Abstract

A new hologram type in spectral hole-burning systems is presented. During exposure, the frequency of narrow-band laser light is swept over a spectral range that corresponds to a few homogeneous linewidths of the spectrally selective recording material. Simultaneously the phase of the hologram is adjusted as a function of frequency—the phase sweep function. Because of the phase-reconstructing properties of holography, this recording technique programs the sample as a spectral amplitude and phase filter. We call this hologram type frequency and phase swept (FPS) holograms. Their properties and applications are summarized, and a straightforward theory is presented that describes all the diffraction phenomena observed to date. Thin FPS holograms show strongly asymmetric diffraction into conjugated diffraction orders, which is an unusual behavior for thin transmission holograms. Investigations demonstrate the advantages of FPS holograms with respect to conventional cw recording techniques in frequency-multiplexed data storage. By choosing appropriate phase sweep functions, various features of holographic data storage can be optimized. Examples for cross-talk reduction, highest diffraction efficiency, and maximal readout stability are demonstrated. The properties of these FPS hologram types are deduced from theoretical considerations and confirmed by experiments.

© 1995 Optical Society of America

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References

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  1. A. Szabo, “Frequency selective optical memory,” U.S. patent3,896,420 (22July1975).
  2. G. Castro, D. Haarer, R. M. Macfarlane, H. P. Trommsdorff, “Frequency selective optical data storage system,” U.S. patent4,101,976 (18July1978).
  3. P. Saari, R. Kaarli, A. Rebane, “Picosecond time- and space-domain holography by photochemical hole burning,” J. Opt. Soc. Am. B 3, 527–533 (1986).
    [Crossref]
  4. T. W. Mossberg, “Time-domain frequency-selective optical data storage,” Opt. Lett. 7, 77–81 (1982).
    [Crossref] [PubMed]
  5. A. Rebane, S. Bernet, A. Renn, U. P. Wild, “Holography in frequency selective media: hologram phase and causality,” Opt. Commun. 86, 7–13 (1991).
    [Crossref]
  6. S. Bernet, B. Kohler, A. Rebane, A. Renn, U. P. Wild, “Spectral hole burning and holography. V: Asymmetric diffraction from thin holograms,” J. Opt. Soc. Am. B 9, 987–991 (1992).
    [Crossref]
  7. F. A. Burkhalter, G. W. Suter, U. P. Wild, V. D. Samoilenko, N. V. Rasumova, R. I. Personov, “Hole burning in the absorption spectrum of chlorin in polymer films: Stark effect and temperature dependence,” Chem. Phys. Lett. 94, 483–487 (1983).
    [Crossref]
  8. W. E. Moerner, ed., Persistent Spectral Hole-Burning: Science and Applications, Vol. 44 of Topics in Current Physics (Springer Verlag, Berlin, 1988), Chap. 2, p. 33.
  9. U. P. Wild, A. Renn, “Molecular computing: a review. I. Data and image storage,” J. Mol. Electron. 7, 1–20 (1991).
  10. B. Kohler, S. Bernet, A. Renn, U. P. Wild, “Storage of 2000 holograms in a photochemical hole-burning system,” Opt. Lett. 18, 2144–2146 (1993).
    [Crossref] [PubMed]
  11. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
  12. A. J. Meixner, A. Renn, U. P. Wild, “Spectral hole burning and holography. I. Transmission and holographic detection of spectral holes,” J. Chem. Phys. 91, 6728–6736 (1989).
    [Crossref]
  13. A. Renn, A. J. Meixner, U. P. Wild, “Spectral hole burning and holography. II. Diffraction properties of two spectrally adjacent holograms,” J. Chem. Phys. 92, 2748–2755 (1990).
    [Crossref]
  14. S. Bernet, “Phasenkontrollierte Holographie in frequenzselektiven Materialien,” Ph.D. thesis (ETH, Zurich, 1993), No. 10292.
  15. J. S. Toll, “Causality and the dispersion relation: logical foundations,” Phys. Rev. 104, 1760–1770 (1956).
    [Crossref]
  16. R. Bracewell, Fourier Transform and Its Applications (McGraw-Hill, New York, 1965), Chap. 12, p. 267.
  17. H. de Vries, D. A. Wiersma, “Photophysical and photochemical molecular hole burning theory,” J. Chem. Phys. 72, 1851–1863 (1980).
    [Crossref]
  18. R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), Chap. 9, p. 261.
  19. S. Bernet, B. Kohler, A. Rebane, A. Renn, U. P. Wild, “Holography in frequency selective media II: controlling the diffraction efficiency,” J. Lumin. 53, 215–218 (1992).
    [Crossref]
  20. E. S. Maniloff, S. B. Altner, S. Bernet, F. R. Graf, A. Renn, U. P. Wild, “Spectral hole burning holography in optical memory systems,” in Photonics for Processors, Neural Networks, and Memories, J. L. Horner, B. Javidi, S. T. Kowel, W. J. Miceli, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2026, 592–603 (1993).
  21. E. S. Maniloff, S. B. Altner, S. Bernet, F. R. Graf, U. P. Wild, “Recording of 6000 holograms using spectral hole burning,” Appl. Opt. to be published.

