Abstract

It is hard to use bulk metals with high nonlinear susceptibilities since they are nearly opaque. Metal–dielectric photonic crystals can be transparent, but the electric field at each metal layer is still low. We theoretically studied the nonlinear response of heterostructures composed of truncated all-dielectric photonic crystals and thick metallic films. Because of the localized interface modes, both transmittance and the electric field in the metal are enhanced greatly. Compared to metal–dielectric photonic crystals, the critical intensity of threshold for bistability in the heterostructures with the same thickness of metal can be reduced by nearly 2 orders of magnitude.

© 2009 Optical Society of America

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  1. M. J. Bloemer and M. Scalora, Appl. Phys. Lett. 72, 1676 (1998).
    [CrossRef]
  2. M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, J. Appl. Phys. 83, 2377 (1998).
    [CrossRef]
  3. M. J. Keskinen, P. Loschialpo, D. Forester, and J. Schelleng, J. Appl. Phys. 88, 5785 (2000).
    [CrossRef]
  4. R. S. Bennink, Y. K. Yoon, R. W. Boyd, and J. E. Sipe, Opt. Lett. 24, 1416 (1999).
    [CrossRef]
  5. N. N. Lepeshkin, A. Schweinsberg, G. Piredda, R. S. Bennink, and R. W. Boyd, Phys. Rev. Lett. 93, 123902 (2004).
    [CrossRef] [PubMed]
  6. M. Scalora, N. Mattiucci, G. D'Aguanno, M. C. Larciprete, and M. J. Bloemer, Phys. Rev. E 73, 016603 (2006).
    [CrossRef]
  7. A. Husakou and J. Herrmaum, Phys. Rev. Lett. 99, 127402 (2007).
    [CrossRef] [PubMed]
  8. A. Alù and N. Engheta, IEEE Trans. Antennas Propag. 51, 2558 (2003).
    [CrossRef]
  9. T. Goto, A. V. Dorofeenko, A. M. Merzlikin, A. V. Baryshev, A. P. Vinogradov, M. Inoue, A. A. Lisyansky, and A. B. Granovsky, Phys. Rev. Lett. 101, 113902 (2008).
    [CrossRef] [PubMed]
  10. J. Y. Guo, Y. Sun, Y. W. Zhang, H. Q. Li, H. T. Jiang, and H. Chen, Phys. Rev. E 78, 026607 (2008).
    [CrossRef]
  11. In previous research by G. Q. Du the experiments on tunneling modes were extended from the microwave region in to visible light in heterostructures with the same structures studied in this Letter. For example, a tunneling mode at wavelength λ=589 nm was observed in a heterostructure, (CD)6A, where A represents silver, C and D denote SiO2, and TiO2, with thicknesses dC=89.0, dD=55.2, and dA=60.2 nm, respectively. The measured transmittance T≈30% is about 30 times larger than that of the silver layer with the same thickness.
  12. M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, Phys. Rev. B 76, 165415 (2007).
    [CrossRef]
  13. M. E. Sasin, R. P. Seisyan, M. A. Kalitteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil'ev, V. S. Mikhrin, and A. V. Kavokin, Appl. Phys. Lett. 92, 251112 (2008).
    [CrossRef]
  14. D. Ricard, Ph. Roussignol, and Chr. Flytzanis, Opt. Lett. 10, 511 (1985).
    [CrossRef] [PubMed]
  15. P. Yeh, Optical Waves in Layered Media (Wiley1988).
  16. J. He and M. Cada, Appl. Phys. Lett. 61, 2150 (1992).
    [CrossRef]

2008 (3)

T. Goto, A. V. Dorofeenko, A. M. Merzlikin, A. V. Baryshev, A. P. Vinogradov, M. Inoue, A. A. Lisyansky, and A. B. Granovsky, Phys. Rev. Lett. 101, 113902 (2008).
[CrossRef] [PubMed]

J. Y. Guo, Y. Sun, Y. W. Zhang, H. Q. Li, H. T. Jiang, and H. Chen, Phys. Rev. E 78, 026607 (2008).
[CrossRef]

M. E. Sasin, R. P. Seisyan, M. A. Kalitteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil'ev, V. S. Mikhrin, and A. V. Kavokin, Appl. Phys. Lett. 92, 251112 (2008).
[CrossRef]

2007 (2)

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, Phys. Rev. B 76, 165415 (2007).
[CrossRef]

A. Husakou and J. Herrmaum, Phys. Rev. Lett. 99, 127402 (2007).
[CrossRef] [PubMed]

2006 (1)

