Comparison study on atomic and molecular ellipticity dependence of high-order harmonic generation

We systematically investigate ellipticity dependence of high-order harmonic generation of Ar and ${\mathrm{N}}_2$ in intense elliptically polarized laser fields. The experimental normalized ratios of low-order harmonic intensity to high-order harmonic intensity increase with ellipticity for both Ar and ${\mathrm{N}}_2$, and quantitatively depend on targets and trajectory paths. The experimental results are well reproduced by a nonadiabatic semiclassical simulation and explained by trajectory-based analysis. In addition, the influence of nuclear distance on the ratios is theoretically investigated. Our work reveals that the difference between atoms and molecules can be attributed to the influence of different ionic potentials, which depends on the molecular structure (internuclear distance) and alignment, on the evolution of the photoelectron.

Figure 1

Normalized experimental ellipticity dependence of ${\mathrm{H}}_{17}/{\mathrm{H}}_{27}$ and ${\mathrm{H}}_{19}/{\mathrm{H}}_{27}$ ratios of (a) Ar and (b) ${\mathrm{N}}_2$ for both long (L) and short (S) trajectories. Normalized calculated results for (c) Ar, (d) ${\mathrm{N}}_2$ with $r_0=2$ a.u., and (e) ${\mathrm{N}}_2$ with $r_0=3$ a.u.

Figure 2

Calculated harmonic order as a function of tunneling instant for Ar with (a) adiabatic calculation at $\varepsilon =0.1$, (b) adiabatic calculation at $\varepsilon =0.4$, (c) nonadiabatic calculation at $\varepsilon =0.1$, and (d) nonadiabatic calculation at $\varepsilon =0.4$.

Figure 3

Initial momentum distributions corresponding to different harmonic orders for short trajectories of (a) Ar at $\varepsilon =0.1$, (b) $\mathrm{Ar}$ at $\varepsilon =0.4$, (c) ${\mathrm{N}}_2$ at $\varepsilon =0.1$, and (d) ${\mathrm{N}}_2$ at $\varepsilon =0.4$, respectively. (e) Initial momentum distributions for different ellipticities, harmonic orders, and targets.

Figure 4

(a) The distribution of the electric field at tunneling instant $t_0$ and recombination instant $t_r$ for short trajectories. The arrows indicate the evolution of the electric field with time increasing. (b) and (c) Typical short trajectories corresponding to different harmonic orders of ${\mathrm{N}}_2$ at $\varepsilon =0.1$ and $\varepsilon =0.4$, respectively. The arrows in (c) indicate the directions of $v_{\mathrm{par}}$ and $v_{\mathrm{perp}}$ for the trajectory of ${\mathrm{H}}_{27}$.

Figure 5

The solid black and dashed red lines display typical time evolutions (in laser cycle $T$) of $r$ (the distance between the electron and the core) for ${\mathrm{H}}_{27}$ at $\varepsilon =0.1$ and $\varepsilon =0.2$, respectively. See text for details of the dotted blue line.

Figure 6

(a) The distribution of the electric field at $t_0$ and $t_r$ for long trajectories. The arrows indicate the evolution of the electric field with increasing time. (b) Typical long trajectories for different ellipticities and harmonic orders. (c) The distribution of initial momenta corresponding to different ellipticities and harmonic orders for long (L) and short (S) trajectories.

Figure 7

(a) Typical short trajectories for ${\mathrm{H}}_{17}$ (the solid blue line) and ${\mathrm{H}}_{27}$ (the dashed brown line) of ${\mathrm{N}}_2$ with $r_0=3$ a.u. when $\varepsilon =0.3$. The nuclear distances for trajectory1 and trajectory2 are 0 and 2 a.u., respectively, and the initial conditions of electrons for trajectory1 and trajectory2 are the same as ${\mathrm{H}}_{17}$ with $r_0=3$ a.u. The nuclear distances for trajectory3 and trajectory4 are 0 and 2 a.u., respectively, and the initial conditions of electrons for trajectory3 and trajectory4 are the same as ${\mathrm{H}}_{27}$ with $r_0=3$ a.u. (b) and (c) The value of $|F_{c3}|-|F_{c2}|$ at different positions when the molecular alignment is along the $z$ direction and the $x$ direction, respectively. Here $F_{c3}$ and $F_{c2}$ denote the value of Coulomb force as a function of position when $r_0=3$ a.u. and $r_0=2$ a.u., respectively.