Abstract

We demonstrate a novel all-optical scheme for measuring the correlation of spectrally phase-coded ultrashort optical waveforms that uses second-harmonic generation (SHG) in long, periodically poled lithium niobate crystals. The SHG yield can be controlled over a range of 30 dB, depending on the correlation of the applied phase codes. Such a spectral phase correlator has applications for ultrashort-pulse optical code-division multiple-access networking and could serve as a nonlinear optical but classical analog for certain schemes for coherent quantum control of multiphoton processes.

© 2000 Optical Society of America

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  1. P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
    [CrossRef]
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    [CrossRef]
  3. A. M. Weiner, Prog. Quantum Electron. 19, 161 (1995).
    [CrossRef]
  4. A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert II, IEEE J. Quantum Electron. 28, 908 (1992).
    [CrossRef]
  5. M. M. Wefers and K. A. Nelson, Opt. Lett. 20, 1047 (1995).
    [CrossRef]
  6. W. H. Glenn, IEEE J. Quantum Electron. QE-5, 284 (1969).
    [CrossRef]
  7. D. Meshulach and Y. Silbergberg, Nature 396, 239 (1998).
    [CrossRef]
  8. J. A. Salehi, A. M. Weiner, and J. P. Heritage, J. Lightwave Technol. 8, 478 (1990).
    [CrossRef]
  9. H. P. Sardesai, C. C. Chang, and A. M. Weiner, J. Lightwave Technol. 16, 1953 (1998).
    [CrossRef]
  10. H. Tsuda, H. Takenouchi, T. Ishii, K. Okamoto, T. Goh, K. Sato, A. Hirano, T. Kurokawa, and C. Amano, Electron. Lett. 35, 1186 (1999).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  14. C. C. Chang, H. P. Sardesai, and A. M. Weiner, Opt. Lett. 23, 283 (1998).
    [CrossRef]
  15. J. G. Proakis, Digital Communications, 3rd ed. (McGraw-Hill, New York, 1995).
  16. M. Harwit and N. J. A. Sloane, Hadamard Transform Optics (Academic, New York, 1979).

1999 (2)

H. Tsuda, H. Takenouchi, T. Ishii, K. Okamoto, T. Goh, K. Sato, A. Hirano, T. Kurokawa, and C. Amano, Electron. Lett. 35, 1186 (1999).
[CrossRef]

Z. Zheng, S. Shen, H. Sardesai, C. C. Chang, J. H. Marsh, M. M. Karkhanehchi, and A. M. Weiner, Opt. Commun. 167, 225 (1999).
[CrossRef]

1998 (4)

1997 (1)

1995 (2)

1992 (2)

A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert II, IEEE J. Quantum Electron. 28, 908 (1992).
[CrossRef]

B. Broerrs, L. D. Noordam, and H. B. van Linden van den Heuvell, Phys. Rev. A 46, 2749 (1992).
[CrossRef]

1990 (1)

J. A. Salehi, A. M. Weiner, and J. P. Heritage, J. Lightwave Technol. 8, 478 (1990).
[CrossRef]

1969 (1)

W. H. Glenn, IEEE J. Quantum Electron. QE-5, 284 (1969).
[CrossRef]

1961 (1)

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Amano, C.

H. Tsuda, H. Takenouchi, T. Ishii, K. Okamoto, T. Goh, K. Sato, A. Hirano, T. Kurokawa, and C. Amano, Electron. Lett. 35, 1186 (1999).
[CrossRef]

Arbore, M. A.

Broerrs, B.

B. Broerrs, L. D. Noordam, and H. B. van Linden van den Heuvell, Phys. Rev. A 46, 2749 (1992).
[CrossRef]

Chang, C. C.

Fejer, M. M.

Franken, P. A.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Glenn, W. H.

W. H. Glenn, IEEE J. Quantum Electron. QE-5, 284 (1969).
[CrossRef]

Goh, T.

H. Tsuda, H. Takenouchi, T. Ishii, K. Okamoto, T. Goh, K. Sato, A. Hirano, T. Kurokawa, and C. Amano, Electron. Lett. 35, 1186 (1999).
[CrossRef]

Harwit, M.

M. Harwit and N. J. A. Sloane, Hadamard Transform Optics (Academic, New York, 1979).

Heritage, J. P.

J. A. Salehi, A. M. Weiner, and J. P. Heritage, J. Lightwave Technol. 8, 478 (1990).
[CrossRef]

Hill, A. E.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Hirano, A.

