Examination of the nonlinear dynamics of a chaotic acousto-optic Bragg modulator with feedback under signal encryption and decryption

Abstract

An acousto-optic Bragg cell with first-order feedback, which exhibits chaotic behavior past the threshold for bistability, was recently examined for possible chaotic encryption and recovery of simple messages (such as low-amplitude periodic signals) applied via the bias input of the sound cell driver. We carry out a thorough examination of the nonlinear dynamics of the Bragg cell under intensity feedback for (i) dc variations of the feedback gain (β) and the phase shift parameter (α 0 ) and (ii) ac variations ofα 0;total under signal encryption, investigating both from two different perspectives: (i) examining chaos in view of the so-called Lyapunov exponent derived recently by Ghosh and Verma and (ii) examining chaos in terms of the familiar bifurcation maps of intensity plotted against the feedback gain and the effective bias. It is shown that overall, the nonlinear dynamical results using the two approaches broadly agree, both for dc (fixed-parameter) analyses and, more importantly, when applied to the case of ac signal encryption cases. This affirms the effectiveness of the nonlinear dynamical theory in predicting and tracking the actual physical behavior of this system for message signal transmission and recovery under complex chaotic encryption.Downloaded From: http://opticalengineering.spiedigitallibrary.org/ on 02/20/2015 Terms of Use: http://spiedl.org/terms Al-Saedi and Chatterjee: Examination of the nonlinear dynamics of a chaotic acousto-optic Bragg modulator : : :Optical Engineering

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

“…Since the application motivating this work is the transmission of encrypted signals, future work will include AC signal modulation at the bias input of the RF driver [12][13][14][15]. As has been shown in recent work [8], the first-order intensity becomes an amplitude-modulated chaotic wave. This process for secure communication has been shown to be feasible for uniform plane wave inputs; the impact of nonuniform plane wave inputs, however, needs to be studied further.…”

“…The behavior of the LE as a function of the feedback system parameters has been explored numerically with the assumption of uniform input beams [8,10]. In this work, we explore the effect of nonuniform Gaussian input beams on the LE and chaos, a necessary and novel development because realistic input beams are not truly uniform.…”

“…At this low value of Q, even though the scattered output appears to be sin 2 , this value ofβ for the hybrid cell is significantly different from that for the uniform case. For uniform plane wave illumination, the threshold value ofβ nominally tends to be 2.41 corresponding to a unit-amplitude plane wave input and zero initial conditions [8,11]. Thus, for profiled propagation, the threshold has been lowered.…”

“…The resulting nonlinear dynamics exhibit monostable, bistable, multistable, and chaotic behavior [5][6][7]. These properties have been exploited for a variety of signal processing applications including signal encryption and decryption [8]. The understanding of the nonlinear dynamics thus far has been limited by the assumption of uniform input beams.…”