Abstract

We predict accurate correction of thermal blooming by phase conjugation, for the case of a nonunity-magnitude reflection coefficient, over a wide range of easily realized experimental conditions. Diffusion relaxes a thermal grating that would otherwise spoil phase-conjugate correction. Phase conjugation is predicted to correct thermal blooming caused by continuous-wave lasers, collimated or loosely focused lasers, pulsed lasers blooming in gases, and broadband lasers.

© 1989 Optical Society of America

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References

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  1. B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, F. S. Faizullov, JETP Lett. 15, 109 (1972).
  2. A. Yariv, IEEE J. Quantum Electron. QE-14, 650 (1978).
    [CrossRef]
  3. A. Yariv, R. A. Fisher, in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), p. 17.
  4. B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985), pp. 4, 24.
  5. D. M. Pepper, A. Yariv, Opt. Lett. 5, 59 (1980).
    [CrossRef] [PubMed]
  6. G. A. Rakuljic, “Photorefractive properties and applications of barium titanate and tungsten-bronze ferroelectrics,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1987), pp. 121–126.
  7. C. J. Wetterer, L. P. Schelonka, M. A. Kramer, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1989), paper MD1; see also C. J. Wetterer, L. P. Schelonka, M. A. Kramer, Opt. Lett. 14, 874 (1989).
    [CrossRef] [PubMed]
  8. R. Y. Chiao, P. L. Kelley, E. Garmire, Phys. Rev. Lett. 17, 1158 (1966).
    [CrossRef]
  9. C. R. Wiley, Advanced Engineering Mathematics, 4th ed. (McGraw-Hill, New York, 1975), p. 328.
  10. M. Sheif-Bahae, A. Said, E. W. Van Stryland, M. J. Soileau, in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1988), paper WZ4.
  11. E. L. Kerr, in Damage in Laser Glass, A. J. Glass, A. H. Guenther, eds. (American Society for Testing and Materials, Philadelphia, Pa., 1969), pp. 23–42.
    [CrossRef]
  12. F. W. Quelle, in Damage in Laser Glass, A. J. Glass, A. H. Guenther, eds. (American Society for Testing and Materials, Philadelphia, Pa., 1969), pp. 110–116.
    [CrossRef]
  13. R. C. Weast, ed., CRC Handbook of Chemistry and Physics, 64th ed. (CRC Press, Boca Raton, Fla., 1983).

1980 (1)

1978 (1)

A. Yariv, IEEE J. Quantum Electron. QE-14, 650 (1978).
[CrossRef]

1972 (1)

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, F. S. Faizullov, JETP Lett. 15, 109 (1972).

1966 (1)

R. Y. Chiao, P. L. Kelley, E. Garmire, Phys. Rev. Lett. 17, 1158 (1966).
[CrossRef]

Chiao, R. Y.

R. Y. Chiao, P. L. Kelley, E. Garmire, Phys. Rev. Lett. 17, 1158 (1966).
[CrossRef]

Faizullov, F. S.

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, F. S. Faizullov, JETP Lett. 15, 109 (1972).

Fisher, R. A.

A. Yariv, R. A. Fisher, in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), p. 17.

Garmire, E.

R. Y. Chiao, P. L. Kelley, E. Garmire, Phys. Rev. Lett. 17, 1158 (1966).
[CrossRef]

Kelley, P. L.

R. Y. Chiao, P. L. Kelley, E. Garmire, Phys. Rev. Lett. 17, 1158 (1966).
[CrossRef]

Kerr, E. L.

E. L. Kerr, in Damage in Laser Glass, A. J. Glass, A. H. Guenther, eds. (American Society for Testing and Materials, Philadelphia, Pa., 1969), pp. 23–42.
[CrossRef]

Kramer, M. A.

C. J. Wetterer, L. P. Schelonka, M. A. Kramer, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1989), paper MD1; see also C. J. Wetterer, L. P. Schelonka, M. A. Kramer, Opt. Lett. 14, 874 (1989).
[CrossRef] [PubMed]

Pepper, D. M.

Pilipetsky, N. F.

B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985), pp. 4, 24.

Popovichev, V. I.

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, F. S. Faizullov, JETP Lett. 15, 109 (1972).

Quelle, F. W.

F. W. Quelle, in Damage in Laser Glass, A. J. Glass, A. H. Guenther, eds. (American Society for Testing and Materials, Philadelphia, Pa., 1969), pp. 110–116.
[CrossRef]

Ragul’skii, V. V.

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, F. S. Faizullov, JETP Lett. 15, 109 (1972).

Rakuljic, G. A.

G. A. Rakuljic, “Photorefractive properties and applications of barium titanate and tungsten-bronze ferroelectrics,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1987), pp. 121–126.

Said, A.

M. Sheif-Bahae, A. Said, E. W. Van Stryland, M. J. Soileau, in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1988), paper WZ4.

Schelonka, L. P.

C. J. Wetterer, L. P. Schelonka, M. A. Kramer, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1989), paper MD1; see also C. J. Wetterer, L. P. Schelonka, M. A. Kramer, Opt. Lett. 14, 874 (1989).
[CrossRef] [PubMed]

Sheif-Bahae, M.

M. Sheif-Bahae, A. Said, E. W. Van Stryland, M. J. Soileau, in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1988), paper WZ4.

Shkunov, V. V.

B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985), pp. 4, 24.

