Abstract

We demonstrate a phase-conjugating mirror that has a continuous-wave power reflectivity much greater than unity (gain ~100). This mirror uses nonresonant degenerate four-wave mixing in a single crystal of barium titanate (BaTiO3). With our mirror we have (1) observed cw self-oscillation in an optical resonator formed by this mirror and a normal mirror, (2) demonstrated a cw oscillator that, in spite of phase-distorting material placed inside the resonator, will always emit a TEM00 mode, and (3) demonstrated an optical image amplifier. This mirror will work at any visible wavelength and with weak (milliwatt or weaker) pump beams.

© 1980 Optical Society of America

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References

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  1. D. M. Bloom, P. F. Liao, N. P. Economou, Opt. Lett. 2, 58 (1978); D. M. Pepper, D. Fekete, A. Yariv, Appl. Phys. Lett. 33, 41 (1978).
    [CrossRef] [PubMed]
  2. R. C. Lind, D. C. Steel, J. F. Lam, R. K. Jain, R. A. McFarlane, J. Opt. Soc. Am. 70, 599 (1980).
  3. F. S. Chen, J. Appl. Phys. 40, 3389 (1969).
    [CrossRef]
  4. J. P. Huignard, J. P. Herriau, P. Aubourg, E. Spitz, Opt. Lett. 4, 21 (1979).
    [CrossRef] [PubMed]
  5. R. W. Hellwarth, J. Opt. Soc. Am. 67, 1 (1977).
    [CrossRef]
  6. J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
    [CrossRef]
  7. H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
  8. D. L. Staebler, J. J. Amodei, J. Appl. Phys. 43, 1042 (1972).
    [CrossRef]
  9. J. Feinberg, in preparation.
  10. A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975).
  11. The light-induced electrostatic field amplitude E is calculated from Ref. 6 by assuming that the charges in BaTiO3 can hop in the x, y, and z directions with equal facility. The present experiment, however, is not sensitive to this assumption. We are pursuing further experiments to search for any anisotropy in the charge-hopping rates.
  12. J. AuYeung, D. Fekete, D. M. Pepper, A. Yariv, IEEE J. Quantum Electron. QE-15, 1180 (1979).
    [CrossRef]

1980 (2)

R. C. Lind, D. C. Steel, J. F. Lam, R. K. Jain, R. A. McFarlane, J. Opt. Soc. Am. 70, 599 (1980).

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
[CrossRef]

1979 (2)

J. P. Huignard, J. P. Herriau, P. Aubourg, E. Spitz, Opt. Lett. 4, 21 (1979).
[CrossRef] [PubMed]

J. AuYeung, D. Fekete, D. M. Pepper, A. Yariv, IEEE J. Quantum Electron. QE-15, 1180 (1979).
[CrossRef]

1978 (1)

1977 (1)

1972 (1)

D. L. Staebler, J. J. Amodei, J. Appl. Phys. 43, 1042 (1972).
[CrossRef]

1969 (2)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

F. S. Chen, J. Appl. Phys. 40, 3389 (1969).
[CrossRef]

Amodei, J. J.

D. L. Staebler, J. J. Amodei, J. Appl. Phys. 43, 1042 (1972).
[CrossRef]

Aubourg, P.

AuYeung, J.

J. AuYeung, D. Fekete, D. M. Pepper, A. Yariv, IEEE J. Quantum Electron. QE-15, 1180 (1979).
[CrossRef]

Bloom, D. M.

Chen, F. S.

F. S. Chen, J. Appl. Phys. 40, 3389 (1969).
[CrossRef]

Economou, N. P.

Feinberg, J.

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
[CrossRef]

J. Feinberg, in preparation.

Fekete, D.

J. AuYeung, D. Fekete, D. M. Pepper, A. Yariv, IEEE J. Quantum Electron. QE-15, 1180 (1979).
[CrossRef]

Heiman, D.

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
[CrossRef]

Hellwarth, R. W.

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
[CrossRef]

R. W. Hellwarth, J. Opt. Soc. Am. 67, 1 (1977).
[CrossRef]

Herriau, J. P.

Huignard, J. P.

Jain, R. K.

R. C. Lind, D. C. Steel, J. F. Lam, R. K. Jain, R. A. McFarlane, J. Opt. Soc. Am. 70, 599 (1980).

Kogelnik, H.

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Lam, J. F.

R. C. Lind, D. C. Steel, J. F. Lam, R. K. Jain, R. A. McFarlane, J. Opt. Soc. Am. 70, 599 (1980).

Liao, P. F.

Lind, R. C.

R. C. Lind, D. C. Steel, J. F. Lam, R. K. Jain, R. A. McFarlane, J. Opt. Soc. Am. 70, 599 (1980).

McFarlane, R. A.