M. Scalora, N. Mattiucci, G. D'Aguanno, M. C. Larciprete, and M. J. Bloemer, Phys. Rev. E 73, 016603 (2006).
[CrossRef]

2004 (1)

N. N. Lepeshkin, A. Schweinsberg, G. Piredda, R. S. Bennink, and R. W. Boyd, Phys. Rev. Lett. 93, 123902 (2004).
[CrossRef] [PubMed]

2003 (1)

A. Alù and N. Engheta, IEEE Trans. Antennas Propag. 51, 2558 (2003).
[CrossRef]

2000 (1)

M. J. Keskinen, P. Loschialpo, D. Forester, and J. Schelleng, J. Appl. Phys. 88, 5785 (2000).
[CrossRef]

1999 (1)

1998 (2)

M. J. Bloemer and M. Scalora, Appl. Phys. Lett. 72, 1676 (1998).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, J. Appl. Phys. 83, 2377 (1998).
[CrossRef]

1992 (1)

J. He and M. Cada, Appl. Phys. Lett. 61, 2150 (1992).
[CrossRef]

1985 (1)

Abram, R. A.

M. E. Sasin, R. P. Seisyan, M. A. Kalitteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil'ev, V. S. Mikhrin, and A. V. Kavokin, Appl. Phys. Lett. 92, 251112 (2008).
[CrossRef]

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, Phys. Rev. B 76, 165415 (2007).
[CrossRef]

Alù, A.

A. Alù and N. Engheta, IEEE Trans. Antennas Propag. 51, 2558 (2003).
[CrossRef]

Baryshev, A. V.

T. Goto, A. V. Dorofeenko, A. M. Merzlikin, A. V. Baryshev, A. P. Vinogradov, M. Inoue, A. A. Lisyansky, and A. B. Granovsky, Phys. Rev. Lett. 101, 113902 (2008).
[CrossRef] [PubMed]

Bennink, R. S.

N. N. Lepeshkin, A. Schweinsberg, G. Piredda, R. S. Bennink, and R. W. Boyd, Phys. Rev. Lett. 93, 123902 (2004).
[CrossRef] [PubMed]

R. S. Bennink, Y. K. Yoon, R. W. Boyd, and J. E. Sipe, Opt. Lett. 24, 1416 (1999).
[CrossRef]

Bloemer, M. J.

M. Scalora, N. Mattiucci, G. D'Aguanno, M. C. Larciprete, and M. J. Bloemer, Phys. Rev. E 73, 016603 (2006).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, J. Appl. Phys. 83, 2377 (1998).
[CrossRef]

M. J. Bloemer and M. Scalora, Appl. Phys. Lett. 72, 1676 (1998).
[CrossRef]

Bowden, C. M.

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, J. Appl. Phys. 83, 2377 (1998).
[CrossRef]

Boyd, R. W.

N. N. Lepeshkin, A. Schweinsberg, G. Piredda, R. S. Bennink, and R. W. Boyd, Phys. Rev. Lett. 93, 123902 (2004).
[CrossRef] [PubMed]

R. S. Bennink, Y. K. Yoon, R. W. Boyd, and J. E. Sipe, Opt. Lett. 24, 1416 (1999).
[CrossRef]

Brand, S.

M. E. Sasin, R. P. Seisyan, M. A. Kalitteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil'ev, V. S. Mikhrin, and A. V. Kavokin, Appl. Phys. Lett. 92, 251112 (2008).
[CrossRef]

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, Phys. Rev. B 76, 165415 (2007).
[CrossRef]

Cada, M.

J. He and M. Cada, Appl. Phys. Lett. 61, 2150 (1992).
[CrossRef]

Chamberlain, J. M.

M. E. Sasin, R. P. Seisyan, M. A. Kalitteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil'ev, V. S. Mikhrin, and A. V. Kavokin, Appl. Phys. Lett. 92, 251112 (2008).
[CrossRef]

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, Phys. Rev. B 76, 165415 (2007).
[CrossRef]

Chen, H.

J. Y. Guo, Y. Sun, Y. W. Zhang, H. Q. Li, H. T. Jiang, and H. Chen, Phys. Rev. E 78, 026607 (2008).
[CrossRef]

D'Aguanno, G.

M. Scalora, N. Mattiucci, G. D'Aguanno, M. C. Larciprete, and M. J. Bloemer, Phys. Rev. E 73, 016603 (2006).
[CrossRef]

Dorofeenko, A. V.

