Abstract

Interferometers based on conjugate-wave generation using three- and four-wave mixing are described theoretically. They are shown to be self-referencing and sensitive to small changes in the phase front.

© 1980 Optical Society of America

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References

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  1. B. Zel’dovich, V. Popvichev, V. Ragul’skii, and F. Faisullov, “Connection between the wave fronts of the reflected and exciting light is stimulated Mandel’shtam Brillouin scattering,” JETP Lett. 15, 109–113 (1972);V. Wang and C. R. Giulliano, “Correction of phase abberations via stimulated Brilloin scattering,” Opt. Lett. 2, 4–6 (1978).
    [Crossref] [PubMed]
  2. A. Yariv, “On transmission and recovery of three-dimensional image information in optical waveguides,” J. Opt. Soc. Am. 66, 301–306 (1976);P. V. Avizonis, F. A. Hopf, W. D. Bomberger, S. F. Jacobs, A. Tomita, and K. H. Womack, “Optical phase conjugation in a LiNb03 crystal,” Appl. Phys. Lett. 31, 435–437 (1977).
    [Crossref]
  3. F. A. Hopf, A. Tomita, K. H. Womack, and J. Jewell, “Optical distortion in nonlinear phase conjugation by three-wave mixing,” J. Opt. Soc. Am. 69, 968–972 (1979).
    [Crossref]
  4. F. A. Hopf, “Distortion in phase conjugation in high-gain three-wave mixing” J. Opt. Soc. Am. 70, 1379–1381 (1980).
    [Crossref]
  5. R. W. Hellwarth, “Generation of time reversal wave fronts by nonlinear refraction,” J. Opt. Soc. Am. 67, 1–3 (1977).
    [Crossref]
  6. D. M. Bloom and G. C. Bjorklund, “Conjugate wave-front generation and image reconstruction by four-wave mixing,” Appl. Phys. Lett. 31, 592–594 (1977);S. M. Jensen and R. W. Hellwarth, “Observation of the time-reversed replica of a monochromatic optical wave,” ibid. 32, 166–168 (1978);D. M. Bloom, P. F. Liao, and N. P. Economou, “Observation of amplified reflection by degenerate four-wave mixing in atomic sodium vapor,” ibid. 32, 58–60 (1978);D. Grischkowsky, N. S. Shiren, and R. J. Bennett, “Generation of time-reversed wavefronts using a resonantly enhanced electronic nonlinearity,” ibid. 33, 805–807 (1978).
    [Crossref]
  7. E. E. Bergmann, K. J. Bigio, B. J. Feldman, and R. A. Fisher, “High efficiency pulsed 10.6 μm phase-conjugate reflection via degenerate four-wave mixing,” Opt. Lett. 3, 82–84 (1978);A. Tomita, “Phase conjugation using gain saturation of a Nd:YAG laser,” Appl. Phys. Lett. 34, 463–464 (1979);R. K. Jain, M. B. Klein, and R. C. Lind, “High-efficiency degenerate four-wave mixing of 1.06 μm radiation in silicon,” Opt. Lett. 4, 328–330 (1979).
    [Crossref] [PubMed]
  8. C. V. Heer and P. F. McManamon, “Wavefront correction with photon echoes,” Opt. Commun. 23, 49–50 (1977);N. C. Griffen and C. V. Heer, “Focusing and phase conjugation of photon echoes in Na vapor,” Appl. Phys. Lett. 33, 865–866 (1978);A. L. Smirl, T. F. Goggess, S. C. Moss, J. R. Lindle, and F. A. Hopf, “Generation of a forward-traveling phase-conjugate wave in germanium,” Opt. Commun. (to be published).
    [Crossref]
  9. Because conjugating interferometers are sensitive to the spatial phase of the pump and to the relative temporal phases of pump and signal they are not self-referencing in quite the same fashion as, for example, a shearing interferometer. The term is used here to convey the insensitivity of the fringe contrast with intensity variation.
  10. W. Koechner, Solid State Laser Engineering (Springer-Verlag, New York, 1976).
    [Crossref]
  11. A. Yariv and D. M. Pepper, “Amplified reflection, phase-conjugation and image reconstruction by four-wave mixing,” Opt. Lett. 116–18 (1977).
    [Crossref]
  12. T. Fu and M. Sargent, “Effects of signal detuning on phase conjugation,” Opt. Lett. 4, 366–368 (1979).
    [Crossref] [PubMed]
  13. F. Zernike and J. E. Midwinter, Applied Nonlinear Optics (Wiley, New York, 1973), p. 42.

