Abstract

Use of acousto-optic (A-O) chaos via the feedback loop in a Bragg cell for signal encryption began as a conceptual demonstration around 2008. Radio frequency (RF) chaos from a hybrid A-O feedback device may be used for secure communications of analog and digital signals. In this paper, modulation of RF chaos via first-order feedback is discussed with results corroborated by nonlinear dynamics, bifurcation maps, and Lyapunov analyses. Applications based on encryption with profiled optical beams, and extended to medical and embedded steganographic data, and video signals are discussed. It is shown that the resulting encryption is significantly robust with key tolerances potentially less than 0.1%. Results are also presented for the use of chaotic encryption for image restoration during propagation through atmospheric turbulence.

© 2018 Optical Society of America

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References

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  1. J. Chrostowski and C. Delisle, “Bistable piezoelectric Fabry–Perot interferometer,” Can. J. Phys. 57, 1376–1379 (1979).
    [Crossref]
  2. J. Chrostowski and C. Delisle, “Bistable optical switching based on Bragg diffraction,” Opt. Commun. 41, 71–74 (1982).
    [Crossref]
  3. M. A. Al-Saedi and M. R. Chatterjee, “Examination of the nonlinear dynamics of a chaotic acousto-optic Bragg modulator with feedback under signal encryption and decryption,” Opt. Eng. 51, 018003 (2012).
    [Crossref]
  4. F. S. Almehmadi and M. R. Chatterjee, “Improved performance of analog and digital acousto-optic modulation with feedback under profiled beam propagation for secure communication using chaos,” Opt. Eng. 53, 126102 (2014).
    [Crossref]
  5. F. S. Almehmadi and M. R. Chatterjee, “Secure chaotic transmission of electrocardiography signals with acousto-optic modulation under profiled beam propagation,” Appl. Opt. 54, 195–203 (2015).
    [Crossref]
  6. F. S. Almehmadi, “Secure Chaotic Transmission of Digital and Analog Signals Under Profiled Beam Propagation in Acousto-Optic Bragg Cells with Feedback,” Doctoral dissertation (University of Dayton, 2015).
  7. M. R. Chatterjee and A. Mohamed, “Anisoplanatic image propagation along a slanted path under lower atmosphere phase turbulence in the presence of encrypted chaos,” Proc. SPIE 10204, 102040G (2017).
    [Crossref]
  8. A. Mohamed and M. R. Chatterjee, “Chaos-based mitigation of image distortion under anisoplanatic electromagnetic signal propagation through turbulence,” in Frontiers in Optics, OSA Technical Digest, Washington, DC, September, 2017, paper JW4A.1.
  9. M. R. Chatterjee and A. Mohamed, “Anisoplanatic electromagnetic image propagation through narrow or extended phase turbulence using altitude-dependent structure parameter,” in Frontiers in Optics, OSA Technical Digest, Rochester, New York, October, 2016, paper JW4A.90.
  10. L. Brillouin, “Diffusion de la lumière et des rayons X par un corps transparent homogène,” Ann. Phys. 9, 88–122 (1922).
    [Crossref]
  11. C. V. Raman and N. S. Nagendra Nath, “The diffraction of light by high frequency sound waves: Part I,” Proc. Indian Acad. Sci. 2, 406–412 (1935).
  12. A. Korpel, Acousto-Optics, 2nd ed. (Marcel Dekker, 1997).
  13. W. R. Klein and B. D. Cook, “Unified approach to ultrasonic light diffraction,” IEEE Trans. Sonics Ultrason. 14, 123–134 (1967).
    [Crossref]
  14. S.-T. Chen and M. R. Chatterjee, “A numerical analysis and expository interpretation of the diffraction of light by ultrasonic waves in the Bragg and Raman–Nath regimes multiple scattering theory,” IEEE Trans. Educ. 39, 56–68 (1996).
    [Crossref]
  15. C. Webb and J. Jones, Handbook of Laser Technology and Applications—Vol. II, 1st ed. (Taylor & Francis, 2004).
  16. A. Korpel and T.-C. Poon, “Explicit formalism for acousto-optic multiple plane-wave scattering,” J. Opt. Soc. Am. 70, 817–820 (1980).
    [Crossref]
