Abstract

If the time-reversal symmetry of a ring phase conjugator is broken, the output of the device is no longer the phase conjugate of the input. For a TEM00 input wave, the output wave can be a higher-order resonator mode, although there is no resonator. Additionally, there will be a frequency shift between the input and output waves that varies discontinuously as the asymmetry in the ring is increased. Experiments using photorefractive BaTiO3 are in good agreement with theory and demonstrate the ability of the system to choose the combination of output mode and frequency that maximizes the mode gain.

© 1987 Optical Society of America

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References

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  1. J. P. Jiang, J. Feinberg, J. Opt. Soc. Am. A 3(13), P34 (1986).
    [CrossRef]
  2. M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 42, 9 (1983).
    [CrossRef]
  3. B. Fischer, S. Sternklar, Appl. Phys. Lett. 47, 1 (1985).
    [CrossRef]
  4. H. Rajbenbach, J. P. Huignard, Opt. Lett. 10, 137 (1985).
    [CrossRef] [PubMed]
  5. P. Pellat-Finet, J. L. de Bougrenet de la Tocnaye, Opt. Commun. 55, 305 (1985).
    [CrossRef]
  6. D. J. Gauthier, P. Narum, R. W. Boyd, Opt. Lett. 11, 623 (1986).
    [CrossRef] [PubMed]
  7. “Dancing Modes,” 16-mm film or VHS video, copyright Jack Feinberg, 1986 (Marmot Productions, Los Angeles, Calif.).
  8. S. Sternklar, S. Weiss, B. Fischer, Opt. Lett. 11, 165 (1986).
    [CrossRef] [PubMed]
  9. K. R. MacDonald, Ph.D. dissertation (University of Southern California, Los Angeles, Calif., 1986) (unpublished).
  10. A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975).

1986 (3)

1985 (3)

B. Fischer, S. Sternklar, Appl. Phys. Lett. 47, 1 (1985).
[CrossRef]

H. Rajbenbach, J. P. Huignard, Opt. Lett. 10, 137 (1985).
[CrossRef] [PubMed]

P. Pellat-Finet, J. L. de Bougrenet de la Tocnaye, Opt. Commun. 55, 305 (1985).
[CrossRef]

1983 (1)

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 42, 9 (1983).
[CrossRef]

Boyd, R. W.

Cronin-Golomb, M.

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 42, 9 (1983).
[CrossRef]

de Bougrenet de la Tocnaye, J. L.

P. Pellat-Finet, J. L. de Bougrenet de la Tocnaye, Opt. Commun. 55, 305 (1985).
[CrossRef]

Feinberg, J.

Fischer, B.

S. Sternklar, S. Weiss, B. Fischer, Opt. Lett. 11, 165 (1986).
[CrossRef] [PubMed]

B. Fischer, S. Sternklar, Appl. Phys. Lett. 47, 1 (1985).
[CrossRef]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 42, 9 (1983).
[CrossRef]

Gauthier, D. J.

Huignard, J. P.

Jiang, J. P.

MacDonald, K. R.

K. R. MacDonald, Ph.D. dissertation (University of Southern California, Los Angeles, Calif., 1986) (unpublished).

Narum, P.

Pellat-Finet, P.

P. Pellat-Finet, J. L. de Bougrenet de la Tocnaye, Opt. Commun. 55, 305 (1985).
[CrossRef]

Rajbenbach, H.

Sternklar, S.

Weiss, S.

White, J. O.

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 42, 9 (1983).
[CrossRef]

Yariv, A.

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 42, 9 (1983).
[CrossRef]

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

Appl. Phys. Lett. (2)

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 42, 9 (1983).
[CrossRef]

B. Fischer, S. Sternklar, Appl. Phys. Lett. 47, 1 (1985).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

P. Pellat-Finet, J. L. de Bougrenet de la Tocnaye, Opt. Commun. 55, 305 (1985).
[CrossRef]

Opt. Lett. (3)

Other (3)

K. R. MacDonald, Ph.D. dissertation (University of Southern California, Los Angeles, Calif., 1986) (unpublished).

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

“Dancing Modes,” 16-mm film or VHS video, copyright Jack Feinberg, 1986 (Marmot Productions, Los Angeles, Calif.).

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Figures (4)

Fig. 1
Fig. 1

The ring phase conjugator. The Faraday rotator and the quarter-wave (λ/4) plates create an optical path difference for the two directions of propagation around the ring while preserving the linear polarization of the beams.

Fig. 2
Fig. 2

The output changes from the initial phase-conjugate TEM00 mode (left) to TEM01 (center) and then TEM02 (right) as the nonreciprocal phase difference Δϕ in the ring is increased. Increasing Δϕ to 360° returns the output to its initial TEM00 mode.

Fig. 3
Fig. 3

The output mode power (■) and the frequency shift (⊡) between the incident and output beams as a function of the nonreciprocal phase difference Δϕ in the ring. The beams were aligned to produce the clearest mode patterns, as shown in Fig. 2. Note the discontinuous jumps in the frequency when the output mode changed.

Fig. 4
Fig. 4

The output mode power (■) and the frequency shift (⊡) between the incident and output beams as a function of the nonreciprocal phase difference Δϕ in the ring. The beams were aligned to give the maximum signal at Δϕ = 0. For Δϕ > 90°, the output beam patterns appeared to be mixtures of higher-order modes.

Equations (6)

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A 4 = exp ( + i ϕ total / 2 ) M + 1 / 2 K ( A 2 ) ,
A 3 * = exp ( - i ϕ total / 2 ) M - 1 / 2 K ( A 1 * ) ,
ϕ total = Δ ϕ - ϑ ,
I ( x ) A 2 A 3 * + A 1 * A 4 + c . c . = exp ( - i ϕ total / 2 ) A 2 M - 1 / 2 K ( A 1 * ) + exp ( + i ϕ total / 2 ) A 1 * M + 1 / 2 K ( A 2 ) + c . c .
exp [ i 2 π L / λ - i ( n + m + 1 ) η ] ,
ϕ total = Δ ϕ - ϑ - ( n + m ) η .

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