Orbital geometry determined by orthogonal high-order harmonic polarization components

We study the polarization state of high-order harmonics produced by linearly polarized light interacting with two-center molecules. By generating high-harmonic polarization maps from Radon transformations of excited electronic wave functions, we show that the polarization of the harmonic radiation can be linked to the geometry of the molecular orbital. While in the Radon transformation the plane-wave approximation for the rescattered electron is implicitly assumed, numerical solutions of the two-dimensional time-dependent Schrodinger equation, in which this approximation is not made, confirm the validity of this topological connection. We also find that measuring two orthogonal amplitude components of the harmonics provides a method for quantum tomography that substantially improves the quality of reconstructed molecular states.