Geometric phases and coherent states for commensurate bichromatic polarization and astigmatic cavities

Both the polarization state of coherent bichromatic fields produced by harmonic generation and a class of anisotropic paraxial optical cavities are examples of commensurate two-dimensional harmonic oscillators. The geometric phase for these systems is studied here, both in the classical/ray and quantum/wave regimes. The quantum geometric phase is described in terms of the coherent states of the system, for which recursive expressions are derived that yield the exact result and are numerically stable even for high modal orders.