Abstract

We demonstrate both analytically and experimentally that second-order nonlinear interaction in a uniaxial crystal produces a holographic replica of one of the incident fields. In particular, we consider difference-frequency generation and directly calculate the field transformation that is produced by the nonlinear interaction for some simple but nontrivial two-dimensional objects, such as a long wire, a circular hole, and a regular net. Finally we show experimental results for such objects that validate the theoretical calculations.

© 2004 Optical Society of America

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References

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  1. A. H. Firester, “Parametric image conversion. I,” J. Appl. Phys. 40, 4842–4849 (1969).
    [CrossRef]
  2. A. H. Firester, “Parametric image conversion. II,” J. Appl. Phys. 40, 4849–4853 (1969).
    [CrossRef]
  3. A. H. Firester, “Image upconversion. III,” J. Appl. Phys. 41, 703–709 (1970).
    [CrossRef]
  4. Yu. N. Denisyuk, A. Andreoni, and M. A. C. Potenza, “Holographic properties of the effect of second-order harmonic cross-correlation of optical wavefields,” Opt. Mem. Neural Netw. 8, 123–137 (1999).
  5. A. Andreoni, M. Bondani, Yu. N. Denisyuk, and M. A. C. Potenza, “Holographic properties of the second harmonic cross-correlation of object and reference optical wave fields,” J. Opt. Soc. Am. B 17, 966–972 (2000).
    [CrossRef]
  6. Yu. N. Denisyuk, A. Andreoni, M. Bondani, and M. A. C. Potenza, “The formation of the holographic image of a diffusing object in the second-harmonic light generated by a non-linear material,” Opt. Spectrosc. 89, 113–120 (2000).
    [CrossRef]
  7. Yu. N. Denisyuk, A. Andreoni, M. Bondani, and M. A. C. Potenza, “Real-time holograms by second-harmonic cross-correlation of object and reference optical wave-fields,” Opt. Lett. 25, 890–892 (2000).
    [CrossRef]
  8. A. Andreoni, M. Bondani, and M. A. C. Potenza, “Combinational tasks performed by second harmonic generated holograms,” Opt. Lett. 25, 1570–1572 (2000).
    [CrossRef]
  9. A. Andreoni, M. Bondani, Yu. N. Denisyuk, M. A. C. Potenza, and E. Puddu, “Boolean algebra operations performed on optical bits by the generation of holographic fields through second-order non-linear interactions,” Rev. Sci. Instrum. 72, 2525–2531 (2001).
    [CrossRef]
  10. M. Bondani and A. Andreoni, “Holographic nature of three-wave mixing,” Phys. Rev. A 66, 033805 (2002).
    [CrossRef]
  11. M. Bondani, A. Allevi, and A. Andreoni, “Holography by nondegenerate χ(2) interactions,” J. Opt. Soc. Am. B 20, 1–13 (2003).
    [CrossRef]
  12. J. E. Midwinter, “Parametric infrared image converters,” IEEE J. Quantum Electron. 4, 716–720 (1968).
    [CrossRef]
  13. J. E. Midwinter, “Image conversion from 1.6 μm to the visible in lithium niobate,” Appl. Phys. Lett. 12, 68–70 (1968).
    [CrossRef]
  14. G. W. Faris and M. Banks, “Upconverting time gate for imaging through highly scattering media,” Opt. Lett. 19, 1813–1815 (1994).
    [CrossRef] [PubMed]
  15. F. Devaux, E. Lantz, A. Lacourt, D. Gindre, H. Maillotte, P. A. Doreau, and T. Laurent, “Picosecond parametric amplification of a monochromatic image,” Nonlinear Opt. 11, 25–37 (1995).
  16. F. Devaux and E. Lantz, “Transfer function of spatial frequencies in parametric image amplification: experimental analysis and application to picosecond spatial filtering,” Opt. Commun. 114, 295–300 (1995).
    [CrossRef]
  17. F. Devaux and E. Lantz, “Ultrahigh-speed imaging by parametric image amplification,” Opt. Commun. 118, 25–27 (1995).
    [CrossRef]
  18. A. Gavrielides, P. Peterson, and D. Cardimona, “Diffractive imaging in three-wave interactions,” J. Appl. Phys. 62, 2640–2645 (1987).
    [CrossRef]
  19. P. V. Avizonis, F. A. Hopf, W. D. Bomberger, S. F. Jacobs, A. Tomita, and K. H. Womack, “Optical phase conjugation in a lithium formate crystal,” Appl. Phys. Lett. 31, 435–437 (1977).
    [CrossRef]
  20. L. Lefort and A. Barthelemy, “Revisiting optical phase conjugation by difference-frequency generation,” Opt. Lett. 21, 848–850 (1996).
    [CrossRef] [PubMed]
  21. V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer-Verlag, Berlin, 1997).
    [CrossRef]
  22. D. Gabor, “Microscopy by reconstructed wave fronts,” Proc. R. Soc. London, Ser. A 197, 454–478 (1949).
    [CrossRef]
  23. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1988), p. 211.
  24. A. M. Gorlanov, N. I. Grishmanova, N. A. Sventsitskaya, and V. D. Solov’yov, “Angular characteristics of radiation from neodymium laser with wavefront conjugation under three-wave parametric interaction,” Kvantovaya Elektron. (Moscow) 5, 415–417 (1982).
  25. D. M. Pepper and A. Yariv, “Optical phase conjugation using three-wave and four-wave mixing via elastic photon scattering in transparent media,” in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), pp. 23–78.
    [CrossRef]
  26. M. R. Fewings and A. L. Gaeta, “Compensation of pulse distortions by phase conjugation via difference-frequency generation,” J. Opt. Soc. Am. B 17, 1522–1525 (2000).
    [CrossRef]
  27. V. N. Mikhailov, M. Bondani, F. Paleari, and A. Andreoni, “Optical-phase conjugation in difference-frequency generation,” J. Opt. Soc. Am. B 20, 1715–1723 (2003).
    [CrossRef]

