Abstract

Spatial-frequency characteristics of the reflectivity and transmissivity of a BaTiO3 phase conjugator (PC) combined with extraordinary rays are investigated and numerical results obtained. It is shown that the reflection of a BaTiO3 PC represents a high-pass or a bandpass filter, whereas its transmission represents a low-pass or a bandpass filter. In addition, the filtering characteristics of this PC can be chosen by using appropriate values of such parameters as the average incident-beam angle from the c axis, the pump-beam intensity ratio, and the applied external electric field. A BaTiO3 PC exhibits characteristics that are quite different from those of a Bi12SiO20 PC, since the latter obtains only a high- or low-spatial-frequency filter.

© 1987 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. O. White and A. Yariv, “Real time image processing via four-wave mixing in a photorefractive medium,” Appl. Phys. Lett. 37, 5–7 (1980).
    [CrossRef]
  2. O. Ikeda, T. Suzuki, and T. Sato, “Image transmission through a turbulent medium using a point reflector and four-wave mixing in BSO crystal,” Appl. Opt. 22, 2192–2195 (1983).
    [CrossRef] [PubMed]
  3. O. Ikeda, T. Sato, and H. Kojima, “Analysis of a high resolution and large dynamic range spatial filter using a pair of facing phase conjugators with gains,” J. Opt. Soc. Am. A 2, 1863–1868 (1985).
    [CrossRef]
  4. O. Ikeda, T. Sato, and H. Kojima, “Construction of Wiener filter using phase conjugate filter,” J. Opt. Soc. Am. A. 3, 645–650 (1986).
    [CrossRef]
  5. J. Feinberg and R. W. Hellwarth, “Phase-conjugating mirror with continuous-wave gain,” Opt. Lett. 5, 519–521 (1980).
    [CrossRef] [PubMed]
  6. H. Rajbenbach, J. P. Huignard, and Ph. Refregior, “Amplified phase-conjugate beam reflection by four-wave mixing with photorefractive Bi12SiO20crystals,” Opt. Lett. 9, 558–560 (1984).
    [CrossRef] [PubMed]
  7. J. P. Huignard, J. P. Herriau, and G. Rivet, “Phase- conjugation and spatial-frequency dependence of wave-front reflectivity in Bi12SiO20crystals,” Opt. Lett. 5, 102–104 (1980).
    [CrossRef]
  8. J. Feinberg, D. Heimann, A. R. Tanguay, and R. W. Hellwarth, “Photorefractive effects and light-induced charge migration in barium titanate,” J. Appl. Phys. 51, 1297–1305 (1980).
    [CrossRef]
  9. F. Laeri, T. Tschudi, and J. Albers, “Coherent cw image amplifier and oscillator using two-wave interaction in a BaTiO3-crystal,” Opt. Commun. 47, 387–390 (1983).
    [CrossRef]
  10. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
    [CrossRef]
  11. M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12–30 (1984).
    [CrossRef]
  12. J. P. Huignard and A. Marrakchi, “Coherent signal beam amplification in two-wave mixing experiments with photorefractive Bi12SiO20crystals,” Opt. Commun. 38, 249–254 (1981).
    [CrossRef]
  13. J. Feinberg, “Asymmetric self-defocusing of an optical beam from the photorefractive effect,” J. Opt. Soc. Am. 72, 46–51 (1982).
    [CrossRef]

1986 (1)

O. Ikeda, T. Sato, and H. Kojima, “Construction of Wiener filter using phase conjugate filter,” J. Opt. Soc. Am. A. 3, 645–650 (1986).
[CrossRef]

1985 (1)

1984 (2)

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12–30 (1984).
[CrossRef]

H. Rajbenbach, J. P. Huignard, and Ph. Refregior, “Amplified phase-conjugate beam reflection by four-wave mixing with photorefractive Bi12SiO20crystals,” Opt. Lett. 9, 558–560 (1984).
[CrossRef] [PubMed]

1983 (2)

F. Laeri, T. Tschudi, and J. Albers, “Coherent cw image amplifier and oscillator using two-wave interaction in a BaTiO3-crystal,” Opt. Commun. 47, 387–390 (1983).
[CrossRef]

O. Ikeda, T. Suzuki, and T. Sato, “Image transmission through a turbulent medium using a point reflector and four-wave mixing in BSO crystal,” Appl. Opt. 22, 2192–2195 (1983).
[CrossRef] [PubMed]

1982 (1)

1981 (1)

J. P. Huignard and A. Marrakchi, “Coherent signal beam amplification in two-wave mixing experiments with photorefractive Bi12SiO20crystals,” Opt. Commun. 38, 249–254 (1981).
[CrossRef]

