Abstract

We describe a nonlinear method for generating, nearly instantaneously, a time-reversed replica of any monochromatic-beam wave pattern. The method employs the interaction of the incident beam, of arbitrary wave front, with counter-propagating plane “pump” waves in a homogeneous, transparent, nonlinear medium. Media are shown to exist in which time-reversed waves can be generated with high efficiency using available laser pump sources.

© 1977 Optical Society of America

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References

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  1. B. Y. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faisullov, “Connection between the wavefronts of the reflected and exciting light in stimulated Mandel’stam-Brillouin scattering,” Sov. Phys. JETP Lett. 15, 109–113 (1972).
  2. O. Y. Nosach, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faisullov, “Cancellation of phase distortions in an amplifying medium with a ‘Brillouin mirror,’” Sov. Phys. JETP Lett. 16, 435–438 (1972).
  3. A. Yariv, “On transmission and recovery of 3-dimensional image information in optical waveguides,” J. Opt. Soc. Am. 66, 301–306 (1976).
    [Crossref]
  4. P. W. Maker and R. W. Terhune, “Study of optical effects due to an induced polarization third-order in the electric field strength,” Phys. Rev. 137, A801–A818 (1965).
    [Crossref]
  5. R. W. Hellwarth, Third-Order Optical Susceptibilities of Liquids and Solids (Pergamon, New York, 1976).
  6. D. Grischkowsky and J. A. Armstrong, “Self-defocusing of light by adiabatic following in rubidium vapor,” Phys. Rev. Lett. 6, 1566–1570 (1972).

1976 (1)

1972 (3)

B. Y. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faisullov, “Connection between the wavefronts of the reflected and exciting light in stimulated Mandel’stam-Brillouin scattering,” Sov. Phys. JETP Lett. 15, 109–113 (1972).

O. Y. Nosach, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faisullov, “Cancellation of phase distortions in an amplifying medium with a ‘Brillouin mirror,’” Sov. Phys. JETP Lett. 16, 435–438 (1972).

D. Grischkowsky and J. A. Armstrong, “Self-defocusing of light by adiabatic following in rubidium vapor,” Phys. Rev. Lett. 6, 1566–1570 (1972).

1965 (1)

P. W. Maker and R. W. Terhune, “Study of optical effects due to an induced polarization third-order in the electric field strength,” Phys. Rev. 137, A801–A818 (1965).
[Crossref]

Armstrong, J. A.

D. Grischkowsky and J. A. Armstrong, “Self-defocusing of light by adiabatic following in rubidium vapor,” Phys. Rev. Lett. 6, 1566–1570 (1972).

Faisullov, F. S.

B. Y. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faisullov, “Connection between the wavefronts of the reflected and exciting light in stimulated Mandel’stam-Brillouin scattering,” Sov. Phys. JETP Lett. 15, 109–113 (1972).

O. Y. Nosach, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faisullov, “Cancellation of phase distortions in an amplifying medium with a ‘Brillouin mirror,’” Sov. Phys. JETP Lett. 16, 435–438 (1972).

Grischkowsky, D.

D. Grischkowsky and J. A. Armstrong, “Self-defocusing of light by adiabatic following in rubidium vapor,” Phys. Rev. Lett. 6, 1566–1570 (1972).

Hellwarth, R. W.

R. W. Hellwarth, Third-Order Optical Susceptibilities of Liquids and Solids (Pergamon, New York, 1976).

Maker, P. W.

P. W. Maker and R. W. Terhune, “Study of optical effects due to an induced polarization third-order in the electric field strength,” Phys. Rev. 137, A801–A818 (1965).
[Crossref]

Nosach, O. Y.

O. Y. Nosach, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faisullov, “Cancellation of phase distortions in an amplifying medium with a ‘Brillouin mirror,’” Sov. Phys. JETP Lett. 16, 435–438 (1972).

Popovichev, V. I.