2003 (2)

2002 (1)

M. Bondani and A. Andreoni, “Holographic nature of three-wave mixing,” Phys. Rev. A 66, 033805 (2002).
[CrossRef]

2001 (1)

A. Andreoni, M. Bondani, Yu. N. Denisyuk, M. A. C. Potenza, and E. Puddu, “Boolean algebra operations performed on optical bits by the generation of holographic fields through second-order non-linear interactions,” Rev. Sci. Instrum. 72, 2525–2531 (2001).
[CrossRef]

2000 (5)

1999 (1)

Yu. N. Denisyuk, A. Andreoni, and M. A. C. Potenza, “Holographic properties of the effect of second-order harmonic cross-correlation of optical wavefields,” Opt. Mem. Neural Netw. 8, 123–137 (1999).

1996 (1)

1995 (3)

F. Devaux, E. Lantz, A. Lacourt, D. Gindre, H. Maillotte, P. A. Doreau, and T. Laurent, “Picosecond parametric amplification of a monochromatic image,” Nonlinear Opt. 11, 25–37 (1995).

F. Devaux and E. Lantz, “Transfer function of spatial frequencies in parametric image amplification: experimental analysis and application to picosecond spatial filtering,” Opt. Commun. 114, 295–300 (1995).
[CrossRef]

F. Devaux and E. Lantz, “Ultrahigh-speed imaging by parametric image amplification,” Opt. Commun. 118, 25–27 (1995).
[CrossRef]

1994 (1)

1987 (1)

A. Gavrielides, P. Peterson, and D. Cardimona, “Diffractive imaging in three-wave interactions,” J. Appl. Phys. 62, 2640–2645 (1987).
[CrossRef]

1982 (1)

A. M. Gorlanov, N. I. Grishmanova, N. A. Sventsitskaya, and V. D. Solov’yov, “Angular characteristics of radiation from neodymium laser with wavefront conjugation under three-wave parametric interaction,” Kvantovaya Elektron. (Moscow) 5, 415–417 (1982).

1977 (1)

P. V. Avizonis, F. A. Hopf, W. D. Bomberger, S. F. Jacobs, A. Tomita, and K. H. Womack, “Optical phase conjugation in a lithium formate crystal,” Appl. Phys. Lett. 31, 435–437 (1977).
[CrossRef]

1970 (1)

A. H. Firester, “Image upconversion. III,” J. Appl. Phys. 41, 703–709 (1970).
[CrossRef]

1969 (2)

A. H. Firester, “Parametric image conversion. I,” J. Appl. Phys. 40, 4842–4849 (1969).
[CrossRef]

A. H. Firester, “Parametric image conversion. II,” J. Appl. Phys. 40, 4849–4853 (1969).
[CrossRef]

1968 (2)

J. E. Midwinter, “Parametric infrared image converters,” IEEE J. Quantum Electron. 4, 716–720 (1968).
[CrossRef]

J. E. Midwinter, “Image conversion from 1.6 μm to the visible in lithium niobate,” Appl. Phys. Lett. 12, 68–70 (1968).
[CrossRef]

1949 (1)

D. Gabor, “Microscopy by reconstructed wave fronts,” Proc. R. Soc. London, Ser. A 197, 454–478 (1949).
[CrossRef]

Allevi, A.

Andreoni, A.

