Two-pulse field-free orientation reveals anisotropy of molecular shape resonance

We report the observation of macroscopic field-free orientation, i.e. more than 73 % of CO molecules pointing in the same direction. This is achieved through an all-optical scheme operating at high particle densities ($>10^{17}$cm$^{-3}$) that combines a one-color ($\omega$) and a two-color ($\omega + 2\omega$) non-resonant femtosecond laser pulses. We show that the achieved orientation solely relies on the hyperpolarizability interaction as opposed to an ionization-depletion mechanism thus opening a wide range of applications. The achieved strong orientation enables us to reveal the molecular-frame anisotropies of the photorecombination amplitudes and phases caused by a shape resonance. The resonance appears as a local maximum in the even-harmonic emission around 28~eV. In contrast, the odd-harmonic emission is suppressed in this spectral region through the combined effects of an asymmetric photorecombination phase and a sub-cycle Stark effect, generic for polar molecules, that we experimentally identify.