Optical bandgaps, level crossings and Berry phase in a rotating Sagnac Interferometer

A Sagnac interferometer’s ring structure enables counter propagating light modes to periodically encounter the same optical elements, effectively simulating infinite periodic potential of a one dimensional crystal. This discrete translational symmetry causes the dispersion of counter propagating beams to acquire a band structure. The band gap between modes arise when their degeneracy is lifted by introducing non-reciprocal effects such as rotation of the interferometer which breaks the time reversal symmetry for all but certain discrete values of angular rotation frequencies at which the two bands cross each other. The coupling between counter propagating modes is examined in a two dimensional state space. We study the interplay between these optical level crossings and Berry curvature to show the accumulation of wave vector dependent Berry phase