Abstract

We consider propagation of light pulses detuned from the atomic resonance in a dense two-level medium and the photonic structures with it. The large density of the medium is important for decreasing the spatial scale of nonlinear effects such as pulse compression, though it does not provide any fundamentally new phenomena as compared to dilute media. Frequency detuning decreases the effectivity of nonlinear phenomena such as pulse compression and dispersion-spreading compensation as well. We propose simple logic gates based on interaction between two pulses in one-dimensional nonlinear photonic crystal. We found that frequency detuning is necessary to obtain ultrafast AND gates, while OR and NOT gates can be realized in the system without detuning.

© 2009 Optical Society of America

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References

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  1. F. A. Hopf, C. M. Bowden, and W. H. Louisell, “Mirrorless optical bistability with the use of the local-field correction,” Phys. Rev. A 29, 2591-2596 (1984).
    [CrossRef]
  2. V. Malyshev and E. C. Jarque, “Spatial effects in nonlinear resonant reflection from the boundary of a dense semi-infinite two-level medium: normal incidence,” J. Opt. Soc. Am. B 14, 1167-1178 (1997).
    [CrossRef]
  3. A. A. Afanas'ev, R. A. Vlasov, N. B. Gubar, and V. M. Volkov, “Hysteresis behavior in light reflection from a dense resonant medium with intrinsic optical bistability,” J. Opt. Soc. Am. B 15, 1160-1167 (1998).
    [CrossRef]
  4. M. E. Crenshaw, M. Scalora, and C. M. Bowden, “Ultrafast intrinsic optical switching in a dense medium of two-level atoms,” Phys. Rev. Lett. 68, 911-914 (1992).
    [CrossRef] [PubMed]
  5. M. Scalora and C. M. Bowden, “Propagation effects and ultrafast optical switching in dense media,” Phys. Rev. A 51, 4048-4056 (1995).
    [CrossRef] [PubMed]
  6. C. M. Bowden, A. Postan, and R. Inguva, “Invariant pulse propagation and self-phase modulation in dense media,” J. Opt. Soc. Am. B 8, 1081-1084 (1991).
    [CrossRef]
  7. A. A. Afanas'ev, R. A. Vlasov, O. K. Khasanov, T. V. Smirnova, and O. M. Fedorova, “Coherent and incoherent solitons of self-induced transparency in dense, resonant media,” J. Opt. Soc. Am. B 19, 911-919 (2002).
    [CrossRef]
  8. D. V. Novitsky and S. Yu. Mikhnevich, “Bistable behavior of reflection and transmission of a one-dimensional photonic crystal with a dense resonant medium as a defect,” J. Opt. Soc. Am. B 25, 1362-1370 (2008).
    [CrossRef]
  9. R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Effect of local-field correction on a strongly pumped resonance,” Phys. Rev. A 40, 2446-2451 (1989).
    [CrossRef] [PubMed]
  10. M. E. Crenshaw, “Quasiadiabatic approximation for a dense collection of two-level atoms,” Phys. Rev. A 54, 3559-3575 (1996).
    [CrossRef] [PubMed]
  11. C. Bowden and J. P. Dowling, “Near dipole-dipole effects in dense media: Generalized Maxwell-Bloch equations,” Phys. Rev. A 47, 1247-1251 (1993).
    [CrossRef] [PubMed]
  12. D. V. Novitsky, “Compression of an intensive light pulse in photonic-band-gap structures with a dense resonant medium,” Phys. Rev. A 79, 023828 (2009).
    [CrossRef]
  13. K. Asakawa, Y. Sugimoto, Y. Watanabe, N. Ozaki, A. Mizutani, Y. Takata, Y. Kitagawa, H. Ishikawa, N. Ikeda, K. Awazu, X. Wang, A. Watanabe, S. Nakamura, S. Ohkouchi, K. Inoue, M.Kristensen, O. Sigmund, P.I. Borel, and R. Baetys, “Photonic crystal and quantum dot technologies for all-optical switch and logic device,” New J. Phys. 8, 208-244 (2006).
    [CrossRef]
  14. P. Andalib and N. Granpayeh, “All-optical ultracompact photonic crystal AND gate based on nonlinear ring resonators,” J. Opt. Soc. Am. B 26, 10-16 (2009).
    [CrossRef]
  15. I. Nefedov, Y. Morozov, V. Gusyatnikov, and A. Zheltikov, “Optically controlling photonic band gap logic element,” in Proceedings of the 2nd International Conference on Transparent Optical Networks (IEEE, 2000), pp. 195-198.

