Abstract

We introduce and experimentally demonstrate a simple and reliable optical technique for matching between two periodic numerical sequences based on optical single-shot measurement of their broadband cross-correlation function in the frequency domain. Each sequence is optically encoded into the shape of the different broadband femtosecond pulse using pulse-shaping techniques. The two corresponding shaped pulses are mixed in a nonlinear medium together with an additional (amplitude-shaped) narrowband pulse. The spectrum of the resulting four-wave mixing signal is measured to provide the cross-correlation function of the two encoded sequences. For identical sequences it is the auto-correlation function that is being measured, allowing also the identification of the sequence period. The high contrast achieved here between cross-correlation and auto-correlation functions allows to determine with a very high reliability whether the two encoded sequences are identical or not. The demonstrated technique might be employed in an optical implementation of CDMA communication protocol.

© 2010 OSA

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References

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  1. L. Harte, R. Levine, and R. Kikta, 3G Wireless Demystified, (McGraw-Hill, New York, 2002).
  2. Optical Code Division Multiple Access, Fundamentals and Applications P. R. Prucnal ed. (CRC, Taylor & Francis, Boca Raton, 2006).
  3. A. M. Weiner, Z. Jiang, and D. E. Leaird, “Spectrally phase-coded O-CDMA,” J. Opt. Netw. 6(6), 728–755 (2007).
    [CrossRef]
  4. J. P. Heritage and A. M. Weiner, “Advances in spectral optical code-division multiple-access communications,” IEEE J. Sel. Top. Quantum Electron. 13(5), 1351–1369 (2007).
    [CrossRef]
  5. A. M. Weiner, “Fourier information optics for the ultrafast time domain,” Appl. Opt. 47(4), A88–A96 (2008).
    [CrossRef] [PubMed]
  6. A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71(5), 1929–1960 (2000).
    [CrossRef]
  7. V. S. Pless and W. C. Huffman eds., Handbook of Coding Theory (Elsevier Science B. V., Amsterdam, 1998).
  8. Z. Zheng and A. M. Weiner, “Spectral phase correlation of coded femtosecond pulses by second-harmonic generation in thick nonlinear crystals,” Opt. Lett. 25(13), 984–986 (2000).
    [CrossRef]
  9. Z. Zheng, A. M. Weiner, K. R. Parameswaran, M. H. Chou, and M. M. Fejer, “Low-power spectral phase correlator using periodically poled LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 13(4), 376–378 (2001).
    [CrossRef]
  10. D. S. Seo, Z. Jiang, D. E. Leaird, and A. M. Weiner, “Pulse shaper in a loop: demonstration of cascadable ultrafast all-optical code translation,” Opt. Lett. 29(16), 1864–1866 (2004).
    [CrossRef] [PubMed]
  11. Z. Jiang, D. S. Seo, S.-D. Yang, D. E. Leaird, R. V. Roussev, C. Langrock, M. M. Fejer, and A. M. Weiner, “Low-power high-contrast coded waveform discrimination at 10 GHz via nonlinear processing,” IEEE Photon. Technol. Lett. 16(7), 1778–1780 (2004).
    [CrossRef]
  12. S. Boztas, A. R. Hammons, and P. V. Kumar, “4-phase sequences with near-optimum correlation properties,” IEEE Trans. Inf. Theory 38(3), 1101–1113 (1992).
    [CrossRef]
  13. P. V. Kumar, T. Helleseth, A. R. Calderbank, and A. R. Hammons, “Large families of quaternary sequences with low correlation,” IEEE Trans. Inf. Theory 42(2), 579–592 (1996).
    [CrossRef]
  14. T. Helleseth and P. V. Kumar, “Sequences with low correlation,” in Handbook of Coding Theory, V. S. Pless and W. C. Huffman eds., (Elsevier Science B. V., Amsterdam, 1998).
  15. A. C. Eckbreth, “BOXCARS: Crossed-beam phase-matched CARS generation in gases,” Appl. Phys. Lett. 32(7), 421–423 (1978).
    [CrossRef]
  16. R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses, (Kluwer Academic Publishers, Norwell, 2000).

