Abstract

We optimize the ring self-pumped phase-conjugate mirror at 1.06 μm. With cw as well as nanosecond illumination the photorefractive efficiency is higher than 90%. Therefore the reflectivity (79%) is limited only by the transmission of the loop. Another relevant characteristic is the time needed to increase the reflectivity from 10% to 90% of its maximum value, which is as little as 12 s at 5 W cm-2 in the cw regime. In the nanosecond regime, 90 J cm-2 is needed. We study the response to an abrupt change in the incident wave front, taking into account the three-prism system inserted in the loop.

[Optical Society of America ]

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  1. S. MacCormack , G. D. Bacher , J. Feinberg , S. O Brien , R. J. Lang , M. B. Klein , and B. A. Wechsler , Powerful, diffraction limited semiconductor laser using photorefractive beam coupling , Opt. Lett. OPLEDP 22 , 227 ( 1997
    [CrossRef] [PubMed]
  2. J. M. Verdiell , H. Rajbenbach , and J. P. Huignard , Injection-locking of gain-guided diode laser arrays: influence of the master beam shape , IEEE Photonics Technol. Lett. IPTLEL 2 , 568 ( 1990
    [CrossRef]
  3. M. Cronin-Golomb , K. Y. Lau , and A. Yariv , Infrared photorefractive passive phase conjugation with BaTiO 3 : demonstration with GaAlAs and 1.09 m Ar + lasers , Appl. Phys. Lett. APPLAB 47 , 567 ( 1985
    [CrossRef]
  4. B. A. Wechsler , M. B. Klein , C. C. Nelson , and R. N. Schwartz , Spectroscopic and photorefractive properties of infrared-sensitive rhodium-doped barium titanate , Opt. Lett. OPLEDP 19 , 536 ( 1994
    [CrossRef] [PubMed]
  5. A. Brignon , D. Geffroy , J. P. Huignard , M. H. Garrett , and I. Mnushkina , Experimental investigations of the photorefractive properties of rhodium-doped BaTiO 3 at 1.06 m , Opt. Commun. OPCOB8 137 , 311 ( 1997
    [CrossRef]
  6. N. Huot , J. M. C. Jonathan , G. Pauliat , D. Rytz , and G. Roosen , Characterization of a photorefractive rhodium doped barium titanate at 1.06 m , Opt. Commun. OPCOB8 135 , 133 ( 1997
    [CrossRef]
  7. N. Huot , J. M. C. Jonathan , G. Roosen , and D. Rytz , Two-wave mixing in photorefractive BaTiO 3 :Rh at 1.06 m in the nanosecond regime , Opt. Lett. OPLEDP 22 , 976 ( 1997
    [CrossRef] [PubMed]
  8. G. C. Valley , Short pulse grating formation in photorefractive materials , IEEE J. Quantum Electron. IEJQA7 QE-19 , 1637 ( 1983
    [CrossRef]
  9. M. J. Damzen and N. Barry , Intensity-dependent hole electron competition and photocarrier saturation in BaTiO 3 when using intense laser pulses , J. Opt. Soc. Am. B JOBPDE 10 , 600 ( 1993
    [CrossRef]
  10. N. Huot , J. M. C. Jonathan , G. Roosen , and D. Rytz , Self-pumped phase conjugation in a ring cavity at 1.06 m in the cw and nanosecond regimes using photorefractive BaTiO 3 :Rh , Opt. Commun. OPCOB8 140 , 296 ( 1997
    [CrossRef]
  11. N. Huot , J. M. C. Jonathan , and G. Roosen , Validity of the three charge state model in photorefractive BaTiO 3 :Rh at 1.06 m in the cw regime , Appl. Phys. B 65 , 489 ( 1997
    [CrossRef]
  12. 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. IEJQA7 QE-20 , 12 ( 1984
    [CrossRef]
  13. M. Cronin-Golomb , J. Paslaski , and A. Yariv , Vibration resistance, short coherence length operation, and mode-locked pumping in passive phase conjugate mirrors , Appl. Phys. Lett. APPLAB 47 , 1131 ( 1985
    [CrossRef]
  14. V. T. Tikhonchuk and A. A. Zozulya , Structure of light beams in self-pumped four-wave mixing geometries for phase conjugation and mutual conjugation , Prog. Quantum Electron. PQUEAH 15 , 231 ( 1991
    [CrossRef]
  15. N. V. Bogodaev , L. I. Ivleva , A. S. Korshunov , A. V. Mamaev , N. N. Poloskov , and A. A. Zozulya , Geometry of a self-pumped passive ring mirror in crystals with strong fanning , J. Opt. Soc. Am. B JOBPDE 10 , 1054 ( 1993
    [CrossRef]
  16. H. Kro se , R. Scharfschwerdt , O. F. Schirmer , and H. Hesse , Light-induced charge transport in BaTiO 3 via three charge states of rhodium , Appl. Phys. B: Photophys. Laser Chem. APPCDL 61 , 1 ( 1995
    [CrossRef]
  17. K. Buse , Light-induced charge transport processes in photorefractive crystals. I. Models and experimental methods , Appl. Phys. B 64 , 273 ( 1997
    [CrossRef]
  18. N. V. Kukhtarev , V. B. Markov , S. G. Odulov , M. S. Soskin , and V. L. Vinetskii , Holographic storage in electrooptic crystals , Ferroelectrics FEROA8 22 , 949 ( 1979
    [CrossRef]
  19. G. Pauliat , M. Ingold , and P. Gu nter , Analysis of the build up of oscillations in self-induced photorefractive light resonators , IEEE J. Quantum Electron. IEJQA7 25 , 201 ( 1989
    [CrossRef]
  20. P. Bernasconi , M. Zgonik , and P. Gu nter , Temperature dependence and dispersion of electro-optic and elasto-optic effect in perovskite crystals , J. Appl. Phys. JAPIAU 78 , 2651 ( 1995
    [CrossRef]
  21. S. A. Korolkov , Y. S. Kuzminov , A. V. Mamaev , V. V. Skhunov , and A. A. Zozulya , Spatial structure of scattered radiation in a self-pumped photorefractive passive ring mirror , J. Opt. Soc. Am. B JOBPDE 9 , 664 ( 1992
    [CrossRef]
  22. L. Mager , C. Lacquarnoy , G. Pauliat , M. H. Garrett , D. Rytz , and G. Roosen , High-quality self-pumped phase conjugation of nanosecond pulses at 532 nm using photorefractive BaTiO 3 , Opt. Lett. OPLEDP 19 , 1508 ( 1994
    [CrossRef] [PubMed]
  23. A. Brignon , J. P. Huignard , M. H. Garrett , and I. Mnushkina , Nd:YAG master-oscillator power amplifier with a rhodium-doped BaTiO 3 self-pumped phase-conjugate mirror , Opt. Lett. OPLEDP 22 , 442 ( 1997
    [CrossRef] [PubMed]