  17. M. R. Chatterjee, T.-C. Poon, and D. N. Sitter, “Transfer function formalism for strong acousto-optic Bragg diffraction of light beams with arbitrary profiles,” Acustica 71, 81–91 (1991).
  18. L. N. Magdich and V. Y. Molchanov, “Diffraction of divergent beam on intense acoustic waves,” Opt. Spectrosc. 42, 533–539 (1977).
  19. V. I. Balakshy, “Acousto-optic cell as a filter of spatial frequencies,” Radio Eng. Electron. 29, 1610–1616 (1984).
  20. V. I. Balakshy, V. N. Parygin, and L. E. Chirkov, Physical Principles of Acousto-Optics (Radio Svyaz, 1985).
  21. P. P. Banerjee, U. Banerjee, and H. Kaplan, “Response of an acousto-optic device with feedback to time-varying inputs,” Appl. Opt. 31, 1842–1852 (1992).
    [Crossref]
  22. V. I. Balakshy, Y. I. Kuznetsov, S. N. Mantsevich, and N. V. Polikarpova, “Dynamic processes in an acousto-optic laser beam intensity stabilization system,” Opt. Laser Technol. 62, 89–94 (2014).
    [Crossref]
  23. M. R. Chatterjee and F. Almehmadi, “Numerical analysis of first-order acousto-optic Bragg diffraction of profiled optical beams using open-loop transfer functions,” Opt. Eng. 53, 036108 (2014).
    [Crossref]
  24. E. I. Gordon, “A review of acoustooptical deflection and modulation devices,” Proc. IEEE 54, 1391–1401 (1966).
    [Crossref]
  25. A. K. Ghosh and P. Verma, “Lyapunov exponent of chaos generated by acousto-optic modulators with feedback,” Opt. Eng. 50, 017005 (2011).
    [Crossref]
  26. J. Durnin, J. J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
    [Crossref]
  27. A. N. Kolmogorov, “The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers,” Proc. R. Soc. A 434, 9–13 (1991).
    [Crossref]
  28. A. N. Kolmogorov, “A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number,” J. Fluid Mech. 13, 82–85 (1962).
    [Crossref]
  29. A. M. Obukhov, “On the distribution of energy in the spectrum of turbulent flow,” Dokl. Akad. Nauk SSSR 32, 22–24 (1941).
  30. A. K. Majumdar, Naval Research Lab, private communication (2014).
  31. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).
  32. M. C. Roggemann and B. M. Welsh, Imaging through Turbulence, 1st ed. (CRC Press, 1996).
  33. M. R. Chatterjee and F. H. A. Mohamed, “Split-step approach to electromagnetic propagation through atmospheric turbulence using the modified von Karman spectrum and planar apertures,” Opt. Eng. 53, 126107 (2014).
    [Crossref]
  34. J. Power, “Modeling anisoplanatic effects from atmospheric turbulence across slanted optical paths in imagery,” Master’s thesis (University of Dayton, 2016).
  35. J. D. Schmidt, Numerical Simulation of Optical Wave Propagation with Examples in Matlab (SPIE, 2010).
  36. A. K. Majumdar, J. C. Ricklin, E. Leitgeb, M. Gebhart, and U. Birnbacher, “Optical networks, last mile access and applications,” in Free-Space Laser Communications (Springer, 2008), Vol. 2, pp. 273–302.
  37. P. P. Banerjee and T.-C. Poon, Principles of Applied Optics (Aksen Associates, 1991).
  38. J. M. Jarem and P. P. Banerjee, Computational Methods for Electromagnetic and Optical Systems, 2nd ed. (CRC Press, 2011).
  39. M. R. Chatterjee and M. Alsaedi, “Examination of chaotic signal encryption and recovery for secure communication using hybrid acousto-optic feedback,” Opt. Eng. 50, 055002 (2011).
    [Crossref]
  40. M. R. Chatterjee and F. Mohamed, “Diffractive propagation and recovery of modulated (including chaotic) electromagnetic waves through uniform atmosphere and modified von Karman phase turbulence,” Proc. SPIE 9833, 98330F (2016).
    [Crossref]

2017 (1)

M. R. Chatterjee and A. Mohamed, “Anisoplanatic image propagation along a slanted path under lower atmosphere phase turbulence in the presence of encrypted chaos,” Proc. SPIE 10204, 102040G (2017).
[Crossref]

2016 (1)

M. R. Chatterjee and F. Mohamed, “Diffractive propagation and recovery of modulated (including chaotic) electromagnetic waves through uniform atmosphere and modified von Karman phase turbulence,” Proc. SPIE 9833, 98330F (2016).
[Crossref]

