Ray and wave instabilities in twisted graded-index optical fibers

We study ray and wave propagation in an elliptical graded-index optical fiber or lens with a twisted axis and show analytically the existence of an instability for both ray trajectories and beam moments in a finite range of axis twist rate embedded within the spatial frequencies of periodically focused rays for the untwisted fiber. By considering the paraxial ray equations and the paraxial wave dynamics in a rotating frame that follows the fiber axis twist, we reduce the dynamical problem of ray trajectories to the classical Blackburn's pendulum, which shows a dynamical instability, corresponding to classical diverging trajectories, due to the competing effects of confining potential, Coriolis force, and centrifugal force. A closed set of linear evolution equations for generalized beam moments are also derived from the paraxial wave equation in the rotating reference frame, revealing the existence of a dynamical moment instability in addition to the trajectory instability. A detailed analysis of beam propagation is presented in case of a Gaussian beam, and different dynamical regimes are discussed