1980 (4)

J. O. White and A. Yariv, “Real time image processing via four-wave mixing in a photorefractive medium,” Appl. Phys. Lett. 37, 5–7 (1980).
[CrossRef]

J. Feinberg and R. W. Hellwarth, “Phase-conjugating mirror with continuous-wave gain,” Opt. Lett. 5, 519–521 (1980).
[CrossRef] [PubMed]

J. P. Huignard, J. P. Herriau, and G. Rivet, “Phase- conjugation and spatial-frequency dependence of wave-front reflectivity in Bi12SiO20crystals,” Opt. Lett. 5, 102–104 (1980).
[CrossRef]

J. Feinberg, D. Heimann, A. R. Tanguay, and R. W. Hellwarth, “Photorefractive effects and light-induced charge migration in barium titanate,” J. Appl. Phys. 51, 1297–1305 (1980).
[CrossRef]

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Albers, J.

F. Laeri, T. Tschudi, and J. Albers, “Coherent cw image amplifier and oscillator using two-wave interaction in a BaTiO3-crystal,” Opt. Commun. 47, 387–390 (1983).
[CrossRef]

Cronin-Golomb, M.

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12–30 (1984).
[CrossRef]

Feinberg, J.

Fischer, B.

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12–30 (1984).
[CrossRef]

Heimann, D.

J. Feinberg, D. Heimann, A. R. Tanguay, and R. W. Hellwarth, “Photorefractive effects and light-induced charge migration in barium titanate,” J. Appl. Phys. 51, 1297–1305 (1980).
[CrossRef]

Hellwarth, R. W.

J. Feinberg, D. Heimann, A. R. Tanguay, and R. W. Hellwarth, “Photorefractive effects and light-induced charge migration in barium titanate,” J. Appl. Phys. 51, 1297–1305 (1980).
[CrossRef]

J. Feinberg and R. W. Hellwarth, “Phase-conjugating mirror with continuous-wave gain,” Opt. Lett. 5, 519–521 (1980).
[CrossRef] [PubMed]

Herriau, J. P.

Huignard, J. P.

Ikeda, O.

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Kojima, H.

Laeri, F.

F. Laeri, T. Tschudi, and J. Albers, “Coherent cw image amplifier and oscillator using two-wave interaction in a BaTiO3-crystal,” Opt. Commun. 47, 387–390 (1983).
[CrossRef]

Marrakchi, A.

J. P. Huignard and A. Marrakchi, “Coherent signal beam amplification in two-wave mixing experiments with photorefractive Bi12SiO20crystals,” Opt. Commun. 38, 249–254 (1981).
[CrossRef]

Rajbenbach, H.

Refregior, Ph.

Rivet, G.

Sato, T.

Suzuki, T.

Tanguay, A. R.

J. Feinberg, D. Heimann, A. R. Tanguay, and R. W. Hellwarth, “Photorefractive effects and light-induced charge migration in barium titanate,” J. Appl. Phys. 51, 1297–1305 (1980).
[CrossRef]

Tschudi, T.

F. Laeri, T. Tschudi, and J. Albers, “Coherent cw image amplifier and oscillator using two-wave interaction in a BaTiO3-crystal,” Opt. Commun. 47, 387–390 (1983).
[CrossRef]

White, J. O.

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12–30 (1984).
[CrossRef]

J. O. White and A. Yariv, “Real time image processing via four-wave mixing in a photorefractive medium,” Appl. Phys. Lett. 37, 5–7 (1980).
[CrossRef]

Yariv, A.

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12–30 (1984).
[CrossRef]

J. O. White and A. Yariv, “Real time image processing via four-wave mixing in a photorefractive medium,” Appl. Phys. Lett. 37, 5–7 (1980).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

J. O. White and A. Yariv, “Real time image processing via four-wave mixing in a photorefractive medium,” Appl. Phys. Lett. 37, 5–7 (1980).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12–30 (1984).
[CrossRef]

J. Appl. Phys. (1)

J. Feinberg, D. Heimann, A. R. Tanguay, and R. W. Hellwarth, “Photorefractive effects and light-induced charge migration in barium titanate,” J. Appl. Phys. 51, 1297–1305 (1980).
[CrossRef]

J. Opt. Soc. Am. (1)

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

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

O. Ikeda, T. Sato, and H. Kojima, “Construction of Wiener filter using phase conjugate filter,” J. Opt. Soc. Am. A. 3, 645–650 (1986).
[CrossRef]

Opt. Commun. (2)

F. Laeri, T. Tschudi, and J. Albers, “Coherent cw image amplifier and oscillator using two-wave interaction in a BaTiO3-crystal,” Opt. Commun. 47, 387–390 (1983).
[CrossRef]

J. P. Huignard and A. Marrakchi, “Coherent signal beam amplification in two-wave mixing experiments with photorefractive Bi12SiO20crystals,” Opt. Commun. 38, 249–254 (1981).
[CrossRef]

Opt. Lett. (3)

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Four-wave mixing in BaTiO3. A1, reference wave; A2, read-out wave; A3, signal wave; A4, reflected wave of A3; A5, transmitted wave of A3. All the incident waves are extraordinary rays. The grating vector kg is parallel to the applied electric field.