2015 (1)

2014 (4)

F. S. Almehmadi and M. R. Chatterjee, “Improved performance of analog and digital acousto-optic modulation with feedback under profiled beam propagation for secure communication using chaos,” Opt. Eng. 53, 126102 (2014).
[Crossref]

V. I. Balakshy, Y. I. Kuznetsov, S. N. Mantsevich, and N. V. Polikarpova, “Dynamic processes in an acousto-optic laser beam intensity stabilization system,” Opt. Laser Technol. 62, 89–94 (2014).
[Crossref]

M. R. Chatterjee and F. Almehmadi, “Numerical analysis of first-order acousto-optic Bragg diffraction of profiled optical beams using open-loop transfer functions,” Opt. Eng. 53, 036108 (2014).
[Crossref]

M. R. Chatterjee and F. H. A. Mohamed, “Split-step approach to electromagnetic propagation through atmospheric turbulence using the modified von Karman spectrum and planar apertures,” Opt. Eng. 53, 126107 (2014).
[Crossref]

2012 (1)

M. A. Al-Saedi and M. R. Chatterjee, “Examination of the nonlinear dynamics of a chaotic acousto-optic Bragg modulator with feedback under signal encryption and decryption,” Opt. Eng. 51, 018003 (2012).
[Crossref]

2011 (2)

M. R. Chatterjee and M. Alsaedi, “Examination of chaotic signal encryption and recovery for secure communication using hybrid acousto-optic feedback,” Opt. Eng. 50, 055002 (2011).
[Crossref]

A. K. Ghosh and P. Verma, “Lyapunov exponent of chaos generated by acousto-optic modulators with feedback,” Opt. Eng. 50, 017005 (2011).
[Crossref]

1996 (1)

S.-T. Chen and M. R. Chatterjee, “A numerical analysis and expository interpretation of the diffraction of light by ultrasonic waves in the Bragg and Raman–Nath regimes multiple scattering theory,” IEEE Trans. Educ. 39, 56–68 (1996).
[Crossref]

1992 (1)

1991 (2)

M. R. Chatterjee, T.-C. Poon, and D. N. Sitter, “Transfer function formalism for strong acousto-optic Bragg diffraction of light beams with arbitrary profiles,” Acustica 71, 81–91 (1991).

A. N. Kolmogorov, “The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers,” Proc. R. Soc. A 434, 9–13 (1991).
[Crossref]

1987 (1)

J. Durnin, J. J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref]

1984 (1)

V. I. Balakshy, “Acousto-optic cell as a filter of spatial frequencies,” Radio Eng. Electron. 29, 1610–1616 (1984).

1982 (1)

J. Chrostowski and C. Delisle, “Bistable optical switching based on Bragg diffraction,” Opt. Commun. 41, 71–74 (1982).
[Crossref]

1980 (1)

1979 (1)

J. Chrostowski and C. Delisle, “Bistable piezoelectric Fabry–Perot interferometer,” Can. J. Phys. 57, 1376–1379 (1979).
[Crossref]

1977 (1)

L. N. Magdich and V. Y. Molchanov, “Diffraction of divergent beam on intense acoustic waves,” Opt. Spectrosc. 42, 533–539 (1977).

1967 (1)

W. R. Klein and B. D. Cook, “Unified approach to ultrasonic light diffraction,” IEEE Trans. Sonics Ultrason. 14, 123–134 (1967).
[Crossref]

1966 (1)

E. I. Gordon, “A review of acoustooptical deflection and modulation devices,” Proc. IEEE 54, 1391–1401 (1966).
[Crossref]

1962 (1)

A. N. Kolmogorov, “A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number,” J. Fluid Mech. 13, 82–85 (1962).
[Crossref]

1941 (1)

A. M. Obukhov, “On the distribution of energy in the spectrum of turbulent flow,” Dokl. Akad. Nauk SSSR 32, 22–24 (1941).

1935 (1)

C. V. Raman and N. S. Nagendra Nath, “The diffraction of light by high frequency sound waves: Part I,” Proc. Indian Acad. Sci. 2, 406–412 (1935).

1922 (1)

L. Brillouin, “Diffusion de la lumière et des rayons X par un corps transparent homogène,” Ann. Phys. 9, 88–122 (1922).
[Crossref]

Almehmadi, F.

