Numerical examination of the nonlinear dynamics of a hybrid acousto-optic Bragg cell with positive feedback under profiled beam propagation

Abstract

In standard weak interaction theory, acousto-optic Bragg analysis typically assumes that the incident light and sound beams are uniform plane waves. Acousto-optic Bragg diffraction with nonuniform profiled input beams is numerically examined under open loop via a transfer function formalism. Unexpected deviations in the first-order diffracted beam from the standard theory are observed for high Q values. These deviations are significant because the corresponding closed-loop system is sensitive to input amplitudes and initial conditions, and the overall impact on the dynamical behavior has not been studied previously in standard analyses. To explore the effect of such nonuniform output profiles on the feedback system, the numerically generated scattered output is fed back to the acoustic driver, and the resulting nonlinear dynamics are manipulated to create novel monostable, bistable, multistable, and chaotic regimes. The effects of the nonuniform input on these regimes are examined using the techniques of Lyapunov exponents and bifurcation maps. The orbital behavior is characterized with quadratic maps, which are an intuitive method of predicting the parametric behavior of the system. The latter trajectory-based approach offers yet a third arm in the process of developing a fuller understanding of the profiled output beam under feedback. The results of this work indicate that the nonlinear dynamical thresholds of the hybrid cell are significantly different for the profiled propagation problem than for the uniform case. The mono and bistable regimes do not coincide with the well-known uniform plane wave results, and the chaotic thresholds, which are critical to understanding encryption applications, are altered noticeably.