Abstract

In this paper we report a new method for double phase conjugation particularly suited to the tungsten bronze crystal strontium barium niobate. It has also been observed to produce conjugate waves in BaTiO3 and BSKNN. This new arrangement is called the bridge conjugator because the two beams enter opposing [100] crystal faces and fan together to form a bridge without reflection off a crystal face. Our measurements indicate that the bridge conjugator is competitive with previously reported double phase conjugate mirrors in reflectivity, response time, ease of alignment, and fidelity.

© 1990 Optical Society of America

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  1. J. Feinberg, R. W. Hellwarth, “Phase-Conjugating Mirror with Continuous-Wave Gain,” Opt. Lett. 5, 519–521 (1980); Erratum, Opt. Lett. 6, 257 (1981).
    [CrossRef] [PubMed]
  2. J. White, M. Cronin-Golomb, B. Fischer, A. Yariv, “Coherent Oscillation by Self-Induced Gratings in the Photorefractive Crystal BaTiO3,” Appl. Phys. Lett. 40, 450–452 (1982); M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Passive (Self-Pumped) Phase Conjugate Mirror: Theoretical and Experimental Investigation,” Appl. Phys. Lett. 41, 689–691 (1982).
    [CrossRef]
  3. J. Feinberg, “Self-Pumped, Continuous-Wave Phase Conjugator Using Internal Reflection,” Opt. Lett. 7, 486–488 (1982).
    [CrossRef] [PubMed]
  4. P. Yeh, T. Y. Chang, M. D. Ewbank, “Model for Mutually Pumped Phase Conjugation,” J. Opt. Soc. Am. B 5, 1743–1749 (1988); S. Weiss, O. Werner, B. Fischer, “Analysis of Coupled Photorefractive Wave Mixing Junctions,” Opt. Lett. 14, 186–188 (1989) and references therein.
    [CrossRef] [PubMed]
  5. J. Feinberg, “Asymmetric Self-Defocusing of an Optical Beam from the Photorefractive Effect,” J. Opt. Soc. Am. 72, 46–51 (1982); V. V. Obukhovskii, A. V. Stoyanov, “Photoinduced Light Scattering in Crystals with a Nonlocal Response,” Sov. J. Quantum Electron. 15, 367–371 (1986); G. C. Valley, “Competition between Forward- and Backward-Stimulated Photorefractive Scattering in BaTiO3,” J. Opt. Soc. Am. B 4, 14–19 (1987); Erratum, J. Opt. Soc. Am B 4, 934 (1987).
    [CrossRef]
  6. J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, “Photorefractive Effects and Light-Induced Charge Migration in Barium Titanate,” J. Appl. Phys. 51, 1297–1305 (1980); Erratum, J. Appl. Phys. 52, 537 (1981).
    [CrossRef]
  7. See for example, R. Fisher, Ed., Optical Phase Conjugation (Academic, New York, 1983).
  8. K. R. MacDonald, J. Feinberg, “Theory of a Self-Pumped Conjugator with Two Coupled Interaction Regions,” J. Opt. Soc. Am. 73, 548–553 (1983).
    [CrossRef]
  9. B. Fischer, S. Weiss, S. Sternklar, “Spatial Light Modulation and Filtering Effects in Photorefractive Wave Mixing,” Appl. Phys. Lett. 50, 483–485 (1987).
    [CrossRef]
  10. S. Weiss, S. Sternklar, B. Fischer, “Double Phase-Conjugate Mirror: Analysis, Demonstrations, and Applications,” Opt. Lett. 12, 114–116 (1987); S. Sternklar, S. Weiss, M. Segev, B. Fischer, “Mach-Zender Interferometer with Multimode Fibers Using the Double-Phase Conjugator Mirror,” Appl. Opt. 25, 4518–4520 (1986); S. Sternklar, S. Weiss, B. Fischer, “Optical Information Processing with the Double Phase Conjugate Mirror,” Opt. Engr. 26, 423–427 (1987).
    [CrossRef] [PubMed]
  11. R. W. Eason, A. M. C. Smout, “Bistability and Noncommutative Behavior of Multiple-Beam Self-Pulsing and Self-Pumping in BaTiO3,” Opt. Lett. 12, 51–53 (1987); A. M. C. Smout, R. W. Eason, “Analysis of Mutually Incoherent Beam Coupling in BaTiO3,” Opt. Lett. 12, 498–500 (1987).
    [CrossRef] [PubMed]
  12. M. D. Ewbank, “Mechanism for Photorefractive Phase Conjugation Using Incoherent Beams,” Opt. Lett. 13, 47–49 (1988); “Incoherent Beams Sharing Photorefractive Holograms,” in Digest of Topical Meeting on Photorefractive Materials, Effects, and Devices (Optical Society of America, Washington, D.C., 1987), p. 179.
    [CrossRef] [PubMed]
  13. G. J. Salamo, M. J. Miller, W. W. Clark, G. L. Wood, E. J. Sharp, R. R. Neurganokar, “Photorefractive Rainbows,” Appl. Opt. 27, 4356–4358 (1988).
    [CrossRef] [PubMed]
  14. P. S. Brody, “Grating Structure in Self-Pumping Barium Titanate by Local Erasure,” in Digest of Topical Meeting on Photorefractive Materials, Effects, and Devices (Optical Society of America, Washington, D.C., 1987), p. 164.
  15. Y. Tomita, R. Yahalom, A. Yariv, “Real-Time Image Subtraction with the Use of Wave Polarization and Phase Conjugation,” Appl. Phys. Lett. 52, 425–427 (1988).
    [CrossRef]
  16. M. D. Ewbank, R. A. Vazquez, P. Yeh, R. R. Neurganonkar, “Frog-Legs Phase Conjugator,” O.S.A. Annual Meeting Technical Digest, Santa Clara, CA, Oct 30, 1988.
  17. P. Yeh, T. Y. Chang, P. H. Beckwith, “Real-Time Optical Image Subtraction Using Dynamic Holographic Interference in Photorefractive Media,” Opt. Lett. 13, 586–588 (1988); S. Kwong, G. Rakuljic, A. Yariv, “Real Time Image Subtraction and ‘Exclusive OR’ Operation Using a Self-Pumped Phase Conjugate Mirror,” Appl. Phys. Lett. 48, 201–203 (1986).
    [CrossRef] [PubMed]

