Abstract

We give a brief overview of nonlinear localized modes in photonic crystals. We explain how photonic crystals can potentially be important in making small scale active devices which operate in an all optical way. Two models to approach nonlinear photonic crystals, the coupled mode theory and the discrete lattice theory using a Green's function, are explained.

© 2002 Optical Society of Korea

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References

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  1. See, e.g. J.D. Joannoupoulos, RB. Meade, and J. N. Winn, Photonic OrystalsiMolding the Flow of Light (Princeton University Press, Princeton N.J., 1995)
  2. J. Heebner, Q-H. Park, and R.W. Boyd, Phys. Rev. E 65, 036619 (2002)
    [CrossRef]
  3. J. Heebner, Q-H. Park, and R.W. Boyd, J. of Opt. Soc. B19, 722 (2002)
    [CrossRef]
  4. See, e.g. M. Scalora et al, Phys. Rev. Lett. 73, 1368 (1994)
    [CrossRef]
  5. P. Than, Phys. Rev. B 52, 10673 (1995)
    [CrossRef]
  6. W. Chen and D.L. Mills, Phys. Rev. Lett. 58, 160 (1987)
    [CrossRef]
  7. D.N. Christodoulides and RI. Joseph, Phys. Rev. Lett. 62, 1746 (1989)
    [CrossRef]
  8. S. John and N. Ak6zbek, Phys. Rev. Lett. 71, 1168 (1993)
    [CrossRef]
  9. N. Ak6zbek and S. John, Phys. Rev. E 57, 2287 (1998)
    [CrossRef]
  10. G. Kuritzki et al., Self-induced transparency and gi ant nonlinearity in doped photonic crystals (quant ph/0204076)
  11. V. Berger, Phys. Rev. Lett. 81, 4136 (1998)
    [CrossRef]
  12. N.G.R Broderick et al., Phys. Rev. Lett. 84, 4345 (2000)
    [CrossRef]
  13. See, e.g. K. Sakoda, Optical Properties of Photonic crystals (Springer-Verlag, Berlin, 2001)
  14. A. R McGurn, Phys. Lett. A 251 322 (1999)
    [CrossRef]
  15. ibid. 260314 (1999)
  16. S.F. Mingaleev, Y.S. Kivshar and RA. Sammut, Phys. Rev. E 62 5777 (2000)
    [CrossRef]
  17. S.F. Mingaleev, Y.S. Kivshar and R.A. Sammut, Phys, Rev. E 62 5777 (2000)
    [CrossRef]

2002 (2)

J. Heebner, Q-H. Park, and R.W. Boyd, Phys. Rev. E 65, 036619 (2002)
[CrossRef]

J. Heebner, Q-H. Park, and R.W. Boyd, J. of Opt. Soc. B19, 722 (2002)
[CrossRef]

2001 (1)

See, e.g. K. Sakoda, Optical Properties of Photonic crystals (Springer-Verlag, Berlin, 2001)

2000 (3)

N.G.R Broderick et al., Phys. Rev. Lett. 84, 4345 (2000)
[CrossRef]

S.F. Mingaleev, Y.S. Kivshar and RA. Sammut, Phys. Rev. E 62 5777 (2000)
[CrossRef]

S.F. Mingaleev, Y.S. Kivshar and R.A. Sammut, Phys, Rev. E 62 5777 (2000)
[CrossRef]

1999 (2)

A. R McGurn, Phys. Lett. A 251 322 (1999)
[CrossRef]

ibid. 260314 (1999)

1998 (2)

N. Ak6zbek and S. John, Phys. Rev. E 57, 2287 (1998)
[CrossRef]

V. Berger, Phys. Rev. Lett. 81, 4136 (1998)
[CrossRef]

1995 (2)

See, e.g. J.D. Joannoupoulos, RB. Meade, and J. N. Winn, Photonic OrystalsiMolding the Flow of Light (Princeton University Press, Princeton N.J., 1995)

P. Than, Phys. Rev. B 52, 10673 (1995)
[CrossRef]

1994 (1)

See, e.g. M. Scalora et al, Phys. Rev. Lett. 73, 1368 (1994)
[CrossRef]

1993 (1)

S. John and N. Ak6zbek, Phys. Rev. Lett. 71, 1168 (1993)
[CrossRef]

1989 (1)

D.N. Christodoulides and RI. Joseph, Phys. Rev. Lett. 62, 1746 (1989)
[CrossRef]

1987 (1)

W. Chen and D.L. Mills, Phys. Rev. Lett. 58, 160 (1987)
[CrossRef]

ibid (1)

ibid. 260314 (1999)

JOSA B (1)

J. Heebner, Q-H. Park, and R.W. Boyd, J. of Opt. Soc. B19, 722 (2002)
[CrossRef]

Phys, Rev. E (2)

S.F. Mingaleev, Y.S. Kivshar and RA. Sammut, Phys. Rev. E 62 5777 (2000)
[CrossRef]

S.F. Mingaleev, Y.S. Kivshar and R.A. Sammut, Phys, Rev. E 62 5777 (2000)
[CrossRef]

Phys. Rev. B (1)

P. Than, Phys. Rev. B 52, 10673 (1995)
[CrossRef]

Phys. Rev. E (2)

J. Heebner, Q-H. Park, and R.W. Boyd, Phys. Rev. E 65, 036619 (2002)
[CrossRef]

N. Ak6zbek and S. John, Phys. Rev. E 57, 2287 (1998)
[CrossRef]

Phys. Rev. Lett. (6)

V. Berger, Phys. Rev. Lett. 81, 4136 (1998)
[CrossRef]

N.G.R Broderick et al., Phys. Rev. Lett. 84, 4345 (2000)
[CrossRef]

See, e.g. M. Scalora et al, Phys. Rev. Lett. 73, 1368 (1994)
[CrossRef]

W. Chen and D.L. Mills, Phys. Rev. Lett. 58, 160 (1987)
[CrossRef]

D.N. Christodoulides and RI. Joseph, Phys. Rev. Lett. 62, 1746 (1989)
[CrossRef]

S. John and N. Ak6zbek, Phys. Rev. Lett. 71, 1168 (1993)
[CrossRef]

Physics Letters A (1)

A. R McGurn, Phys. Lett. A 251 322 (1999)
[CrossRef]

Other (3)

See, e.g. K. Sakoda, Optical Properties of Photonic crystals (Springer-Verlag, Berlin, 2001)

G. Kuritzki et al., Self-induced transparency and gi ant nonlinearity in doped photonic crystals (quant ph/0204076)

See, e.g. J.D. Joannoupoulos, RB. Meade, and J. N. Winn, Photonic OrystalsiMolding the Flow of Light (Princeton University Press, Princeton N.J., 1995)

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