Abstract

A broad-bandwidth persistent spectral hole-burning organic material is used as a fast optical processor that compares an input temporal-frequency profile with a recorded reference spectral shape. This pattern-recognition procedure relies on a subpicosecond temporal cross-correlation process. The size of the phase-encoding spectral interval exceeds 1 THz. The storage material, the spectral encoder, and the interferometric detector are examined in detail for optimal pattern discrimination. Experimental temporal pattern-recognition results are reported.

© 1999 Optical Society of America

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References

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  1. T. W. Mossberg, “Time-domain frequency-selective optical data storage,” Opt. Lett. 7, 77–79 (1982).
    [CrossRef] [PubMed]
  2. A. Rebane, R. Kaarli, P. Saari, A. Anijalg, and K. Timpmann, “Photochemical time-domain holography of weak picosecond pulses,” Opt. Commun. 47, 173–176 (1983).
    [CrossRef]
  3. P. Saari, R. Kaarli, and A. Rebane, “Picosecond time- and space-domain holography by photochemical hole-burning,” J. Opt. Soc. Am. B 3, 527–533 (1986).
    [CrossRef]
  4. A. Rebane, J. Aaviksoo, and J. Kuhl, “Storage and time reversal of femtosecond light signals via persistent spectral hole burning holography,” Appl. Phys. Lett. 54, 93–95 (1989).
    [CrossRef]
  5. M. Mitsunaga, R. Yano, and N. Uesugi, “Time- and frequency-domain hybrid optical memory: 1.6-kbit data storage in Eu3+:Y2SiO5,” Opt. Lett. 16, 1890–1892 (1991).
    [CrossRef] [PubMed]
  6. H. Lin, T. Wang, and T. W. Mossberg, “Demonstration of 8 Gbit/in2 areal storage density based on swept-carrier frequency-selective optical memory,” Opt. Lett. 20, 1658–1660 (1995).
    [CrossRef] [PubMed]
  7. A. Rebane, “Compression and recovery of temporal profiles of picosecond light signals by persistent spectral hole-burning holograms,” Opt. Commun. 67, 301–304 (1988).
    [CrossRef]
  8. H. Schwoerer, D. Erni, and A. Rebane, “Holography in frequency-selective media. III. Spectral synthesis of arbitrary time-domain pulse shapes,” J. Opt. Soc. Am. B 12, 1083–1093 (1995).
    [CrossRef]
  9. K. D. Merkel and W. R. Babbitt, “Optical coherent transient true-time-delay regenerator,” Opt. Lett. 21, 1102–1104 (1996).
    [CrossRef] [PubMed]
  10. T. Wang, H. Lin, and T. W. Mossberg, “Optical bit-rate conversion and bit-stream time reversal by the use of swept-carrier frequency-selective optical data storage techniques,” Opt. Lett. 20, 2033–2035 (1995).
    [CrossRef] [PubMed]
  11. X. A. Shen, Y. S. Bai, and R. Kachru, “Reprogrammable optical matched filter for biphase-coded pulse compression,” Opt. Lett. 17, 1079–1081 (1992).
    [CrossRef] [PubMed]
  12. M. Zhu, W. R. Babbitt, and C. M. Jefferson, “Continuous coherent transient optical processing in a solid,” Opt. Lett. 20, 2514–2516 (1995).
    [CrossRef] [PubMed]
  13. M. Rätsep, M. Tian, I. Lorgeré, F. Grelet, and J.-L. Le Gouët, “Fast random access to frequency-selective optical memory,” Opt. Lett. 21, 83–85 (1996).
    [CrossRef]
  14. A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
  15. H. Sonajalg, A. Débarre, J.-L. Le Gouët, I. Lorgeré, and P. Tchénio, “Phase-encoding technique in time-domain holography: theoretical estimation,” J. Opt. Soc. Am. B 12, 1448–1456 (1995).
    [CrossRef]
  16. A. Débarre, J.-C. Keller, J.-L. Le Gouët, A. Richard, and P. Tchénio, “An amplitude correlator for broadband laser source characterization,” Opt. Commun. 73, 309–313 (1989).
    [CrossRef]
  17. A. K. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1989).
  18. C. Froehly, B. Colombeau, and M. Vampouille, “Shaping and analysis of picosecond light pulses,” Prog. Opt. 20, 115–121 (1983).
  19. A. M. Weiner, D. E. Laird, J. S. Patel, and J. R. Wullert, “Programmable shaping of femtosecond optical pulses by use of 128 element liquid crystal phase modulator,” IEEE J. Quantum Electron. 28, 908–919 (1992).
    [CrossRef]
  20. I. Lorgeré, M. Rätsep, J.-L. Le Gouët, F. Grelet, M. Tian, A. Débarre, and P. Tchénio, “Storage of a spectral shaped hologram in a frequency selective material,” J. Phys. B 28, L565–L569 (1995).
    [CrossRef]
  21. O. E. Martinez, “Grating and prism compressors in the case of finite beam size,” J. Opt. Soc. Am. B 3, 929–934 (1986).
    [CrossRef]
  22. M. Tian, J. Zhang, I. Lorgeré, J.-P. Galaup, and J.-L. Le Gouët, “Phototautomerization and broadband spectral holography,” J. Opt. Soc. Am. B 15, 2216–2225 (1998).
    [CrossRef]
  23. S. Volker and J. H. Van der Waals, “Laser-induced photochemical isomerization of free base porphyrin in a n-octane crystal at 4.2 K,” Mol. Phys. 32, 1703–1718 (1976).
    [CrossRef]
  24. W. R. Babbitt and T. W. Mossberg, “Spatial routing of optical beams through time-domain spatial-spectral filtering,” Opt. Lett. 20, 910–912 (1995).
    [CrossRef] [PubMed]
  25. T. Wang, H. Lin, and T. W. Mossberg, “Experimental demonstration of temporal-waveform-controlled spatial routing of optical beams via spatial-spectral filtering,” Opt. Lett. 20, 2541–2543 (1995).
    [CrossRef]
  26. M. Ratsep, M. Tian, F. Grelet, J.-L. Le Gouët, C. Sigel, and M.-L. Roblin, “Time-encoded spatial routing in a photorefractive crystal,” Opt. Lett. 21, 1292–1294 (1996).
    [CrossRef] [PubMed]