1988

1987

1983

1982

1980

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, “Photorefractive Effects and Light-Induced Charge Migration in Barium Titanate,” J. Appl. Phys. 51, 1297–1305 (1980); Erratum, J. Appl. Phys. 52, 537 (1981).
[CrossRef]

J. Feinberg, R. W. Hellwarth, “Phase-Conjugating Mirror with Continuous-Wave Gain,” Opt. Lett. 5, 519–521 (1980); Erratum, Opt. Lett. 6, 257 (1981).
[CrossRef] [PubMed]

Beckwith, P. H.

Brody, P. S.

P. S. Brody, “Grating Structure in Self-Pumping Barium Titanate by Local Erasure,” in Digest of Topical Meeting on Photorefractive Materials, Effects, and Devices (Optical Society of America, Washington, D.C., 1987), p. 164.

Chang, T. Y.

Clark, W. W.

Cronin-Golomb, M.

J. White, M. Cronin-Golomb, B. Fischer, A. Yariv, “Coherent Oscillation by Self-Induced Gratings in the Photorefractive Crystal BaTiO3,” Appl. Phys. Lett. 40, 450–452 (1982); M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Passive (Self-Pumped) Phase Conjugate Mirror: Theoretical and Experimental Investigation,” Appl. Phys. Lett. 41, 689–691 (1982).
[CrossRef]

Eason, R. W.

Ewbank, M. D.

Feinberg, J.

Fischer, B.

B. Fischer, S. Weiss, S. Sternklar, “Spatial Light Modulation and Filtering Effects in Photorefractive Wave Mixing,” Appl. Phys. Lett. 50, 483–485 (1987).
[CrossRef]

S. Weiss, S. Sternklar, B. Fischer, “Double Phase-Conjugate Mirror: Analysis, Demonstrations, and Applications,” Opt. Lett. 12, 114–116 (1987); S. Sternklar, S. Weiss, M. Segev, B. Fischer, “Mach-Zender Interferometer with Multimode Fibers Using the Double-Phase Conjugator Mirror,” Appl. Opt. 25, 4518–4520 (1986); S. Sternklar, S. Weiss, B. Fischer, “Optical Information Processing with the Double Phase Conjugate Mirror,” Opt. Engr. 26, 423–427 (1987).
[CrossRef] [PubMed]

J. White, M. Cronin-Golomb, B. Fischer, A. Yariv, “Coherent Oscillation by Self-Induced Gratings in the Photorefractive Crystal BaTiO3,” Appl. Phys. Lett. 40, 450–452 (1982); M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Passive (Self-Pumped) Phase Conjugate Mirror: Theoretical and Experimental Investigation,” Appl. Phys. Lett. 41, 689–691 (1982).
[CrossRef]

Heiman, D.