T. Goto, A. V. Dorofeenko, A. M. Merzlikin, A. V. Baryshev, A. P. Vinogradov, M. Inoue, A. A. Lisyansky, and A. B. Granovsky, Phys. Rev. Lett. 101, 113902 (2008).
[CrossRef] [PubMed]

Dowling, J. P.

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, J. Appl. Phys. 83, 2377 (1998).
[CrossRef]

Egorov, A. Yu.

M. E. Sasin, R. P. Seisyan, M. A. Kalitteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil'ev, V. S. Mikhrin, and A. V. Kavokin, Appl. Phys. Lett. 92, 251112 (2008).
[CrossRef]

Engheta, N.

A. Alù and N. Engheta, IEEE Trans. Antennas Propag. 51, 2558 (2003).
[CrossRef]

Flytzanis, Chr.

Forester, D.

M. J. Keskinen, P. Loschialpo, D. Forester, and J. Schelleng, J. Appl. Phys. 88, 5785 (2000).
[CrossRef]

Goto, T.

T. Goto, A. V. Dorofeenko, A. M. Merzlikin, A. V. Baryshev, A. P. Vinogradov, M. Inoue, A. A. Lisyansky, and A. B. Granovsky, Phys. Rev. Lett. 101, 113902 (2008).
[CrossRef] [PubMed]

Granovsky, A. B.

T. Goto, A. V. Dorofeenko, A. M. Merzlikin, A. V. Baryshev, A. P. Vinogradov, M. Inoue, A. A. Lisyansky, and A. B. Granovsky, Phys. Rev. Lett. 101, 113902 (2008).
[CrossRef] [PubMed]

Guo, J. Y.

J. Y. Guo, Y. Sun, Y. W. Zhang, H. Q. Li, H. T. Jiang, and H. Chen, Phys. Rev. E 78, 026607 (2008).
[CrossRef]

He, J.

J. He and M. Cada, Appl. Phys. Lett. 61, 2150 (1992).
[CrossRef]

Herrmaum, J.

A. Husakou and J. Herrmaum, Phys. Rev. Lett. 99, 127402 (2007).
[CrossRef] [PubMed]

Husakou, A.

A. Husakou and J. Herrmaum, Phys. Rev. Lett. 99, 127402 (2007).
[CrossRef] [PubMed]

Inoue, M.

T. Goto, A. V. Dorofeenko, A. M. Merzlikin, A. V. Baryshev, A. P. Vinogradov, M. Inoue, A. A. Lisyansky, and A. B. Granovsky, Phys. Rev. Lett. 101, 113902 (2008).
[CrossRef] [PubMed]

Iorsh, I.

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, Phys. Rev. B 76, 165415 (2007).
[CrossRef]

Jiang, H. T.

J. Y. Guo, Y. Sun, Y. W. Zhang, H. Q. Li, H. T. Jiang, and H. Chen, Phys. Rev. E 78, 026607 (2008).
[CrossRef]

Kaliteevski, M.

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, Phys. Rev. B 76, 165415 (2007).
[CrossRef]

Kalitteevski, M. A.

M. E. Sasin, R. P. Seisyan, M. A. Kalitteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil'ev, V. S. Mikhrin, and A. V. Kavokin, Appl. Phys. Lett. 92, 251112 (2008).
[CrossRef]

Kavokin, A. V.

M. E. Sasin, R. P. Seisyan, M. A. Kalitteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil'ev, V. S. Mikhrin, and A. V. Kavokin, Appl. Phys. Lett. 92, 251112 (2008).
[CrossRef]

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, Phys. Rev. B 76, 165415 (2007).
[CrossRef]

Keskinen, M. J.

M. J. Keskinen, P. Loschialpo, D. Forester, and J. Schelleng, J. Appl. Phys. 88, 5785 (2000).
[CrossRef]

Larciprete, M. C.

M. Scalora, N. Mattiucci, G. D'Aguanno, M. C. Larciprete, and M. J. Bloemer, Phys. Rev. E 73, 016603 (2006).
[CrossRef]

Lepeshkin, N. N.

N. N. Lepeshkin, A. Schweinsberg, G. Piredda, R. S. Bennink, and R. W. Boyd, Phys. Rev. Lett. 93, 123902 (2004).
[CrossRef] [PubMed]

Li, H. Q.

J. Y. Guo, Y. Sun, Y. W. Zhang, H. Q. Li, H. T. Jiang, and H. Chen, Phys. Rev. E 78, 026607 (2008).
[CrossRef]

Lisyansky, A. A.