2009 (2)

D. V. Novitsky, “Compression of an intensive light pulse in photonic-band-gap structures with a dense resonant medium,” Phys. Rev. A 79, 023828 (2009).
[CrossRef]

P. Andalib and N. Granpayeh, “All-optical ultracompact photonic crystal AND gate based on nonlinear ring resonators,” J. Opt. Soc. Am. B 26, 10-16 (2009).
[CrossRef]

2008 (1)

2006 (1)

K. Asakawa, Y. Sugimoto, Y. Watanabe, N. Ozaki, A. Mizutani, Y. Takata, Y. Kitagawa, H. Ishikawa, N. Ikeda, K. Awazu, X. Wang, A. Watanabe, S. Nakamura, S. Ohkouchi, K. Inoue, M.Kristensen, O. Sigmund, P.I. Borel, and R. Baetys, “Photonic crystal and quantum dot technologies for all-optical switch and logic device,” New J. Phys. 8, 208-244 (2006).
[CrossRef]

2002 (1)

1998 (1)

1997 (1)

1996 (1)

M. E. Crenshaw, “Quasiadiabatic approximation for a dense collection of two-level atoms,” Phys. Rev. A 54, 3559-3575 (1996).
[CrossRef] [PubMed]

1995 (1)

M. Scalora and C. M. Bowden, “Propagation effects and ultrafast optical switching in dense media,” Phys. Rev. A 51, 4048-4056 (1995).
[CrossRef] [PubMed]

1993 (1)

C. Bowden and J. P. Dowling, “Near dipole-dipole effects in dense media: Generalized Maxwell-Bloch equations,” Phys. Rev. A 47, 1247-1251 (1993).
[CrossRef] [PubMed]

1992 (1)

M. E. Crenshaw, M. Scalora, and C. M. Bowden, “Ultrafast intrinsic optical switching in a dense medium of two-level atoms,” Phys. Rev. Lett. 68, 911-914 (1992).
[CrossRef] [PubMed]

1991 (1)

1989 (1)

R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Effect of local-field correction on a strongly pumped resonance,” Phys. Rev. A 40, 2446-2451 (1989).
[CrossRef] [PubMed]

1984 (1)

F. A. Hopf, C. M. Bowden, and W. H. Louisell, “Mirrorless optical bistability with the use of the local-field correction,” Phys. Rev. A 29, 2591-2596 (1984).
[CrossRef]

Afanas'ev, A. A.

Andalib, P.

Asakawa, K.

K. Asakawa, Y. Sugimoto, Y. Watanabe, N. Ozaki, A. Mizutani, Y. Takata, Y. Kitagawa, H. Ishikawa, N. Ikeda, K. Awazu, X. Wang, A. Watanabe, S. Nakamura, S. Ohkouchi, K. Inoue, M.Kristensen, O. Sigmund, P.I. Borel, and R. Baetys, “Photonic crystal and quantum dot technologies for all-optical switch and logic device,” New J. Phys. 8, 208-244 (2006).
[CrossRef]

Awazu, K.

K. Asakawa, Y. Sugimoto, Y. Watanabe, N. Ozaki, A. Mizutani, Y. Takata, Y. Kitagawa, H. Ishikawa, N. Ikeda, K. Awazu, X. Wang, A. Watanabe, S. Nakamura, S. Ohkouchi, K. Inoue, M.Kristensen, O. Sigmund, P.I. Borel, and R. Baetys, “Photonic crystal and quantum dot technologies for all-optical switch and logic device,” New J. Phys. 8, 208-244 (2006).
[CrossRef]

Baetys, R.