1998 (1)

1996 (3)

1995 (8)

T. Wang, H. Lin, and T. W. Mossberg, “Optical bit-rate conversion and bit-stream time reversal by the use of swept-carrier frequency-selective optical data storage techniques,” Opt. Lett. 20, 2033–2035 (1995).
[CrossRef] [PubMed]

H. Sonajalg, A. Débarre, J.-L. Le Gouët, I. Lorgeré, and P. Tchénio, “Phase-encoding technique in time-domain holography: theoretical estimation,” J. Opt. Soc. Am. B 12, 1448–1456 (1995).
[CrossRef]

M. Zhu, W. R. Babbitt, and C. M. Jefferson, “Continuous coherent transient optical processing in a solid,” Opt. Lett. 20, 2514–2516 (1995).
[CrossRef] [PubMed]

H. Lin, T. Wang, and T. W. Mossberg, “Demonstration of 8 Gbit/in2 areal storage density based on swept-carrier frequency-selective optical memory,” Opt. Lett. 20, 1658–1660 (1995).
[CrossRef] [PubMed]

H. Schwoerer, D. Erni, and A. Rebane, “Holography in frequency-selective media. III. Spectral synthesis of arbitrary time-domain pulse shapes,” J. Opt. Soc. Am. B 12, 1083–1093 (1995).
[CrossRef]

W. R. Babbitt and T. W. Mossberg, “Spatial routing of optical beams through time-domain spatial-spectral filtering,” Opt. Lett. 20, 910–912 (1995).
[CrossRef] [PubMed]

T. Wang, H. Lin, and T. W. Mossberg, “Experimental demonstration of temporal-waveform-controlled spatial routing of optical beams via spatial-spectral filtering,” Opt. Lett. 20, 2541–2543 (1995).
[CrossRef]

I. Lorgeré, M. Rätsep, J.-L. Le Gouët, F. Grelet, M. Tian, A. Débarre, and P. Tchénio, “Storage of a spectral shaped hologram in a frequency selective material,” J. Phys. B 28, L565–L569 (1995).
[CrossRef]

1992 (2)

A. M. Weiner, D. E. Laird, J. S. Patel, and J. R. Wullert, “Programmable shaping of femtosecond optical pulses by use of 128 element liquid crystal phase modulator,” IEEE J. Quantum Electron. 28, 908–919 (1992).
[CrossRef]

X. A. Shen, Y. S. Bai, and R. Kachru, “Reprogrammable optical matched filter for biphase-coded pulse compression,” Opt. Lett. 17, 1079–1081 (1992).
[CrossRef] [PubMed]

1991 (1)

1989 (2)