2008 (1)

2007 (2)

A. M. Weiner, Z. Jiang, and D. E. Leaird, “Spectrally phase-coded O-CDMA,” J. Opt. Netw. 6(6), 728–755 (2007).
[CrossRef]

J. P. Heritage and A. M. Weiner, “Advances in spectral optical code-division multiple-access communications,” IEEE J. Sel. Top. Quantum Electron. 13(5), 1351–1369 (2007).
[CrossRef]

2004 (2)

Z. Jiang, D. S. Seo, S.-D. Yang, D. E. Leaird, R. V. Roussev, C. Langrock, M. M. Fejer, and A. M. Weiner, “Low-power high-contrast coded waveform discrimination at 10 GHz via nonlinear processing,” IEEE Photon. Technol. Lett. 16(7), 1778–1780 (2004).
[CrossRef]

D. S. Seo, Z. Jiang, D. E. Leaird, and A. M. Weiner, “Pulse shaper in a loop: demonstration of cascadable ultrafast all-optical code translation,” Opt. Lett. 29(16), 1864–1866 (2004).
[CrossRef] [PubMed]

2001 (1)

Z. Zheng, A. M. Weiner, K. R. Parameswaran, M. H. Chou, and M. M. Fejer, “Low-power spectral phase correlator using periodically poled LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 13(4), 376–378 (2001).
[CrossRef]

2000 (2)

1996 (1)

P. V. Kumar, T. Helleseth, A. R. Calderbank, and A. R. Hammons, “Large families of quaternary sequences with low correlation,” IEEE Trans. Inf. Theory 42(2), 579–592 (1996).
[CrossRef]

1992 (1)

S. Boztas, A. R. Hammons, and P. V. Kumar, “4-phase sequences with near-optimum correlation properties,” IEEE Trans. Inf. Theory 38(3), 1101–1113 (1992).
[CrossRef]

1978 (1)

A. C. Eckbreth, “BOXCARS: Crossed-beam phase-matched CARS generation in gases,” Appl. Phys. Lett. 32(7), 421–423 (1978).
[CrossRef]

Boztas, S.

S. Boztas, A. R. Hammons, and P. V. Kumar, “4-phase sequences with near-optimum correlation properties,” IEEE Trans. Inf. Theory 38(3), 1101–1113 (1992).
[CrossRef]

Calderbank, A. R.

P. V. Kumar, T. Helleseth, A. R. Calderbank, and A. R. Hammons, “Large families of quaternary sequences with low correlation,” IEEE Trans. Inf. Theory 42(2), 579–592 (1996).
[CrossRef]

Chou, M. H.

Z. Zheng, A. M. Weiner, K. R. Parameswaran, M. H. Chou, and M. M. Fejer, “Low-power spectral phase correlator using periodically poled LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 13(4), 376–378 (2001).
[CrossRef]

Eckbreth, A. C.

A. C. Eckbreth, “BOXCARS: Crossed-beam phase-matched CARS generation in gases,” Appl. Phys. Lett. 32(7), 421–423 (1978).
[CrossRef]

Fejer, M. M.

Z. Jiang, D. S. Seo, S.-D. Yang, D. E. Leaird, R. V. Roussev, C. Langrock, M. M. Fejer, and A. M. Weiner, “Low-power high-contrast coded waveform discrimination at 10 GHz via nonlinear processing,” IEEE Photon. Technol. Lett. 16(7), 1778–1780 (2004).
[CrossRef]

Z. Zheng, A. M. Weiner, K. R. Parameswaran, M. H. Chou, and M. M. Fejer, “Low-power spectral phase correlator using periodically poled LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 13(4), 376–378 (2001).
[CrossRef]

Hammons, A. R.