Geffroy, D

A. Brignon , D. Geffroy , J. P. Huignard , M. H. Garrett , and I. Mnushkina , Experimental investigations of the photorefractive properties of rhodium-doped BaTiO 3 at 1.06 m , Opt. Commun. OPCOB8 137 , 311 ( 1997
[CrossRef]

Huot, N

N. Huot , J. M. C. Jonathan , G. Pauliat , D. Rytz , and G. Roosen , Characterization of a photorefractive rhodium doped barium titanate at 1.06 m , Opt. Commun. OPCOB8 135 , 133 ( 1997
[CrossRef]

Ingold, M

G. Pauliat , M. Ingold , and P. Gu nter , Analysis of the build up of oscillations in self-induced photorefractive light resonators , IEEE J. Quantum Electron. IEJQA7 25 , 201 ( 1989
[CrossRef]

Lacquarnoy, C

Mager, L

Poloskov, N. N

Skhunov, V. V

Other (23)

J. M. Verdiell , H. Rajbenbach , and J. P. Huignard , Injection-locking of gain-guided diode laser arrays: influence of the master beam shape , IEEE Photonics Technol. Lett. IPTLEL 2 , 568 ( 1990
[CrossRef]

M. Cronin-Golomb , K. Y. Lau , and A. Yariv , Infrared photorefractive passive phase conjugation with BaTiO 3 : demonstration with GaAlAs and 1.09 m Ar + lasers , Appl. Phys. Lett. APPLAB 47 , 567 ( 1985
[CrossRef]

A. Brignon , D. Geffroy , J. P. Huignard , M. H. Garrett , and I. Mnushkina , Experimental investigations of the photorefractive properties of rhodium-doped BaTiO 3 at 1.06 m , Opt. Commun. OPCOB8 137 , 311 ( 1997
[CrossRef]

N. Huot , J. M. C. Jonathan , G. Pauliat , D. Rytz , and G. Roosen , Characterization of a photorefractive rhodium doped barium titanate at 1.06 m , Opt. Commun. OPCOB8 135 , 133 ( 1997
[CrossRef]

N. Huot , J. M. C. Jonathan , G. Roosen , and D. Rytz , Self-pumped phase conjugation in a ring cavity at 1.06 m in the cw and nanosecond regimes using photorefractive BaTiO 3 :Rh , Opt. Commun. OPCOB8 140 , 296 ( 1997
[CrossRef]

N. Huot , J. M. C. Jonathan , and G. Roosen , Validity of the three charge state model in photorefractive BaTiO 3 :Rh at 1.06 m in the cw regime , Appl. Phys. B 65 , 489 ( 1997
[CrossRef]

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. IEJQA7 QE-20 , 12 ( 1984
[CrossRef]

