Angular Tunneling Ionization Probability of Fixed-in-Space ${\mathrm{H}}_2$ Molecules in Intense Laser Pulses

We propose a new approach to obtain molecular frame photoelectron angular distributions from molecules ionized by intense laser pulses. With our method we study the angular tunnel ionization probability of ${\mathrm{H}}_2$ at a wavelength of 800 nm over an intensity range of $2–4.5\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$. We find an anisotropy that is stronger than predicted by any existing model. To explain the observed anisotropy and its strong intensity dependence we develop an analytical model in the framework of the strong-field approximation. It expresses molecular ionization as a product of atomic ionization rate and a Fourier transform of the highest occupied molecular orbital filtered by the strong-field ionization process.

Figure 1

(a) Sketch of the experiment. The same circularly polarized laser pulse ionizes (left) and subsequently dissociates (right) the molecule. (b) Potential energy curves of ${\mathrm{H}}_2$ and ${\mathrm{H}}_2^{+}$ indicating the pathways leading to 1 photon and net-2 photon dissociation of ${\mathrm{H}}_2^{+}$. (c) Top: Measured proton momentum distribution produced by dissociating ${\mathrm{H}}_2^{+}$ in the polarization plane of a circularly polarized, 800 nm, 40 fs pulse at $3.0\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$. Bottom: electron momentum distribution produced by single ionization of ${\mathrm{H}}_2$ under identical conditions.

Figure 2

(a) MFPAD of ${\mathrm{H}}_2$ ($X^1{\Sigma }_g^{+}$) in circularly polarized, 40 fs, 800 nm laser pulses at $2.3\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$. (b) Ratio of the ionization rates $w_{\parallel }/w_{\perp }$ as a function of intensity for experiment and theory. Dashed line: MOADK [28], solid star: Hartree-Fock calculation [14]. Solid line: our model—length-gauge MOSFA (see text for details).