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## Signal encryption strategies based on acoustooptic chaos and mitigation of phase turbulence using encrypted chaos propagation

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The phenomenon of acousto-optic (A-O) diffraction, first studied extensively in the late 1920s and 1930s, is used in many areas of signal processing, although this behavior is complex, and despite extensive generalized analyses and applications, comprehension of the phenomenon in its entirety is still incomplete. A-O diffraction refers to the interaction of light and sound waves, and it is used to controllably diffract light beams. The behavior of an A-O cell depends on several system parameters, and, in particular, the thickness of the crystal L and the wave numbers of both sound (K) and light (k). These quantities are summarized as a figure-of-merit by the Klein-Cook parameter (Q) which is used to characterize the regimes of A-O operation. For strict Bragg operation, which finds the most applications for these devices in practice, Chatterjee and Chen showed that Q should be larger than 8π. In this regime, under perfect Bragg-matching, there is only one diffracted order. If Q is much smaller than one, the mode of operation is called the Raman-Nath regime, which is characterized by multiple diffracted orders with intensities given by Bessel functions. Weak interaction theory is used in the analyses of AO diffraction, and this theory rests upon the assumption of uniform plane waves of sound and light. These assumptions, though not physically realistic, allow for tractable analyses and lead to observable results. The transfer function approach utilizes a plane wave angular spectrum of the field distribution (valid for small deviations from the exact Bragg angle), which allows the scattered fields to be represented by Fourier integrals in the angular domain. This makes it possible to apply the FFT algorithm to numerically generate the scattered fields of arbitrary inputs. Transfer function expressions for both Bragg orders are developed and may be readily applied in the Fourier transform domain. These expressions are convenient for modeling the effects of various parameters (such as phase shift and Q), as well as arbitrary input profiles.

Chapter Contents:

• 13.1 A-O Bragg diffraction of profiled optical beams
• 13.2 Transfer function formalism (TFF) for arbitrary optical profiles
• 13.3 Examination of the nonlinear dynamics under profiled beam propagation
• 13.4 Examination of dynamical behavior based on both Lyapunov exponent and bifurcation maps
• 13.5 Chaotic encryption and decryption in hybrid acousto-optic feedback (HAOF) devices
• 13.6 Preliminary results for chaotic encryption and decryption
• 13.7 Propagation of a profiled beam through MVKS type phase turbulence
• 13.7.1 An overview
• 13.7.2 The von Karman spectrum
• 13.7.3 Thin-phase screen generation
• 13.8 Spectral approach to the propagation of a (non-chaotic) EM wave through turbulence using SVEA and Fourier transforms
• 13.9 A uniform (nonturbulent) propagation prototype
• 13.9.1 Propagation through weak turbulence
• 13.9.1.1 Propagation through weak turbulence with mean frequency fT = 20 Hz
• 13.9.1.2 Propagation through weak turbulence with mean frequency fT = 50 Hz
• 13.9.1.3 Propagation through weak turbulence with mean frequency fT = 100 Hz
• 13.9.2 Propagation through strong turbulence
• 13.9.2.1 Propagation through strong turbulence with mean frequency fT = 20 Hz
• 13.9.2.2 Propagation through strong turbulence with mean frequency fT = 50 Hz
• 13.9.2.3 Propagation through strong turbulence with mean frequency fT = 100 Hz
• 13.10 Spectral approach to encrypted chaotic wave propagation through turbulence using SVEA and Fourier transforms
• 13.10.1 Numerical simulations, results, and interpretations
• 13.10.1.1 A uniform (nonturbulent) propagation prototype
• 13.10.1.2 Chaotic propagation through weak turbulence with mean frequency fT = 50 Hz
• 13.10.1.3 Chaotic propagation through strong turbulence with mean frequency fT = 50 Hz
• 13.11 Propagation through phase turbulence using altitude-dependent structure parameter without and with A-O chaos
• 13.11.1 Hufnagel-Valley (HV) model
• 13.11.2 Plane EM wave propagation through a transparency-thin lens combination with turbulence
• 13.11.3 Fixed LT and LD distances for different turbulence strengths
• 13.11.4 Fixed Cn 2 and LT for three different (nonturbulent) distances LD
• 13.11.5 Fixed Cn 2 and LD, for three different turbulence distances LT
• 13.11.6 Modulated EM wave (non-chaotic and chaotic) with a digitized image pattern
• 13.11.7 Fixed LT and LD distances for different turbulence strengths under a modulated EM wave propagation
• 13.11.8 Fixed Cn 2 and LD for three different destination distances LD
• 13.11.9 Fixed Cn 2 and LD for three different destination distances LT
• References

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