K. Asakawa, Y. Sugimoto, Y. Watanabe, N. Ozaki, A. Mizutani, Y. Takata, Y. Kitagawa, H. Ishikawa, N. Ikeda, K. Awazu, X. Wang, A. Watanabe, S. Nakamura, S. Ohkouchi, K. Inoue, M.Kristensen, O. Sigmund, P.I. Borel, and R. Baetys, “Photonic crystal and quantum dot technologies for all-optical switch and logic device,” New J. Phys. 8, 208-244 (2006).
[CrossRef]

Borel, P. I.

K. Asakawa, Y. Sugimoto, Y. Watanabe, N. Ozaki, A. Mizutani, Y. Takata, Y. Kitagawa, H. Ishikawa, N. Ikeda, K. Awazu, X. Wang, A. Watanabe, S. Nakamura, S. Ohkouchi, K. Inoue, M.Kristensen, O. Sigmund, P.I. Borel, and R. Baetys, “Photonic crystal and quantum dot technologies for all-optical switch and logic device,” New J. Phys. 8, 208-244 (2006).
[CrossRef]

Bowden, C.

C. Bowden and J. P. Dowling, “Near dipole-dipole effects in dense media: Generalized Maxwell-Bloch equations,” Phys. Rev. A 47, 1247-1251 (1993).
[CrossRef] [PubMed]

Bowden, C. M.

M. Scalora and C. M. Bowden, “Propagation effects and ultrafast optical switching in dense media,” Phys. Rev. A 51, 4048-4056 (1995).
[CrossRef] [PubMed]

M. E. Crenshaw, M. Scalora, and C. M. Bowden, “Ultrafast intrinsic optical switching in a dense medium of two-level atoms,” Phys. Rev. Lett. 68, 911-914 (1992).
[CrossRef] [PubMed]

C. M. Bowden, A. Postan, and R. Inguva, “Invariant pulse propagation and self-phase modulation in dense media,” J. Opt. Soc. Am. B 8, 1081-1084 (1991).
[CrossRef]

F. A. Hopf, C. M. Bowden, and W. H. Louisell, “Mirrorless optical bistability with the use of the local-field correction,” Phys. Rev. A 29, 2591-2596 (1984).
[CrossRef]

Crenshaw, M. E.

M. E. Crenshaw, “Quasiadiabatic approximation for a dense collection of two-level atoms,” Phys. Rev. A 54, 3559-3575 (1996).
[CrossRef] [PubMed]

M. E. Crenshaw, M. Scalora, and C. M. Bowden, “Ultrafast intrinsic optical switching in a dense medium of two-level atoms,” Phys. Rev. Lett. 68, 911-914 (1992).
[CrossRef] [PubMed]

Dowling, J. P.

C. Bowden and J. P. Dowling, “Near dipole-dipole effects in dense media: Generalized Maxwell-Bloch equations,” Phys. Rev. A 47, 1247-1251 (1993).
[CrossRef] [PubMed]

Fedorova, O. M.

Friedberg, R.

R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Effect of local-field correction on a strongly pumped resonance,” Phys. Rev. A 40, 2446-2451 (1989).
[CrossRef] [PubMed]

Granpayeh, N.

Gubar, N. B.

Gusyatnikov, V.

I. Nefedov, Y. Morozov, V. Gusyatnikov, and A. Zheltikov, “Optically controlling photonic band gap logic element,” in Proceedings of the 2nd International Conference on Transparent Optical Networks (IEEE, 2000), pp. 195-198.

Hartmann, S. R.

R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Effect of local-field correction on a strongly pumped resonance,” Phys. Rev. A 40, 2446-2451 (1989).
[CrossRef] [PubMed]

Hopf, F. A.

