The nonlinear dynamics of a hybrid acousto-optic device was examined from the perspective of the Lyapunov exponent (LE) and bifurcation maps. The plots for LE versus system parameters and bifurcation maps have recently been examined against known simulation results including chaotic encryption experiments [1]. It is verified that the "loop gain" (feedback gain (β) times incident light amplitude (Iin) needs to be greater than one as a necessary , but not sufficient condition for the onset of chaos.

It is found that for certain combinations of β, Iin, net bias voltage (αtοt), and the initial value of the first-order scattered light (I1(0)), there are pronounced regions of chaos in the parameter field, while for others, chaos is minimal. It is also observed that in some cases, the negative "spikes" in the LE are far larger than its positive amplitudes, hence indicating a greater tendency to become non-chaotic. Additionally, we have examined the bifurcation plots versus the two most salient system parameters, αtοt and β. These maps have revealed behavior that is by no means uniformly chaotic. It is found that the system moves in and out of chaos within distinct bands along the αtοt and β axes. These results imply strong sensitivity vis-Ã -vis these parameters around the passbands and stopbands , and may indicate control of chaos by appropriate parameter adjustment. Such control may have applications in biological chaos, such as arresting malignant, chaotic cell multiplication.

Overall, the dynamical results compare favorably with time-domain characteristics of encrypted chaotic waveforms in signal modulation and transmission applications.