T. Goto, A. V. Dorofeenko, A. M. Merzlikin, A. V. Baryshev, A. P. Vinogradov, M. Inoue, A. A. Lisyansky, and A. B. Granovsky, Phys. Rev. Lett. 101, 113902 (2008).
[CrossRef] [PubMed]

Loschialpo, P.

M. J. Keskinen, P. Loschialpo, D. Forester, and J. Schelleng, J. Appl. Phys. 88, 5785 (2000).
[CrossRef]

Manka, A. S.

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, J. Appl. Phys. 83, 2377 (1998).
[CrossRef]

Mattiucci, N.

M. Scalora, N. Mattiucci, G. D'Aguanno, M. C. Larciprete, and M. J. Bloemer, Phys. Rev. E 73, 016603 (2006).
[CrossRef]

Merzlikin, A. M.

T. Goto, A. V. Dorofeenko, A. M. Merzlikin, A. V. Baryshev, A. P. Vinogradov, M. Inoue, A. A. Lisyansky, and A. B. Granovsky, Phys. Rev. Lett. 101, 113902 (2008).
[CrossRef] [PubMed]

Mikhrin, V. S.

M. E. Sasin, R. P. Seisyan, M. A. Kalitteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil'ev, V. S. Mikhrin, and A. V. Kavokin, Appl. Phys. Lett. 92, 251112 (2008).
[CrossRef]

Pethel, A. S.

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, J. Appl. Phys. 83, 2377 (1998).
[CrossRef]

Piredda, G.

N. N. Lepeshkin, A. Schweinsberg, G. Piredda, R. S. Bennink, and R. W. Boyd, Phys. Rev. Lett. 93, 123902 (2004).
[CrossRef] [PubMed]

Ricard, D.

Roussignol, Ph.

Sasin, M. E.

M. E. Sasin, R. P. Seisyan, M. A. Kalitteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil'ev, V. S. Mikhrin, and A. V. Kavokin, Appl. Phys. Lett. 92, 251112 (2008).
[CrossRef]

Scalora, M.

M. Scalora, N. Mattiucci, G. D'Aguanno, M. C. Larciprete, and M. J. Bloemer, Phys. Rev. E 73, 016603 (2006).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, J. Appl. Phys. 83, 2377 (1998).
[CrossRef]

M. J. Bloemer and M. Scalora, Appl. Phys. Lett. 72, 1676 (1998).
[CrossRef]

Schelleng, J.

M. J. Keskinen, P. Loschialpo, D. Forester, and J. Schelleng, J. Appl. Phys. 88, 5785 (2000).
[CrossRef]

Schweinsberg, A.

N. N. Lepeshkin, A. Schweinsberg, G. Piredda, R. S. Bennink, and R. W. Boyd, Phys. Rev. Lett. 93, 123902 (2004).
[CrossRef] [PubMed]

Seisyan, R. P.

M. E. Sasin, R. P. Seisyan, M. A. Kalitteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil'ev, V. S. Mikhrin, and A. V. Kavokin, Appl. Phys. Lett. 92, 251112 (2008).
[CrossRef]

Shelykh, I. A.

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, Phys. Rev. B 76, 165415 (2007).
[CrossRef]

Sipe, J. E.

Sun, Y.

J. Y. Guo, Y. Sun, Y. W. Zhang, H. Q. Li, H. T. Jiang, and H. Chen, Phys. Rev. E 78, 026607 (2008).
[CrossRef]

Vasil'ev, A. P.

M. E. Sasin, R. P. Seisyan, M. A. Kalitteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil'ev, V. S. Mikhrin, and A. V. Kavokin, Appl. Phys. Lett. 92, 251112 (2008).
[CrossRef]

Vinogradov, A. P.

T. Goto, A. V. Dorofeenko, A. M. Merzlikin, A. V. Baryshev, A. P. Vinogradov, M. Inoue, A. A. Lisyansky, and A. B. Granovsky, Phys. Rev. Lett. 101, 113902 (2008).
[CrossRef] [PubMed]

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley1988).

Yoon, Y. K.

Zhang, Y. W.