1980 (1)

1979 (2)

1978 (1)

1977 (4)

C. V. Heer and P. F. McManamon, “Wavefront correction with photon echoes,” Opt. Commun. 23, 49–50 (1977);N. C. Griffen and C. V. Heer, “Focusing and phase conjugation of photon echoes in Na vapor,” Appl. Phys. Lett. 33, 865–866 (1978);A. L. Smirl, T. F. Goggess, S. C. Moss, J. R. Lindle, and F. A. Hopf, “Generation of a forward-traveling phase-conjugate wave in germanium,” Opt. Commun. (to be published).
[Crossref]

A. Yariv and D. M. Pepper, “Amplified reflection, phase-conjugation and image reconstruction by four-wave mixing,” Opt. Lett. 116–18 (1977).
[Crossref]

R. W. Hellwarth, “Generation of time reversal wave fronts by nonlinear refraction,” J. Opt. Soc. Am. 67, 1–3 (1977).
[Crossref]

D. M. Bloom and G. C. Bjorklund, “Conjugate wave-front generation and image reconstruction by four-wave mixing,” Appl. Phys. Lett. 31, 592–594 (1977);S. M. Jensen and R. W. Hellwarth, “Observation of the time-reversed replica of a monochromatic optical wave,” ibid. 32, 166–168 (1978);D. M. Bloom, P. F. Liao, and N. P. Economou, “Observation of amplified reflection by degenerate four-wave mixing in atomic sodium vapor,” ibid. 32, 58–60 (1978);D. Grischkowsky, N. S. Shiren, and R. J. Bennett, “Generation of time-reversed wavefronts using a resonantly enhanced electronic nonlinearity,” ibid. 33, 805–807 (1978).
[Crossref]

1976 (1)

1972 (1)

B. Zel’dovich, V. Popvichev, V. Ragul’skii, and F. Faisullov, “Connection between the wave fronts of the reflected and exciting light is stimulated Mandel’shtam Brillouin scattering,” JETP Lett. 15, 109–113 (1972);V. Wang and C. R. Giulliano, “Correction of phase abberations via stimulated Brilloin scattering,” Opt. Lett. 2, 4–6 (1978).
[Crossref] [PubMed]

Bergmann, E. E.

Bigio, K. J.

Bjorklund, G. C.

D. M. Bloom and G. C. Bjorklund, “Conjugate wave-front generation and image reconstruction by four-wave mixing,” Appl. Phys. Lett. 31, 592–594 (1977);S. M. Jensen and R. W. Hellwarth, “Observation of the time-reversed replica of a monochromatic optical wave,” ibid. 32, 166–168 (1978);D. M. Bloom, P. F. Liao, and N. P. Economou, “Observation of amplified reflection by degenerate four-wave mixing in atomic sodium vapor,” ibid. 32, 58–60 (1978);D. Grischkowsky, N. S. Shiren, and R. J. Bennett, “Generation of time-reversed wavefronts using a resonantly enhanced electronic nonlinearity,” ibid. 33, 805–807 (1978).
[Crossref]

Bloom, D. M.

D. M. Bloom and G. C. Bjorklund, “Conjugate wave-front generation and image reconstruction by four-wave mixing,” Appl. Phys. Lett. 31, 592–594 (1977);S. M. Jensen and R. W. Hellwarth, “Observation of the time-reversed replica of a monochromatic optical wave,” ibid. 32, 166–168 (1978);D. M. Bloom, P. F. Liao, and N. P. Economou, “Observation of amplified reflection by degenerate four-wave mixing in atomic sodium vapor,” ibid. 32, 58–60 (1978);D. Grischkowsky, N. S. Shiren, and R. J. Bennett, “Generation of time-reversed wavefronts using a resonantly enhanced electronic nonlinearity,” ibid. 33, 805–807 (1978).
[Crossref]

Faisullov, F.

