Abstract

A nonlinear optical technique is described that performs, essentially instantaneously, the functions of spatial correlation and convolution of spatially encoded waves. These real-time operations are accomplished by mixing spatially dependent optical fields in the Fourier-transform plane of a lens system. The use of a degenerate four-wave mixing scheme eliminates (in the Fresnel approximation) phase-matching restrictions and (optical) frequency-scaling factors. Spatial bandwidth-gain considerations and numerical examples, as well as applications to nonlinear microscopy, are presented.

© 1978 Optical Society of America

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  1. A. B. Van der Lugt, IEEE Trans. Inform. Theory IT-10, 2 (1964).
  2. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  3. A. Yariv, Appl. Phys. Lett. 28, 89 (1976).
    [CrossRef]
  4. A. Yariv, J. Opt. Soc. Am. 66, 301 (1976).
    [CrossRef]
  5. R. A. Eremeeva, V. A. Kudryashov, I. N. Matrieev, T. G. Usacheva, A. I. Chekemenev, Sov. J. Quantum Electron. 5, 1429 (1976).
    [CrossRef]
  6. R. W. Hellwarth, J. Opt. Soc. Am. 67, 1 (1977).
    [CrossRef]
  7. A. Yariv, D. M. Pepper, Opt. Lett. 1, 16 (1977).
    [CrossRef] [PubMed]
  8. P. D. Maker, R. W. Terhune, Phys. Rev. 137, A801 (1965).
    [CrossRef]
  9. See, for example, A. Yariv, Quantum Electronics (Wiley, New York, 1975), 2nd ed.
  10. D. M. Pepper, D. Fekete, A. Yariv, “Observation of amplified phase conjugate reflection and optical parametric oscillation by degenerate four-wave mixing in a transparent medium,” submitted to Appl. Phys. Lett.; D. M. Bloom, P. F. Liao, N. P. Economou, Opt. Lett. 2, 58 (1978).
  11. D. M. Bloom, G. C. Bjorklund, Appl. Phys. Lett. 31, 592 (1977); S. M. Jensen, R. W. Hellwarth, Appl. Phys. Lett. 32, 166 (1978).
    [CrossRef]
  12. A. Yariv, Opt. Commun. 25, 23 (1978).
    [CrossRef]
  13. See, for example, B. Chen, E. Marom, A. Lee, Appl. Phys. Lett. 31, 263 (1977), and references therein.
    [CrossRef]
  14. A. Yariv, J. AuYeung, D. Fekete, D. M. Pepper, Appl. Phys. Lett. 32, 635 (1978).
    [CrossRef]
  15. R. W. Hellwarth, P. Christensen, Opt. Commun. 12, 318 (1974).
    [CrossRef]

1978

A. Yariv, Opt. Commun. 25, 23 (1978).
[CrossRef]

A. Yariv, J. AuYeung, D. Fekete, D. M. Pepper, Appl. Phys. Lett. 32, 635 (1978).
[CrossRef]

1977

See, for example, B. Chen, E. Marom, A. Lee, Appl. Phys. Lett. 31, 263 (1977), and references therein.
[CrossRef]

D. M. Bloom, G. C. Bjorklund, Appl. Phys. Lett. 31, 592 (1977); S. M. Jensen, R. W. Hellwarth, Appl. Phys. Lett. 32, 166 (1978).
[CrossRef]

A. Yariv, D. M. Pepper, Opt. Lett. 1, 16 (1977).
[CrossRef] [PubMed]

R. W. Hellwarth, J. Opt. Soc. Am. 67, 1 (1977).
[CrossRef]

1976

A. Yariv, J. Opt. Soc. Am. 66, 301 (1976).
[CrossRef]

A. Yariv, Appl. Phys. Lett. 28, 89 (1976).
[CrossRef]

R. A. Eremeeva, V. A. Kudryashov, I. N. Matrieev, T. G. Usacheva, A. I. Chekemenev, Sov. J. Quantum Electron. 5, 1429 (1976).
[CrossRef]

1974

R. W. Hellwarth, P. Christensen, Opt. Commun. 12, 318 (1974).
[CrossRef]

1965

P. D. Maker, R. W. Terhune, Phys. Rev. 137, A801 (1965).
[CrossRef]

1964

A. B. Van der Lugt, IEEE Trans. Inform. Theory IT-10, 2 (1964).

AuYeung, J.

A. Yariv, J. AuYeung, D. Fekete, D. M. Pepper, Appl. Phys. Lett. 32, 635 (1978).
[CrossRef]

Bjorklund, G. C.

D. M. Bloom, G. C. Bjorklund, Appl. Phys. Lett. 31, 592 (1977); S. M. Jensen, R. W. Hellwarth, Appl. Phys. Lett. 32, 166 (1978).
[CrossRef]

Bloom, D. M.

D. M. Bloom, G. C. Bjorklund, Appl. Phys. Lett. 31, 592 (1977); S. M. Jensen, R. W. Hellwarth, Appl. Phys. Lett. 32, 166 (1978).
[CrossRef]

Chekemenev, A. I.

R. A. Eremeeva, V. A. Kudryashov, I. N. Matrieev, T. G. Usacheva, A. I. Chekemenev, Sov. J. Quantum Electron. 5, 1429 (1976).
[CrossRef]

Chen, B.

See, for example, B. Chen, E. Marom, A. Lee, Appl. Phys. Lett. 31, 263 (1977), and references therein.
[CrossRef]

Christensen, P.

R. W. Hellwarth, P. Christensen, Opt. Commun. 12, 318 (1974).
[CrossRef]

Eremeeva, R. A.