1993 (1)

1992 (2)

S. Bernet, B. Kohler, A. Rebane, A. Renn, U. P. Wild, “Spectral hole burning and holography. V: Asymmetric diffraction from thin holograms,” J. Opt. Soc. Am. B 9, 987–991 (1992).
[Crossref]

S. Bernet, B. Kohler, A. Rebane, A. Renn, U. P. Wild, “Holography in frequency selective media II: controlling the diffraction efficiency,” J. Lumin. 53, 215–218 (1992).
[Crossref]

1991 (2)

A. Rebane, S. Bernet, A. Renn, U. P. Wild, “Holography in frequency selective media: hologram phase and causality,” Opt. Commun. 86, 7–13 (1991).
[Crossref]

U. P. Wild, A. Renn, “Molecular computing: a review. I. Data and image storage,” J. Mol. Electron. 7, 1–20 (1991).

1990 (1)

A. Renn, A. J. Meixner, U. P. Wild, “Spectral hole burning and holography. II. Diffraction properties of two spectrally adjacent holograms,” J. Chem. Phys. 92, 2748–2755 (1990).
[Crossref]

1989 (1)

A. J. Meixner, A. Renn, U. P. Wild, “Spectral hole burning and holography. I. Transmission and holographic detection of spectral holes,” J. Chem. Phys. 91, 6728–6736 (1989).
[Crossref]

1986 (1)

1983 (1)

F. A. Burkhalter, G. W. Suter, U. P. Wild, V. D. Samoilenko, N. V. Rasumova, R. I. Personov, “Hole burning in the absorption spectrum of chlorin in polymer films: Stark effect and temperature dependence,” Chem. Phys. Lett. 94, 483–487 (1983).
[Crossref]

1982 (1)

1980 (1)

H. de Vries, D. A. Wiersma, “Photophysical and photochemical molecular hole burning theory,” J. Chem. Phys. 72, 1851–1863 (1980).
[Crossref]

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

1956 (1)

J. S. Toll, “Causality and the dispersion relation: logical foundations,” Phys. Rev. 104, 1760–1770 (1956).
[Crossref]

Altner, S. B.

E. S. Maniloff, S. B. Altner, S. Bernet, F. R. Graf, A. Renn, U. P. Wild, “Spectral hole burning holography in optical memory systems,” in Photonics for Processors, Neural Networks, and Memories, J. L. Horner, B. Javidi, S. T. Kowel, W. J. Miceli, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2026, 592–603 (1993).

E. S. Maniloff, S. B. Altner, S. Bernet, F. R. Graf, U. P. Wild, “Recording of 6000 holograms using spectral hole burning,” Appl. Opt. to be published.

Bernet, S.

B. Kohler, S. Bernet, A. Renn, U. P. Wild, “Storage of 2000 holograms in a photochemical hole-burning system,” Opt. Lett. 18, 2144–2146 (1993).
[Crossref] [PubMed]

S. Bernet, B. Kohler, A. Rebane, A. Renn, U. P. Wild, “Spectral hole burning and holography. V: Asymmetric diffraction from thin holograms,” J. Opt. Soc. Am. B 9, 987–991 (1992).
[Crossref]

S. Bernet, B. Kohler, A. Rebane, A. Renn, U. P. Wild, “Holography in frequency selective media II: controlling the diffraction efficiency,” J. Lumin. 53, 215–218 (1992).
[Crossref]

A. Rebane, S. Bernet, A. Renn, U. P. Wild, “Holography in frequency selective media: hologram phase and causality,” Opt. Commun. 86, 7–13 (1991).
[Crossref]

S. Bernet, “Phasenkontrollierte Holographie in frequenzselektiven Materialien,” Ph.D. thesis (ETH, Zurich, 1993), No. 10292.