M. Bondani, A. Allevi, and A. Andreoni, “Holography by nondegenerate χ(2) interactions,” J. Opt. Soc. Am. B 20, 1–13 (2003).
[CrossRef]

V. N. Mikhailov, M. Bondani, F. Paleari, and A. Andreoni, “Optical-phase conjugation in difference-frequency generation,” J. Opt. Soc. Am. B 20, 1715–1723 (2003).
[CrossRef]

M. Bondani and A. Andreoni, “Holographic nature of three-wave mixing,” Phys. Rev. A 66, 033805 (2002).
[CrossRef]

A. Andreoni, M. Bondani, Yu. N. Denisyuk, M. A. C. Potenza, and E. Puddu, “Boolean algebra operations performed on optical bits by the generation of holographic fields through second-order non-linear interactions,” Rev. Sci. Instrum. 72, 2525–2531 (2001).
[CrossRef]

Yu. N. Denisyuk, A. Andreoni, M. Bondani, and M. A. C. Potenza, “The formation of the holographic image of a diffusing object in the second-harmonic light generated by a non-linear material,” Opt. Spectrosc. 89, 113–120 (2000).
[CrossRef]

A. Andreoni, M. Bondani, Yu. N. Denisyuk, and M. A. C. Potenza, “Holographic properties of the second harmonic cross-correlation of object and reference optical wave fields,” J. Opt. Soc. Am. B 17, 966–972 (2000).
[CrossRef]

Yu. N. Denisyuk, A. Andreoni, M. Bondani, and M. A. C. Potenza, “Real-time holograms by second-harmonic cross-correlation of object and reference optical wave-fields,” Opt. Lett. 25, 890–892 (2000).
[CrossRef]

A. Andreoni, M. Bondani, and M. A. C. Potenza, “Combinational tasks performed by second harmonic generated holograms,” Opt. Lett. 25, 1570–1572 (2000).
[CrossRef]

Yu. N. Denisyuk, A. Andreoni, and M. A. C. Potenza, “Holographic properties of the effect of second-order harmonic cross-correlation of optical wavefields,” Opt. Mem. Neural Netw. 8, 123–137 (1999).

Avizonis, P. V.

P. V. Avizonis, F. A. Hopf, W. D. Bomberger, S. F. Jacobs, A. Tomita, and K. H. Womack, “Optical phase conjugation in a lithium formate crystal,” Appl. Phys. Lett. 31, 435–437 (1977).
[CrossRef]

Banks, M.

Barthelemy, A.

Bomberger, W. D.

P. V. Avizonis, F. A. Hopf, W. D. Bomberger, S. F. Jacobs, A. Tomita, and K. H. Womack, “Optical phase conjugation in a lithium formate crystal,” Appl. Phys. Lett. 31, 435–437 (1977).
[CrossRef]

Bondani, M.

M. Bondani, A. Allevi, and A. Andreoni, “Holography by nondegenerate χ(2) interactions,” J. Opt. Soc. Am. B 20, 1–13 (2003).
[CrossRef]

V. N. Mikhailov, M. Bondani, F. Paleari, and A. Andreoni, “Optical-phase conjugation in difference-frequency generation,” J. Opt. Soc. Am. B 20, 1715–1723 (2003).
[CrossRef]

M. Bondani and A. Andreoni, “Holographic nature of three-wave mixing,” Phys. Rev. A 66, 033805 (2002).
[CrossRef]

A. Andreoni, M. Bondani, Yu. N. Denisyuk, M. A. C. Potenza, and E. Puddu, “Boolean algebra operations performed on optical bits by the generation of holographic fields through second-order non-linear interactions,” Rev. Sci. Instrum. 72, 2525–2531 (2001).
[CrossRef]

Yu. N. Denisyuk, A. Andreoni, M. Bondani, and M. A. C. Potenza, “The formation of the holographic image of a diffusing object in the second-harmonic light generated by a non-linear material,” Opt. Spectrosc. 89, 113–120 (2000).
[CrossRef]

Yu. N. Denisyuk, A. Andreoni, M. Bondani, and M. A. C. Potenza, “Real-time holograms by second-harmonic cross-correlation of object and reference optical wave-fields,” Opt. Lett. 25, 890–892 (2000).
[CrossRef]

A. Andreoni, M. Bondani, Yu. N. Denisyuk, and M. A. C. Potenza, “Holographic properties of the second harmonic cross-correlation of object and reference optical wave fields,” J. Opt. Soc. Am. B 17, 966–972 (2000).
[CrossRef]

A. Andreoni, M. Bondani, and M. A. C. Potenza, “Combinational tasks performed by second harmonic generated holograms,” Opt. Lett. 25, 1570–1572 (2000).
[CrossRef]

Cardimona, D.

A. Gavrielides, P. Peterson, and D. Cardimona, “Diffractive imaging in three-wave interactions,” J. Appl. Phys. 62, 2640–2645 (1987).
[CrossRef]

Denisyuk, Yu. N.

