Stability of periodic paraxial optical systems.

Based on ray propagation of paraxial geometric optics, we show that any stable periodic paraxial system or optical resonator becomes unstable in presence of stochastic perturbations of the the periodic sequence along which the rays are propagated. The exponential divergence with distance of ray displacements from the optical axis bears a close connection to the phenomenon of Anderson localization in disordered systems. The stability of the periodic focusing system is restored when finite aperture effects are accounted for and complex paraxial optics is used to describe wave propagation.