M. R. Chatterjee and F. Almehmadi, “Numerical analysis of first-order acousto-optic Bragg diffraction of profiled optical beams using open-loop transfer functions,” Opt. Eng. 53, 036108 (2014).
[Crossref]

Almehmadi, F. S.

F. S. Almehmadi and M. R. Chatterjee, “Secure chaotic transmission of electrocardiography signals with acousto-optic modulation under profiled beam propagation,” Appl. Opt. 54, 195–203 (2015).
[Crossref]

F. S. Almehmadi and M. R. Chatterjee, “Improved performance of analog and digital acousto-optic modulation with feedback under profiled beam propagation for secure communication using chaos,” Opt. Eng. 53, 126102 (2014).
[Crossref]

F. S. Almehmadi, “Secure Chaotic Transmission of Digital and Analog Signals Under Profiled Beam Propagation in Acousto-Optic Bragg Cells with Feedback,” Doctoral dissertation (University of Dayton, 2015).

Alsaedi, M.

M. R. Chatterjee and M. Alsaedi, “Examination of chaotic signal encryption and recovery for secure communication using hybrid acousto-optic feedback,” Opt. Eng. 50, 055002 (2011).
[Crossref]

Al-Saedi, M. A.

M. A. Al-Saedi and M. R. Chatterjee, “Examination of the nonlinear dynamics of a chaotic acousto-optic Bragg modulator with feedback under signal encryption and decryption,” Opt. Eng. 51, 018003 (2012).
[Crossref]

Andrews, L. C.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).

Balakshy, V. I.

V. I. Balakshy, Y. I. Kuznetsov, S. N. Mantsevich, and N. V. Polikarpova, “Dynamic processes in an acousto-optic laser beam intensity stabilization system,” Opt. Laser Technol. 62, 89–94 (2014).
[Crossref]

V. I. Balakshy, “Acousto-optic cell as a filter of spatial frequencies,” Radio Eng. Electron. 29, 1610–1616 (1984).

V. I. Balakshy, V. N. Parygin, and L. E. Chirkov, Physical Principles of Acousto-Optics (Radio Svyaz, 1985).

Banerjee, P. P.

P. P. Banerjee, U. Banerjee, and H. Kaplan, “Response of an acousto-optic device with feedback to time-varying inputs,” Appl. Opt. 31, 1842–1852 (1992).
[Crossref]

J. M. Jarem and P. P. Banerjee, Computational Methods for Electromagnetic and Optical Systems, 2nd ed. (CRC Press, 2011).

P. P. Banerjee and T.-C. Poon, Principles of Applied Optics (Aksen Associates, 1991).

Banerjee, U.

Birnbacher, U.

A. K. Majumdar, J. C. Ricklin, E. Leitgeb, M. Gebhart, and U. Birnbacher, “Optical networks, last mile access and applications,” in Free-Space Laser Communications (Springer, 2008), Vol. 2, pp. 273–302.

Brillouin, L.

L. Brillouin, “Diffusion de la lumière et des rayons X par un corps transparent homogène,” Ann. Phys. 9, 88–122 (1922).
[Crossref]

Chatterjee, M. R.

M. R. Chatterjee and A. Mohamed, “Anisoplanatic image propagation along a slanted path under lower atmosphere phase turbulence in the presence of encrypted chaos,” Proc. SPIE 10204, 102040G (2017).
[Crossref]

M. R. Chatterjee and F. Mohamed, “Diffractive propagation and recovery of modulated (including chaotic) electromagnetic waves through uniform atmosphere and modified von Karman phase turbulence,” Proc. SPIE 9833, 98330F (2016).
[Crossref]

F. S. Almehmadi and M. R. Chatterjee, “Secure chaotic transmission of electrocardiography signals with acousto-optic modulation under profiled beam propagation,” Appl. Opt. 54, 195–203 (2015).
[Crossref]

F. S. Almehmadi and M. R. Chatterjee, “Improved performance of analog and digital acousto-optic modulation with feedback under profiled beam propagation for secure communication using chaos,” Opt. Eng. 53, 126102 (2014).
[Crossref]

M. R. Chatterjee and F. Almehmadi, “Numerical analysis of first-order acousto-optic Bragg diffraction of profiled optical beams using open-loop transfer functions,” Opt. Eng. 53, 036108 (2014).
[Crossref]

M. R. Chatterjee and F. H. A. Mohamed, “Split-step approach to electromagnetic propagation through atmospheric turbulence using the modified von Karman spectrum and planar apertures,” Opt. Eng. 53, 126107 (2014).
[Crossref]