Fig. 2
Fig. 2

Amplitude reflectivity |R| and transmissivity |T| for which the pump-wave intensity ratio q (= |A2|2/|A1|2) = 5 and the applied electric field E0 = 0. |R| monotonically increases with increasing Λ−1, and the increasing rate depends on the value of q. In the range of Λ−1 exceeding 1000 mm−1, which may not in practice be important, |R| saturates once at Λ−1 ~ 1800 mm−1 and then decreases with increasing Λ−1, in agreement with Feinberg et al.8 The change is more significant for smaller q.

Fig. 3
Fig. 3

Amplitude reflectivity |R| and transmissivity |T| for which the average incident-beam angle relative to the c axis θ [= (α + β)/2] = 108° and E0 = 0.

Fig. 4
Fig. 4

Amplitude reflectivity |R| and transmissivity |T| for which q = 5 and θ = 108°.

Fig. 5
Fig. 5

Amplitude reflectivity |R| for (a) θ = variable (E0 = variable) and q = 5 and for (b) θ = 110° and q = variable (E0 = variable).

Fig. 6
Fig. 6

Plot of the center frequencies of the bandpass filters obtained at discrete values of E0, for which q = 5 and θ = 110°.

Fig. 7
Fig. 7

Schematic of a two-dimensional PC filter. FI’s, Faraday isolators; ST, SR, shutters; PW’s, plane pump waves; M’s, mirrors; BS’s, beam splitters; L’s, lenses. Pump waves impinge so that the grating vectors in PC(X) and PC(Y) are orthogonal to each other, and the insertion of Faraday isolators may be required to prevent interaction between the two PC’s.

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

d A 4 / d z = γ ( A 1 A 3 * + A 2 * A 4 ) A 2 / I 0 ,
d A 3 / d z = γ * ( A 1 * A 3 + A 2 A 4 * ) A 1 / I 0 ,
A 4 ( z ) = exp [ γ ( z - 1 ) ] - 1 q - 1 exp ( - γ 1 ) + 1 ( A 1 / A 2 * ) A 3 * ( 0 ) ,
A 3 * ( z ) = 1 + q - 1 exp [ γ ( z - 1 ) ] 1 + q - 1 exp ( - γ 1 ) A 3 * ( 0 ) ,
q = A 2 2 / A 1 2 .
A 4 ( 0 ) = R ( A 1 / A 1 ) ( A 2 / A 2 ) A 3 * ( 0 ) ,
A 3 ( 1 ) = T A 3 ( 0 ) ,
R = - sinh ( γ 1 / 2 ) cosh ( γ 1 / 2 + ln q / 2 ) ,
T * = exp ( γ 1 / 2 ) cosh ( ln q / 2 ) cosh ( γ 1 / 2 + ln q / 2 ) .
A 4 ( X ) = a 3 * ( f ) R ( f ) exp [ j 2 π f · X ] d 2 f ,
A 5 ( X ) = a 3 ( f ) T ( f ) exp [ - j 2 π f · X ] d 2 f ,
A 3 ( X ) = a 3 ( f ) exp [ - j 2 π f · X ] d 2 f
γ = - j k r eff E exp ( - j ϕ ) 2 cos [ ( α - β ) / 2 ] ,
E = E p [ E 0 2 + E d 2 E 0 2 + ( E d + E p ) 2 ] 1 / 2 ,
r eff = { n 0 4 r 13 cos α cos β + 2 n 0 2 n e 2 r 42 cos 2 [ ( α + β ) / 2 ] + n e 4 r 33 sin α sin β } sin [ ( α + β ) / 2 ] / n ,
ϕ = tan - 1 { [ E d ( E d + E p ) + E 0 2 ] / E 0 E p } ,
E p = e P d Λ / 2 π ,
E d = 2 π k B T / e Λ ,
Λ = π / k n sin [ ( α - β ) / 2 ] ,
= { cos 2 [ ( α + β ) / 2 ] / 1 2 + sin 2 [ ( α + β ) / 2 ] / 2 2 } - 1 / 2 .

Metrics