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, “Photorefractive Effects and Light-Induced Charge Migration in Barium Titanate,” J. Appl. Phys. 51, 1297–1305 (1980); Erratum, J. Appl. Phys. 52, 537 (1981).
[CrossRef]

Hellwarth, R. W.

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, “Photorefractive Effects and Light-Induced Charge Migration in Barium Titanate,” J. Appl. Phys. 51, 1297–1305 (1980); Erratum, J. Appl. Phys. 52, 537 (1981).
[CrossRef]

J. Feinberg, R. W. Hellwarth, “Phase-Conjugating Mirror with Continuous-Wave Gain,” Opt. Lett. 5, 519–521 (1980); Erratum, Opt. Lett. 6, 257 (1981).
[CrossRef] [PubMed]

MacDonald, K. R.

Miller, M. J.

Neurganokar, R. R.

Neurganonkar, R. R.

M. D. Ewbank, R. A. Vazquez, P. Yeh, R. R. Neurganonkar, “Frog-Legs Phase Conjugator,” O.S.A. Annual Meeting Technical Digest, Santa Clara, CA, Oct 30, 1988.

Salamo, G. J.

Sharp, E. J.

Smout, A. M. C.

Sternklar, S.

Tanguay, A. R.

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, “Photorefractive Effects and Light-Induced Charge Migration in Barium Titanate,” J. Appl. Phys. 51, 1297–1305 (1980); Erratum, J. Appl. Phys. 52, 537 (1981).
[CrossRef]

Tomita, Y.

Y. Tomita, R. Yahalom, A. Yariv, “Real-Time Image Subtraction with the Use of Wave Polarization and Phase Conjugation,” Appl. Phys. Lett. 52, 425–427 (1988).
[CrossRef]

Vazquez, R. A.

M. D. Ewbank, R. A. Vazquez, P. Yeh, R. R. Neurganonkar, “Frog-Legs Phase Conjugator,” O.S.A. Annual Meeting Technical Digest, Santa Clara, CA, Oct 30, 1988.

Weiss, S.

White, J.

J. White, M. Cronin-Golomb, B. Fischer, A. Yariv, “Coherent Oscillation by Self-Induced Gratings in the Photorefractive Crystal BaTiO3,” Appl. Phys. Lett. 40, 450–452 (1982); M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Passive (Self-Pumped) Phase Conjugate Mirror: Theoretical and Experimental Investigation,” Appl. Phys. Lett. 41, 689–691 (1982).
[CrossRef]

Wood, G. L.

Yahalom, R.

Y. Tomita, R. Yahalom, A. Yariv, “Real-Time Image Subtraction with the Use of Wave Polarization and Phase Conjugation,” Appl. Phys. Lett. 52, 425–427 (1988).
[CrossRef]

Yariv, A.

Y. Tomita, R. Yahalom, A. Yariv, “Real-Time Image Subtraction with the Use of Wave Polarization and Phase Conjugation,” Appl. Phys. Lett. 52, 425–427 (1988).
[CrossRef]

J. White, M. Cronin-Golomb, B. Fischer, A. Yariv, “Coherent Oscillation by Self-Induced Gratings in the Photorefractive Crystal BaTiO3,” Appl. Phys. Lett. 40, 450–452 (1982); M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Passive (Self-Pumped) Phase Conjugate Mirror: Theoretical and Experimental Investigation,” Appl. Phys. Lett. 41, 689–691 (1982).
[CrossRef]

Yeh, P.

Appl. Opt.

Appl. Phys. Lett.