E. S. Maniloff, S. B. Altner, S. Bernet, F. R. Graf, A. Renn, U. P. Wild, “Spectral hole burning holography in optical memory systems,” in Photonics for Processors, Neural Networks, and Memories, J. L. Horner, B. Javidi, S. T. Kowel, W. J. Miceli, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2026, 592–603 (1993).

E. S. Maniloff, S. B. Altner, S. Bernet, F. R. Graf, U. P. Wild, “Recording of 6000 holograms using spectral hole burning,” Appl. Opt. to be published.

Bracewell, R.

R. Bracewell, Fourier Transform and Its Applications (McGraw-Hill, New York, 1965), Chap. 12, p. 267.

Burckhardt, C. B.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), Chap. 9, p. 261.

Burkhalter, F. A.

F. A. Burkhalter, G. W. Suter, U. P. Wild, V. D. Samoilenko, N. V. Rasumova, R. I. Personov, “Hole burning in the absorption spectrum of chlorin in polymer films: Stark effect and temperature dependence,” Chem. Phys. Lett. 94, 483–487 (1983).
[Crossref]

Castro, G.

G. Castro, D. Haarer, R. M. Macfarlane, H. P. Trommsdorff, “Frequency selective optical data storage system,” U.S. patent4,101,976 (18July1978).

Collier, R. J.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), Chap. 9, p. 261.

de Vries, H.

H. de Vries, D. A. Wiersma, “Photophysical and photochemical molecular hole burning theory,” J. Chem. Phys. 72, 1851–1863 (1980).
[Crossref]

Graf, F. R.

E. S. Maniloff, S. B. Altner, S. Bernet, F. R. Graf, A. Renn, U. P. Wild, “Spectral hole burning holography in optical memory systems,” in Photonics for Processors, Neural Networks, and Memories, J. L. Horner, B. Javidi, S. T. Kowel, W. J. Miceli, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2026, 592–603 (1993).

E. S. Maniloff, S. B. Altner, S. Bernet, F. R. Graf, U. P. Wild, “Recording of 6000 holograms using spectral hole burning,” Appl. Opt. to be published.

Haarer, D.

G. Castro, D. Haarer, R. M. Macfarlane, H. P. Trommsdorff, “Frequency selective optical data storage system,” U.S. patent4,101,976 (18July1978).

Kaarli, R.

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Kohler, B.

Lin, L. H.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), Chap. 9, p. 261.

Macfarlane, R. M.

G. Castro, D. Haarer, R. M. Macfarlane, H. P. Trommsdorff, “Frequency selective optical data storage system,” U.S. patent4,101,976 (18July1978).

Maniloff, E. S.

E. S. Maniloff, S. B. Altner, S. Bernet, F. R. Graf, A. Renn, U. P. Wild, “Spectral hole burning holography in optical memory systems,” in Photonics for Processors, Neural Networks, and Memories, J. L. Horner, B. Javidi, S. T. Kowel, W. J. Miceli, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2026, 592–603 (1993).

E. S. Maniloff, S. B. Altner, S. Bernet, F. R. Graf, U. P. Wild, “Recording of 6000 holograms using spectral hole burning,” Appl. Opt. to be published.

Meixner, A. J.

A. Renn, A. J. Meixner, U. P. Wild, “Spectral hole burning and holography. II. Diffraction properties of two spectrally adjacent holograms,” J. Chem. Phys. 92, 2748–2755 (1990).
[Crossref]

A. J. Meixner, A. Renn, U. P. Wild, “Spectral hole burning and holography. I. Transmission and holographic detection of spectral holes,” J. Chem. Phys. 91, 6728–6736 (1989).
[Crossref]

Mossberg, T. W.

Personov, R. I.

F. A. Burkhalter, G. W. Suter, U. P. Wild, V. D. Samoilenko, N. V. Rasumova, R. I. Personov, “Hole burning in the absorption spectrum of chlorin in polymer films: Stark effect and temperature dependence,” Chem. Phys. Lett. 94, 483–487 (1983).
[Crossref]

Rasumova, N. V.

