Angle dependence of dissociative tunneling ionization of NO in asymmetric two-color intense laser fields

Dissociative tunneling ionization of nitric oxide (NO) in linearly polarized phase-locked two-color femtosecond intense laser fields (45 fs, $\lambda =800$ and 400 nm, total field intensity $I=1\times {10}^{14}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$) has been studied by three-dimensional ion momentum imaging. The ${\mathrm{N}}^{+}$ fragment produced by the dissociative ionization, $\mathrm{NO}\to \mathrm{N}{\mathrm{O}}^{+}+e^{-}\to {\mathrm{N}}^{+}+\mathrm{O}+e^{-}$, exhibits a butterflylike momentum distribution peaked at finite angles with respect to the laser polarization direction. In addition, a clear dependence on the relative phase between the two laser fields is observed, showing that the tunneling ionization occurs efficiently when the electric field points from N to O. For the highest kinetic energy component, the observed orientation dependence is well explained with theoretical calculations by the weak-field asymptotic theory for the 2π highest occupied molecular orbital (HOMO). On the other hand, the peak angle shifts toward the laser polarization direction as the kinetic energy decreases, indicating that pathways other than direct ionization from the HOMO contribute to the dissociative ionization.

Figure 1

(a) Potential energy curves of selected electronic states of $\mathrm{N}{\mathrm{O}}^{+}$ [41, 42] and NO. Possible dissociative ionization pathways are schematically shown, which involves electron rescattering excitation after the tunneling ionization to populate the dissociative $B{}^1\mathrm{\Pi }$ and $c{}^3\mathrm{\Pi }$ states in the Franck-Condon (FC) region, or photodissociation in the non-FC region, from the bound excited states of $\mathrm{N}{\mathrm{O}}^{+}$ (see text for details). (b) Relevant molecular orbitals of NO, 2π, 1π, and 5σ.

Figure 2

(a) Schematic of the experimental setup. The fundamental femtosecond laser pulses (ω) (45 fs, 800 nm, 1 kHz) and the second harmonics (2ω) generated by a β-barium borate (BBO, type I) crystal are collinearly introduced to the three-dimensional ion momentum imaging spectrometer. The time delay between ω and 2ω pulses is controlled by birefringent α-BBO crystals and a pair of fused silica wedges. The relative phase is locked by a feedback loop utilizing the 2ω-2ω interference spectrum. The fragment ions produced from the interaction region are guided by a uniform electric field (61 V/cm) to reach a PSD through a field-free region. DWP: dual-wavelength wave plate; PSD: position-sensitive detector. (b) Temporal profiles of the two-color laser electric fields [Eq. (3)] for the relative phases of $\varphi =0,\pi /2$, and π, respectively, with the intensity ratio of $I_{2\omega }/I_{\omega }=0.04$. The Gaussian functions are assumed for the envelopes, ${\overline{F}}_{\omega }\left(t\right)$ and ${\overline{F}}_{2\omega }\left(t\right)$. See Eq. (2) and inset of (a) for the definition of the field direction.

Figure 3

Two-dimensional momentum images of the ${\mathrm{N}}^{+}$ fragment ions produced in (a) one-color intense laser fields ($800\mathrm{nm},1\times {10}^{14}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2,45\mathrm{fs}$), (b) phase-locked two-color intense laser fields ($800\mathrm{nm}+400\mathrm{nm},1\times {10}^{14}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2,45\mathrm{fs},I_{2\omega }/I_{\omega }=0.04$) with a relative phase of $\varphi =0.1\pi$. The momentum map represents a thin slice (with a slice width of ±0.5 a.u.) of the three-dimensional momentum distribution in the plane containing the $z$ axis (laser polarization direction). The momentum components parallel and perpendicular to the $z$ axis are denoted with $p_z$ and $p_{\perp }$, respectively. The laser polarization direction is denoted as ε with the arrow representing the direction of the larger amplitude.

Figure 4

(a) The asymmetry parameter A(ϕ) of the ${\mathrm{N}}^{+}$ fragment ions in phase-locked two-color intense laser fields, integrated over the entire $E_{\mathrm{kin}}$ range ($0\le E_{\mathrm{kin}}\le 4\mathrm{eV}$) (solid circle). Theoretical asymmetry parameter calculated by ME-WFAT is plotted for comparison (dotted line). (b) Observed asymmetry parameter A(ϕ) plotted against the kinetic energy release $E_{\mathrm{kin}}$.

Figure 5

(a) The total kinetic energy release, $E_{\mathrm{kin}}$, spectra calculated by the momentum conservation from the ${\mathrm{N}}^{+}$ fragment ions produced in two-color 45-fs intense laser fields $\varphi =0.1\pi$ (solid line), one-color 45-fs intense laser fields (broken line), and one-color 8-fs laser fields [11] (dotted line). (b) Two-dimensional plot of yields of the ${\mathrm{N}}^{+}$ fragment ions produced in two-color intense laser fields ($1\times {10}^{14}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2,I_{2\omega }/I_{\omega }=0.04,\varphi =0.1\pi$) against the angle θ with respect to the laser polarization direction and $E_{\mathrm{kin}}$.

Figure 6

Polar plot of θ angle distribution of the ${\mathrm{N}}^{+}$ fragment ions produced by the dissociative ionization $\mathrm{NO}\to {\mathrm{N}}^{+}+\mathrm{O}+e^{-}$ in two-color intense laser fields. The relative phase of $\varphi =0.1\pi$. (a) Peak I ($0.14\le E_{\mathrm{kin}}\le 0.36\mathrm{eV}$), (b) peak II ($0.50\le E_{\mathrm{kin}}\le 1.0\mathrm{eV}$), (c) peak III ($1.2\le E_{\mathrm{kin}}\le 1.7\mathrm{eV}$), and (d) peak IV ($1.8\le E_{\mathrm{kin}}\le 4.0\mathrm{eV}$). The laser polarization direction is denoted as ε with the larger arrow representing the direction of the larger amplitude.

Figure 7

Structure factors of NO plotted against orientation angle β between the electric field and the molecular axis. (a) $|G_{00}\left(\beta \right){|}^2$ (solid line) and $|{G_{01}}^{(+)}\left(\beta \right){|}^2$ (dashed line) for $2\pi \left(yz\right)$ HOMO and (b) $|{G_{01}}^{(–)}\left(\beta \right){|}^2$ for $2\pi \left(xz\right)$ HOMO.

Figure 8

Dependence of the angular distribution of peak IV on the relative phase ϕ. The laser polarization direction is along the horizontal axis. Experimental results show clear dependence on the phase (open circle). Theoretical results obtained by ME-WFAT ($1\times {10}^{14}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$) are shown in the first and second quadrants (solid line) for comparison.