M. A. Al-Saedi and M. R. Chatterjee, “Examination of the nonlinear dynamics of a chaotic acousto-optic Bragg modulator with feedback under signal encryption and decryption,” Opt. Eng. 51, 018003 (2012).
[Crossref]

M. R. Chatterjee and M. Alsaedi, “Examination of chaotic signal encryption and recovery for secure communication using hybrid acousto-optic feedback,” Opt. Eng. 50, 055002 (2011).
[Crossref]

S.-T. Chen and M. R. Chatterjee, “A numerical analysis and expository interpretation of the diffraction of light by ultrasonic waves in the Bragg and Raman–Nath regimes multiple scattering theory,” IEEE Trans. Educ. 39, 56–68 (1996).
[Crossref]

M. R. Chatterjee, T.-C. Poon, and D. N. Sitter, “Transfer function formalism for strong acousto-optic Bragg diffraction of light beams with arbitrary profiles,” Acustica 71, 81–91 (1991).

A. Mohamed and M. R. Chatterjee, “Chaos-based mitigation of image distortion under anisoplanatic electromagnetic signal propagation through turbulence,” in Frontiers in Optics, OSA Technical Digest, Washington, DC, September, 2017, paper JW4A.1.

M. R. Chatterjee and A. Mohamed, “Anisoplanatic electromagnetic image propagation through narrow or extended phase turbulence using altitude-dependent structure parameter,” in Frontiers in Optics, OSA Technical Digest, Rochester, New York, October, 2016, paper JW4A.90.

Chen, S.-T.

S.-T. Chen and M. R. Chatterjee, “A numerical analysis and expository interpretation of the diffraction of light by ultrasonic waves in the Bragg and Raman–Nath regimes multiple scattering theory,” IEEE Trans. Educ. 39, 56–68 (1996).
[Crossref]

Chirkov, L. E.

V. I. Balakshy, V. N. Parygin, and L. E. Chirkov, Physical Principles of Acousto-Optics (Radio Svyaz, 1985).

Chrostowski, J.

J. Chrostowski and C. Delisle, “Bistable optical switching based on Bragg diffraction,” Opt. Commun. 41, 71–74 (1982).
[Crossref]

J. Chrostowski and C. Delisle, “Bistable piezoelectric Fabry–Perot interferometer,” Can. J. Phys. 57, 1376–1379 (1979).
[Crossref]

Cook, B. D.

W. R. Klein and B. D. Cook, “Unified approach to ultrasonic light diffraction,” IEEE Trans. Sonics Ultrason. 14, 123–134 (1967).
[Crossref]

Delisle, C.

J. Chrostowski and C. Delisle, “Bistable optical switching based on Bragg diffraction,” Opt. Commun. 41, 71–74 (1982).
[Crossref]

J. Chrostowski and C. Delisle, “Bistable piezoelectric Fabry–Perot interferometer,” Can. J. Phys. 57, 1376–1379 (1979).
[Crossref]

Durnin, J.

J. Durnin, J. J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref]

Eberly, J.

J. Durnin, J. J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref]

Gebhart, M.

A. K. Majumdar, J. C. Ricklin, E. Leitgeb, M. Gebhart, and U. Birnbacher, “Optical networks, last mile access and applications,” in Free-Space Laser Communications (Springer, 2008), Vol. 2, pp. 273–302.

Ghosh, A. K.

A. K. Ghosh and P. Verma, “Lyapunov exponent of chaos generated by acousto-optic modulators with feedback,” Opt. Eng. 50, 017005 (2011).
[Crossref]

Gordon, E. I.

E. I. Gordon, “A review of acoustooptical deflection and modulation devices,” Proc. IEEE 54, 1391–1401 (1966).
[Crossref]

Jarem, J. M.

J. M. Jarem and P. P. Banerjee, Computational Methods for Electromagnetic and Optical Systems, 2nd ed. (CRC Press, 2011).

Jones, J.

C. Webb and J. Jones, Handbook of Laser Technology and Applications—Vol. II, 1st ed. (Taylor & Francis, 2004).

Kaplan, H.

Klein, W. R.

W. R. Klein and B. D. Cook, “Unified approach to ultrasonic light diffraction,” IEEE Trans. Sonics Ultrason. 14, 123–134 (1967).
[Crossref]

Kolmogorov, A. N.

