Abstract

We show that two superimposed time-and-space-domain holograms in a persistent spectral hole-burning material can produce destructive interference, even if the path-length difference of the writing beams is constant. The cancellation of the amplitudes in the −1 diffraction order occurs when the two holograms have specially chosen spectral envelopes that represent a pair of complementary functions. By controlling the spectrum of the holograms we are able to perform coherent subtraction and addition of images.

© 1995 Optical Society of America

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  1. A. Rebane, R. Kaarli, P. Saari, A. Anijalg, K. Timpmann, Opt. Commun. 47, 173 (1983).
    [CrossRef]
  2. P. Saari, R. Kaarli, A. Rebane, J. Opt. Soc. Am. B 3, 527 (1986); P. Saari, A. Rebane, Proc. Acad. Sci. Eston. SSR Phys. Math. 33, 322 (1984).
    [CrossRef]
  3. T. W. Mossberg, Opt. Lett. 7, 77 (1982).
    [CrossRef] [PubMed]
  4. A. Rebane, R. Kaarli, P. Saari, Opt. Spectrosc. (USSR) 55, 405 (1983).
  5. D. A. Wiersma, in Advances in Chemical Physics XLVII, J. Jortner, R. D. Levine, S. A. Rice, eds. (Wiley, New York, 1981), p. 421.
    [CrossRef]
  6. T. W. Mossberg, R. Kachru, S. R. Hartmann, Phys. Rev. A 20, 1976 (1979); V. A. Zuikov, V. V. Samartesev, R. G. Usmanov, JETP Lett. 32, 270 (1980).
    [CrossRef]
  7. A. Rebane, O. Ollikainen, Opt. Commun. 78, 327 (1990); A. Rebane, J. Aaviksoo, Opt. Lett. 13, 993 (1988).
    [CrossRef]
  8. N. N. Akhmediev, Opt. Lett. 15, 1035 (1990).
    [CrossRef] [PubMed]
  9. R. Kaarli, P. Saari, R. Sarapuu, H. Sõnajalg, Opt. Commun. 86, 211 (1991).
    [CrossRef]
  10. M. Arend, E. Block, S. R. Hartmann, Opt. Lett. 18, 1789 (1993).
    [CrossRef] [PubMed]
  11. U. P. Wild, A. Renn, C. De Caro, S. Bernet, Appl. Opt. 29, 4329 (1990).
    [CrossRef] [PubMed]
  12. A. Rebane, S. Bernet, A. Renn, U. P. Wild, Opt. Commun. 86, 7 (1991); S. Bernet, B. Kohler, A. Rebane, A. Renn, U. P. Wild, J. Opt. Soc. Am. B 9, 987 (1992).
    [CrossRef]
  13. E. Y. Xu, S. Kröll, D. L. Huestis, R. Kachru, M. K. Kim, Opt. Lett. 15, 562 (1990); M. Mitsunaga, N. Uesugi, H. Sasaki, K. Karaki, Opt. Lett. 19, 752 (1994).
    [CrossRef] [PubMed]

1993 (1)

1991 (2)

R. Kaarli, P. Saari, R. Sarapuu, H. Sõnajalg, Opt. Commun. 86, 211 (1991).
[CrossRef]

A. Rebane, S. Bernet, A. Renn, U. P. Wild, Opt. Commun. 86, 7 (1991); S. Bernet, B. Kohler, A. Rebane, A. Renn, U. P. Wild, J. Opt. Soc. Am. B 9, 987 (1992).
[CrossRef]

1990 (4)

1986 (1)

1983 (2)

A. Rebane, R. Kaarli, P. Saari, A. Anijalg, K. Timpmann, Opt. Commun. 47, 173 (1983).
[CrossRef]

A. Rebane, R. Kaarli, P. Saari, Opt. Spectrosc. (USSR) 55, 405 (1983).

1982 (1)

1979 (1)

T. W. Mossberg, R. Kachru, S. R. Hartmann, Phys. Rev. A 20, 1976 (1979); V. A. Zuikov, V. V. Samartesev, R. G. Usmanov, JETP Lett. 32, 270 (1980).
[CrossRef]

Akhmediev, N. N.

Anijalg, A.

A. Rebane, R. Kaarli, P. Saari, A. Anijalg, K. Timpmann, Opt. Commun. 47, 173 (1983).
[CrossRef]

Arend, M.

