  Resonant light interacting with matter can support different phases of a
polarizable medium, and optical bistability where two such phases coexist. Here
we identify signatures of optical phase transitions and optical bistability
mapped onto scattered light in planar arrays of cold atoms. Methods on how to
explore such systems in superradiant, and extreme subradiant states existing
outside the light cone, are proposed. The cooperativity threshold and intensity
regimes for the intrinsic optical bistability, supported by resonant
dipole-dipole interactions alone, are derived in several cases of interest
analytically. Subradiant states require lower intensities, but stronger
cooperativity for the existence of non-trivial phases than superradiant states.
The transmitted light reveals the onset of phase transitions and bistability
that are predicted by mean-field theory as large jumps in coherent and
incoherent signals and hysteresis. In the quantum solution, traces of phase
transitions are identified in enhanced quantum fluctuations of excited level
populations.
