Examination of chaotic signal encryption and recovery for secure communication using hybrid acousto-optic feedback

Abstract

Generation of chaos from acousto-optic (A-O)Bragg cell modulators with an electronic feedback has been studied for over 3 decades. Since an acousto-optic Bragg cell with zeroth-and first-order feedback exhibits chaotic behavior past the threshold for bistability, such a system was recently examined for possible chaotic encryption of simple messages (such as a low-amplitude sinusoidal signal) applied via the bias input of the sound cell driver. Subsequent recovery of the message signal was carried out via a heterodyne-type strategy employing a locally generated chaotic carrier, with threshold parameters matched to the transmitting Bragg cell. In this paper, we present numerical results and detailed interpretations for signal encryption and recovery under hybrid A-O electronic feedback using a heterodyne strategy. Important features of this setup, such as the system robustness in terms of parameter matching (feedback gain, dc bias, and time delay) are also examined in some detail. C 2011 Society of Photo-Optical Instrumentation Engineers (SPIE). IntroductionIn an acousto-optic (A-O) modulator, an RF signal applied to a piezo-electric transducer, bonded to a suitable crystal, will generate an acoustic wave. It is well known that the acoustic wave acts like a "phase grating" that diffracts any incident laser beam into a number of diffracted orders. The Raman-Nath regime is characterized by multiple scattered orders while in the Bragg regime there are typically only two scattered orders (zeroth-and first-orders). 1 Around 1978, it was reported that A-O devices with positive feedback gain exhibit bistability characteristics. 2 In an A-O device, the amplitude of the diffracted fields that operate in the Bragg regime, i.e., the zeroth-and first-orders, which appear at the output of the Bragg cell, are related through a set of coupled differential equations. In Refs. 3 and 4, Chrostowski and co-workers present experimental results for A-O bistability and chaos using an equivalent circuit model of the Bragg cell with feedback. In a standard setup, a Bragg cell is driven by an ultrasonic sound wave from an RF generator at 40 MHz, and the resulting sound grating diffracts an incident He-Ne laser beam into the first Bragg order under Bragg condition. The first-order is then picked up by a linear photodetector, fed to an amplifier, and then returned to the bias input of the RF generator. The arrangement is shown in Fig. 1. Nominally, the scattered light beam is intrinsically frequency or phase modulated (with the acoustic frequency). In typical waveform sources, the external bias input amplitude modulates the RF waveform. A plot of the first order intensity (I 1 ) versus the bias inputα 0 yields the well known bistable and hysteretic behavior. 3,4 The bistability and hysteresis characteristics depend strongly on the feedback gain (β), the feedback time delay (TD), and the amplitude (I inc ) of the incident

Diffractive propagation and recovery of modulated (including chaotic) electromagnetic waves through uniform atmosphere and modified von Karman phase turbulence

“…When the message is embedded in a chaotic carrier, it is seen that even after passage though relatively weak chaos, the message is recovered with noticeably higher integrity (see Fig.16 (f)). Although this finding is relatively limited in scope, it nevertheless holds out the promise that a message wave may be secured and protected from a turbulent environment by packaging it inside a chaos wave via the RF encryption methodology which has been developed by our group [16,17]. As is shown later, when the turbulence becomes stronger, the recovery of the message from the chaos wave is subject to some degree of distortion, and is not entirely distortion-free.…”

“…It has been verified that in an acousto-optic Bragg cell with first-order feedback, the time-dependent chaos wave generated is approximately amplitude modulated when the signal wave is applied via the RF (sound) input [16]. We note that the chaotic waveform in eq.…”

“…As described, a sinc-type message waveform is therefore embedded onto the chaotic carrier at the output of a Bragg cell (not shown here; see ref. [16] for details). The resulting numerical data for the encrypted chaos wave is used to amplitude-modulate the optical carrier.…”

“…We note that the chaotic waveform in eq. (14) is essentially RF in nature, and manifests itself in the feedback loop as a current in the photodetector [16]. However, the chaos wave in turn rides on the optical carrier at the output of the Bragg cell (here assumed to be in first order), and is therefore manifested as envelope modulation of the optical carrier.…”

“…From Fig.15, we observe that the profile of the EM beam is broadened due to diffraction during passage through the (homogenous) medium ( Fig.15 (a) and (d)). Also, Fig.15 (f) shows that the received signal is recovered without any distortion using a simple heterodyne receiver used to filter out the chaos frequency and its harmonics in the photocurrent, thereby enabling recovery of the message signal [16].…”