Bernet, S.

A. Rebane, S. Bernet, A. Renn, U. P. Wild, Opt. Commun. 86, 7 (1991); S. Bernet, B. Kohler, A. Rebane, A. Renn, U. P. Wild, J. Opt. Soc. Am. B 9, 987 (1992).
[CrossRef]

U. P. Wild, A. Renn, C. De Caro, S. Bernet, Appl. Opt. 29, 4329 (1990).
[CrossRef] [PubMed]

Block, E.

De Caro, C.

Hartmann, S. R.

M. Arend, E. Block, S. R. Hartmann, Opt. Lett. 18, 1789 (1993).
[CrossRef] [PubMed]

T. W. Mossberg, R. Kachru, S. R. Hartmann, Phys. Rev. A 20, 1976 (1979); V. A. Zuikov, V. V. Samartesev, R. G. Usmanov, JETP Lett. 32, 270 (1980).
[CrossRef]

Huestis, D. L.

Kaarli, R.

R. Kaarli, P. Saari, R. Sarapuu, H. Sõnajalg, Opt. Commun. 86, 211 (1991).
[CrossRef]

P. Saari, R. Kaarli, A. Rebane, J. Opt. Soc. Am. B 3, 527 (1986); P. Saari, A. Rebane, Proc. Acad. Sci. Eston. SSR Phys. Math. 33, 322 (1984).
[CrossRef]

A. Rebane, R. Kaarli, P. Saari, Opt. Spectrosc. (USSR) 55, 405 (1983).

A. Rebane, R. Kaarli, P. Saari, A. Anijalg, K. Timpmann, Opt. Commun. 47, 173 (1983).
[CrossRef]

Kachru, R.

E. Y. Xu, S. Kröll, D. L. Huestis, R. Kachru, M. K. Kim, Opt. Lett. 15, 562 (1990); M. Mitsunaga, N. Uesugi, H. Sasaki, K. Karaki, Opt. Lett. 19, 752 (1994).
[CrossRef] [PubMed]

T. W. Mossberg, R. Kachru, S. R. Hartmann, Phys. Rev. A 20, 1976 (1979); V. A. Zuikov, V. V. Samartesev, R. G. Usmanov, JETP Lett. 32, 270 (1980).
[CrossRef]

Kim, M. K.

Kröll, S.

Mossberg, T. W.

T. W. Mossberg, Opt. Lett. 7, 77 (1982).
[CrossRef] [PubMed]

T. W. Mossberg, R. Kachru, S. R. Hartmann, Phys. Rev. A 20, 1976 (1979); V. A. Zuikov, V. V. Samartesev, R. G. Usmanov, JETP Lett. 32, 270 (1980).
[CrossRef]

Ollikainen, O.

A. Rebane, O. Ollikainen, Opt. Commun. 78, 327 (1990); A. Rebane, J. Aaviksoo, Opt. Lett. 13, 993 (1988).
[CrossRef]

Rebane, A.

A. Rebane, S. Bernet, A. Renn, U. P. Wild, Opt. Commun. 86, 7 (1991); S. Bernet, B. Kohler, A. Rebane, A. Renn, U. P. Wild, J. Opt. Soc. Am. B 9, 987 (1992).
[CrossRef]

A. Rebane, O. Ollikainen, Opt. Commun. 78, 327 (1990); A. Rebane, J. Aaviksoo, Opt. Lett. 13, 993 (1988).
[CrossRef]

P. Saari, R. Kaarli, A. Rebane, J. Opt. Soc. Am. B 3, 527 (1986); P. Saari, A. Rebane, Proc. Acad. Sci. Eston. SSR Phys. Math. 33, 322 (1984).
[CrossRef]

A. Rebane, R. Kaarli, P. Saari, Opt. Spectrosc. (USSR) 55, 405 (1983).

A. Rebane, R. Kaarli, P. Saari, A. Anijalg, K. Timpmann, Opt. Commun. 47, 173 (1983).
[CrossRef]

Renn, A.

A. Rebane, S. Bernet, A. Renn, U. P. Wild, Opt. Commun. 86, 7 (1991); S. Bernet, B. Kohler, A. Rebane, A. Renn, U. P. Wild, J. Opt. Soc. Am. B 9, 987 (1992).
[CrossRef]

U. P. Wild, A. Renn, C. De Caro, S. Bernet, Appl. Opt. 29, 4329 (1990).
[CrossRef] [PubMed]

Saari, P.