J. Y. Guo, Y. Sun, Y. W. Zhang, H. Q. Li, H. T. Jiang, and H. Chen, Phys. Rev. E 78, 026607 (2008).
[CrossRef]

Appl. Phys. Lett. (3)

M. E. Sasin, R. P. Seisyan, M. A. Kalitteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasil'ev, V. S. Mikhrin, and A. V. Kavokin, Appl. Phys. Lett. 92, 251112 (2008).
[CrossRef]

M. J. Bloemer and M. Scalora, Appl. Phys. Lett. 72, 1676 (1998).
[CrossRef]

J. He and M. Cada, Appl. Phys. Lett. 61, 2150 (1992).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

A. Alù and N. Engheta, IEEE Trans. Antennas Propag. 51, 2558 (2003).
[CrossRef]

J. Appl. Phys. (2)

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, J. Appl. Phys. 83, 2377 (1998).
[CrossRef]

M. J. Keskinen, P. Loschialpo, D. Forester, and J. Schelleng, J. Appl. Phys. 88, 5785 (2000).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. B (1)

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, Phys. Rev. B 76, 165415 (2007).
[CrossRef]

Phys. Rev. E (2)

J. Y. Guo, Y. Sun, Y. W. Zhang, H. Q. Li, H. T. Jiang, and H. Chen, Phys. Rev. E 78, 026607 (2008).
[CrossRef]

M. Scalora, N. Mattiucci, G. D'Aguanno, M. C. Larciprete, and M. J. Bloemer, Phys. Rev. E 73, 016603 (2006).
[CrossRef]

Phys. Rev. Lett. (3)

A. Husakou and J. Herrmaum, Phys. Rev. Lett. 99, 127402 (2007).
[CrossRef] [PubMed]

T. Goto, A. V. Dorofeenko, A. M. Merzlikin, A. V. Baryshev, A. P. Vinogradov, M. Inoue, A. A. Lisyansky, and A. B. Granovsky, Phys. Rev. Lett. 101, 113902 (2008).
[CrossRef] [PubMed]

N. N. Lepeshkin, A. Schweinsberg, G. Piredda, R. S. Bennink, and R. W. Boyd, Phys. Rev. Lett. 93, 123902 (2004).
[CrossRef] [PubMed]

Other (2)

In previous research by G. Q. Du the experiments on tunneling modes were extended from the microwave region in to visible light in heterostructures with the same structures studied in this Letter. For example, a tunneling mode at wavelength λ=589 nm was observed in a heterostructure, (CD)6A, where A represents silver, C and D denote SiO2, and TiO2, with thicknesses dC=89.0, dD=55.2, and dA=60.2 nm, respectively. The measured transmittance T≈30% is about 30 times larger than that of the silver layer with the same thickness.

P. Yeh, Optical Waves in Layered Media (Wiley1988).

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Figures (4)

Fig. 1
Fig. 1

(a) Transmittance of a heterostructure ( C D ) 7 A without considering χ 3 of Ag (denoted by A); n C = 1.443 , n D = 2.327 , d C = 85.5 nm , d D = 53.0 nm , and d A = 67.2 nm . The frequency of the tunneling mode is f 0 = 525 THz . (b) Distributions of intensities of EM fields in the structure at f 0 . The thickness of Ag in the schematic is 3 times its real thickness.

Fig. 2
Fig. 2

Nonlinear properties of the structure ( χ 3 = 2.4 × 10 9 esu ) in Fig. 1. (a) Output versus input intensity at three different frequencies (521.5, 520.6, and 519.5 THz ). (b) Intensities of thresholds for bistability versus frequencies of the incident wave. The critical intensity of threshold E in 1 2 = E in 2 2 = 1.17 GW cm 2 .

Fig. 3
Fig. 3

(a) Transmittance of a 1D Si O 2 Ag photonic crystal with seven periods without considering χ 3 of Ag. The thicknesses of Ag layer and Si O 2 layer are 9.6 and 176.96 nm , respectively. The total thickness of Ag is the same as that of the Ag in Fig. 1. (b) Distribution of E 2 in the structure at the high band-edge frequency ( f 0 = 525 THz ) as indicated in (a).

Fig. 4
Fig. 4

Nonlinear properties of the structure ( χ 3 = 2.4 × 10 9 esu ) in Fig. 3. (a) Output versus input intensity at three different frequencies (492.5, 485.5, and 477.5 THz ). (b) Intensities of thresholds for bistability versus frequencies of incident wave. The critical intensity of threshold E in 1 2 = E in 2 2 = 48.6 GW cm 2 .

Equations (2)

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ε Ag L = 1.0 ω p 2 ω 2 + i γ ω ,
ε Ag NL = ε Ag L + ε 0 χ 3 E 2 ,

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