A. N. Kolmogorov, “The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers,” Proc. R. Soc. A 434, 9–13 (1991).
[Crossref]

A. N. Kolmogorov, “A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number,” J. Fluid Mech. 13, 82–85 (1962).
[Crossref]

Korpel, A.

Kuznetsov, Y. I.

V. I. Balakshy, Y. I. Kuznetsov, S. N. Mantsevich, and N. V. Polikarpova, “Dynamic processes in an acousto-optic laser beam intensity stabilization system,” Opt. Laser Technol. 62, 89–94 (2014).
[Crossref]

Leitgeb, E.

A. K. Majumdar, J. C. Ricklin, E. Leitgeb, M. Gebhart, and U. Birnbacher, “Optical networks, last mile access and applications,” in Free-Space Laser Communications (Springer, 2008), Vol. 2, pp. 273–302.

Magdich, L. N.

L. N. Magdich and V. Y. Molchanov, “Diffraction of divergent beam on intense acoustic waves,” Opt. Spectrosc. 42, 533–539 (1977).

Majumdar, A. K.

A. K. Majumdar, J. C. Ricklin, E. Leitgeb, M. Gebhart, and U. Birnbacher, “Optical networks, last mile access and applications,” in Free-Space Laser Communications (Springer, 2008), Vol. 2, pp. 273–302.

A. K. Majumdar, Naval Research Lab, private communication (2014).

Mantsevich, S. N.

V. I. Balakshy, Y. I. Kuznetsov, S. N. Mantsevich, and N. V. Polikarpova, “Dynamic processes in an acousto-optic laser beam intensity stabilization system,” Opt. Laser Technol. 62, 89–94 (2014).
[Crossref]

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref]

Mohamed, A.

M. R. Chatterjee and A. Mohamed, “Anisoplanatic image propagation along a slanted path under lower atmosphere phase turbulence in the presence of encrypted chaos,” Proc. SPIE 10204, 102040G (2017).
[Crossref]

A. Mohamed and M. R. Chatterjee, “Chaos-based mitigation of image distortion under anisoplanatic electromagnetic signal propagation through turbulence,” in Frontiers in Optics, OSA Technical Digest, Washington, DC, September, 2017, paper JW4A.1.

M. R. Chatterjee and A. Mohamed, “Anisoplanatic electromagnetic image propagation through narrow or extended phase turbulence using altitude-dependent structure parameter,” in Frontiers in Optics, OSA Technical Digest, Rochester, New York, October, 2016, paper JW4A.90.

Mohamed, F.

M. R. Chatterjee and F. Mohamed, “Diffractive propagation and recovery of modulated (including chaotic) electromagnetic waves through uniform atmosphere and modified von Karman phase turbulence,” Proc. SPIE 9833, 98330F (2016).
[Crossref]

Mohamed, F. H. A.

M. R. Chatterjee and F. H. A. Mohamed, “Split-step approach to electromagnetic propagation through atmospheric turbulence using the modified von Karman spectrum and planar apertures,” Opt. Eng. 53, 126107 (2014).
[Crossref]

Molchanov, V. Y.

L. N. Magdich and V. Y. Molchanov, “Diffraction of divergent beam on intense acoustic waves,” Opt. Spectrosc. 42, 533–539 (1977).

Nagendra Nath, N. S.

C. V. Raman and N. S. Nagendra Nath, “The diffraction of light by high frequency sound waves: Part I,” Proc. Indian Acad. Sci. 2, 406–412 (1935).

Obukhov, A. M.

A. M. Obukhov, “On the distribution of energy in the spectrum of turbulent flow,” Dokl. Akad. Nauk SSSR 32, 22–24 (1941).

Parygin, V. N.

V. I. Balakshy, V. N. Parygin, and L. E. Chirkov, Physical Principles of Acousto-Optics (Radio Svyaz, 1985).

Phillips, R. L.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).

Polikarpova, N. V.

V. I. Balakshy, Y. I. Kuznetsov, S. N. Mantsevich, and N. V. Polikarpova, “Dynamic processes in an acousto-optic laser beam intensity stabilization system,” Opt. Laser Technol. 62, 89–94 (2014).
[Crossref]

Poon, T.-C.

M. R. Chatterjee, T.-C. Poon, and D. N. Sitter, “Transfer function formalism for strong acousto-optic Bragg diffraction of light beams with arbitrary profiles,” Acustica 71, 81–91 (1991).