A. Rebane, J. Aaviksoo, and J. Kuhl, “Storage and time reversal of femtosecond light signals via persistent spectral hole burning holography,” Appl. Phys. Lett. 54, 93–95 (1989).
[CrossRef]

A. Débarre, J.-C. Keller, J.-L. Le Gouët, A. Richard, and P. Tchénio, “An amplitude correlator for broadband laser source characterization,” Opt. Commun. 73, 309–313 (1989).
[CrossRef]

1988 (1)

A. Rebane, “Compression and recovery of temporal profiles of picosecond light signals by persistent spectral hole-burning holograms,” Opt. Commun. 67, 301–304 (1988).
[CrossRef]

1986 (2)

1983 (2)

A. Rebane, R. Kaarli, P. Saari, A. Anijalg, and K. Timpmann, “Photochemical time-domain holography of weak picosecond pulses,” Opt. Commun. 47, 173–176 (1983).
[CrossRef]

C. Froehly, B. Colombeau, and M. Vampouille, “Shaping and analysis of picosecond light pulses,” Prog. Opt. 20, 115–121 (1983).

1982 (1)

1976 (1)

S. Volker and J. H. Van der Waals, “Laser-induced photochemical isomerization of free base porphyrin in a n-octane crystal at 4.2 K,” Mol. Phys. 32, 1703–1718 (1976).
[CrossRef]

1964 (1)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

Aaviksoo, J.

A. Rebane, J. Aaviksoo, and J. Kuhl, “Storage and time reversal of femtosecond light signals via persistent spectral hole burning holography,” Appl. Phys. Lett. 54, 93–95 (1989).
[CrossRef]

Anijalg, A.

A. Rebane, R. Kaarli, P. Saari, A. Anijalg, and K. Timpmann, “Photochemical time-domain holography of weak picosecond pulses,” Opt. Commun. 47, 173–176 (1983).
[CrossRef]

Babbitt, W. R.

Bai, Y. S.

Colombeau, B.

C. Froehly, B. Colombeau, and M. Vampouille, “Shaping and analysis of picosecond light pulses,” Prog. Opt. 20, 115–121 (1983).

Débarre, A.

H. Sonajalg, A. Débarre, J.-L. Le Gouët, I. Lorgeré, and P. Tchénio, “Phase-encoding technique in time-domain holography: theoretical estimation,” J. Opt. Soc. Am. B 12, 1448–1456 (1995).
[CrossRef]

I. Lorgeré, M. Rätsep, J.-L. Le Gouët, F. Grelet, M. Tian, A. Débarre, and P. Tchénio, “Storage of a spectral shaped hologram in a frequency selective material,” J. Phys. B 28, L565–L569 (1995).
[CrossRef]

A. Débarre, J.-C. Keller, J.-L. Le Gouët, A. Richard, and P. Tchénio, “An amplitude correlator for broadband laser source characterization,” Opt. Commun. 73, 309–313 (1989).
[CrossRef]

Erni, D.

Froehly, C.

C. Froehly, B. Colombeau, and M. Vampouille, “Shaping and analysis of picosecond light pulses,” Prog. Opt. 20, 115–121 (1983).

Galaup, J.-P.

Grelet, F.

Jefferson, C. M.

Kaarli, R.

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

A. Rebane, R. Kaarli, P. Saari, A. Anijalg, and K. Timpmann, “Photochemical time-domain holography of weak picosecond pulses,” Opt. Commun. 47, 173–176 (1983).
[CrossRef]

Kachru, R.

Keller, J.-C.

A. Débarre, J.-C. Keller, J.-L. Le Gouët, A. Richard, and P. Tchénio, “An amplitude correlator for broadband laser source characterization,” Opt. Commun. 73, 309–313 (1989).
[CrossRef]

Kuhl, J.

A. Rebane, J. Aaviksoo, and J. Kuhl, “Storage and time reversal of femtosecond light signals via persistent spectral hole burning holography,” Appl. Phys. Lett. 54, 93–95 (1989).
[CrossRef]

Laird, D. E.

A. M. Weiner, D. E. Laird, J. S. Patel, and J. R. Wullert, “Programmable shaping of femtosecond optical pulses by use of 128 element liquid crystal phase modulator,” IEEE J. Quantum Electron. 28, 908–919 (1992).
[CrossRef]

Le Gouët, J.-L.

Lin, H.

Lorgeré, I.

Martinez, O. E.

Merkel, K. D.

Mitsunaga, M.

Mossberg, T. W.

Patel, J. S.