P. V. Kumar, T. Helleseth, A. R. Calderbank, and A. R. Hammons, “Large families of quaternary sequences with low correlation,” IEEE Trans. Inf. Theory 42(2), 579–592 (1996).
[CrossRef]

S. Boztas, A. R. Hammons, and P. V. Kumar, “4-phase sequences with near-optimum correlation properties,” IEEE Trans. Inf. Theory 38(3), 1101–1113 (1992).
[CrossRef]

Helleseth, T.

P. V. Kumar, T. Helleseth, A. R. Calderbank, and A. R. Hammons, “Large families of quaternary sequences with low correlation,” IEEE Trans. Inf. Theory 42(2), 579–592 (1996).
[CrossRef]

Heritage, J. P.

J. P. Heritage and A. M. Weiner, “Advances in spectral optical code-division multiple-access communications,” IEEE J. Sel. Top. Quantum Electron. 13(5), 1351–1369 (2007).
[CrossRef]

Jiang, Z.

A. M. Weiner, Z. Jiang, and D. E. Leaird, “Spectrally phase-coded O-CDMA,” J. Opt. Netw. 6(6), 728–755 (2007).
[CrossRef]

D. S. Seo, Z. Jiang, D. E. Leaird, and A. M. Weiner, “Pulse shaper in a loop: demonstration of cascadable ultrafast all-optical code translation,” Opt. Lett. 29(16), 1864–1866 (2004).
[CrossRef] [PubMed]

Z. Jiang, D. S. Seo, S.-D. Yang, D. E. Leaird, R. V. Roussev, C. Langrock, M. M. Fejer, and A. M. Weiner, “Low-power high-contrast coded waveform discrimination at 10 GHz via nonlinear processing,” IEEE Photon. Technol. Lett. 16(7), 1778–1780 (2004).
[CrossRef]

Kumar, P. V.

P. V. Kumar, T. Helleseth, A. R. Calderbank, and A. R. Hammons, “Large families of quaternary sequences with low correlation,” IEEE Trans. Inf. Theory 42(2), 579–592 (1996).
[CrossRef]

S. Boztas, A. R. Hammons, and P. V. Kumar, “4-phase sequences with near-optimum correlation properties,” IEEE Trans. Inf. Theory 38(3), 1101–1113 (1992).
[CrossRef]

Langrock, C.

Z. Jiang, D. S. Seo, S.-D. Yang, D. E. Leaird, R. V. Roussev, C. Langrock, M. M. Fejer, and A. M. Weiner, “Low-power high-contrast coded waveform discrimination at 10 GHz via nonlinear processing,” IEEE Photon. Technol. Lett. 16(7), 1778–1780 (2004).
[CrossRef]

Leaird, D. E.

A. M. Weiner, Z. Jiang, and D. E. Leaird, “Spectrally phase-coded O-CDMA,” J. Opt. Netw. 6(6), 728–755 (2007).
[CrossRef]

D. S. Seo, Z. Jiang, D. E. Leaird, and A. M. Weiner, “Pulse shaper in a loop: demonstration of cascadable ultrafast all-optical code translation,” Opt. Lett. 29(16), 1864–1866 (2004).
[CrossRef] [PubMed]

Z. Jiang, D. S. Seo, S.-D. Yang, D. E. Leaird, R. V. Roussev, C. Langrock, M. M. Fejer, and A. M. Weiner, “Low-power high-contrast coded waveform discrimination at 10 GHz via nonlinear processing,” IEEE Photon. Technol. Lett. 16(7), 1778–1780 (2004).
[CrossRef]

Parameswaran, K. R.

Z. Zheng, A. M. Weiner, K. R. Parameswaran, M. H. Chou, and M. M. Fejer, “Low-power spectral phase correlator using periodically poled LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 13(4), 376–378 (2001).
[CrossRef]

Roussev, R. V.

Z. Jiang, D. S. Seo, S.-D. Yang, D. E. Leaird, R. V. Roussev, C. Langrock, M. M. Fejer, and A. M. Weiner, “Low-power high-contrast coded waveform discrimination at 10 GHz via nonlinear processing,” IEEE Photon. Technol. Lett. 16(7), 1778–1780 (2004).
[CrossRef]

Seo, D. S.