R. Kaarli, P. Saari, R. Sarapuu, H. Sõnajalg, Opt. Commun. 86, 211 (1991).
[CrossRef]

P. Saari, R. Kaarli, A. Rebane, J. Opt. Soc. Am. B 3, 527 (1986); P. Saari, A. Rebane, Proc. Acad. Sci. Eston. SSR Phys. Math. 33, 322 (1984).
[CrossRef]

A. Rebane, R. Kaarli, P. Saari, Opt. Spectrosc. (USSR) 55, 405 (1983).

A. Rebane, R. Kaarli, P. Saari, A. Anijalg, K. Timpmann, Opt. Commun. 47, 173 (1983).
[CrossRef]

Sarapuu, R.

R. Kaarli, P. Saari, R. Sarapuu, H. Sõnajalg, Opt. Commun. 86, 211 (1991).
[CrossRef]

Sõnajalg, H.

R. Kaarli, P. Saari, R. Sarapuu, H. Sõnajalg, Opt. Commun. 86, 211 (1991).
[CrossRef]

Timpmann, K.

A. Rebane, R. Kaarli, P. Saari, A. Anijalg, K. Timpmann, Opt. Commun. 47, 173 (1983).
[CrossRef]

Wiersma, D. A.

D. A. Wiersma, in Advances in Chemical Physics XLVII, J. Jortner, R. D. Levine, S. A. Rice, eds. (Wiley, New York, 1981), p. 421.
[CrossRef]

Wild, U. P.

A. Rebane, S. Bernet, A. Renn, U. P. Wild, Opt. Commun. 86, 7 (1991); S. Bernet, B. Kohler, A. Rebane, A. Renn, U. P. Wild, J. Opt. Soc. Am. B 9, 987 (1992).
[CrossRef]

U. P. Wild, A. Renn, C. De Caro, S. Bernet, Appl. Opt. 29, 4329 (1990).
[CrossRef] [PubMed]

Xu, E. Y.

Appl. Opt. (1)

J. Opt. Soc. Am. B (1)

Opt. Commun. (4)

A. Rebane, O. Ollikainen, Opt. Commun. 78, 327 (1990); A. Rebane, J. Aaviksoo, Opt. Lett. 13, 993 (1988).
[CrossRef]

A. Rebane, R. Kaarli, P. Saari, A. Anijalg, K. Timpmann, Opt. Commun. 47, 173 (1983).
[CrossRef]

R. Kaarli, P. Saari, R. Sarapuu, H. Sõnajalg, Opt. Commun. 86, 211 (1991).
[CrossRef]

A. Rebane, S. Bernet, A. Renn, U. P. Wild, Opt. Commun. 86, 7 (1991); S. Bernet, B. Kohler, A. Rebane, A. Renn, U. P. Wild, J. Opt. Soc. Am. B 9, 987 (1992).
[CrossRef]

Opt. Lett. (4)

Opt. Spectrosc. (1)

A. Rebane, R. Kaarli, P. Saari, Opt. Spectrosc. (USSR) 55, 405 (1983).

Phys. Rev. A (1)

T. W. Mossberg, R. Kachru, S. R. Hartmann, Phys. Rev. A 20, 1976 (1979); V. A. Zuikov, V. V. Samartesev, R. G. Usmanov, JETP Lett. 32, 270 (1980).
[CrossRef]

Other (1)

D. A. Wiersma, in Advances in Chemical Physics XLVII, J. Jortner, R. D. Levine, S. A. Rice, eds. (Wiley, New York, 1981), p. 421.
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Experimental setup: BE, beam expander; BS, beam splitter; M, spatial mask; H, hole-burning sample.

Fig. 2
Fig. 2

Spectral envelopes at the output of the interferometer measured with a grating monochromator: (a), (b) Spectra used to record the first and the second holograms, respectively. The dashed curve is the spectrum of the picosecond laser.

Fig. 3
Fig. 3

Images recorded by the CCD camera: (a), (b) Holographic image of the two different masks observed in the −1 diffraction order; (c) image from the double-exposure hologram observed in the −1 diffraction order, (d) the same double-exposure hologram observed in the +1 diffraction order.

Equations (1)

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S ( ν ) = S 1 ( ν ) + S 2 ( ν ) ,

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