H. Tsuda, H. Takenouchi, T. Ishii, K. Okamoto, T. Goh, K. Sato, A. Hirano, T. Kurokawa, and C. Amano, Electron. Lett. 35, 1186 (1999).
[CrossRef]

Ishii, T.

H. Tsuda, H. Takenouchi, T. Ishii, K. Okamoto, T. Goh, K. Sato, A. Hirano, T. Kurokawa, and C. Amano, Electron. Lett. 35, 1186 (1999).
[CrossRef]

Kan'an, A. M.

Karkhanehchi, M. M.

Z. Zheng, S. Shen, H. Sardesai, C. C. Chang, J. H. Marsh, M. M. Karkhanehchi, and A. M. Weiner, Opt. Commun. 167, 225 (1999).
[CrossRef]

Kurokawa, T.

H. Tsuda, H. Takenouchi, T. Ishii, K. Okamoto, T. Goh, K. Sato, A. Hirano, T. Kurokawa, and C. Amano, Electron. Lett. 35, 1186 (1999).
[CrossRef]

Leaird, D. E.

A. M. Weiner, A. M. Kan'an, and D. E. Leaird, Opt. Lett. 23, 1441 (1998).
[CrossRef]

A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert II, IEEE J. Quantum Electron. 28, 908 (1992).
[CrossRef]

Marco, O.

Marsh, J. H.

Z. Zheng, S. Shen, H. Sardesai, C. C. Chang, J. H. Marsh, M. M. Karkhanehchi, and A. M. Weiner, Opt. Commun. 167, 225 (1999).
[CrossRef]

Meshulach, D.

D. Meshulach and Y. Silbergberg, Nature 396, 239 (1998).
[CrossRef]

Nelson, K. A.

Noordam, L. D.

B. Broerrs, L. D. Noordam, and H. B. van Linden van den Heuvell, Phys. Rev. A 46, 2749 (1992).
[CrossRef]

Okamoto, K.

H. Tsuda, H. Takenouchi, T. Ishii, K. Okamoto, T. Goh, K. Sato, A. Hirano, T. Kurokawa, and C. Amano, Electron. Lett. 35, 1186 (1999).
[CrossRef]

Patel, J. S.

A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert II, IEEE J. Quantum Electron. 28, 908 (1992).
[CrossRef]

Peters, C. W.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Proakis, J. G.

J. G. Proakis, Digital Communications, 3rd ed. (McGraw-Hill, New York, 1995).

Salehi, J. A.

J. A. Salehi, A. M. Weiner, and J. P. Heritage, J. Lightwave Technol. 8, 478 (1990).
[CrossRef]

Sardesai, H.

Z. Zheng, S. Shen, H. Sardesai, C. C. Chang, J. H. Marsh, M. M. Karkhanehchi, and A. M. Weiner, Opt. Commun. 167, 225 (1999).
[CrossRef]

Sardesai, H. P.

Sato, K.

H. Tsuda, H. Takenouchi, T. Ishii, K. Okamoto, T. Goh, K. Sato, A. Hirano, T. Kurokawa, and C. Amano, Electron. Lett. 35, 1186 (1999).
[CrossRef]

Shen, S.

Z. Zheng, S. Shen, H. Sardesai, C. C. Chang, J. H. Marsh, M. M. Karkhanehchi, and A. M. Weiner, Opt. Commun. 167, 225 (1999).
[CrossRef]

Silbergberg, Y.

D. Meshulach and Y. Silbergberg, Nature 396, 239 (1998).
[CrossRef]

Sloane, N. J. A.

M. Harwit and N. J. A. Sloane, Hadamard Transform Optics (Academic, New York, 1979).

Takenouchi, H.

H. Tsuda, H. Takenouchi, T. Ishii, K. Okamoto, T. Goh, K. Sato, A. Hirano, T. Kurokawa, and C. Amano, Electron. Lett. 35, 1186 (1999).
[CrossRef]

Tsuda, H.

H. Tsuda, H. Takenouchi, T. Ishii, K. Okamoto, T. Goh, K. Sato, A. Hirano, T. Kurokawa, and C. Amano, Electron. Lett. 35, 1186 (1999).
[CrossRef]

van Linden van den Heuvell, H. B.

B. Broerrs, L. D. Noordam, and H. B. van Linden van den Heuvell, Phys. Rev. A 46, 2749 (1992).
[CrossRef]

Wefers, M. M.

Weiner, A. M.