A. Andreoni, M. Bondani, Yu. N. Denisyuk, M. A. C. Potenza, and E. Puddu, “Boolean algebra operations performed on optical bits by the generation of holographic fields through second-order non-linear interactions,” Rev. Sci. Instrum. 72, 2525–2531 (2001).
[CrossRef]

Yu. N. Denisyuk, A. Andreoni, M. Bondani, and M. A. C. Potenza, “The formation of the holographic image of a diffusing object in the second-harmonic light generated by a non-linear material,” Opt. Spectrosc. 89, 113–120 (2000).
[CrossRef]

A. Andreoni, M. Bondani, Yu. N. Denisyuk, and M. A. C. Potenza, “Holographic properties of the second harmonic cross-correlation of object and reference optical wave fields,” J. Opt. Soc. Am. B 17, 966–972 (2000).
[CrossRef]

Yu. N. Denisyuk, A. Andreoni, M. Bondani, and M. A. C. Potenza, “Real-time holograms by second-harmonic cross-correlation of object and reference optical wave-fields,” Opt. Lett. 25, 890–892 (2000).
[CrossRef]

Yu. N. Denisyuk, A. Andreoni, and M. A. C. Potenza, “Holographic properties of the effect of second-order harmonic cross-correlation of optical wavefields,” Opt. Mem. Neural Netw. 8, 123–137 (1999).

Devaux, F.

F. Devaux, E. Lantz, A. Lacourt, D. Gindre, H. Maillotte, P. A. Doreau, and T. Laurent, “Picosecond parametric amplification of a monochromatic image,” Nonlinear Opt. 11, 25–37 (1995).

F. Devaux and E. Lantz, “Transfer function of spatial frequencies in parametric image amplification: experimental analysis and application to picosecond spatial filtering,” Opt. Commun. 114, 295–300 (1995).
[CrossRef]

F. Devaux and E. Lantz, “Ultrahigh-speed imaging by parametric image amplification,” Opt. Commun. 118, 25–27 (1995).
[CrossRef]

Doreau, P. A.

F. Devaux, E. Lantz, A. Lacourt, D. Gindre, H. Maillotte, P. A. Doreau, and T. Laurent, “Picosecond parametric amplification of a monochromatic image,” Nonlinear Opt. 11, 25–37 (1995).

Faris, G. W.

Fewings, M. R.

Firester, A. H.

A. H. Firester, “Image upconversion. III,” J. Appl. Phys. 41, 703–709 (1970).
[CrossRef]

A. H. Firester, “Parametric image conversion. I,” J. Appl. Phys. 40, 4842–4849 (1969).
[CrossRef]

A. H. Firester, “Parametric image conversion. II,” J. Appl. Phys. 40, 4849–4853 (1969).
[CrossRef]

Gabor, D.

D. Gabor, “Microscopy by reconstructed wave fronts,” Proc. R. Soc. London, Ser. A 197, 454–478 (1949).
[CrossRef]

Gaeta, A. L.

Gavrielides, A.

A. Gavrielides, P. Peterson, and D. Cardimona, “Diffractive imaging in three-wave interactions,” J. Appl. Phys. 62, 2640–2645 (1987).
[CrossRef]

Gindre, D.

F. Devaux, E. Lantz, A. Lacourt, D. Gindre, H. Maillotte, P. A. Doreau, and T. Laurent, “Picosecond parametric amplification of a monochromatic image,” Nonlinear Opt. 11, 25–37 (1995).

Gorlanov, A. M.

A. M. Gorlanov, N. I. Grishmanova, N. A. Sventsitskaya, and V. D. Solov’yov, “Angular characteristics of radiation from neodymium laser with wavefront conjugation under three-wave parametric interaction,” Kvantovaya Elektron. (Moscow) 5, 415–417 (1982).

Grishmanova, N. I.

A. M. Gorlanov, N. I. Grishmanova, N. A. Sventsitskaya, and V. D. Solov’yov, “Angular characteristics of radiation from neodymium laser with wavefront conjugation under three-wave parametric interaction,” Kvantovaya Elektron. (Moscow) 5, 415–417 (1982).

Hopf, F. A.

P. V. Avizonis, F. A. Hopf, W. D. Bomberger, S. F. Jacobs, A. Tomita, and K. H. Womack, “Optical phase conjugation in a lithium formate crystal,” Appl. Phys. Lett. 31, 435–437 (1977).
[CrossRef]

Jacobs, S. F.

P. V. Avizonis, F. A. Hopf, W. D. Bomberger, S. F. Jacobs, A. Tomita, and K. H. Womack, “Optical phase conjugation in a lithium formate crystal,” Appl. Phys. Lett. 31, 435–437 (1977).
[CrossRef]

Lacourt, A.

F. Devaux, E. Lantz, A. Lacourt, D. Gindre, H. Maillotte, P. A. Doreau, and T. Laurent, “Picosecond parametric amplification of a monochromatic image,” Nonlinear Opt. 11, 25–37 (1995).