F. A. Burkhalter, G. W. Suter, U. P. Wild, V. D. Samoilenko, N. V. Rasumova, R. I. Personov, “Hole burning in the absorption spectrum of chlorin in polymer films: Stark effect and temperature dependence,” Chem. Phys. Lett. 94, 483–487 (1983).
[Crossref]

Rebane, A.

S. Bernet, B. Kohler, A. Rebane, A. Renn, U. P. Wild, “Spectral hole burning and holography. V: Asymmetric diffraction from thin holograms,” J. Opt. Soc. Am. B 9, 987–991 (1992).
[Crossref]

S. Bernet, B. Kohler, A. Rebane, A. Renn, U. P. Wild, “Holography in frequency selective media II: controlling the diffraction efficiency,” J. Lumin. 53, 215–218 (1992).
[Crossref]

A. Rebane, S. Bernet, A. Renn, U. P. Wild, “Holography in frequency selective media: hologram phase and causality,” Opt. Commun. 86, 7–13 (1991).
[Crossref]

P. Saari, R. Kaarli, A. Rebane, “Picosecond time- and space-domain holography by photochemical hole burning,” J. Opt. Soc. Am. B 3, 527–533 (1986).
[Crossref]

Renn, A.

B. Kohler, S. Bernet, A. Renn, U. P. Wild, “Storage of 2000 holograms in a photochemical hole-burning system,” Opt. Lett. 18, 2144–2146 (1993).
[Crossref] [PubMed]

S. Bernet, B. Kohler, A. Rebane, A. Renn, U. P. Wild, “Spectral hole burning and holography. V: Asymmetric diffraction from thin holograms,” J. Opt. Soc. Am. B 9, 987–991 (1992).
[Crossref]

S. Bernet, B. Kohler, A. Rebane, A. Renn, U. P. Wild, “Holography in frequency selective media II: controlling the diffraction efficiency,” J. Lumin. 53, 215–218 (1992).
[Crossref]

A. Rebane, S. Bernet, A. Renn, U. P. Wild, “Holography in frequency selective media: hologram phase and causality,” Opt. Commun. 86, 7–13 (1991).
[Crossref]

U. P. Wild, A. Renn, “Molecular computing: a review. I. Data and image storage,” J. Mol. Electron. 7, 1–20 (1991).

A. Renn, A. J. Meixner, U. P. Wild, “Spectral hole burning and holography. II. Diffraction properties of two spectrally adjacent holograms,” J. Chem. Phys. 92, 2748–2755 (1990).
[Crossref]

A. J. Meixner, A. Renn, U. P. Wild, “Spectral hole burning and holography. I. Transmission and holographic detection of spectral holes,” J. Chem. Phys. 91, 6728–6736 (1989).
[Crossref]

E. S. Maniloff, S. B. Altner, S. Bernet, F. R. Graf, A. Renn, U. P. Wild, “Spectral hole burning holography in optical memory systems,” in Photonics for Processors, Neural Networks, and Memories, J. L. Horner, B. Javidi, S. T. Kowel, W. J. Miceli, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2026, 592–603 (1993).

Saari, P.

Samoilenko, V. D.

F. A. Burkhalter, G. W. Suter, U. P. Wild, V. D. Samoilenko, N. V. Rasumova, R. I. Personov, “Hole burning in the absorption spectrum of chlorin in polymer films: Stark effect and temperature dependence,” Chem. Phys. Lett. 94, 483–487 (1983).
[Crossref]

Suter, G. W.

F. A. Burkhalter, G. W. Suter, U. P. Wild, V. D. Samoilenko, N. V. Rasumova, R. I. Personov, “Hole burning in the absorption spectrum of chlorin in polymer films: Stark effect and temperature dependence,” Chem. Phys. Lett. 94, 483–487 (1983).
[Crossref]

Szabo, A.

A. Szabo, “Frequency selective optical memory,” U.S. patent3,896,420 (22July1975).

Toll, J. S.

J. S. Toll, “Causality and the dispersion relation: logical foundations,” Phys. Rev. 104, 1760–1770 (1956).
[Crossref]

Trommsdorff, H. P.