A. M. Weiner, D. E. Laird, J. S. Patel, and J. R. Wullert, “Programmable shaping of femtosecond optical pulses by use of 128 element liquid crystal phase modulator,” IEEE J. Quantum Electron. 28, 908–919 (1992).
[CrossRef]

Ratsep, M.

Rätsep, M.

M. Rätsep, M. Tian, I. Lorgeré, F. Grelet, and J.-L. Le Gouët, “Fast random access to frequency-selective optical memory,” Opt. Lett. 21, 83–85 (1996).
[CrossRef]

I. Lorgeré, M. Rätsep, J.-L. Le Gouët, F. Grelet, M. Tian, A. Débarre, and P. Tchénio, “Storage of a spectral shaped hologram in a frequency selective material,” J. Phys. B 28, L565–L569 (1995).
[CrossRef]

Rebane, A.

H. Schwoerer, D. Erni, and A. Rebane, “Holography in frequency-selective media. III. Spectral synthesis of arbitrary time-domain pulse shapes,” J. Opt. Soc. Am. B 12, 1083–1093 (1995).
[CrossRef]

A. Rebane, J. Aaviksoo, and J. Kuhl, “Storage and time reversal of femtosecond light signals via persistent spectral hole burning holography,” Appl. Phys. Lett. 54, 93–95 (1989).
[CrossRef]

A. Rebane, “Compression and recovery of temporal profiles of picosecond light signals by persistent spectral hole-burning holograms,” Opt. Commun. 67, 301–304 (1988).
[CrossRef]

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

A. Rebane, R. Kaarli, P. Saari, A. Anijalg, and K. Timpmann, “Photochemical time-domain holography of weak picosecond pulses,” Opt. Commun. 47, 173–176 (1983).
[CrossRef]

Richard, A.

A. Débarre, J.-C. Keller, J.-L. Le Gouët, A. Richard, and P. Tchénio, “An amplitude correlator for broadband laser source characterization,” Opt. Commun. 73, 309–313 (1989).
[CrossRef]

Roblin, M.-L.

Saari, P.

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

A. Rebane, R. Kaarli, P. Saari, A. Anijalg, and K. Timpmann, “Photochemical time-domain holography of weak picosecond pulses,” Opt. Commun. 47, 173–176 (1983).
[CrossRef]

Schwoerer, H.

Shen, X. A.

Sigel, C.

Sonajalg, H.

Tchénio, P.

H. Sonajalg, A. Débarre, J.-L. Le Gouët, I. Lorgeré, and P. Tchénio, “Phase-encoding technique in time-domain holography: theoretical estimation,” J. Opt. Soc. Am. B 12, 1448–1456 (1995).
[CrossRef]

I. Lorgeré, M. Rätsep, J.-L. Le Gouët, F. Grelet, M. Tian, A. Débarre, and P. Tchénio, “Storage of a spectral shaped hologram in a frequency selective material,” J. Phys. B 28, L565–L569 (1995).
[CrossRef]

A. Débarre, J.-C. Keller, J.-L. Le Gouët, A. Richard, and P. Tchénio, “An amplitude correlator for broadband laser source characterization,” Opt. Commun. 73, 309–313 (1989).
[CrossRef]

Tian, M.

Timpmann, K.

A. Rebane, R. Kaarli, P. Saari, A. Anijalg, and K. Timpmann, “Photochemical time-domain holography of weak picosecond pulses,” Opt. Commun. 47, 173–176 (1983).
[CrossRef]

Uesugi, N.

Vampouille, M.

C. Froehly, B. Colombeau, and M. Vampouille, “Shaping and analysis of picosecond light pulses,” Prog. Opt. 20, 115–121 (1983).

Van der Waals, J. H.

S. Volker and J. H. Van der Waals, “Laser-induced photochemical isomerization of free base porphyrin in a n-octane crystal at 4.2 K,” Mol. Phys. 32, 1703–1718 (1976).
[CrossRef]

VanderLugt, A.

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

Volker, S.

S. Volker and J. H. Van der Waals, “Laser-induced photochemical isomerization of free base porphyrin in a n-octane crystal at 4.2 K,” Mol. Phys. 32, 1703–1718 (1976).
[CrossRef]

Wang, T.

Weiner, A. M.

A. M. Weiner, D. E. Laird, J. S. Patel, and J. R. Wullert, “Programmable shaping of femtosecond optical pulses by use of 128 element liquid crystal phase modulator,” IEEE J. Quantum Electron. 28, 908–919 (1992).
[CrossRef]

Wullert, J. R.