A. Korpel and T.-C. Poon, “Explicit formalism for acousto-optic multiple plane-wave scattering,” J. Opt. Soc. Am. 70, 817–820 (1980).
[Crossref]

P. P. Banerjee and T.-C. Poon, Principles of Applied Optics (Aksen Associates, 1991).

Power, J.

J. Power, “Modeling anisoplanatic effects from atmospheric turbulence across slanted optical paths in imagery,” Master’s thesis (University of Dayton, 2016).

Raman, C. V.

C. V. Raman and N. S. Nagendra Nath, “The diffraction of light by high frequency sound waves: Part I,” Proc. Indian Acad. Sci. 2, 406–412 (1935).

Ricklin, J. C.

A. K. Majumdar, J. C. Ricklin, E. Leitgeb, M. Gebhart, and U. Birnbacher, “Optical networks, last mile access and applications,” in Free-Space Laser Communications (Springer, 2008), Vol. 2, pp. 273–302.

Roggemann, M. C.

M. C. Roggemann and B. M. Welsh, Imaging through Turbulence, 1st ed. (CRC Press, 1996).

Schmidt, J. D.

J. D. Schmidt, Numerical Simulation of Optical Wave Propagation with Examples in Matlab (SPIE, 2010).

Sitter, D. N.

M. R. Chatterjee, T.-C. Poon, and D. N. Sitter, “Transfer function formalism for strong acousto-optic Bragg diffraction of light beams with arbitrary profiles,” Acustica 71, 81–91 (1991).

Verma, P.

A. K. Ghosh and P. Verma, “Lyapunov exponent of chaos generated by acousto-optic modulators with feedback,” Opt. Eng. 50, 017005 (2011).
[Crossref]

Webb, C.

C. Webb and J. Jones, Handbook of Laser Technology and Applications—Vol. II, 1st ed. (Taylor & Francis, 2004).

Welsh, B. M.

M. C. Roggemann and B. M. Welsh, Imaging through Turbulence, 1st ed. (CRC Press, 1996).

Acustica (1)

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F. S. Almehmadi and M. R. Chatterjee, “Improved performance of analog and digital acousto-optic modulation with feedback under profiled beam propagation for secure communication using chaos,” Opt. Eng. 53, 126102 (2014).
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M. R. Chatterjee and M. Alsaedi, “Examination of chaotic signal encryption and recovery for secure communication using hybrid acousto-optic feedback,” Opt. Eng. 50, 055002 (2011).
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M. R. Chatterjee and F. Almehmadi, “Numerical analysis of first-order acousto-optic Bragg diffraction of profiled optical beams using open-loop transfer functions,” Opt. Eng. 53, 036108 (2014).
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Figures (21)

Fig. 1.
Fig. 1. Bragg diffraction with an arbitrary incident beam profile.
Fig. 2.
Fig. 2. A-O closed-loop hybrid system with an arbitrary incident beam profile.
Fig. 3.
Fig. 3. Chaotic oscillations for uniform-profiled plane wave input when β ˜ increased to 3.
Fig. 4.
Fig. 4. First-order intensity Bragg diffraction versus the optical phase shift for Q = 20 , 17, 177, and 533.
Fig. 5.
Fig. 5. Hysteresis loop with an arbitrary Gaussian incident beam profile for Q = 20 .
Fig. 6.
Fig. 6. Nonlinear dynamics versus optical phase shift with a profiled Gaussian incident beam when β ˜ increased to 1.6 for Q = 20 .
Fig. 7.
Fig. 7. Nonlinear dynamics versus optical phase shift with a profiled Gaussian incident beam when β ˜ increased to 2.2 for Q = 20 .
Fig. 8.
Fig. 8. Lyapunov exponent and bifurcation maps versus the optical phase shift when β ˜ = 2 .
Fig. 9.
Fig. 9. Lyapunov exponent and bifurcation maps versus the effective feedback gain when α ^ = 3 and I inc = 2 .
Fig. 10.
Fig. 10. Heterodyne scheme for encrypting and decrypting using A-O chaos.
Fig. 11.
Fig. 11. Encryption and recovery with matched keys, β ˜ = 3 , TD = 0.05    μs , α ^ 0 = 2 .
Fig. 12.
Fig. 12. Recovered Peppers images with three levels of mismatch in the β ˜ parameter: (a) 0.1% mismatch, (b) 0.2% mismatch, and (c) 0.4% mismatch.
Fig. 13.
Fig. 13. Bit error rate curves for percent mismatch in β ˜ : (a) Gaussian-profiled beam simulation, (b) uniform-profiled beam simulation.
Fig. 14.
Fig. 14. Bit error rate curves for two digital communication systems: binary phase shift keying and A-O chaotic encryption system.
Fig. 15.
Fig. 15. Block diagram of multilayer security technique combining steganography with chaotic image encryption to transmit ECG combined with patient identification.
Fig. 16.
Fig. 16. (a) Recovered ECG image with slight mismatch. (b) Recovered text message with slight mismatch.
Fig. 17.
Fig. 17. Numerical model for slant path propagation.
Fig. 18.
Fig. 18. (a) Digitized image; (b) encrypted chaotic image signal; (c) cross-correlation for nonchaotic versus chaotic under weak, moderate, and strong turbulence and L T = L D at 3.5 km.
Fig. 19.
Fig. 19. Received image signal. (a) With chaotic transmission; (b) thresholding the recovered signal in (a). (c) With nonchaotic transmission; (d) thresholding the recovered signal in (c). L T = 14    km and strong turbulence.
Fig. 20.
Fig. 20. Received image. (a) With nonchaotic transmission; (b) with chaotic transmission C n 2 = 3.5 × 10 15    m 2 / 3 .
Fig. 21.
Fig. 21. (a) Cross-correlation and (b) mean square error for nonchaotic versus chaotic with ( L T = 3.5 , 7, and 10.5 km) strong turbulence.

