates of ${\text{N}}_2$ (black solid curves) and ${\text{O}}_2$ (red dashed curves) as functions of the ellipticity $\epsilon$ for fixed electrons energy of 58.5 eV, Upper panel: $\theta ={\theta }_{\text{L}}=0°$; bottom panel: $\theta ={\theta }_{\text{L}}=90°$. Laser intensity and wavelength are the same as in Fig. 1.

Figure 4

(Color online) Differential ionization rates of ${\text{N}}_2$ (black solid curves) and ${\text{O}}_2$ (red dashed curves) as functions of the ellipticity $\epsilon \ge 0$ for fixed electron energy of 58.5 eV, calculated for $\theta ={\theta }_{\text{L}}$ and: ${\theta }_{\text{L}}=5°$ (upper panel), $45°$ (middle panel), and $85°$ (bottom panel). Laser intensity and wavelength are the same as in Fig. 1.

Figure 5

(Color online) Polar diagrams which represent the high-energy ionization rates of ${\text{N}}_2$ as functions of the polar angle $\psi$, for the peak intensity $1.2\times {10}^{14}\text{W}/{\text{cm}}^2$ and wavelength 800 nm. The laser field is linearly polarized. Calculations are carried out for fixed value of energy $E_{\mathbf{p}}=43\text{eV}$, for ${\theta }_{\text{L}}=0°$ (left-hand panels) and ${\theta }_{\text{L}}=60°$ (right-hand panels), and for the total yield (top panels), and yields of partial contributions: $T^{++--}$ (panels in the second row), $T^{+-}$ (third row), and $T^{-+}$ (bottom row). The rates for ${\theta }_{\text{L}}=0°$ (left-hand panels) are in multiples of $x\times {10}^{-10}\text{a}\text{.u}\text{.}$, with $x=1.092$, 9.85, 3.23, and 3.23, from top to bottom (in all panels the radial coordinate goes from 0 to 1, as denoted). For ${\theta }_{\text{L}}=60°$ (right-hand panels) we have $x=5.7$, 2.59, 2.01, and 2.01, respectively.

Figure 6

(Color online) Same as in Fig. 5 but for ${\text{O}}_2$, ${\theta }_{\text{L}}=1°$ (left-hand panels) and ${\theta }_{\text{L}}=30°$ (right-hand panels). The rates for ${\theta }_{\text{L}}=1°$ are in multiples of $x\times {10}^{-12}\text{a}\text{.u}\text{.}$, with $x=0.471$, 3.75, 1.45, and 1.45, from top to bottom, while for ${\theta }_{\text{L}}=30°$ we have $x\times {10}^{-9}\text{a}\text{.u}\text{.}$, where $x=0.925$, 2.58, 1.12, and 1.12, respectively.

Figure 7

(Color online) Same as in Fig. 5 but for ${\theta }_{\text{L}}=0°$ and elliptically polarized field for two values of the ellipticity: $\epsilon =0.17$ (left-hand panels), $\epsilon =-0.17$ (right-hand panels). The rates are in multiples of $x\times {10}^{-10}\text{a}\text{.u}\text{.}$, with $x=2.89$, 4.01, 1.2, and 1.2, from top to bottom, respectively.

Figure 8

(Color online) Same as in Fig. 7, but for ${\theta }_{\text{L}}=60°$. The rates for $\epsilon =0.17$ are in multiples of $x\times {10}^{-10}\text{a}\text{.u}\text{.}$, with $x=3.07$, 1.17, 0.915, and 0.915, while for $\epsilon =-0.17$ we have $x=1.17$, 1.04, 7.13, and 7.13.

Figure 9

(Color online) Same as in Fig. 6 but for ${\theta }_{\text{L}}=0°$ and $\epsilon =0.34$ (left-hand panels) or $\epsilon =-0.34$ (right-hand panels). The rates are in multiples of $x\times {10}^{-11}\text{a}\text{.u}\text{.}$, with $x=1.29$, 7.04, 3.27, and 3.27, from top to bottom, respectively.

Figure 10

(Color online) Same as in Fig. 9, but for ${\theta }_{\text{L}}=30°$. The rates for $\epsilon =0.34$ are in multiples of $x\times {10}^{-11}\text{a}\text{.u}\text{.}$, with $x=3.8$, 9.57, 6.28, and 6.28, while for $\epsilon =-0.34$ we have $x=5.41$, 1.08, 4.62, and 4.62.