R. C. Lind, D. C. Steel, J. F. Lam, R. K. Jain, R. A. McFarlane, J. Opt. Soc. Am. 70, 599 (1980).

Pepper, D. M.

J. AuYeung, D. Fekete, D. M. Pepper, A. Yariv, IEEE J. Quantum Electron. QE-15, 1180 (1979).
[CrossRef]

Spitz, E.

Staebler, D. L.

D. L. Staebler, J. J. Amodei, J. Appl. Phys. 43, 1042 (1972).
[CrossRef]

Steel, D. C.

R. C. Lind, D. C. Steel, J. F. Lam, R. K. Jain, R. A. McFarlane, J. Opt. Soc. Am. 70, 599 (1980).

Tanguay, A. R.

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
[CrossRef]

Yariv, A.

J. AuYeung, D. Fekete, D. M. Pepper, A. Yariv, IEEE J. Quantum Electron. QE-15, 1180 (1979).
[CrossRef]

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975).

Bell Syst. Tech. J. (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

IEEE J. Quantum Electron. (1)

J. AuYeung, D. Fekete, D. M. Pepper, A. Yariv, IEEE J. Quantum Electron. QE-15, 1180 (1979).
[CrossRef]

J. Appl. Phys. (3)

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
[CrossRef]

D. L. Staebler, J. J. Amodei, J. Appl. Phys. 43, 1042 (1972).
[CrossRef]

F. S. Chen, J. Appl. Phys. 40, 3389 (1969).
[CrossRef]

J. Opt. Soc. Am. (2)

R. C. Lind, D. C. Steel, J. F. Lam, R. K. Jain, R. A. McFarlane, J. Opt. Soc. Am. 70, 599 (1980).

R. W. Hellwarth, J. Opt. Soc. Am. 67, 1 (1977).
[CrossRef]

Opt. Lett. (2)

Other (3)

J. Feinberg, in preparation.

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975).

The light-induced electrostatic field amplitude E is calculated from Ref. 6 by assuming that the charges in BaTiO3 can hop in the x, y, and z directions with equal facility. The present experiment, however, is not sensitive to this assumption. We are pursuing further experiments to search for any anisotropy in the charge-hopping rates.

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Figures (5)

Fig. 1
Fig. 1

The reference writing beam (1) and the image writing beam (2) interfere in a crystal of undoped BaTiO3 to make a refractive-index grating with wave vector k. The reading beam (3) Bragg scatters off this grating to produce the phase-conjugate signal beam (4). The crystal is immersed in index-matching oil.

Fig. 2
Fig. 2

A plot of the measured mirror reflectivity RextI4/I2 as a function of the reading-beam intensity I3. The object-beam intensity was fixed at I2 = I1/4, and the angles of the incident beams were α1 = 16°, α2 = 24°, and θ = 20° (see Fig. 1). In this plot, I3 has been normalized by the fixed intensityI2.

Fig. 3
Fig. 3

Optical setup for observing cw self-oscillation. The incident beams 1 and 3 are both linearly polarized in the plane of the figure and are extraordinary rays in the crystal. Self-oscillation is observed to grow between the crystal and a 94% reflectivity plane mirror M. Here L’s are lenses with a focal length F = 100 mm, and P is a variable pinhole used to control the transverse-mode structure of the oscillation. The phase aberrator A is formed by bubbles of transparent glue on a microscope slide. The angles of the beams are about the same as in Fig. 2.

Fig. 4
Fig. 4

Photographs of far-field mode patterns of self-oscillation with a severe phase aberrator in the resonator cavity. (See Fig. 3.) With no aperture in the resonator cavity: mode pattern transmitted (a) through the back of the crystal and (b)through the 94% mirror. With a 1-mm-diameter pinhole in the cavity: mode pattern (c) from the back side of the crystal and (d) transmitted through the 94% mirror. These mode patterns were displayed on a white card 2 m from the cavity, photographed with Kodak Plus-X (ASA 125) film, and printed on high-contrast paper.

Fig. 5
Fig. 5

Photograph of the real image of a resolution test chart (wheel diameter, 1 cm) formed in the object plane. The intensity of the image beam was measured to be ~10 times the intensity of the object beam, demonstrating optical image amplification. The bright spot seen on the left-hand side is from self-oscillation between the crystal and one of the faces of the glass cuvette that holds the crystal. This image was photographed with Kodak Plus-X (ASA 125) film and printed on high-contrast paper. The angles of the beams are about the same as in Figs. 2 and 3.

Equations (2)

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R ord = | ωLEη 4 c n o 3 r 13 cos θ | 2
R ext = | ωLEη 4 c n 3 cos θ ( n e r 33 sin α 1 sin α 2 + 2 n e 2 n o 2 r 42 sin 2 θ + n o 4 r 13 cos α 1 cos α 2 ) | 2

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