F. A. Hopf, C. M. Bowden, and W. H. Louisell, “Mirrorless optical bistability with the use of the local-field correction,” Phys. Rev. A 29, 2591-2596 (1984).
[CrossRef]

Ikeda, N.

K. Asakawa, Y. Sugimoto, Y. Watanabe, N. Ozaki, A. Mizutani, Y. Takata, Y. Kitagawa, H. Ishikawa, N. Ikeda, K. Awazu, X. Wang, A. Watanabe, S. Nakamura, S. Ohkouchi, K. Inoue, M.Kristensen, O. Sigmund, P.I. Borel, and R. Baetys, “Photonic crystal and quantum dot technologies for all-optical switch and logic device,” New J. Phys. 8, 208-244 (2006).
[CrossRef]

Inguva, R.

Inoue, K.

K. Asakawa, Y. Sugimoto, Y. Watanabe, N. Ozaki, A. Mizutani, Y. Takata, Y. Kitagawa, H. Ishikawa, N. Ikeda, K. Awazu, X. Wang, A. Watanabe, S. Nakamura, S. Ohkouchi, K. Inoue, M.Kristensen, O. Sigmund, P.I. Borel, and R. Baetys, “Photonic crystal and quantum dot technologies for all-optical switch and logic device,” New J. Phys. 8, 208-244 (2006).
[CrossRef]

Ishikawa, H.

K. Asakawa, Y. Sugimoto, Y. Watanabe, N. Ozaki, A. Mizutani, Y. Takata, Y. Kitagawa, H. Ishikawa, N. Ikeda, K. Awazu, X. Wang, A. Watanabe, S. Nakamura, S. Ohkouchi, K. Inoue, M.Kristensen, O. Sigmund, P.I. Borel, and R. Baetys, “Photonic crystal and quantum dot technologies for all-optical switch and logic device,” New J. Phys. 8, 208-244 (2006).
[CrossRef]

Jarque, E. C.

Khasanov, O. K.

Kitagawa, Y.

K. Asakawa, Y. Sugimoto, Y. Watanabe, N. Ozaki, A. Mizutani, Y. Takata, Y. Kitagawa, H. Ishikawa, N. Ikeda, K. Awazu, X. Wang, A. Watanabe, S. Nakamura, S. Ohkouchi, K. Inoue, M.Kristensen, O. Sigmund, P.I. Borel, and R. Baetys, “Photonic crystal and quantum dot technologies for all-optical switch and logic device,” New J. Phys. 8, 208-244 (2006).
[CrossRef]

Kristensen, M.

K. Asakawa, Y. Sugimoto, Y. Watanabe, N. Ozaki, A. Mizutani, Y. Takata, Y. Kitagawa, H. Ishikawa, N. Ikeda, K. Awazu, X. Wang, A. Watanabe, S. Nakamura, S. Ohkouchi, K. Inoue, M.Kristensen, O. Sigmund, P.I. Borel, and R. Baetys, “Photonic crystal and quantum dot technologies for all-optical switch and logic device,” New J. Phys. 8, 208-244 (2006).
[CrossRef]

Louisell, W. H.

F. A. Hopf, C. M. Bowden, and W. H. Louisell, “Mirrorless optical bistability with the use of the local-field correction,” Phys. Rev. A 29, 2591-2596 (1984).
[CrossRef]

Malyshev, V.

Manassah, J. T.

R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Effect of local-field correction on a strongly pumped resonance,” Phys. Rev. A 40, 2446-2451 (1989).
[CrossRef] [PubMed]

Mikhnevich, S. Yu.

Mizutani, A.

K. Asakawa, Y. Sugimoto, Y. Watanabe, N. Ozaki, A. Mizutani, Y. Takata, Y. Kitagawa, H. Ishikawa, N. Ikeda, K. Awazu, X. Wang, A. Watanabe, S. Nakamura, S. Ohkouchi, K. Inoue, M.Kristensen, O. Sigmund, P.I. Borel, and R. Baetys, “Photonic crystal and quantum dot technologies for all-optical switch and logic device,” New J. Phys. 8, 208-244 (2006).
[CrossRef]

Morozov, Y.