Lantz, E.

F. Devaux, E. Lantz, A. Lacourt, D. Gindre, H. Maillotte, P. A. Doreau, and T. Laurent, “Picosecond parametric amplification of a monochromatic image,” Nonlinear Opt. 11, 25–37 (1995).

F. Devaux and E. Lantz, “Ultrahigh-speed imaging by parametric image amplification,” Opt. Commun. 118, 25–27 (1995).
[CrossRef]

F. Devaux and E. Lantz, “Transfer function of spatial frequencies in parametric image amplification: experimental analysis and application to picosecond spatial filtering,” Opt. Commun. 114, 295–300 (1995).
[CrossRef]

Laurent, T.

F. Devaux, E. Lantz, A. Lacourt, D. Gindre, H. Maillotte, P. A. Doreau, and T. Laurent, “Picosecond parametric amplification of a monochromatic image,” Nonlinear Opt. 11, 25–37 (1995).

Lefort, L.

Maillotte, H.

F. Devaux, E. Lantz, A. Lacourt, D. Gindre, H. Maillotte, P. A. Doreau, and T. Laurent, “Picosecond parametric amplification of a monochromatic image,” Nonlinear Opt. 11, 25–37 (1995).

Midwinter, J. E.

J. E. Midwinter, “Parametric infrared image converters,” IEEE J. Quantum Electron. 4, 716–720 (1968).
[CrossRef]

J. E. Midwinter, “Image conversion from 1.6 μm to the visible in lithium niobate,” Appl. Phys. Lett. 12, 68–70 (1968).
[CrossRef]

Mikhailov, V. N.

Paleari, F.

Peterson, P.

A. Gavrielides, P. Peterson, and D. Cardimona, “Diffractive imaging in three-wave interactions,” J. Appl. Phys. 62, 2640–2645 (1987).
[CrossRef]

Potenza, M. A. C.

A. Andreoni, M. Bondani, Yu. N. Denisyuk, M. A. C. Potenza, and E. Puddu, “Boolean algebra operations performed on optical bits by the generation of holographic fields through second-order non-linear interactions,” Rev. Sci. Instrum. 72, 2525–2531 (2001).
[CrossRef]

Yu. N. Denisyuk, A. Andreoni, M. Bondani, and M. A. C. Potenza, “The formation of the holographic image of a diffusing object in the second-harmonic light generated by a non-linear material,” Opt. Spectrosc. 89, 113–120 (2000).
[CrossRef]

A. Andreoni, M. Bondani, and M. A. C. Potenza, “Combinational tasks performed by second harmonic generated holograms,” Opt. Lett. 25, 1570–1572 (2000).
[CrossRef]

Yu. N. Denisyuk, A. Andreoni, M. Bondani, and M. A. C. Potenza, “Real-time holograms by second-harmonic cross-correlation of object and reference optical wave-fields,” Opt. Lett. 25, 890–892 (2000).
[CrossRef]

A. Andreoni, M. Bondani, Yu. N. Denisyuk, and M. A. C. Potenza, “Holographic properties of the second harmonic cross-correlation of object and reference optical wave fields,” J. Opt. Soc. Am. B 17, 966–972 (2000).
[CrossRef]

Yu. N. Denisyuk, A. Andreoni, and M. A. C. Potenza, “Holographic properties of the effect of second-order harmonic cross-correlation of optical wavefields,” Opt. Mem. Neural Netw. 8, 123–137 (1999).

Puddu, E.

A. Andreoni, M. Bondani, Yu. N. Denisyuk, M. A. C. Potenza, and E. Puddu, “Boolean algebra operations performed on optical bits by the generation of holographic fields through second-order non-linear interactions,” Rev. Sci. Instrum. 72, 2525–2531 (2001).
[CrossRef]

Solov’yov, V. D.

A. M. Gorlanov, N. I. Grishmanova, N. A. Sventsitskaya, and V. D. Solov’yov, “Angular characteristics of radiation from neodymium laser with wavefront conjugation under three-wave parametric interaction,” Kvantovaya Elektron. (Moscow) 5, 415–417 (1982).

Sventsitskaya, N. A.

A. M. Gorlanov, N. I. Grishmanova, N. A. Sventsitskaya, and V. D. Solov’yov, “Angular characteristics of radiation from neodymium laser with wavefront conjugation under three-wave parametric interaction,” Kvantovaya Elektron. (Moscow) 5, 415–417 (1982).

Tomita, A.

P. V. Avizonis, F. A. Hopf, W. D. Bomberger, S. F. Jacobs, A. Tomita, and K. H. Womack, “Optical phase conjugation in a lithium formate crystal,” Appl. Phys. Lett. 31, 435–437 (1977).
[CrossRef]

Womack, K. H.