Y. Tomita, R. Yahalom, A. Yariv, “Real-Time Image Subtraction with the Use of Wave Polarization and Phase Conjugation,” Appl. Phys. Lett. 52, 425–427 (1988).
[CrossRef]

J. White, M. Cronin-Golomb, B. Fischer, A. Yariv, “Coherent Oscillation by Self-Induced Gratings in the Photorefractive Crystal BaTiO3,” Appl. Phys. Lett. 40, 450–452 (1982); M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Passive (Self-Pumped) Phase Conjugate Mirror: Theoretical and Experimental Investigation,” Appl. Phys. Lett. 41, 689–691 (1982).
[CrossRef]

B. Fischer, S. Weiss, S. Sternklar, “Spatial Light Modulation and Filtering Effects in Photorefractive Wave Mixing,” Appl. Phys. Lett. 50, 483–485 (1987).
[CrossRef]

J. Appl. Phys.

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, “Photorefractive Effects and Light-Induced Charge Migration in Barium Titanate,” J. Appl. Phys. 51, 1297–1305 (1980); Erratum, J. Appl. Phys. 52, 537 (1981).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. B

Opt. Lett.

J. Feinberg, R. W. Hellwarth, “Phase-Conjugating Mirror with Continuous-Wave Gain,” Opt. Lett. 5, 519–521 (1980); Erratum, Opt. Lett. 6, 257 (1981).
[CrossRef] [PubMed]

J. Feinberg, “Self-Pumped, Continuous-Wave Phase Conjugator Using Internal Reflection,” Opt. Lett. 7, 486–488 (1982).
[CrossRef] [PubMed]

R. W. Eason, A. M. C. Smout, “Bistability and Noncommutative Behavior of Multiple-Beam Self-Pulsing and Self-Pumping in BaTiO3,” Opt. Lett. 12, 51–53 (1987); A. M. C. Smout, R. W. Eason, “Analysis of Mutually Incoherent Beam Coupling in BaTiO3,” Opt. Lett. 12, 498–500 (1987).
[CrossRef] [PubMed]

S. Weiss, S. Sternklar, B. Fischer, “Double Phase-Conjugate Mirror: Analysis, Demonstrations, and Applications,” Opt. Lett. 12, 114–116 (1987); S. Sternklar, S. Weiss, M. Segev, B. Fischer, “Mach-Zender Interferometer with Multimode Fibers Using the Double-Phase Conjugator Mirror,” Appl. Opt. 25, 4518–4520 (1986); S. Sternklar, S. Weiss, B. Fischer, “Optical Information Processing with the Double Phase Conjugate Mirror,” Opt. Engr. 26, 423–427 (1987).
[CrossRef] [PubMed]

M. D. Ewbank, “Mechanism for Photorefractive Phase Conjugation Using Incoherent Beams,” Opt. Lett. 13, 47–49 (1988); “Incoherent Beams Sharing Photorefractive Holograms,” in Digest of Topical Meeting on Photorefractive Materials, Effects, and Devices (Optical Society of America, Washington, D.C., 1987), p. 179.
[CrossRef] [PubMed]

P. Yeh, T. Y. Chang, P. H. Beckwith, “Real-Time Optical Image Subtraction Using Dynamic Holographic Interference in Photorefractive Media,” Opt. Lett. 13, 586–588 (1988); S. Kwong, G. Rakuljic, A. Yariv, “Real Time Image Subtraction and ‘Exclusive OR’ Operation Using a Self-Pumped Phase Conjugate Mirror,” Appl. Phys. Lett. 48, 201–203 (1986).
[CrossRef] [PubMed]

Other

See for example, R. Fisher, Ed., Optical Phase Conjugation (Academic, New York, 1983).

P. S. Brody, “Grating Structure in Self-Pumping Barium Titanate by Local Erasure,” in Digest of Topical Meeting on Photorefractive Materials, Effects, and Devices (Optical Society of America, Washington, D.C., 1987), p. 164.

M. D. Ewbank, R. A. Vazquez, P. Yeh, R. R. Neurganonkar, “Frog-Legs Phase Conjugator,” O.S.A. Annual Meeting Technical Digest, Santa Clara, CA, Oct 30, 1988.

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Figures (19)

Fig. 1
Fig. 1

Photographs illustrating the bridge formation: (a) The two incident beams at time t = 0 before the bridge formation. (b) The two incident beams after having bridged together. The c-axis is directed from top to bottom in these photos.

