  Recent years have seen vast progress in the generation and detection of
structured light, with potential applications in high capacity optical data
storage and continuous variable quantum technologies. Here we measure the
transmission of structured light through cold rubidium atoms and observe
regions of electromagnetically induced transparency (EIT). We use q-plates to
generate a probe beam with azimuthally varying phase and polarisation
structure, and its right and left circular polarisation components provide the
probe and control of an EIT transition. We observe an azimuthal modulation of
the absorption profile that is dictated by the phase and polarisation structure
of the probe laser. Conventional EIT systems do not exhibit phase sensitivity.
We show, however, that a weak transverse magnetic field closes the EIT
transitions, thereby generating phase dependent dark states which in turn lead
to phase dependent transparency, in agreement with our measurements.