Z. Jiang, D. S. Seo, S.-D. Yang, D. E. Leaird, R. V. Roussev, C. Langrock, M. M. Fejer, and A. M. Weiner, “Low-power high-contrast coded waveform discrimination at 10 GHz via nonlinear processing,” IEEE Photon. Technol. Lett. 16(7), 1778–1780 (2004).
[CrossRef]

D. S. Seo, Z. Jiang, D. E. Leaird, and A. M. Weiner, “Pulse shaper in a loop: demonstration of cascadable ultrafast all-optical code translation,” Opt. Lett. 29(16), 1864–1866 (2004).
[CrossRef] [PubMed]

Weiner, A. M.

A. M. Weiner, “Fourier information optics for the ultrafast time domain,” Appl. Opt. 47(4), A88–A96 (2008).
[CrossRef] [PubMed]

A. M. Weiner, Z. Jiang, and D. E. Leaird, “Spectrally phase-coded O-CDMA,” J. Opt. Netw. 6(6), 728–755 (2007).
[CrossRef]

J. P. Heritage and A. M. Weiner, “Advances in spectral optical code-division multiple-access communications,” IEEE J. Sel. Top. Quantum Electron. 13(5), 1351–1369 (2007).
[CrossRef]

Z. Jiang, D. S. Seo, S.-D. Yang, D. E. Leaird, R. V. Roussev, C. Langrock, M. M. Fejer, and A. M. Weiner, “Low-power high-contrast coded waveform discrimination at 10 GHz via nonlinear processing,” IEEE Photon. Technol. Lett. 16(7), 1778–1780 (2004).
[CrossRef]

D. S. Seo, Z. Jiang, D. E. Leaird, and A. M. Weiner, “Pulse shaper in a loop: demonstration of cascadable ultrafast all-optical code translation,” Opt. Lett. 29(16), 1864–1866 (2004).
[CrossRef] [PubMed]

Z. Zheng, A. M. Weiner, K. R. Parameswaran, M. H. Chou, and M. M. Fejer, “Low-power spectral phase correlator using periodically poled LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 13(4), 376–378 (2001).
[CrossRef]

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71(5), 1929–1960 (2000).
[CrossRef]

Z. Zheng and A. M. Weiner, “Spectral phase correlation of coded femtosecond pulses by second-harmonic generation in thick nonlinear crystals,” Opt. Lett. 25(13), 984–986 (2000).
[CrossRef]

Yang, S.-D.

Z. Jiang, D. S. Seo, S.-D. Yang, D. E. Leaird, R. V. Roussev, C. Langrock, M. M. Fejer, and A. M. Weiner, “Low-power high-contrast coded waveform discrimination at 10 GHz via nonlinear processing,” IEEE Photon. Technol. Lett. 16(7), 1778–1780 (2004).
[CrossRef]

Zheng, Z.

Z. Zheng, A. M. Weiner, K. R. Parameswaran, M. H. Chou, and M. M. Fejer, “Low-power spectral phase correlator using periodically poled LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 13(4), 376–378 (2001).
[CrossRef]

Z. Zheng and A. M. Weiner, “Spectral phase correlation of coded femtosecond pulses by second-harmonic generation in thick nonlinear crystals,” Opt. Lett. 25(13), 984–986 (2000).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

A. C. Eckbreth, “BOXCARS: Crossed-beam phase-matched CARS generation in gases,” Appl. Phys. Lett. 32(7), 421–423 (1978).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

J. P. Heritage and A. M. Weiner, “Advances in spectral optical code-division multiple-access communications,” IEEE J. Sel. Top. Quantum Electron. 13(5), 1351–1369 (2007).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

Z. Zheng, A. M. Weiner, K. R. Parameswaran, M. H. Chou, and M. M. Fejer, “Low-power spectral phase correlator using periodically poled LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 13(4), 376–378 (2001).
[CrossRef]