I. Nefedov, Y. Morozov, V. Gusyatnikov, and A. Zheltikov, “Optically controlling photonic band gap logic element,” in Proceedings of the 2nd International Conference on Transparent Optical Networks (IEEE, 2000), pp. 195-198.

Nakamura, S.

K. Asakawa, Y. Sugimoto, Y. Watanabe, N. Ozaki, A. Mizutani, Y. Takata, Y. Kitagawa, H. Ishikawa, N. Ikeda, K. Awazu, X. Wang, A. Watanabe, S. Nakamura, S. Ohkouchi, K. Inoue, M.Kristensen, O. Sigmund, P.I. Borel, and R. Baetys, “Photonic crystal and quantum dot technologies for all-optical switch and logic device,” New J. Phys. 8, 208-244 (2006).
[CrossRef]

Nefedov, I.

I. Nefedov, Y. Morozov, V. Gusyatnikov, and A. Zheltikov, “Optically controlling photonic band gap logic element,” in Proceedings of the 2nd International Conference on Transparent Optical Networks (IEEE, 2000), pp. 195-198.

Novitsky, D. V.

Ohkouchi, S.

K. Asakawa, Y. Sugimoto, Y. Watanabe, N. Ozaki, A. Mizutani, Y. Takata, Y. Kitagawa, H. Ishikawa, N. Ikeda, K. Awazu, X. Wang, A. Watanabe, S. Nakamura, S. Ohkouchi, K. Inoue, M.Kristensen, O. Sigmund, P.I. Borel, and R. Baetys, “Photonic crystal and quantum dot technologies for all-optical switch and logic device,” New J. Phys. 8, 208-244 (2006).
[CrossRef]

Ozaki, N.

K. Asakawa, Y. Sugimoto, Y. Watanabe, N. Ozaki, A. Mizutani, Y. Takata, Y. Kitagawa, H. Ishikawa, N. Ikeda, K. Awazu, X. Wang, A. Watanabe, S. Nakamura, S. Ohkouchi, K. Inoue, M.Kristensen, O. Sigmund, P.I. Borel, and R. Baetys, “Photonic crystal and quantum dot technologies for all-optical switch and logic device,” New J. Phys. 8, 208-244 (2006).
[CrossRef]

Postan, A.

Scalora, M.

M. Scalora and C. M. Bowden, “Propagation effects and ultrafast optical switching in dense media,” Phys. Rev. A 51, 4048-4056 (1995).
[CrossRef] [PubMed]

M. E. Crenshaw, M. Scalora, and C. M. Bowden, “Ultrafast intrinsic optical switching in a dense medium of two-level atoms,” Phys. Rev. Lett. 68, 911-914 (1992).
[CrossRef] [PubMed]

Sigmund, O.

K. Asakawa, Y. Sugimoto, Y. Watanabe, N. Ozaki, A. Mizutani, Y. Takata, Y. Kitagawa, H. Ishikawa, N. Ikeda, K. Awazu, X. Wang, A. Watanabe, S. Nakamura, S. Ohkouchi, K. Inoue, M.Kristensen, O. Sigmund, P.I. Borel, and R. Baetys, “Photonic crystal and quantum dot technologies for all-optical switch and logic device,” New J. Phys. 8, 208-244 (2006).
[CrossRef]

Smirnova, T. V.

Sugimoto, Y.

K. Asakawa, Y. Sugimoto, Y. Watanabe, N. Ozaki, A. Mizutani, Y. Takata, Y. Kitagawa, H. Ishikawa, N. Ikeda, K. Awazu, X. Wang, A. Watanabe, S. Nakamura, S. Ohkouchi, K. Inoue, M.Kristensen, O. Sigmund, P.I. Borel, and R. Baetys, “Photonic crystal and quantum dot technologies for all-optical switch and logic device,” New J. Phys. 8, 208-244 (2006).
[CrossRef]

Takata, Y.