Fig. 2
Fig. 2

Fictional depiction of the self-pumped phase conjugate mirror where the radiation of laser #1 is blocked by the beam block (B.B.) and beam #2 is supplied by laser #2 and mirror M.

Fig. 3
Fig. 3

Generic schematic for double phase conjugation. E 1 * and E 2 * are the incident fields while El and E2 are the corresponding conjugate fields.

Fig. 4
Fig. 4

Geometries which have been employed to observe double phase conjugation (DPC). (a) The first reported observation of DPC (Ref. 10); (b) DPC using two laser beams entering the crystal from the same side (Ref. 11); (c) the bird-wing configuration using total internal reflection (Ref. 12); and (d) the bridge conjugator reported here. Since the DPCs reported in (a), (b), and (c) were observed in BaTiO3, the beam fanning direction is in the same direction as the c-axis. For the bridge conjugator in (d), however, the observation was made in SBN, so that the fanning direction opposes the c-axis direction.

Fig. 5
Fig. 5

Experimental apparatus used to study the reflectivity, angular sensitivity, and time response of the bridge conjugator. D, detector; P, polarization rotator; and BS, beamsplitter.

Fig. 6
Fig. 6

Reflectivity of the bridge conjugator as a function of incidence angle. No adjustment of data for Fresnel losses has been made.

Fig. 7
Fig. 7

Schematic diagram showing the ring pattern which is observed for incidence angles <10°.

Fig. 8
Fig. 8

Time response as a function of input intensity in cerium-doped SBN:60 for: (a) Self-pumping configuration; (b) Bridge conjugator (E1 = E2, ϕ1 = ϕ2 = 45°); (c) Beam fanning.

Fig. 9
Fig. 9

(a) Time response for the bridge conjugator as a function of E1 with E2 held fixed at 3.8 W/cm2. (b) Time response as a function of E2 with E1 held fixed at 1 W/cm2. ϕ1 = ϕ2 = 45° for both measurements.

Fig. 10
Fig. 10

Schematic diagram depicting the alignment angle θ, which is defined as the angle formed as E2 is raised out of the plane defined by beam E1 and the c-axis.

Fig. 11
Fig. 11

Phase conjugate signal as a function of the angle between the input beams in the vertical plane θ. The angles ϕ1 and ϕ2 were held fixed at 45°.

Fig. 12
Fig. 12

Apparatus used to erase a selected section of the bridge gratings. The erase beam is brought into the crystal via a cylindrical lens (not shown).

Fig. 13
Fig. 13

Relative strength of the conjugate signal as a function of the erase–probe position. The point CP represents the crossing point at t = 0.

Fig. 14
Fig. 14

Schematic diagram illustrating the formation of the bridge conjugator. Two points are shown where each beam scatters off identical gratings in the direction of the other beam.

Fig. 15
Fig. 15

Plot of the coupling constant γ for SBN:60 vs α2 for various values of α1. The curves are for 442-nm light and are based on the following values: N ~ 7 × 1016 cm−3, 11 = 470, 33 = 1100, n0 = 2.30, ne = 2.27, r13 = 55 pm/V, r42 = 80 pm/V, and r33 = 224 pm/V.

Fig. 16
Fig. 16

Plot of the coupling constant γ for BaTiO3 vs α2 for various values of α1. The curves are for 442-nm light and are based on the following values: N ~ 2 2 × 1017 cm−3, 11 = 300, 33 = 3000, n0 = 2.30, ne = 2.27, r13 = 29 pm/V, r42 = 1640 pm/V, and r33 = 97 pm/V.

Fig. 17
Fig. 17

Geometrical arrangement which resulted in a modified bridge formation in BaTiO3.

Fig. 18
Fig. 18

Experimental apparatus used to observe addition and subtraction of images and the fidelity of phase conjugation for the bridge conjugator. LASER, He–Cd laser; P, polarizer; BX, beam expander; L, lens; BS, beam splitters; S, screen; T, Transparency; and M, mirror.

Fig. 19
Fig. 19

(a) Photograph of E 2 * added to E 1 * taken at S1 in Fig. 18. (b) Photo of E 1 * subtracted from E 2 * taken at S2 in Fig. 18.

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