G. Castro, D. Haarer, R. M. Macfarlane, H. P. Trommsdorff, “Frequency selective optical data storage system,” U.S. patent4,101,976 (18July1978).

Wiersma, D. A.

H. de Vries, D. A. Wiersma, “Photophysical and photochemical molecular hole burning theory,” J. Chem. Phys. 72, 1851–1863 (1980).
[Crossref]

Wild, U. P.

B. Kohler, S. Bernet, A. Renn, U. P. Wild, “Storage of 2000 holograms in a photochemical hole-burning system,” Opt. Lett. 18, 2144–2146 (1993).
[Crossref] [PubMed]

S. Bernet, B. Kohler, A. Rebane, A. Renn, U. P. Wild, “Spectral hole burning and holography. V: Asymmetric diffraction from thin holograms,” J. Opt. Soc. Am. B 9, 987–991 (1992).
[Crossref]

S. Bernet, B. Kohler, A. Rebane, A. Renn, U. P. Wild, “Holography in frequency selective media II: controlling the diffraction efficiency,” J. Lumin. 53, 215–218 (1992).
[Crossref]

A. Rebane, S. Bernet, A. Renn, U. P. Wild, “Holography in frequency selective media: hologram phase and causality,” Opt. Commun. 86, 7–13 (1991).
[Crossref]

U. P. Wild, A. Renn, “Molecular computing: a review. I. Data and image storage,” J. Mol. Electron. 7, 1–20 (1991).

A. Renn, A. J. Meixner, U. P. Wild, “Spectral hole burning and holography. II. Diffraction properties of two spectrally adjacent holograms,” J. Chem. Phys. 92, 2748–2755 (1990).
[Crossref]

A. J. Meixner, A. Renn, U. P. Wild, “Spectral hole burning and holography. I. Transmission and holographic detection of spectral holes,” J. Chem. Phys. 91, 6728–6736 (1989).
[Crossref]

F. A. Burkhalter, G. W. Suter, U. P. Wild, V. D. Samoilenko, N. V. Rasumova, R. I. Personov, “Hole burning in the absorption spectrum of chlorin in polymer films: Stark effect and temperature dependence,” Chem. Phys. Lett. 94, 483–487 (1983).
[Crossref]

E. S. Maniloff, S. B. Altner, S. Bernet, F. R. Graf, U. P. Wild, “Recording of 6000 holograms using spectral hole burning,” Appl. Opt. to be published.

E. S. Maniloff, S. B. Altner, S. Bernet, F. R. Graf, A. Renn, U. P. Wild, “Spectral hole burning holography in optical memory systems,” in Photonics for Processors, Neural Networks, and Memories, J. L. Horner, B. Javidi, S. T. Kowel, W. J. Miceli, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2026, 592–603 (1993).

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Chem. Phys. Lett. (1)

F. A. Burkhalter, G. W. Suter, U. P. Wild, V. D. Samoilenko, N. V. Rasumova, R. I. Personov, “Hole burning in the absorption spectrum of chlorin in polymer films: Stark effect and temperature dependence,” Chem. Phys. Lett. 94, 483–487 (1983).
[Crossref]

J. Chem. Phys. (3)

A. J. Meixner, A. Renn, U. P. Wild, “Spectral hole burning and holography. I. Transmission and holographic detection of spectral holes,” J. Chem. Phys. 91, 6728–6736 (1989).
[Crossref]

A. Renn, A. J. Meixner, U. P. Wild, “Spectral hole burning and holography. II. Diffraction properties of two spectrally adjacent holograms,” J. Chem. Phys. 92, 2748–2755 (1990).
[Crossref]

H. de Vries, D. A. Wiersma, “Photophysical and photochemical molecular hole burning theory,” J. Chem. Phys. 72, 1851–1863 (1980).
[Crossref]

J. Lumin. (1)

S. Bernet, B. Kohler, A. Rebane, A. Renn, U. P. Wild, “Holography in frequency selective media II: controlling the diffraction efficiency,” J. Lumin. 53, 215–218 (1992).
[Crossref]

J. Mol. Electron. (1)

U. P. Wild, A. Renn, “Molecular computing: a review. I. Data and image storage,” J. Mol. Electron. 7, 1–20 (1991).

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

A. Rebane, S. Bernet, A. Renn, U. P. Wild, “Holography in frequency selective media: hologram phase and causality,” Opt. Commun. 86, 7–13 (1991).
[Crossref]

Opt. Lett. (2)

Phys. Rev. (1)

J. S. Toll, “Causality and the dispersion relation: logical foundations,” Phys. Rev. 104, 1760–1770 (1956).
[Crossref]

Other (8)

R. Bracewell, Fourier Transform and Its Applications (McGraw-Hill, New York, 1965), Chap. 12, p. 267.

S. Bernet, “Phasenkontrollierte Holographie in frequenzselektiven Materialien,” Ph.D. thesis (ETH, Zurich, 1993), No. 10292.