B. Zel’dovich, V. Popvichev, V. Ragul’skii, and F. Faisullov, “Connection between the wave fronts of the reflected and exciting light is stimulated Mandel’shtam Brillouin scattering,” JETP Lett. 15, 109–113 (1972);V. Wang and C. R. Giulliano, “Correction of phase abberations via stimulated Brilloin scattering,” Opt. Lett. 2, 4–6 (1978).
[Crossref] [PubMed]

Feldman, B. J.

Fisher, R. A.

Fu, T.

Heer, C. V.

C. V. Heer and P. F. McManamon, “Wavefront correction with photon echoes,” Opt. Commun. 23, 49–50 (1977);N. C. Griffen and C. V. Heer, “Focusing and phase conjugation of photon echoes in Na vapor,” Appl. Phys. Lett. 33, 865–866 (1978);A. L. Smirl, T. F. Goggess, S. C. Moss, J. R. Lindle, and F. A. Hopf, “Generation of a forward-traveling phase-conjugate wave in germanium,” Opt. Commun. (to be published).
[Crossref]

Hellwarth, R. W.

Hopf, F. A.

Jewell, J.

Koechner, W.

W. Koechner, Solid State Laser Engineering (Springer-Verlag, New York, 1976).
[Crossref]

McManamon, P. F.

C. V. Heer and P. F. McManamon, “Wavefront correction with photon echoes,” Opt. Commun. 23, 49–50 (1977);N. C. Griffen and C. V. Heer, “Focusing and phase conjugation of photon echoes in Na vapor,” Appl. Phys. Lett. 33, 865–866 (1978);A. L. Smirl, T. F. Goggess, S. C. Moss, J. R. Lindle, and F. A. Hopf, “Generation of a forward-traveling phase-conjugate wave in germanium,” Opt. Commun. (to be published).
[Crossref]

Midwinter, J. E.

F. Zernike and J. E. Midwinter, Applied Nonlinear Optics (Wiley, New York, 1973), p. 42.

Pepper, D. M.

Popvichev, V.

B. Zel’dovich, V. Popvichev, V. Ragul’skii, and F. Faisullov, “Connection between the wave fronts of the reflected and exciting light is stimulated Mandel’shtam Brillouin scattering,” JETP Lett. 15, 109–113 (1972);V. Wang and C. R. Giulliano, “Correction of phase abberations via stimulated Brilloin scattering,” Opt. Lett. 2, 4–6 (1978).
[Crossref] [PubMed]

Ragul’skii, V.

B. Zel’dovich, V. Popvichev, V. Ragul’skii, and F. Faisullov, “Connection between the wave fronts of the reflected and exciting light is stimulated Mandel’shtam Brillouin scattering,” JETP Lett. 15, 109–113 (1972);V. Wang and C. R. Giulliano, “Correction of phase abberations via stimulated Brilloin scattering,” Opt. Lett. 2, 4–6 (1978).
[Crossref] [PubMed]

Sargent, M.

Tomita, A.

Womack, K. H.

Yariv, A.

Zel’dovich, B.

B. Zel’dovich, V. Popvichev, V. Ragul’skii, and F. Faisullov, “Connection between the wave fronts of the reflected and exciting light is stimulated Mandel’shtam Brillouin scattering,” JETP Lett. 15, 109–113 (1972);V. Wang and C. R. Giulliano, “Correction of phase abberations via stimulated Brilloin scattering,” Opt. Lett. 2, 4–6 (1978).
[Crossref] [PubMed]

Zernike, F.

