The use of acousto-optic chaos, as manifested via first-order feedback in an acousto-optic Bragg cell, in
encrypting a message wave and subsequently recovering the message in the receiver using a chaotic heterodyne
strategy, has been reported recently [1-3]. In examining the dynamical system analytically using computer
simulation, (expected) modulated chaos waveforms are obtained within specified observation windows. Because of
the relatively random nature inherent in chaos waveforms, it is essentially impossible to ascertain from the visual
display of the chaotic wave whether a given message signal has in fact modulated the chaotic "carrier". In fact, it
has been observed from earlier work that by appropriately controlling the chaos parameters, one may "hide" the
silhouette of the message from the envelope of the modulated chaos [1]. This was found to be especially true for
low-frequency chaos (in the KHz range). For chaos in the mid-RF (up to 10s of MHz) range, it is seen that the
silhouette is more difficult to suppress (even though this does not affect the robustness of the encryption). To
adequately determine whether modulation has in fact occurred by passing the AC signal through the sound cell bias
input, one needs to examine the spectral content of the chaos wave. In this paper, we discuss the results of such
spectral analyses using two different approaches, (i) fast Fourier transforms applied to the displayed waveform; and
(ii) transferring the intensity-vs-time data to an Excel spreadsheet, and then applying this information to a laboratory
spectrum analyzer with adequate bandwidth. The results are mutually compared and interpreted in terms of
encryption and decryption properties.
In recent work, low-frequency AC signal encryption, decryption and retrieval using system-parameter based
keys at the receiver stage of an acousto-optic (A-O) Bragg cell under first-order feedback have been demonstrated [1,2].
The corresponding nonlinear dynamics have also been investigated using the Lyapunov exponent and the so-called
bifurcation maps [3]. The results were essentially restricted to A-O chaos around 10 KHz, and (baseband) signal
bandwidths in the 1-4 KHz range. The results have generally been satisfactory, and parameter tolerances (prior to severe
signal distortion at the output) in the ±5% - ±10% range have been obtained. Periodic AC waveforms, and a short audio
clip have been examined in this series of investigations. Obviously, a main drawback in the above series of simulations
has been the low and impractical signal bandwidths used. The effort to increase the bandwidth involves designing a
feedback system with much higher chaos frequency that would then be amenable to higher BW information. In this
paper, we re-visit the problem for the case where the feedback delay time is reduced considerably, and the system
parameters in the transmitter adjusted in order to drive the system with a DC driver bias into chaos. Reducing the
feedback time delay to less than 1 μs, an average chaos frequency of about 10 MHz was achieved after a few trials. For
the AC application, a chaos region was chosen that would allow a large enough dynamic range for the width of the
available passband. Based on these dynamic choices, periodic AC signals with 1 MHz (fundamental) bandwidth were used for the RF bias driver (along with a DC bias). A triangular wave and a rectangular pulse train were chosen as examples. Results for these cases are presented here, along with comments on the system performance, and the possibility of including (static) images for signal encryption. Overall, the results are encouraging, and affirm the possibility of using A-O chaos for securely transmitting and retrieving information in the mid-RF range (a few 10s of MHz).
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