P. V. Avizonis, F. A. Hopf, W. D. Bomberger, S. F. Jacobs, A. Tomita, and K. H. Womack, “Optical phase conjugation in a lithium formate crystal,” Appl. Phys. Lett. 31, 435–437 (1977).
[CrossRef]

Appl. Phys. Lett. (2)

P. V. Avizonis, F. A. Hopf, W. D. Bomberger, S. F. Jacobs, A. Tomita, and K. H. Womack, “Optical phase conjugation in a lithium formate crystal,” Appl. Phys. Lett. 31, 435–437 (1977).
[CrossRef]

J. E. Midwinter, “Image conversion from 1.6 μm to the visible in lithium niobate,” Appl. Phys. Lett. 12, 68–70 (1968).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. E. Midwinter, “Parametric infrared image converters,” IEEE J. Quantum Electron. 4, 716–720 (1968).
[CrossRef]

J. Appl. Phys. (4)

A. H. Firester, “Parametric image conversion. I,” J. Appl. Phys. 40, 4842–4849 (1969).
[CrossRef]

A. H. Firester, “Parametric image conversion. II,” J. Appl. Phys. 40, 4849–4853 (1969).
[CrossRef]

A. H. Firester, “Image upconversion. III,” J. Appl. Phys. 41, 703–709 (1970).
[CrossRef]

A. Gavrielides, P. Peterson, and D. Cardimona, “Diffractive imaging in three-wave interactions,” J. Appl. Phys. 62, 2640–2645 (1987).
[CrossRef]

J. Opt. Soc. Am. B (4)

Kvantovaya Elektron. (Moscow) (1)

A. M. Gorlanov, N. I. Grishmanova, N. A. Sventsitskaya, and V. D. Solov’yov, “Angular characteristics of radiation from neodymium laser with wavefront conjugation under three-wave parametric interaction,” Kvantovaya Elektron. (Moscow) 5, 415–417 (1982).

Nonlinear Opt. (1)

F. Devaux, E. Lantz, A. Lacourt, D. Gindre, H. Maillotte, P. A. Doreau, and T. Laurent, “Picosecond parametric amplification of a monochromatic image,” Nonlinear Opt. 11, 25–37 (1995).

Opt. Commun. (2)

F. Devaux and E. Lantz, “Transfer function of spatial frequencies in parametric image amplification: experimental analysis and application to picosecond spatial filtering,” Opt. Commun. 114, 295–300 (1995).
[CrossRef]

F. Devaux and E. Lantz, “Ultrahigh-speed imaging by parametric image amplification,” Opt. Commun. 118, 25–27 (1995).
[CrossRef]

Opt. Lett. (4)

Opt. Mem. Neural Netw. (1)

Yu. N. Denisyuk, A. Andreoni, and M. A. C. Potenza, “Holographic properties of the effect of second-order harmonic cross-correlation of optical wavefields,” Opt. Mem. Neural Netw. 8, 123–137 (1999).

Opt. Spectrosc. (1)

Yu. N. Denisyuk, A. Andreoni, M. Bondani, and M. A. C. Potenza, “The formation of the holographic image of a diffusing object in the second-harmonic light generated by a non-linear material,” Opt. Spectrosc. 89, 113–120 (2000).
[CrossRef]

Phys. Rev. A (1)

M. Bondani and A. Andreoni, “Holographic nature of three-wave mixing,” Phys. Rev. A 66, 033805 (2002).
[CrossRef]

Proc. R. Soc. London, Ser. A (1)

D. Gabor, “Microscopy by reconstructed wave fronts,” Proc. R. Soc. London, Ser. A 197, 454–478 (1949).
[CrossRef]

Rev. Sci. Instrum. (1)

A. Andreoni, M. Bondani, Yu. N. Denisyuk, M. A. C. Potenza, and E. Puddu, “Boolean algebra operations performed on optical bits by the generation of holographic fields through second-order non-linear interactions,” Rev. Sci. Instrum. 72, 2525–2531 (2001).
[CrossRef]

Other (3)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1988), p. 211.

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer-Verlag, Berlin, 1997).
[CrossRef]

D. M. Pepper and A. Yariv, “Optical phase conjugation using three-wave and four-wave mixing via elastic photon scattering in transparent media,” in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), pp. 23–78.
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Noncollinear three-wave interaction in a type I uniaxial crystal. (X, Y, Z), crystal reference frame with Z parallel to the optical axis; (x, y, z), laboratory reference frame with the (x, y) plane coinciding with the crystal entrance face; α, tuning angle.

Fig. 2
Fig. 2

Schematics of the experimental setups cases (a) and (b). See text for details.

Fig. 3
Fig. 3

Propagation geometry for the field diffracted by the object and for the holographic field generated by the nonlinear crystal whose entrance face is located at the Fraunhofer diffraction plane.