M. Cronin-Golomb , J. Paslaski , and A. Yariv , Vibration resistance, short coherence length operation, and mode-locked pumping in passive phase conjugate mirrors , Appl. Phys. Lett. APPLAB 47 , 1131 ( 1985
[CrossRef]

V. T. Tikhonchuk and A. A. Zozulya , Structure of light beams in self-pumped four-wave mixing geometries for phase conjugation and mutual conjugation , Prog. Quantum Electron. PQUEAH 15 , 231 ( 1991
[CrossRef]

H. Kro se , R. Scharfschwerdt , O. F. Schirmer , and H. Hesse , Light-induced charge transport in BaTiO 3 via three charge states of rhodium , Appl. Phys. B: Photophys. Laser Chem. APPCDL 61 , 1 ( 1995
[CrossRef]

K. Buse , Light-induced charge transport processes in photorefractive crystals. I. Models and experimental methods , Appl. Phys. B 64 , 273 ( 1997
[CrossRef]

N. V. Kukhtarev , V. B. Markov , S. G. Odulov , M. S. Soskin , and V. L. Vinetskii , Holographic storage in electrooptic crystals , Ferroelectrics FEROA8 22 , 949 ( 1979
[CrossRef]

G. Pauliat , M. Ingold , and P. Gu nter , Analysis of the build up of oscillations in self-induced photorefractive light resonators , IEEE J. Quantum Electron. IEJQA7 25 , 201 ( 1989
[CrossRef]

P. Bernasconi , M. Zgonik , and P. Gu nter , Temperature dependence and dispersion of electro-optic and elasto-optic effect in perovskite crystals , J. Appl. Phys. JAPIAU 78 , 2651 ( 1995
[CrossRef]

G. C. Valley , Short pulse grating formation in photorefractive materials , IEEE J. Quantum Electron. IEJQA7 QE-19 , 1637 ( 1983
[CrossRef]

S. A. Korolkov , Y. S. Kuzminov , A. V. Mamaev , V. V. Skhunov , and A. A. Zozulya , Spatial structure of scattered radiation in a self-pumped photorefractive passive ring mirror , J. Opt. Soc. Am. B JOBPDE 9 , 664 ( 1992
[CrossRef]

M. J. Damzen and N. Barry , Intensity-dependent hole electron competition and photocarrier saturation in BaTiO 3 when using intense laser pulses , J. Opt. Soc. Am. B JOBPDE 10 , 600 ( 1993
[CrossRef]

N. V. Bogodaev , L. I. Ivleva , A. S. Korshunov , A. V. Mamaev , N. N. Poloskov , and A. A. Zozulya , Geometry of a self-pumped passive ring mirror in crystals with strong fanning , J. Opt. Soc. Am. B JOBPDE 10 , 1054 ( 1993
[CrossRef]

B. A. Wechsler , M. B. Klein , C. C. Nelson , and R. N. Schwartz , Spectroscopic and photorefractive properties of infrared-sensitive rhodium-doped barium titanate , Opt. Lett. OPLEDP 19 , 536 ( 1994
[CrossRef] [PubMed]

L. Mager , C. Lacquarnoy , G. Pauliat , M. H. Garrett , D. Rytz , and G. Roosen , High-quality self-pumped phase conjugation of nanosecond pulses at 532 nm using photorefractive BaTiO 3 , Opt. Lett. OPLEDP 19 , 1508 ( 1994
[CrossRef] [PubMed]

S. MacCormack , G. D. Bacher , J. Feinberg , S. O Brien , R. J. Lang , M. B. Klein , and B. A. Wechsler , Powerful, diffraction limited semiconductor laser using photorefractive beam coupling , Opt. Lett. OPLEDP 22 , 227 ( 1997
[CrossRef] [PubMed]

A. Brignon , J. P. Huignard , M. H. Garrett , and I. Mnushkina , Nd:YAG master-oscillator power amplifier with a rhodium-doped BaTiO 3 self-pumped phase-conjugate mirror , Opt. Lett. OPLEDP 22 , 442 ( 1997
[CrossRef] [PubMed]

N. Huot , J. M. C. Jonathan , G. Roosen , and D. Rytz , Two-wave mixing in photorefractive BaTiO 3 :Rh at 1.06 m in the nanosecond regime , Opt. Lett. OPLEDP 22 , 976 ( 1997
[CrossRef] [PubMed]

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Figures (11)

Fig. 1
Fig. 1

Schematic of the ring self-pumped phase-conjugate mirror. Phase-conjugate beams are observed in optical plane (P). PZT, piezo mirror used in the cw illumination regime.

Fig. 2
Fig. 2

Reflectivity of the ring self-pumped phase-conjugate mirror versus transmission of the loop in the cw illumination regime at 1.06 μm. Experimental data are fitted by theoretical curves obtained with different values of the product Γl.

