Here, we describe progress toward realization of a vector magnetometer based on all-optical excitation
of an atomic ensemble in a vapor cell under the conditions of electromagnetically induced transparency (EIT). The EIT resonance amplitudes depend on relative orientations of the three key vectors: laser wave-vector, polarization,
and the direction of the magnetic field. By analyzing possible two-photon transitions and their combinations, we can,
in principle, analytically calculate the amplitude of various EIT resonances as functions of the relative angles between
the magnetic field, polarization and laser propagation vectors. By locking the polarization to
one of these maxima, one can determine the plane formed by the magnetic field and the light wave vector to the
accuracy better than 0.001 rad. Analysis of the relative resonance amplitude may be used to extract the full information
about the magnetic field direction.
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