Soileau, M. J.

M. Sheif-Bahae, A. Said, E. W. Van Stryland, M. J. Soileau, in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1988), paper WZ4.

Van Stryland, E. W.

M. Sheif-Bahae, A. Said, E. W. Van Stryland, M. J. Soileau, in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1988), paper WZ4.

Wetterer, C. J.

C. J. Wetterer, L. P. Schelonka, M. A. Kramer, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1989), paper MD1; see also C. J. Wetterer, L. P. Schelonka, M. A. Kramer, Opt. Lett. 14, 874 (1989).
[CrossRef] [PubMed]

Wiley, C. R.

C. R. Wiley, Advanced Engineering Mathematics, 4th ed. (McGraw-Hill, New York, 1975), p. 328.

Yariv, A.

D. M. Pepper, A. Yariv, Opt. Lett. 5, 59 (1980).
[CrossRef] [PubMed]

A. Yariv, IEEE J. Quantum Electron. QE-14, 650 (1978).
[CrossRef]

A. Yariv, R. A. Fisher, in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), p. 17.

Zel’dovich, B. Ya.

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, F. S. Faizullov, JETP Lett. 15, 109 (1972).

B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985), pp. 4, 24.

IEEE J. Quantum Electron. (1)

A. Yariv, IEEE J. Quantum Electron. QE-14, 650 (1978).
[CrossRef]

JETP Lett. (1)

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, F. S. Faizullov, JETP Lett. 15, 109 (1972).

Opt. Lett. (1)

Phys. Rev. Lett. (1)

R. Y. Chiao, P. L. Kelley, E. Garmire, Phys. Rev. Lett. 17, 1158 (1966).
[CrossRef]

Other (9)

C. R. Wiley, Advanced Engineering Mathematics, 4th ed. (McGraw-Hill, New York, 1975), p. 328.

M. Sheif-Bahae, A. Said, E. W. Van Stryland, M. J. Soileau, in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1988), paper WZ4.

E. L. Kerr, in Damage in Laser Glass, A. J. Glass, A. H. Guenther, eds. (American Society for Testing and Materials, Philadelphia, Pa., 1969), pp. 23–42.
[CrossRef]

F. W. Quelle, in Damage in Laser Glass, A. J. Glass, A. H. Guenther, eds. (American Society for Testing and Materials, Philadelphia, Pa., 1969), pp. 110–116.
[CrossRef]

R. C. Weast, ed., CRC Handbook of Chemistry and Physics, 64th ed. (CRC Press, Boca Raton, Fla., 1983).

G. A. Rakuljic, “Photorefractive properties and applications of barium titanate and tungsten-bronze ferroelectrics,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1987), pp. 121–126.

C. J. Wetterer, L. P. Schelonka, M. A. Kramer, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1989), paper MD1; see also C. J. Wetterer, L. P. Schelonka, M. A. Kramer, Opt. Lett. 14, 874 (1989).
[CrossRef] [PubMed]

A. Yariv, R. A. Fisher, in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), p. 17.

B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985), pp. 4, 24.

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Figures (2)

Fig. 1
Fig. 1

Schematic of the thermal blooming phase-conjugation problem. The dashed curves indicate equiphase surfaces.

Fig. 2
Fig. 2

Characteristic scale sizes in the thermal blooming medium. Λ is the thermal grating spacing (≈λ/2), and 2w is the spot diameter.

Tables (1)

Tables Icon

Table 1 Thermal Constants and Characteristic Times for Air and Methanola

Equations (9)

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

E 1 = ψ ( r ¯ 1 , t 1 ) exp [ i ( ω 1 t 1 k 1 z 1 ) ] + c . c .
E 2 = f ( r ¯ 2 , t 2 ) exp [ i ( ω 2 t 2 + k 2 z 2 ) ] + c . c . ,
E = ψ ( r ¯ 1 , t 1 ) exp [ i ( ω 1 t 1 k 1 z 1 ) ] + f ( r ¯ 2 , t 2 ) × exp [ i ( ω 2 t 2 + k 2 z 2 ) ] + c . c .
2 E μ c 2 2 E t 2 = 0 ,
( r ¯ , t ) = 0 ( r ¯ , t ) + d 3 r 1 d 3 r 2 d t 1 d t 2 × 2 ( r ¯ r ¯ 1 , r ¯ r ¯ 2 , t t 1 , t t 2 ) × | E ( r ¯ 1 , r ¯ 2 , t 1 , t 2 ) | 2 .
2 ( r ¯ , t ) | E | 2 = 2 ( r ¯ , t ) { | ψ | 2 + | f | 2 + ψf * exp [ i ( ω 1 ω 2 ) t ( k 1 + k 2 ) z ] + c . c . } ,
( r ¯ , t ) = 0 ( r ¯ , t ) + d 3 r 1 d 3 r 2 d t 1 d t 2 × { 2 ( r ¯ r ¯ 1 , r ¯ r ¯ 2 , t t 1 , t t 2 ) × [ | ψ ( r ¯ 1 , t 1 ) | 2 + | f ( r ¯ 2 , t 2 ) | 2 + ψ ( r ¯ 1 , t 1 ) f * ( r ¯ 2 , t 2 ) + c . c . ] } .
2 u c p ρ k c u t = F ( r ¯ , t ) ,
= 0 + 2 ( r ¯ , t ) | E | 2 τ a ,

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