We perform an accurate polarimetry measurement of high-order harmonic emission from aligned molecules. We find that harmonic emission from ${\mathrm{N}}_2$ can be strongly elliptically polarized even when driven by linearly polarized laser fields. These data have broad implications for understanding molecules in strong fields because they cannot be explained by simple theories based on the strong field approximation and single active electron models. Finally, this work also shows that it is possible to engineer the polarization properties of harmonic emission by carefully preparing a molecular medium.

We use extreme-ultraviolet interferometry to measure the phase of high-order harmonic generation from transiently aligned ${\mathrm{CO}}_2$ molecules. We unambiguously observe a reversal in phase of the high-order harmonic emission for higher harmonic orders with a sufficient degree of alignment. This results from molecular-scale quantum interferences between the molecular electronic wave function and the recolliding electron as it recombines with the molecule, and is consistent with a two-center model. Furthermore, using the combined harmonic intensity and phase information, we extract accurate information on the dispersion relation of the returning electron wave packet as a function of harmonic order. This analysis shows evidence of the effect of the molecular potential on the recolliding electron wave.