A. Szabo, “Frequency selective optical memory,” U.S. patent3,896,420 (22July1975).

G. Castro, D. Haarer, R. M. Macfarlane, H. P. Trommsdorff, “Frequency selective optical data storage system,” U.S. patent4,101,976 (18July1978).

W. E. Moerner, ed., Persistent Spectral Hole-Burning: Science and Applications, Vol. 44 of Topics in Current Physics (Springer Verlag, Berlin, 1988), Chap. 2, p. 33.

E. S. Maniloff, S. B. Altner, S. Bernet, F. R. Graf, A. Renn, U. P. Wild, “Spectral hole burning holography in optical memory systems,” in Photonics for Processors, Neural Networks, and Memories, J. L. Horner, B. Javidi, S. T. Kowel, W. J. Miceli, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2026, 592–603 (1993).

E. S. Maniloff, S. B. Altner, S. Bernet, F. R. Graf, U. P. Wild, “Recording of 6000 holograms using spectral hole burning,” Appl. Opt. to be published.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), Chap. 9, p. 261.

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Figures (8)

Fig. 1
Fig. 1

Complex phasor representation of the electric field amplitudes diffracted by a single-frequency hologram. The Lorentzian and the dispersion curves in the real and imaginary planes correspond to the electric field components diffracted by the absorption and the refractive-index gratings, respectively. The total diffracted electric field amplitude is obtained by a complex summation over both contributions, at which the absolute value and the phase of the resulting phasor yields the corresponding information about the electric field amplitude. This is indicated for one selected frequency position. On the right-hand side the absolute values and phases for the electric field components diffracted by the absorption (gray) and the refractive-index gratings (black) are displayed a second time in an absolute value/phase representation, which is also used in Figs. 2 and 3.

Fig. 2
Fig. 2

Illustration of a linear FPS hologram with a phase shift of (−π). The linear FPS hologram is considered a linear superposition of spectrally adjacent single-frequency holograms with a frequency-dependent phase. The externally applied phase shift in the complex representation corresponds to a rotation around the frequency axis. The top of the figure demonstrates this for the absorption part of the FPS hologram. The continuous case is shown on the right-hand side in an absolute value/phase representation. The burning range is indicated by the dashed vertical lines. Below, the same procedure is shown for the refractive-index contribution. To obtain the correct phase relation between both diffraction contributions it is important to maintain the correct phase relation between the absorption and refractive-index parts of each of the sampling single-frequency holograms. The total diffracted field amplitude might be obtained by a complex addition of both contributions and would yield an increase compared with the single contributions because they are almost exactly in phase in the burning interval. An analogous calculation for a positive phase sweep would result in a suppression of the relative diffraction efficiency, because both diffraction contributions were exactly out of phase in the burning interval.

Fig. 3
Fig. 3

Comparison of a single-frequency hologram and several FPS hologram types. The columns correspond to holograms of a single frequency (A), a pure frequency swept (B), a (−2π) linear (C), an arctangent (D), and a π-jump FPS (E). Row 1 displays the phase sweep functions of all the hologram types. All the FPS holograms are assumed to be burnt in a frequency interval that corresponds to six hole widths (12Γh), which is indicated by the dashed vertical lines. Row 2 shows the absolute values of the electric field amplitudes diffracted by the absorption (blue) and refractive-index gratings (red) separately. Row 3 displays the corresponding phases. Row 4 shows the phases of the total electric field, as calculated by a complex addition of the absorption and the refractive-index contributions. Row 5 represents the corresponding relative diffraction efficiencies with correct quantitative relations.