K. Asakawa, Y. Sugimoto, Y. Watanabe, N. Ozaki, A. Mizutani, Y. Takata, Y. Kitagawa, H. Ishikawa, N. Ikeda, K. Awazu, X. Wang, A. Watanabe, S. Nakamura, S. Ohkouchi, K. Inoue, M.Kristensen, O. Sigmund, P.I. Borel, and R. Baetys, “Photonic crystal and quantum dot technologies for all-optical switch and logic device,” New J. Phys. 8, 208-244 (2006).
[CrossRef]

Vlasov, R. A.

Volkov, V. M.

Wang, X.

K. Asakawa, Y. Sugimoto, Y. Watanabe, N. Ozaki, A. Mizutani, Y. Takata, Y. Kitagawa, H. Ishikawa, N. Ikeda, K. Awazu, X. Wang, A. Watanabe, S. Nakamura, S. Ohkouchi, K. Inoue, M.Kristensen, O. Sigmund, P.I. Borel, and R. Baetys, “Photonic crystal and quantum dot technologies for all-optical switch and logic device,” New J. Phys. 8, 208-244 (2006).
[CrossRef]

Watanabe, A.

K. Asakawa, Y. Sugimoto, Y. Watanabe, N. Ozaki, A. Mizutani, Y. Takata, Y. Kitagawa, H. Ishikawa, N. Ikeda, K. Awazu, X. Wang, A. Watanabe, S. Nakamura, S. Ohkouchi, K. Inoue, M.Kristensen, O. Sigmund, P.I. Borel, and R. Baetys, “Photonic crystal and quantum dot technologies for all-optical switch and logic device,” New J. Phys. 8, 208-244 (2006).
[CrossRef]

Watanabe, Y.

K. Asakawa, Y. Sugimoto, Y. Watanabe, N. Ozaki, A. Mizutani, Y. Takata, Y. Kitagawa, H. Ishikawa, N. Ikeda, K. Awazu, X. Wang, A. Watanabe, S. Nakamura, S. Ohkouchi, K. Inoue, M.Kristensen, O. Sigmund, P.I. Borel, and R. Baetys, “Photonic crystal and quantum dot technologies for all-optical switch and logic device,” New J. Phys. 8, 208-244 (2006).
[CrossRef]

Zheltikov, A.

I. Nefedov, Y. Morozov, V. Gusyatnikov, and A. Zheltikov, “Optically controlling photonic band gap logic element,” in Proceedings of the 2nd International Conference on Transparent Optical Networks (IEEE, 2000), pp. 195-198.

J. Opt. Soc. Am. B (6)

New J. Phys. (1)

K. Asakawa, Y. Sugimoto, Y. Watanabe, N. Ozaki, A. Mizutani, Y. Takata, Y. Kitagawa, H. Ishikawa, N. Ikeda, K. Awazu, X. Wang, A. Watanabe, S. Nakamura, S. Ohkouchi, K. Inoue, M.Kristensen, O. Sigmund, P.I. Borel, and R. Baetys, “Photonic crystal and quantum dot technologies for all-optical switch and logic device,” New J. Phys. 8, 208-244 (2006).
[CrossRef]

Phys. Rev. A (6)

R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Effect of local-field correction on a strongly pumped resonance,” Phys. Rev. A 40, 2446-2451 (1989).
[CrossRef] [PubMed]

M. E. Crenshaw, “Quasiadiabatic approximation for a dense collection of two-level atoms,” Phys. Rev. A 54, 3559-3575 (1996).
[CrossRef] [PubMed]

C. Bowden and J. P. Dowling, “Near dipole-dipole effects in dense media: Generalized Maxwell-Bloch equations,” Phys. Rev. A 47, 1247-1251 (1993).
[CrossRef] [PubMed]

D. V. Novitsky, “Compression of an intensive light pulse in photonic-band-gap structures with a dense resonant medium,” Phys. Rev. A 79, 023828 (2009).
[CrossRef]