O. Y. Nosach, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faisullov, “Cancellation of phase distortions in an amplifying medium with a ‘Brillouin mirror,’” Sov. Phys. JETP Lett. 16, 435–438 (1972).

B. Y. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faisullov, “Connection between the wavefronts of the reflected and exciting light in stimulated Mandel’stam-Brillouin scattering,” Sov. Phys. JETP Lett. 15, 109–113 (1972).

Ragul’skii, V. V.

B. Y. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faisullov, “Connection between the wavefronts of the reflected and exciting light in stimulated Mandel’stam-Brillouin scattering,” Sov. Phys. JETP Lett. 15, 109–113 (1972).

O. Y. Nosach, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faisullov, “Cancellation of phase distortions in an amplifying medium with a ‘Brillouin mirror,’” Sov. Phys. JETP Lett. 16, 435–438 (1972).

Terhune, R. W.

P. W. Maker and R. W. Terhune, “Study of optical effects due to an induced polarization third-order in the electric field strength,” Phys. Rev. 137, A801–A818 (1965).
[Crossref]

Yariv, A.

Zel’dovich, B. Y.

B. Y. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faisullov, “Connection between the wavefronts of the reflected and exciting light in stimulated Mandel’stam-Brillouin scattering,” Sov. Phys. JETP Lett. 15, 109–113 (1972).

J. Opt. Soc. Am. (1)

Phys. Rev. (1)

P. W. Maker and R. W. Terhune, “Study of optical effects due to an induced polarization third-order in the electric field strength,” Phys. Rev. 137, A801–A818 (1965).
[Crossref]

Phys. Rev. Lett. (1)

D. Grischkowsky and J. A. Armstrong, “Self-defocusing of light by adiabatic following in rubidium vapor,” Phys. Rev. Lett. 6, 1566–1570 (1972).

Sov. Phys. JETP Lett. (2)

B. Y. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faisullov, “Connection between the wavefronts of the reflected and exciting light in stimulated Mandel’stam-Brillouin scattering,” Sov. Phys. JETP Lett. 15, 109–113 (1972).

O. Y. Nosach, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faisullov, “Cancellation of phase distortions in an amplifying medium with a ‘Brillouin mirror,’” Sov. Phys. JETP Lett. 16, 435–438 (1972).

Other (1)

R. W. Hellwarth, Third-Order Optical Susceptibilities of Liquids and Solids (Pergamon, New York, 1976).

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Figures (2)

FIG. 1
FIG. 1

Schematic and nomenclature for calculation of time-reversed wave fields.

FIG. 2
FIG. 2

Schematic diagram of apparatus described in text for observing generation of a time-reversed wave by nonlinear refraction in medium A.

Equations (12)

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Re [ E i ( r ) e - i ω t + G i e i k 0 z - i ω 0 t + H i e - i k 0 z - i ω 0 t ] .
P i N L = X i j E j * .
X i j = 6 c i j k l ( - ν , - ω , ω 0 , ω 0 ) G k H l ,
E i ( ξ , η , z ) = - i k d x d y E i ( x , y , 0 ) K e i k r / ( 2 π r ) ,
F i ( x , y , 0 ) = q 2 z 1 z 2 d z d ξ d η T i j X j k E k * ( ξ , η , z ) e i q s / s .
q s - k r = Δ k z + 1 2 ( q ρ 2 - k ρ 2 ) / z + ( k x - q x ) · ξ / z + 1 2 Δ k σ 2 / z + O [ k σ 4 / z 3 ] .
z d 2 Δ k
z k d 4 / z 2 .
F i ( x , y , 0 ) = 2 π i q 2 k - 1 z 1 z 2 d z e i Δ k z ξ ( z ) T i j X j k E k * ( q k x , q k y , 0 ) ,
F i ( r ) = 2 π i k L X i j E j * ( r ) .
R = I G I H β 2 L 2 ,
β = 96 π 2 c - 2 ω c i j k l f i * e j * g k h l .