Fig. 4
Fig. 4

Comparison of theory and experiment for hologram types of arctangent, a (−2 π) linear, and a π-jump FPS as discussed in Fig. 3. In the experiment all the hologram types were swept with equal exposure energy in the same frequency range of 3 GHz, which corresponds to six hole widths. The inset shows the result of the calculations.

Fig. 5
Fig. 5

Theoretical and experimental data showing the absorption hole depth of linear FPS holograms that have been recorded with equal exposure energies in variable burning intervals. The stars represent experimental data for the absorption hole depths at the center frequencies of the holograms, measured from the transmission of the sample, and normalized to the absorption hole depth of a single-frequency hologram burnt with equal recording energy. The theoretical curve according to Eq. (11) fits the experimental data without any adjustable parameters. Therefore, in a low-modulation limit, at which the absorption hole depth depends linearly on the burning energy, the inverse of this relation can be used to adapt the exposure energy to a varying recording range in order to get equal absorption hole depths, resulting in similar levels of saturation.

Fig. 6
Fig. 6

Comparison of the cross talk between single-frequency and (−2π)-linear FPS holograms. The top shows a group of five single-frequency holograms that were recorded with a frequency separation of 4 GHz (16Γh, upper curve, indicated in the graph). Afterward 30 single-frequency holograms were stored with equal relative distances on each side of the original group. A second scan over the hologram group (lower curve) shows strong cross talk with the spectral neighbors resulting in extremely distorted signals. Below, the same procedure was performed with a group of five (−2π)-linear FPS holograms, each recorded at a frequency interval of 1 GHz (4 Γh). After recording 30 FPS holograms on each side of the burning range, much less cross talk was observed than in the previous case.

Fig. 7
Fig. 7

Comparison of the absolute diffraction efficiencies of single-frequency and arctangent FPS holograms. The single-frequency hologram, exposed for 60 s, shows typical saturation behavior: a small dip in its center. The maximum diffraction efficiency reaches 0.5% and is decreased by additional recording. The arctangent FPS holograms reach a diffraction efficiency of 4.8% using a sweeping range of 5 GHz (20Γh) and five to six times more burning energy than the single-frequency holograms.

Fig. 8
Fig. 8

Bleaching curves for different hologram types. After recording, the holograms were bleached with the reference light in the center of their burning intervals. The diffraction efficiencies were measured as a function of the bleaching energy and normalized to their initial values. The energy axis is normalized in units of the recording energy that was used for each hologram type. Whereas the single-frequency hologram decays continuously, the efficiency of the FPS holograms increases at first and then decays slowly after a maximum value is passed. This behavior is most pronounced for the π-jump FPS hologram.

Equations (13)

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E A b ( ν ) = C Γ h ( ν C - ν ) 2 + Γ h 2 = L ( ν ) , E R I ( ν ) = i C ν C - ν ( ν C - ν ) 2 + Γ h 2 = i D ( ν ) ,
E Dif ( ν ) = E Ab ( ν ) + E RI ( ν ) = L ( ν ) + i D ( ν ) .
η rel ( ν ) E Dif ( ν ) 2 ,             η abs ( ν ) = η rel ( ν ) T ( ν ) .
E Dif FPS ( ν ) = E Ab ( ν ) S ( ν ) + E RI ( ν ) S ( ν ) .
S ( ν ) = A ( ν ) exp [ - i φ ( ν ) ] .
D ( ν ) = H ^ [ L ( ν ) ] ,             L ( ν ) = - H ^ [ D ( ν ) ] ,
H ^ [ f ] = - 1 / ( π ν ) f .
E Dif FPS = ( S + i H ^ [ S ] ) L .
φ ( ν ) = arctan ( ν C - ν Γ h ) with ν = ( ν C - 6 Γ h , ν C + 6 Γ h ) .
Δ A FPS = C Δ ν FPS - 1 / 2 Δ ν FPS + 1 / 2 Δ ν FPS Γ h Γ h 2 + ν 2 d ν = 2 Δ ν FPS arctan Δ ν FPS 2 Γ h .
Δ A FPS Δ A SF = arctan ( Δ ν FPS / 2 Γ h ) Δ ν FPS / 2 Γ h
η rel SF η rel FPS = 4 π 2 ( ν C - ν Δ ν FPS ) 2
φ ( ν ) = arctan Im ( E ) Re ( E ) = arctan ν C - ν Γ / 2 ,

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