Light propagation through an atomic vapor with non-orthogonal electric field modes

Alkali-metal atomic vapors are the foundation of an ever-growing range of applications, driven by a comprehensive understanding of their interaction with light. In particular, many models have been developed which characterize this interaction for low intensity laser fields. An atomic medium subject to an external magnetic field of arbitrary direction exhibits two electric field modes that, in general, are non-orthogonal. Mode non-orthogonality is currently neglected by the models used in this context. We derive a new light propagation formalism which takes into account the non-zero overlap of the two modes. We verify the theory using weak-probe spectroscopy of the Rb D$_{2}$ line, showing excellent agreement with experiment. The predictions of the new theory can be exploited, and optimized, to design better atomic photonic devices.