Fig. 4
Fig. 4

Images of the wire. Top, 60×-magnified image; bottom, virtual holographic image [case (a)] detected by the CCD sensor on insertion of a converging lens between the BBO crystal and the CCD camera.

Fig. 5
Fig. 5

Images of the hole. Top, 200×-magnified image; bottom, real holographic image [case (b)] detected by the CCD sensor.

Fig. 6
Fig. 6

Images of the net. Top, virtual holographic image [case (a)] detected by the CCD sensor on insertion of a converging lens between the BBO crystal and the CCD camera. Center, 200×-magnified image. Bottom real holographic image [case (b)] detected by the CCD sensor.

Fig. 7
Fig. 7

Virtual holographic image of a stainless-steel net made from ∼40-µm wires spaced apart by squares ∼40 µm2 on a side [case (a)] detected by the CCD sensor on insertion of a converging lens between the BBO crystal and the CCD camera.

Equations (47)

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E1(r, t)=xˆ2 2η0ω1n11/2a1(r)exp[-i(k1 sin ϑ1y+k1 cos ϑ1z-ω1t)]+c.c.,
E2(r, t)=xˆ2 2η0ω2n21/2a2(r)exp[-i(k2 sin ϑ2y+k2 cos ϑ2z-ω2t)]+c.c.,
E3(r, t)=12 2η0ω3n31/2[yˆa3y(r)+zˆa3z(r)]×exp[-i(k3 sin ϑ3y+k3 cos ϑ3z-ω3t)]+c.c.,
sin ϑ1 a1(r)y+cos ϑ1 a1(r)z
=i[g+a3y(r)+g-a3z(r)]a2*(r)×exp[-i(Δky+Δkz)],
sin ϑ2 a2(r)y+cos ϑ2 a2(r)z
=i[g+a3y(r)+g-a3z(r)]a1*(r)×exp[-i(Δky+Δkz)],
sin ϑ3 a3y(r)y+cos ϑ3 a3y(r)z
=ig+a1(r)a2(r)exp[i(Δky+Δkz)],
sin ϑ3 a3z(r)y+cos ϑ3 a3z(r)z
=ig-a1(r)a2(r)exp[i(Δky+Δkz)],
g+=2ω1ω2ω3η03n1n2n31/2[d22 cos(α-ϑ3)+d31 sin(α-ϑ3)],
g-=2ω1ω2ω3η03n1n2n31/2[d22 sin(α-ϑ3)-d31 cos(α-ϑ3)],
Δk=k3 cos ϑ3-k1 cos ϑ1-k2 cos ϑ2,
Δk=k3 sin ϑ3-k1 sin ϑ1-k2 sin ϑ2
a2(y, z)=a2(0, 0) cosg|a1(0, 0)|sin(ϑ2-ϑ3)[(cos ϑ3-cos ϑ1)y-(sin ϑ3-sin ϑ1)z]+i geffga3(0, 0) a1*(0, 0)|a1(0, 0)| sing|a1(0, 0)|sin(ϑ1-ϑ3)×[(cos ϑ3-cos ϑ1)y-(sin ϑ3-sin ϑ1)z],
a3(y, z)=geffga3(0, 0)cosg|a1(0, 0)|sin(ϑ2-ϑ3)[(cos ϑ3-cos ϑ1)y-(sin ϑ3-sin ϑ1)z]+ia2(0, 0) a1*(0, 0)|a1(0, 0)| sing|a1(0, 0)|sin(ϑ1-ϑ3)×[(cos ϑ3-cos ϑ1)y-(sin ϑ3-sin ϑ1)z],
a1(y, z)=a1(0, 0)coshgeff |a3(0, 0)|sin(ϑ1-ϑ2)[(cos ϑ2-cos ϑ1)y-(sin ϑ2-sin ϑ1)z]+ia2*(0, 0) a3(0, 0)|a3(0, 0)| sinhgeff |a3(0, 0)|sin(ϑ1-ϑ2)×[(cos ϑ2-cos ϑ1)y-(sin ϑ2-sin ϑ1)z],
a2(y, z)=a2(0, 0)coshgeff |a3(0, 0)|sin(ϑ1-ϑ2)[(cos ϑ2-cos ϑ1)y-(sin ϑ2-sin ϑ1)z]+ia1*(0, 0) a3(0, 0)|a3(0, 0)| sinhgeff |a3(0, 0)|sin(ϑ1-ϑ2)×[(cos ϑ2-cos ϑ1)y-(sin ϑ2-sin ϑ1)z],