Equations (15)

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d E ˜ n d ξ = j ( α ^ 2 ) [ e { j ( 1 2 ) [ ϕ inc ϕ B + ( 2 n 1 ) ] Q ξ } E ˜ n 1 + e { j ( 1 2 ) [ ϕ inc ϕ B + ( 2 n + 1 ) ] Q ξ } E ˜ n + 1 ] .
H ˜ 0 ( δ ) = E ˜ 0 ( ξ ) ξ = 1 E ˜ inc = e j δ Q 4 ( δ Q 4 ) 2 + ( α ^ 2 ) 2 ( ( δ Q 4 ) 2 + ( α ^ 2 ) 2 × cos ( ( δ Q 4 ) 2 + ( α ^ 2 ) 2 ) + j δ Q 4 sin ( ( δ Q 4 ) 2 + ( α ^ 2 ) 2 ) ) ,
H ˜ 1 ( δ ) = E ˜ 1 ( ξ ) ξ = 1 E ˜ inc = j ( α ^ 2 ) e j δ Q 4 ( δ Q 4 ) 2 + ( α ^ 2 ) 2 × ( sin ( ( δ Q 4 ) 2 + ( α ^ 2 ) 2 ) ) ,
E out ( r ) = E ˜ inc ( δ ) H ( δ ) e j 2 π λ δ ϕ B r ( ϕ B λ ) d δ .
I 1 ( t ) = I inc sin 2 { 1 2 [ α ^ 0 ( t ) + β ˜ I 1 ( t TD ) ] } .
I ph ( t ) = | f ( 1 2 [ α ^ 0 ( t ) + β ˜ ( I ph ( t TD ) ) ] ) | 2 .
Δ I 1 ϵ e n λ ,
ϕ n ( k ) = 0.033 C n 2 exp ( k 2 k m 2 ) ( k 2 + k o 2 ) 11 6 , 0 k ,
ϕ p ( k ) = 0.23    r 0 5 3    exp ( k 2 k m 2 ) ( k 2 + k o 2 ) 11 6 .
C n 2 ( h ) = A e ( h 100 ) + 5.94 × 10 53 × ( v 27 ) 2 h 10 e ( h 1000 ) + 2.7 × 10 16 e ( h 1500 ) .
E AM ( x , y , z , t ) = E o ( x , y , z ) [ 1 + m s ( t ) ] cos ( ω o t k z ) ,
E o ( x , y , z ) = A ˜ w o w ( z ) e r 2 / w 2 ( z ) ,
S ch ( t ) = A c [ 1 + m s ( t ) ] cos ω ch t ,
E AM ( x , y , z , t ) = E o ( x , y , z ) [ 1 + m ˜    S ch ( t ) ] cos ( ω o t k z ) ,
E AM ( x , y , z , t ) = A w o w ( z ) e ( x 2 + y 2 ) w 2 ( z ) { 1 + A c m ˜ [ 1 + m s ( t ) ] cos ω ch t } cos ( ω o t k z ) .

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