Propagation dynamics of spatio-temporal wave packets

Qian Cao


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]. It is well-known that this system offers interesting dynamical properties, including bistability and chaos under a range of parameter thresholds. Thus, for fixed values of the bias voltage feedback gain, feedback time delay incident optical intensity and initial first-order intensity, the hybrid system may be operated in regimes where it is bistable (thus leading to possible logical applications), or chaotic (within which it may exhibit period-2, period-3 and similar characteristics). In recent work, the analysis of the system was extended to include bistable maps and bifurcation specific to chaotic regimes whereby chaotic passbands and stopbands were established. Additionally, the system was utilized for signal encryption and decryption applications under chaos for uniform plane waves. The present work originated with the problem of a variable aperture opening relative to the first-order light. This potentially complex problem is simplified by assuming instead a variable feedback gain, which leads to considerably different nonlinear dynamics. This research explores initially the simpler stages of this problem by examining the nonlinear dynamics versus the bias voltage for different variable feed back-conditions, including very slow and likewise 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 feed back gain. We have generated constant feedback gain and the variable feedback gain chaos characteristics of the hybrid A-O network. Chaos as an equivalent carrier has been used to encrypt messages, and this strategy may be used as a means of ensuring information security in keeping the information safe. A receiver scheme was developed using a second Bragg cell with a matched bias input to generate local chaos that was used to extract message using a heterodyne reception technique, 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.