g=(g+2+g-2)1/2,
geff2ω1ω2ω3η03n1n2n31/2(d22 cos α+d31 sin α).
a2(y, z)=geffg|a3(0, 0)|sing|a1(0, 0)|sin(ϑ1-ϑ3)×[(cos ϑ3-cos ϑ1)y-(sin ϑ3-sin ϑ1)z]×expiΛ3(0, 0)-Λ1(0, 0)+π2.
E2(r, t)=xˆ2 2η0ω2n21/2 geffg|a3(0, 0)|×sing|a1(0, 0)|sin(ϑ1-ϑ3)[(cos ϑ3-cos ϑ1)y-(sin ϑ3-sin ϑ1)z]×expiΛ3(0, 0)-Λ1(0, 0)+π2×exp[-i(k2 sin ϑ2y+k2 cos ϑ2z-ω2t)]+c.c.
a2(y, z)=|a1(0, 0)|sinhgeff |a3(0, 0)|sin(ϑ1-ϑ2)[(cos ϑ2-cos ϑ1)y-(sin ϑ2-sin ϑ1)z]×expiΛ3(0, 0)-Λ1(0, 0)+π2
E2(r, t)=xˆ2 2η0ω2n21/2|a1(0, 0)|×sinhgeff |a3(0, 0)|sin(ϑ1-ϑ2)[(cos ϑ2-cos ϑ1)y-(sin ϑ2-sin ϑ1)z]×expiΛ3(0, 0)-Λ1(0, 0)+π2×exp[-i(k2 sin ϑ2y+k2 cos ϑ2z-ω2t)]+c.c.
φ2(r)=Λ3(0, 0)-Λ1(0, 0)+π2-k2·r,
U(xF, yF, zF)=k2πizF exp(-ikzF)exp-i k(xF2+yF22zF×UO(xO, yO, zO)×expi kzF(xFxO+yFyO)dxOdyO,
Uw(xF, yF, zF)=AOwδ[kyF/(2πzF)]-AOw d2πizF exp(-ikzF)×exp-i kyF22zF sin[kdyF/(2πzF)][kdyF/(2πzF)].
Uh(xF, yF, zF)=AOh kR2izF exp(-ikzF)×exp-i k(xF2+yF2)2zF×J1[kR(xF2+yF2)1/2/zF][kR(xF2+yF2)1/2/zF],
Um(xF, yF, zF)
=AOm 2kl2iπzF exp(-ikzF)exp-i k(xF2+yF2)2zF×m=0Mexp-i kxF4zF(d+l)(2m+1)×n=0Nexp-i kyF4zF(d+l)(2n+1)×sin[klxF/(2zF)][klxF/(2zF)] sin[klyF/(2zF)][klyF/(2zF)].
E2(xout, yout, zout, t)
=xˆ2 2η0ω2n21/2|a1(xF, yF, zF)|×expiΛ3(xF, yF, zF)-Λ1(xF, yF, zF)+π2×sinhgeff |a3(xF, yF, zF)|sin(ϑ1-ϑ2)×[(cos ϑ2-cos ϑ1)(yout-yF)-(sin ϑ2-sin ϑ1)×(zout-zF)]exp[-i(k2 sin ϑ2(yout-yF)+k2 cos ϑ2(zout-zF)-ω2t)]+c.c.
E2(xout, yout, zout, t)
=xˆ2 2η0ω2n21/2|a1(xF, yF, zF)|×expiΛ3(xF, yF, zF)-Λ1(xF, yF, zF)+π2×sinhgeff|a3(xF, yF, zF)|cos ϑ2L×exp-ik2cos ϑ2L-ω2t+c.c.,
|a1(xF, yF, zF)|
AOh k1R2zF J1[k1R(xF2+yF2)1/2/zF][k1R(xF2+yF2)1/2/zF]AOh k1R2zF J1[k1R(sin β12+sin ϑ12)1/2]k1R(sin β12+sin ϑ12)1/2,
Λ1(xF, yF, zF)
-π2-ik1zF-i k1(xF2+yF2)2zF-π2-ik1zF-i k12zF(sin β12+sin ϑ12),
E2(xout, yout, zout, t)
xˆ2 2η0ω2n21/2
×AOh k2R2izH J1[k2R(sin β22+sin ϑ22)1/2]k2R(sin β22+sin ϑ22)1/2×exp(-ik2zH)×exp-i k22zH(sin β22+sin ϑ22)×expiΛ3(xF, yF, zF)+π2×sinhgeff|a3(xF, yF, zF)|cos ϑ2L×exp-ik2cos ϑ2L-ω2t+c.c.,
zH=-(k2/k1)zF.
E2(xout, yout, zout, t)
xˆ2 2η0ω2n21/2 geffg
×AOh k2R2izH J1[k2R(sin β22+sin ϑ22)1/2]k2R(sin β22+sin ϑ22)1/2×exp(ik2zH)×expi k22zH(sin β22+sin ϑ22)×expi-Λ1(xF, yF, zF)+π2×sinhg|a3(xF, yF, zF)|cos ϑ2L×exp-ik2cos ϑ2L-ω2t+c.c.,
zH=(k2/k3)zF.

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