Numerical investigation of the nonlinear dynamics of a hybrid acousto-optic Bragg cell with a variable feedback gain

Since around 1979, the operation of an acousto-optic Bragg cell under positive first-order feedback via amplification and delay in the loop has been studied extensively by several groups [1-3]. In recent work, the analysis of the nonlinear dynamics (NLD) of the system was extended to include bistable maps and Lyapunov exponents, and application of the chaos for signal encryption and decryption for uniform plane waves. The present work originated with the problem of a variable photodetector aperture opening relative to the first-order light. This potentially complex problem is simplified by assuming instead a variable feedback gain ( β ~ (t)), which leads to considerably different NLD. This paper examines initially the NLD versus the (DC) bias voltage for different variable- β ~ conditions, including slow and fast rates of change of the gain with time in relation to the feedback delay. It is found that the response depends critically on the rate of rise of the feedback gain, and also that the resulting chaotic regimes are generally significantly different from those for fixed values of β ~ . We have generated constant feedback gain and the variable feedback gain (t) chaos characteristics of the hybrid A-O network. Chaos as an equivalent carrier has been used to encrypt messages for both fixed and variable β ~ . The transmitted signal is detected from the encrypted carrier using a heterodyne method, using a slave Bragg cell with matched keys to generate local chaos followed by a low pass filter and a phase inverter. Results between variable- and fixed-gain systems are compared in terms of advantages and disadvantages.