R. A. Eremeeva, V. A. Kudryashov, I. N. Matrieev, T. G. Usacheva, A. I. Chekemenev, Sov. J. Quantum Electron. 5, 1429 (1976).
[CrossRef]

Fekete, D.

A. Yariv, J. AuYeung, D. Fekete, D. M. Pepper, Appl. Phys. Lett. 32, 635 (1978).
[CrossRef]

D. M. Pepper, D. Fekete, A. Yariv, “Observation of amplified phase conjugate reflection and optical parametric oscillation by degenerate four-wave mixing in a transparent medium,” submitted to Appl. Phys. Lett.; D. M. Bloom, P. F. Liao, N. P. Economou, Opt. Lett. 2, 58 (1978).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Hellwarth, R. W.

R. W. Hellwarth, J. Opt. Soc. Am. 67, 1 (1977).
[CrossRef]

R. W. Hellwarth, P. Christensen, Opt. Commun. 12, 318 (1974).
[CrossRef]

Kudryashov, V. A.

R. A. Eremeeva, V. A. Kudryashov, I. N. Matrieev, T. G. Usacheva, A. I. Chekemenev, Sov. J. Quantum Electron. 5, 1429 (1976).
[CrossRef]

Lee, A.

See, for example, B. Chen, E. Marom, A. Lee, Appl. Phys. Lett. 31, 263 (1977), and references therein.
[CrossRef]

Maker, P. D.

P. D. Maker, R. W. Terhune, Phys. Rev. 137, A801 (1965).
[CrossRef]

Marom, E.

See, for example, B. Chen, E. Marom, A. Lee, Appl. Phys. Lett. 31, 263 (1977), and references therein.
[CrossRef]

Matrieev, I. N.

R. A. Eremeeva, V. A. Kudryashov, I. N. Matrieev, T. G. Usacheva, A. I. Chekemenev, Sov. J. Quantum Electron. 5, 1429 (1976).
[CrossRef]

Pepper, D. M.

A. Yariv, J. AuYeung, D. Fekete, D. M. Pepper, Appl. Phys. Lett. 32, 635 (1978).
[CrossRef]

A. Yariv, D. M. Pepper, Opt. Lett. 1, 16 (1977).
[CrossRef] [PubMed]

D. M. Pepper, D. Fekete, A. Yariv, “Observation of amplified phase conjugate reflection and optical parametric oscillation by degenerate four-wave mixing in a transparent medium,” submitted to Appl. Phys. Lett.; D. M. Bloom, P. F. Liao, N. P. Economou, Opt. Lett. 2, 58 (1978).

Terhune, R. W.

P. D. Maker, R. W. Terhune, Phys. Rev. 137, A801 (1965).
[CrossRef]

Usacheva, T. G.

R. A. Eremeeva, V. A. Kudryashov, I. N. Matrieev, T. G. Usacheva, A. I. Chekemenev, Sov. J. Quantum Electron. 5, 1429 (1976).
[CrossRef]

Van der Lugt, A. B.

A. B. Van der Lugt, IEEE Trans. Inform. Theory IT-10, 2 (1964).

Yariv, A.

A. Yariv, J. AuYeung, D. Fekete, D. M. Pepper, Appl. Phys. Lett. 32, 635 (1978).
[CrossRef]

A. Yariv, Opt. Commun. 25, 23 (1978).
[CrossRef]

A. Yariv, D. M. Pepper, Opt. Lett. 1, 16 (1977).
[CrossRef] [PubMed]

A. Yariv, Appl. Phys. Lett. 28, 89 (1976).
[CrossRef]

A. Yariv, J. Opt. Soc. Am. 66, 301 (1976).
[CrossRef]

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

D. M. Pepper, D. Fekete, A. Yariv, “Observation of amplified phase conjugate reflection and optical parametric oscillation by degenerate four-wave mixing in a transparent medium,” submitted to Appl. Phys. Lett.; D. M. Bloom, P. F. Liao, N. P. Economou, Opt. Lett. 2, 58 (1978).

Appl. Phys. Lett.

D. M. Bloom, G. C. Bjorklund, Appl. Phys. Lett. 31, 592 (1977); S. M. Jensen, R. W. Hellwarth, Appl. Phys. Lett. 32, 166 (1978).
[CrossRef]

See, for example, B. Chen, E. Marom, A. Lee, Appl. Phys. Lett. 31, 263 (1977), and references therein.
[CrossRef]

A. Yariv, J. AuYeung, D. Fekete, D. M. Pepper, Appl. Phys. Lett. 32, 635 (1978).
[CrossRef]

A. Yariv, Appl. Phys. Lett. 28, 89 (1976).
[CrossRef]

IEEE Trans. Inform. Theory

A. B. Van der Lugt, IEEE Trans. Inform. Theory IT-10, 2 (1964).

J. Opt. Soc. Am.

Opt. Commun.

R. W. Hellwarth, P. Christensen, Opt. Commun. 12, 318 (1974).
[CrossRef]

A. Yariv, Opt. Commun. 25, 23 (1978).
[CrossRef]

Opt. Lett.

Phys. Rev.

P. D. Maker, R. W. Terhune, Phys. Rev. 137, A801 (1965).
[CrossRef]

Sov. J. Quantum Electron.

R. A. Eremeeva, V. A. Kudryashov, I. N. Matrieev, T. G. Usacheva, A. I. Chekemenev, Sov. J. Quantum Electron. 5, 1429 (1976).
[CrossRef]

Other

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

D. M. Pepper, D. Fekete, A. Yariv, “Observation of amplified phase conjugate reflection and optical parametric oscillation by degenerate four-wave mixing in a transparent medium,” submitted to Appl. Phys. Lett.; D. M. Bloom, P. F. Liao, N. P. Economou, Opt. Lett. 2, 58 (1978).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

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