A. M. Weiner, D. E. Laird, J. S. Patel, and J. R. Wullert, “Programmable shaping of femtosecond optical pulses by use of 128 element liquid crystal phase modulator,” IEEE J. Quantum Electron. 28, 908–919 (1992).
[CrossRef]

Yano, R.

Zhang, J.

Zhu, M.

Appl. Phys. Lett. (1)

A. Rebane, J. Aaviksoo, and J. Kuhl, “Storage and time reversal of femtosecond light signals via persistent spectral hole burning holography,” Appl. Phys. Lett. 54, 93–95 (1989).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. M. Weiner, D. E. Laird, J. S. Patel, and J. R. Wullert, “Programmable shaping of femtosecond optical pulses by use of 128 element liquid crystal phase modulator,” IEEE J. Quantum Electron. 28, 908–919 (1992).
[CrossRef]

IEEE Trans. Inf. Theory (1)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

J. Opt. Soc. Am. B (5)

J. Phys. B (1)

I. Lorgeré, M. Rätsep, J.-L. Le Gouët, F. Grelet, M. Tian, A. Débarre, and P. Tchénio, “Storage of a spectral shaped hologram in a frequency selective material,” J. Phys. B 28, L565–L569 (1995).
[CrossRef]

Mol. Phys. (1)

S. Volker and J. H. Van der Waals, “Laser-induced photochemical isomerization of free base porphyrin in a n-octane crystal at 4.2 K,” Mol. Phys. 32, 1703–1718 (1976).
[CrossRef]

Opt. Commun. (3)

A. Rebane, “Compression and recovery of temporal profiles of picosecond light signals by persistent spectral hole-burning holograms,” Opt. Commun. 67, 301–304 (1988).
[CrossRef]

A. Débarre, J.-C. Keller, J.-L. Le Gouët, A. Richard, and P. Tchénio, “An amplitude correlator for broadband laser source characterization,” Opt. Commun. 73, 309–313 (1989).
[CrossRef]

A. Rebane, R. Kaarli, P. Saari, A. Anijalg, and K. Timpmann, “Photochemical time-domain holography of weak picosecond pulses,” Opt. Commun. 47, 173–176 (1983).
[CrossRef]

Opt. Lett. (11)

T. W. Mossberg, “Time-domain frequency-selective optical data storage,” Opt. Lett. 7, 77–79 (1982).
[CrossRef] [PubMed]

M. Mitsunaga, R. Yano, and N. Uesugi, “Time- and frequency-domain hybrid optical memory: 1.6-kbit data storage in Eu3+:Y2SiO5,” Opt. Lett. 16, 1890–1892 (1991).
[CrossRef] [PubMed]

H. Lin, T. Wang, and T. W. Mossberg, “Demonstration of 8 Gbit/in2 areal storage density based on swept-carrier frequency-selective optical memory,” Opt. Lett. 20, 1658–1660 (1995).
[CrossRef] [PubMed]

K. D. Merkel and W. R. Babbitt, “Optical coherent transient true-time-delay regenerator,” Opt. Lett. 21, 1102–1104 (1996).
[CrossRef] [PubMed]

T. Wang, H. Lin, and T. W. Mossberg, “Optical bit-rate conversion and bit-stream time reversal by the use of swept-carrier frequency-selective optical data storage techniques,” Opt. Lett. 20, 2033–2035 (1995).
[CrossRef] [PubMed]

X. A. Shen, Y. S. Bai, and R. Kachru, “Reprogrammable optical matched filter for biphase-coded pulse compression,” Opt. Lett. 17, 1079–1081 (1992).
[CrossRef] [PubMed]

M. Zhu, W. R. Babbitt, and C. M. Jefferson, “Continuous coherent transient optical processing in a solid,” Opt. Lett. 20, 2514–2516 (1995).
[CrossRef] [PubMed]

M. Rätsep, M. Tian, I. Lorgeré, F. Grelet, and J.-L. Le Gouët, “Fast random access to frequency-selective optical memory,” Opt. Lett. 21, 83–85 (1996).
[CrossRef]

W. R. Babbitt and T. W. Mossberg, “Spatial routing of optical beams through time-domain spatial-spectral filtering,” Opt. Lett. 20, 910–912 (1995).
[CrossRef] [PubMed]

T. Wang, H. Lin, and T. W. Mossberg, “Experimental demonstration of temporal-waveform-controlled spatial routing of optical beams via spatial-spectral filtering,” Opt. Lett. 20, 2541–2543 (1995).
[CrossRef]

M. Ratsep, M. Tian, F. Grelet, J.-L. Le Gouët, C. Sigel, and M.-L. Roblin, “Time-encoded spatial routing in a photorefractive crystal,” Opt. Lett. 21, 1292–1294 (1996).
[CrossRef] [PubMed]

Prog. Opt. (1)

C. Froehly, B. Colombeau, and M. Vampouille, “Shaping and analysis of picosecond light pulses,” Prog. Opt. 20, 115–121 (1983).