F. Zernike and J. E. Midwinter, Applied Nonlinear Optics (Wiley, New York, 1973), p. 42.

Appl. Phys. Lett. (1)

D. M. Bloom and G. C. Bjorklund, “Conjugate wave-front generation and image reconstruction by four-wave mixing,” Appl. Phys. Lett. 31, 592–594 (1977);S. M. Jensen and R. W. Hellwarth, “Observation of the time-reversed replica of a monochromatic optical wave,” ibid. 32, 166–168 (1978);D. M. Bloom, P. F. Liao, and N. P. Economou, “Observation of amplified reflection by degenerate four-wave mixing in atomic sodium vapor,” ibid. 32, 58–60 (1978);D. Grischkowsky, N. S. Shiren, and R. J. Bennett, “Generation of time-reversed wavefronts using a resonantly enhanced electronic nonlinearity,” ibid. 33, 805–807 (1978).
[Crossref]

J. Opt. Soc. Am. (4)

JETP Lett. (1)

B. Zel’dovich, V. Popvichev, V. Ragul’skii, and F. Faisullov, “Connection between the wave fronts of the reflected and exciting light is stimulated Mandel’shtam Brillouin scattering,” JETP Lett. 15, 109–113 (1972);V. Wang and C. R. Giulliano, “Correction of phase abberations via stimulated Brilloin scattering,” Opt. Lett. 2, 4–6 (1978).
[Crossref] [PubMed]

Opt. Commun. (1)

C. V. Heer and P. F. McManamon, “Wavefront correction with photon echoes,” Opt. Commun. 23, 49–50 (1977);N. C. Griffen and C. V. Heer, “Focusing and phase conjugation of photon echoes in Na vapor,” Appl. Phys. Lett. 33, 865–866 (1978);A. L. Smirl, T. F. Goggess, S. C. Moss, J. R. Lindle, and F. A. Hopf, “Generation of a forward-traveling phase-conjugate wave in germanium,” Opt. Commun. (to be published).
[Crossref]

Opt. Lett. (3)

Other (3)

F. Zernike and J. E. Midwinter, Applied Nonlinear Optics (Wiley, New York, 1973), p. 42.

Because conjugating interferometers are sensitive to the spatial phase of the pump and to the relative temporal phases of pump and signal they are not self-referencing in quite the same fashion as, for example, a shearing interferometer. The term is used here to convey the insensitivity of the fringe contrast with intensity variation.

W. Koechner, Solid State Laser Engineering (Springer-Verlag, New York, 1976).
[Crossref]

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Figures (3)

FIG. 1
FIG. 1

Schematic of a conjugating interferometer based on four-wave mixing: L—lenses; BS1—50% beamsplitter; BS2—33% beamsplitter oriented to reflect 33% of the signal; M—100% reflecting mirrors. L1 images the object onto BS1. L2 images BS1 onto the observation plane.

FIG. 2
FIG. 2

L are the lenses; BS1 is the dichroic beamsplitter. The signal and pump are orthogonally polarized, so the pump can be rejected with a polarizer or a dichroic beamsplitter placed between the crystal and L2.

FIG. 3
FIG. 3

Intensity I and phase ϕ of (a) the best image of the conjugate (note the phase is plotted in a negative sense), (b) the signal when all image planes are at the center of the crystal, and (c) the best image of the signal. In each case the dotted curves represent the values of I and ϕ for the undistorted image.

Equations (9)

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I = c 48 π | Ɛ in ( x , y ) | 2 sec 2 ( L l OPA ) × { [ 2 cos 2 ( L l OPA ) ] [ 2 sin ( L l OPA ) ] cos ( 2 ϕ in ) } .
I ( x , y ) = c 8 π | Ɛ in ( x , y ) | 2 cosh ( 2 L / l OPA ) × [ 1 + tanh ( 2 L / l OPA ) cos ( 2 ϕ in ) ] .
S f z + i π f 2 λ S f n = 8 π 2 λ n d eff Ɛ p S f * .
1 l OPA = 8 π 2 λ n d eff Ɛ p .
S f ( z ) = S f 0 ( z ) K s e i ( π f 2 λ Δ / n ) + S f 0 * ( z ) K c e i ( π f 2 λ Δ / n ) ,
K c = sinh ( d L ) / d ,
K s = cosh ( d L ) + i ( π f 2 λ / n ) sinh ( d L ) / d ,
d = [ 1 l OPA 2 ( π f 2 λ n ) 2 ] 1 / 2 ,
Δ = tanh ( d L ) / d ( π f 0 2 λ / n ) 2 [ tanh ( d L ) / d 2 L sech 2 ( d L ) / d ] 1 + ( π f 0 2 λ / n ) 2 tanh 2 ( d L ) / d 2 ,