Z. Zheng, S. Shen, H. Sardesai, C. C. Chang, J. H. Marsh, M. M. Karkhanehchi, and A. M. Weiner, Opt. Commun. 167, 225 (1999).
[CrossRef]

H. P. Sardesai, C. C. Chang, and A. M. Weiner, J. Lightwave Technol. 16, 1953 (1998).
[CrossRef]

A. M. Weiner, A. M. Kan'an, and D. E. Leaird, Opt. Lett. 23, 1441 (1998).
[CrossRef]

C. C. Chang, H. P. Sardesai, and A. M. Weiner, Opt. Lett. 23, 283 (1998).
[CrossRef]

A. M. Weiner, Prog. Quantum Electron. 19, 161 (1995).
[CrossRef]

A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert II, IEEE J. Quantum Electron. 28, 908 (1992).
[CrossRef]

J. A. Salehi, A. M. Weiner, and J. P. Heritage, J. Lightwave Technol. 8, 478 (1990).
[CrossRef]

Weinreich, G.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Wullert II, J. R.

A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert II, IEEE J. Quantum Electron. 28, 908 (1992).
[CrossRef]

Zheng, Z.

Z. Zheng, S. Shen, H. Sardesai, C. C. Chang, J. H. Marsh, M. M. Karkhanehchi, and A. M. Weiner, Opt. Commun. 167, 225 (1999).
[CrossRef]

Electron. Lett. (1)

H. Tsuda, H. Takenouchi, T. Ishii, K. Okamoto, T. Goh, K. Sato, A. Hirano, T. Kurokawa, and C. Amano, Electron. Lett. 35, 1186 (1999).
[CrossRef]

IEEE J. Quantum Electron. (2)

A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert II, IEEE J. Quantum Electron. 28, 908 (1992).
[CrossRef]

W. H. Glenn, IEEE J. Quantum Electron. QE-5, 284 (1969).
[CrossRef]

J. Lightwave Technol. (2)

J. A. Salehi, A. M. Weiner, and J. P. Heritage, J. Lightwave Technol. 8, 478 (1990).
[CrossRef]

H. P. Sardesai, C. C. Chang, and A. M. Weiner, J. Lightwave Technol. 16, 1953 (1998).
[CrossRef]

Nature (1)

D. Meshulach and Y. Silbergberg, Nature 396, 239 (1998).
[CrossRef]

Opt. Commun. (1)

Z. Zheng, S. Shen, H. Sardesai, C. C. Chang, J. H. Marsh, M. M. Karkhanehchi, and A. M. Weiner, Opt. Commun. 167, 225 (1999).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. A (1)

B. Broerrs, L. D. Noordam, and H. B. van Linden van den Heuvell, Phys. Rev. A 46, 2749 (1992).
[CrossRef]

Phys. Rev. Lett. (1)

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Prog. Quantum Electron. (1)

A. M. Weiner, Prog. Quantum Electron. 19, 161 (1995).
[CrossRef]

Other (2)

J. G. Proakis, Digital Communications, 3rd ed. (McGraw-Hill, New York, 1995).

M. Harwit and N. J. A. Sloane, Hadamard Transform Optics (Academic, New York, 1979).

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Figures (3)

Fig. 1
Fig. 1

Schematic of optical phase coding for the control of SHG by ultrashort pulses.

Fig. 2
Fig. 2

Theoretical intensity profiles and experimental intensity cross-correlation data of spectrally coded pulses. (a) Phase code {1 -1 1 -1 1 -1 1-1-1 1 -1 1 -1 1 -1 1} was used, and it consisted of C1 and C2 with the bits in C1 arranged from right to left and the bits in C2 arranged from left to right (as shown in Fig. 1). Here C1 and C2 were the same: {-1 1 -1 1 -1 1 -1 1}, the second code word in the Hadamard matrix (see Ref. 16). Inset, uncoded pulse versus coded pulse. (b) Phase code {1 -1 1 -1 1 -1 1-1-1 1 -1 1 -1 1 -1 1} was used, with C1 kept the same and C2 being the sixth word: {-1 1 -1 1 1 1 -1 1 -1}.

Fig. 3
Fig. 3

SHG spectra measured in different spectral phase-coding situations: I, no phase code was applied to the pump pulses; II, phase codes C1 and C2 are the same; III, data for fixed C1, for all choices of C2C1. (a) C1 and C2 chosen from length-8 Hadamard codes; (b) C1 and C2 chosen from length-7 M-sequence codes, given by all the cyclic permutations of {-1-1 1 1 1 -1 1}.

Equations (4)

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A2Ω=0A1Ω/2+ΩA1Ω/2-ΩdΩ×DΩ,
DΩ=ΓL sinc ΩαL/2,
-A2Ω2dΩ=2πΓ2L×0A1ΩA1-ΩdΩ 2/α,
PSHGi=1N expjΦiexpjΦ-i2.

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