Z. Jiang, D. S. Seo, S.-D. Yang, D. E. Leaird, R. V. Roussev, C. Langrock, M. M. Fejer, and A. M. Weiner, “Low-power high-contrast coded waveform discrimination at 10 GHz via nonlinear processing,” IEEE Photon. Technol. Lett. 16(7), 1778–1780 (2004).
[CrossRef]

IEEE Trans. Inf. Theory (2)

S. Boztas, A. R. Hammons, and P. V. Kumar, “4-phase sequences with near-optimum correlation properties,” IEEE Trans. Inf. Theory 38(3), 1101–1113 (1992).
[CrossRef]

P. V. Kumar, T. Helleseth, A. R. Calderbank, and A. R. Hammons, “Large families of quaternary sequences with low correlation,” IEEE Trans. Inf. Theory 42(2), 579–592 (1996).
[CrossRef]

J. Opt. Netw. (1)

Opt. Lett. (2)

Rev. Sci. Instrum. (1)

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71(5), 1929–1960 (2000).
[CrossRef]

Other (5)

V. S. Pless and W. C. Huffman eds., Handbook of Coding Theory (Elsevier Science B. V., Amsterdam, 1998).

L. Harte, R. Levine, and R. Kikta, 3G Wireless Demystified, (McGraw-Hill, New York, 2002).

Optical Code Division Multiple Access, Fundamentals and Applications P. R. Prucnal ed. (CRC, Taylor & Francis, Boca Raton, 2006).

T. Helleseth and P. V. Kumar, “Sequences with low correlation,” in Handbook of Coding Theory, V. S. Pless and W. C. Huffman eds., (Elsevier Science B. V., Amsterdam, 1998).

R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses, (Kluwer Academic Publishers, Norwell, 2000).

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Figures (4)

Fig. 1
Fig. 1

The experimental setup and four-wave mixing excitation scheme.

Fig. 2
Fig. 2

Typical experimental spectrum of I s i g ( ω ) for the cases of identical [k = r, auto-correlation, black line] and different codes [k≠r. cross-correlation, red line]. The distance between the peaks for the case of k = r corresponds to the period Δ L .

Fig. 3
Fig. 3

Histograms of the measured code period Δ L obtained for 432 different codes belonging to the family S(1) for six different values of the programmed code period (corresponding to n = 3-8; see text). The distributions reflect the signal-to-noise experimental ratio: (a) 3.3±0.8, (b) 4.0±0.13, (c) 5.0±0.12, (d) 6.0±0.08, (e) 7.0±0.1, (f) 7.9±0.13. Overall, the correct recognition of the code period is for the 98% of the sequences.

Fig. 4
Fig. 4

Two-dimensional color maps of the normalized correlation measurements between different code pairs k (x-axis) and r (y-axis). The diagonal corresponds to the auto-correlation cases. Each line is normalized by the value of its auto-correlation case. (a) Results for the family S(0), l = 3. (b) Results for the family S(1), l = 3. See the text for details.

Equations (5)

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c ( k , r , τ ) = t = 0 L 1 ω p s k ( t + τ ) s r ( t ) ,
ξ ( k , r , Δ ) = E k ( ω ) E r ( ω + Δ ) d ω = | E k ( ω ) | · | E r ( ω + Δ ) | e i [ Φ k ( ω ) Φ r ( ω + Δ ) ] d ω .
E s i g ( ω ) E p u m p ( ω ) d ω E k ( ω ) E r ( ω + ω ω ) d ω .
E p u m p n a r r o w ( ω ) = E p u m p ( ω ) δ ( ω 0 ω ) d ω .
E s i g ( ω 0 + Δ ) E p u m p ( ω 0 ) E k ( ω ) E r ( ω + Δ ) d ω = E p u m p ( ω 0 ) | E k ( ω ) | | E r ( ω + Δ ) | e i [ Φ k ( ω ) Φ r ( ω + Δ ) ] d ω .

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