F. A. Hopf, C. M. Bowden, and W. H. Louisell, “Mirrorless optical bistability with the use of the local-field correction,” Phys. Rev. A 29, 2591-2596 (1984).
[CrossRef]

M. Scalora and C. M. Bowden, “Propagation effects and ultrafast optical switching in dense media,” Phys. Rev. A 51, 4048-4056 (1995).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

M. E. Crenshaw, M. Scalora, and C. M. Bowden, “Ultrafast intrinsic optical switching in a dense medium of two-level atoms,” Phys. Rev. Lett. 68, 911-914 (1992).
[CrossRef] [PubMed]

Other (1)

I. Nefedov, Y. Morozov, V. Gusyatnikov, and A. Zheltikov, “Optically controlling photonic band gap logic element,” in Proceedings of the 2nd International Conference on Transparent Optical Networks (IEEE, 2000), pp. 195-198.

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Figures (6)

Fig. 1
Fig. 1

(a) Dynamics of population difference on the entrance of the layer of the dense resonant medium after pulse passage and (b) transmitted pulse form transformation for different values of frequency detuning δ. The amplitude of pulse is Ω 0 = 1.5 . Layer thickness is L = 100 λ .

Fig. 2
Fig. 2

Comparison of transmitted pulse forms for different signs of frequency detuning δ. The amplitude of pulse is Ω 0 = 1.5 . Layer thickness is L = 100 λ . The inset shows corresponding dynamics of population difference.

Fig. 3
Fig. 3

Comparison of transmitted pulse forms for different frequency detunings δ at different layer thicknesses. The amplitude of pulse is Ω 0 = 1.5 .

Fig. 4
Fig. 4

The forms of pulses transmitted through the photonic crystal with (a) nonlinear layers d 1 , (b) both nonlinear layers d 1 and d 2 at different values of frequency detuning δ. The number of periods is 250, the thicknesses d 1 = 0.4 , d 2 = 0.13 μ m , background refractive indices n 1 = 1 , n 2 = 3.5 . The amplitude of pulse is Ω 0 = 1.5 .

Fig. 5
Fig. 5

Shapes of transmitted pulses for different input signals corresponding to (a) OR gate, (b) AND gate, (c) NOT gate. The number of periods is 250, the thicknesses of the layers d 1 = 0.4 μ m , d 2 = 0.1301 μ m , background refractive indices n 1 = 1 , n 2 = 3.5 . Frequency detuning is δ = 0 .

Fig. 6
Fig. 6

Shapes of transmitted pulses for two sequential single-pulse inputs with time interval of 200 t p between them. Input pulse intensities are (a) Ω 0 = 1 at δ = 0 (OR gate), (b) Ω 0 = 1.5 at different δ (AND gate). Other parameters are the same as in Fig. 5.

Tables (1)

Tables Icon

Table 1 Table of Output Peak Intensities (Truth Tables)

Equations (7)

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b > 2 δ + 6 ( 1 + δ 2 ) 1 3 Re ( δ + i ) 1 3 ,
d P d t = i μ E N + i P ( Δ ω + 4 π μ 2 C 3 N ) γ 2 P ,
d N d t = 2 i μ ( E * P P * E ) γ 1 ( N 1 ) ,
2 Σ z 2 1 c 2 2 ɛ bg Σ t 2 = 4 π c 2 2 P nl t 2 ,
d P d τ = i Ω ̃ N + i P ( δ ̃ + ε N ) γ ̃ 2 P ,
d N d τ = 2 i ( Ω ̃ * P P * Ω ̃ ) γ ̃ 1 ( N 1 ) ,
2 Ω ̃ ξ 2 ɛ bg 2 Ω ̃ τ 2 + 2 i Ω ̃ ξ + 2 i ɛ bg Ω ̃ τ + ( ɛ bg 1 ) Ω ̃ = 3 ε ( 2 P τ 2 2 i P τ P ) .

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