Other (1)

A. K. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1989).

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Figures (7)

Fig. 1
Fig. 1

Experimental setup.

Fig. 2
Fig. 2

Spectral shaping device. The spectral components of the incident beam are dispersed by grating G1 and focused in plane F by lens L1. They are collimated by lens L2 and collected by grating G2 into a single beam that is focused on the memory element by the lens system Lg. Coordinates x, ξ, and X are orthogonal to the optical axis. The angles of incidence and of diffraction on G1 are represented by φ0 and θ0, respectively.

Fig. 3
Fig. 3

Asymmetric operation of the two-grating device. The diffraction spot size on the LCM is determined by the incident beam diameter, but, as for the imaging of the LCD on the sample, the diffraction limit depends on the output optics aperture.

Fig. 4
Fig. 4

Experiment side: contrast of the interference fringes of the laser beam with its time-delayed, spectrally shaped replica. Theory side: frequency-to-time Fourier transform of the spectral shapes that are drawn in insets. Function numbers refer to their position in a 32-code Hadamard set.

Fig. 5
Fig. 5

(a) Laser spectrum. (b) Optical density of the sample before engraving. (c) Optical density after engraving within a 1.1 T-Hz window, with an average laser energy of 0.7 µJ/THz/shot for 6 min. (d) Diffracted-energy spectrum.

Fig. 6
Fig. 6

Experimental cross correlation between a recorded reference pattern and 32 input codes. The interferometric signal is detected at fixed delay τ=T. Three different shapes (Nos 16, 12, and 1 in the 32-code Hadamard set) are successively stored in the PSHB material.

Fig. 7
Fig. 7

(a), (b) Interferometric detection of the diffracted field, as a function of the time delay (τ-T). Function No 12 is stored as the reference pattern. Readout is performed by input functions No 28 (a) and No 12 (b). (c), (d) Interferometric detection of the laser field shaped by the codes No 16 (c) and No 0 (d).

Equations (25)

Equations on this page are rendered with MathJax. Learn more.

Hˆ[f(ν)]=1πf(ν)ν-νdν.
Es(t)=E˜(ν)m2(ν)exp(2iπνt)×(1-iHˆ)[|E˜(ν)|2m1*(ν)exp(-2iπνT)]dν.
Hˆ[m1*(ν)exp(-2iπνT)]im1*(ν)exp(-2iπνT),
Es(t)=2SE˜(ν)m2(ν)m1*(ν)exp[2iπν(t-T)]dν.
E(t)=dνE˜(ν)exp(2iπνt).
C(τ)dνE˜S(ν)E˜*(ν)exp(2iπντ),
C(τ)S|E˜(ν)|2m2(ν)m1*(ν)exp[2iπν(t-T)].
C(τ=T)m2(ν)m1*(ν)dν.
m(i)(ν)m(j)*(ν)dν=δij.
m(i)(ν)=1Δn=0N-1n(i)νδ-n,
n=0N-1n(i)n(j)=Nδij.
H2(p+1)=[H2(p)][H2(p)][H2(p)]-[H2(p)],
H2=111-1.
Ei(x, ν)=E(x)J(ν).
EF(ξ, ν)=E˜ξ-β(ν-ν0)fαλ0fJ(ν),
β=θνν0=-λ02ac cos θ0
α=θφν0=-cos φ0cos θ0
EP(X, ν)=E˜Xgλ0fmαXgβf+νJ(ν).
C(τ=T)dXE˜Xgλ0f2×m2αXgβf+νm1*αXgβf+νdνm2(ν)m1*(ν)dν.
Φ(2)(ν)=πuλ0λ0acos(θ0)2ν-ν0ν02,
C(τ)dν|E˜(ν)|2 exp[2iπντ+iΦ(ν)].
C(τ)dνE˜*(ν)E˜m(ν)exp(2iπντ).
E˜m(ν)=E˜(ν)m(ν).
C(τ)dνm(ν)exp(2iπντ),
C(τ)dνm*(ν)m(0)(ν)exp(-2iπντ),

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