Fig. 3
Fig. 3

Typical experimental time evolution of the reflectivity of the ring self-pumped phase-conjugate mirror at 1.06 μm in the cw illumination regime. This curve is obtained for an intensity of 5 W cm-2.

Fig. 4
Fig. 4

Predicted Γl, photorefractive rise time τph, and reflectivity rise time τ90%-τ10% versus incidence angle θ on the photorefractive crystal (see text for choice of parameters).

Fig. 5
Fig. 5

Experimental values of τ90%-τ10% for several incidence angles θ. To compensate for the variations of transmission T of the loop with θ, for a given θ τ90%-τ10% is to be compared with the value obtained at θ=20° for the same T.

Fig. 6
Fig. 6

Ring self-pumped phase-conjugate mirror with a three-prism system performing a 90° rotation of the beam cross section. The loop length is 12 cm.

Fig. 7
Fig. 7

a, Phase-conjugate beam profile from a loop using conventional mirrors. The poor fidelity of the phase conjugation appears in the vertical structure of the image. b, Phase-conjugate beam profile with the three prisms. c, Incident beam profile. All the images were obtained in the nanosecond illumination regime at 1.06 μm.

Fig. 8
Fig. 8

Notation used in Section 5. y=0 is the incidence plane. The mirror signs represent the loop mirrors. The loop length is assumed to be much smaller than the focal length of the thermal lens to be corrected for. Wave A2R converges at C2R (x2R, 0, z2R). At steady state it is diffracted as A3R originating from C3R (x2R, 0,-z2R). The photorefractive crystal is centered at (0, 0, 0). A2A is the wave resulting from an abrupt change in the thermal lens; it is now converging at C2A (x2A, 0, z2A); it is diffracted as A3A originating from C3A (x3A, 0, -z3A).

Fig. 9
Fig. 9

Experimental check on relation (13) at 1.06 μm in the nanosecond illumination regime: a, phase-conjugate beam image without aberration (lens) in the incident beam path; b, calculated and c, observed transient beam image when an f=1.3 m focal-length lens is inserted into the incident beam path. d, e, The same results with f=0.5 m. Although the experimental result is a distorted version of the predicted cross pattern, it is quite reproducible. All the images are calculated with no free parameter.

Fig. 10
Fig. 10

Computed variations of the reflectivity and of the overlap integral between the real and the expected transient phase-conjugate beams versus the convergence of the aberrator introduced on the incident collimated beam. For clarity these values are normalized to their maxima.

Fig. 11
Fig. 11

Experimental time evolution of the reflectivity. At t=25 min a diverging lens (f=-1 m) is introduced into the incident beam. The slower recovery is caused by the poor overlap integral between the transient diffracted beam and the phase-conjugate beam obtained only at steady state.

Tables (1)

Tables Icon

Table 1 Relevant Parameters for BaTiO3:Rh Crystals Characterized at 1.06 μm in the cw Illumination Regime a

Equations (17)

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A1(z, t)z=i Γ4Esc E1(z, t)A4(z, t),
A2*(z, t)z=i Γ4Esc E1(z, t)A3*(z, t),
A3(z, t)z=-i Γ4Esc E1(z, t)A2(z, t),
A4*(z, t)z=-i Γ4Esc E1(z, t)A1*(z, t),
E1(z, t)t=-1τph [E1(z, t)-im(z, t)Esc],
m(z, t)=2(A1A4*+A2*A3)/I0.
A2R=e^y a2Rr2R exp(-iωt)exp[ik(z-z2R)]×exp-iπλz2R [(x-x2R)2+y2]1+zz2R,
A3R=e^y a3Rr2R exp(-iωt)exp[ik(z+z2R)]×expiπλz2R [(x-x2R)2+y2]1-zz2R,
ΔnΔn0 exp(2ikz2R)exp2i πλz2R [(x-x2R)2+y2].
A2A=e^y a2Ar2A exp(-iωt)exp[ik(z-z2A)]×exp-iπλz2A [(x-x2A)2+y2]1+zz2A,
2A3A+k2A3A=-k2 [Δε]n2 A2A,
e^y*[Δε]e^y=2nΔn.
A3A=e^y a3A(x, y, z)r3A exp(-iωt)exp[ik(z+z3A)]×expiπλz3A [(x-x3A)2+y2]1-zz3A,
x3Az3A=x2Az2A=x2Rz2R,1z3A+1z2A=2z2R,
a3A(l)sinc(x-x3A)2+y2z3A2-(x-x2A)2+y2z2A2 l2λ.
Isinc(x-x3A)2+y2z3A2-(x-x2A)2+y2z2A2 l2λ+sinc(y-x3A)2+x2z3A2-(y-x2A)2+x2z2A2 l2λ2.
Δαtt=0,I=1.1 W cm-2

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