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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  1. A. H. Firester, “Parametric image conversion. I,” J. Appl. Phys. 40, 4842–4849 (1969).
  2. A. H. Firester, “Parametric image conversion. II,” J. Appl. Phys. 40, 4849–4853 (1969).
  3. A. H. Firester, “Image upconversion. III,” J. Appl. Phys. 41, 703–709 (1970).
  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).
  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).
  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).
  8. A. Andreoni, M. Bondani, and M. A. C. Potenza, “Combinational tasks performed by second harmonic generated holograms,” Opt. Lett. 25, 1570–1572 (2000).
  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).
  10. M. Bondani and A. Andreoni, “Holographic nature of three-wave mixing,” Phys. Rev. A 66, 033805 (2002).
  11. M. Bondani, A. Allevi, and A. Andreoni, “Holography by nondegenerate χ(2) interactions,” J. Opt. Soc. Am. B 20, 1–13 (2003).
  12. J. E. Midwinter, “Parametric infrared image converters,” IEEE J. Quantum Electron. 4, 716–720 (1968).
  13. J. E. Midwinter, “Image conversion from 1.6 μm to the visible in lithium niobate,” Appl. Phys. Lett. 12, 68–70 (1968).
  14. G. W. Faris and M. Banks, “Upconverting time gate for imaging through highly scattering media,” Opt. Lett. 19, 1813–1815 (1994).
  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).
  17. F. Devaux and E. Lantz, “Ultrahigh-speed imaging by parametric image amplification,” Opt. Commun. 118, 25–27 (1995).
  18. A. Gavrielides, P. Peterson, and D. Cardimona, “Diffractive imaging in three-wave interactions,” J. Appl. Phys. 62, 2640–2645 (1987).
  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).
  20. L. Lefort and A. Barthelemy, “Revisiting optical phase conjugation by difference-frequency generation,” Opt. Lett. 21, 848–850 (1996).
  21. V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer-Verlag, Berlin, 1997).
  22. D. Gabor, “Microscopy by reconstructed wave fronts,” Proc. R. Soc. London, Ser. A 197, 454–478 (1949).
  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.
  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).
  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).

2003

2002

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

2001

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).

2000

1999

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

1995

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).

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

1994

1987

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

1982

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

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).

1970

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

1969

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

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

1968

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

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

1949

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

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).

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).

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

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).

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).

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

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).

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).

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).

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).

Bondani, M.

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).

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

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

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).

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).

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

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).

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).

Cardimona, D.

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

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).

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).

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).

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).

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).

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

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).

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

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

Gabor, D.

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

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).

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).

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).

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

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

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).

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

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).

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).

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).

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

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).

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).

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).

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).

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).

Appl. Phys. Lett.

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).

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

IEEE J. Quantum Electron.

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

J. Appl. Phys.

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

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

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

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

J. Opt. Soc. Am. B

Kvantovaya Elektron. (Moscow)

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.

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.

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).

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

Opt. Lett.

Opt. Mem. Neural Netw.

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.

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).

Phys. Rev. A

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

Proc. R. Soc. London, Ser. A

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

Rev. Sci. Instrum.

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).

Other

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).

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.

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