Abstract

We investigate nonlinear transmission in a layered structure consisting of a slab of positive index material with Kerr-type nonlinearity and a subwavelength layer of linear negative index material (NIM) sandwiched between semi-infinite linear dielectrics. We find that a thin layer of NIM leads to significant changes in the hysteresis width when the nonlinear slab is illuminated at an angle near that of total internal reflection. Unidirectional diodelike transmission with enhanced operational range is demonstrated. These results may be useful for NIMs characterization and for designing novel NIMs-based devices.

© 2006 Optical Society of America

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References

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  1. V. M. Shalaev, W. Cai, U. K. Chettiar, H. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, Opt. Lett. 30, 3356 (2005).
    [CrossRef]
  2. S. Zhang, W. Fan, C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. Brueck, Phys. Rev. Lett. 95, 137404 (2005).
    [CrossRef] [PubMed]
  3. A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, Nature 438, 335 (2005).
    [CrossRef] [PubMed]
  4. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, Opt. Lett. 31, 1800 (2006).
    [CrossRef] [PubMed]
  5. V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, Phys. Rev. B 69, 165112 (2004).
    [CrossRef]
  6. G. D'Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Phys. Rev. Lett. 93, 213902 (2004).
    [CrossRef] [PubMed]
  7. A. A. Zharov, N. A. Zharova, I. V. Shadrivov, and Yu. S. Kivshar, Appl. Phys. Lett. 87, 091104 (2005).
    [CrossRef]
  8. M. W. Feise, I. V. Shadrivov, and Yu. S. Kivshar, Phys. Rev. E 71, 037602 (2005).
    [CrossRef]
  9. R. S. Hegde and H. Winful, Opt. Lett. 30, 1852 (2005).
    [CrossRef] [PubMed]
  10. A. K. Popov and V. M. Shalaev, Opt. Lett. 31, 2169 (2006).
    [CrossRef] [PubMed]
  11. A. K. Popov and V. M. Shalaev, Appl. Phys. B 84, 131 (2006).
    [CrossRef]
  12. H. M. Gibbs, Optical Bistability (Academic, 1985).
  13. A. L. Efros and A. L. Pokrovsky, Solid State Commun. 129, 643 (2004).
    [CrossRef]

2006 (3)

2005 (6)

A. A. Zharov, N. A. Zharova, I. V. Shadrivov, and Yu. S. Kivshar, Appl. Phys. Lett. 87, 091104 (2005).
[CrossRef]

M. W. Feise, I. V. Shadrivov, and Yu. S. Kivshar, Phys. Rev. E 71, 037602 (2005).
[CrossRef]

R. S. Hegde and H. Winful, Opt. Lett. 30, 1852 (2005).
[CrossRef] [PubMed]

V. M. Shalaev, W. Cai, U. K. Chettiar, H. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, Opt. Lett. 30, 3356 (2005).
[CrossRef]

S. Zhang, W. Fan, C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. Brueck, Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, Nature 438, 335 (2005).
[CrossRef] [PubMed]

2004 (3)

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, Phys. Rev. B 69, 165112 (2004).
[CrossRef]

G. D'Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Phys. Rev. Lett. 93, 213902 (2004).
[CrossRef] [PubMed]

A. L. Efros and A. L. Pokrovsky, Solid State Commun. 129, 643 (2004).
[CrossRef]

Agranovich, V. M.

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, Phys. Rev. B 69, 165112 (2004).
[CrossRef]

Baughman, R. H.

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, Phys. Rev. B 69, 165112 (2004).
[CrossRef]

Bloemer, M. J.

G. D'Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Phys. Rev. Lett. 93, 213902 (2004).
[CrossRef] [PubMed]

Brueck, S. R.

S. Zhang, W. Fan, C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. Brueck, Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

Cai, W.

Chettiar, U. K.

D'Aguanno, G.

G. D'Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Phys. Rev. Lett. 93, 213902 (2004).
[CrossRef] [PubMed]

Dolling, G.

Drachev, V. P.

Efros, A. L.

A. L. Efros and A. L. Pokrovsky, Solid State Commun. 129, 643 (2004).
[CrossRef]

Enkrich, C.

Fan, W.

S. Zhang, W. Fan, C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. Brueck, Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

Feise, M. W.

M. W. Feise, I. V. Shadrivov, and Yu. S. Kivshar, Phys. Rev. E 71, 037602 (2005).
[CrossRef]

Firsov, A. A.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, Nature 438, 335 (2005).
[CrossRef] [PubMed]

Geim, A. K.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, Nature 438, 335 (2005).
[CrossRef] [PubMed]

Gibbs, H. M.

H. M. Gibbs, Optical Bistability (Academic, 1985).

Gleeson, H. F.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, Nature 438, 335 (2005).
[CrossRef] [PubMed]

Grigorenko, A. N.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, Nature 438, 335 (2005).
[CrossRef] [PubMed]

Hegde, R. S.

Khrushchev, I. Y.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, Nature 438, 335 (2005).
[CrossRef] [PubMed]

Kildishev, A. V.

Kivshar, Yu. S.

A. A. Zharov, N. A. Zharova, I. V. Shadrivov, and Yu. S. Kivshar, Appl. Phys. Lett. 87, 091104 (2005).
[CrossRef]

M. W. Feise, I. V. Shadrivov, and Yu. S. Kivshar, Phys. Rev. E 71, 037602 (2005).
[CrossRef]

Linden, S.

Malloy, K. J.

S. Zhang, W. Fan, C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. Brueck, Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

Mattiucci, N.

G. D'Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Phys. Rev. Lett. 93, 213902 (2004).
[CrossRef] [PubMed]

Osgood, R. M.

S. Zhang, W. Fan, C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. Brueck, Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

Panoiu, C.

S. Zhang, W. Fan, C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. Brueck, Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

Petrovic, J.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, Nature 438, 335 (2005).
[CrossRef] [PubMed]

Pokrovsky, A. L.

A. L. Efros and A. L. Pokrovsky, Solid State Commun. 129, 643 (2004).
[CrossRef]

Popov, A. K.

A. K. Popov and V. M. Shalaev, Appl. Phys. B 84, 131 (2006).
[CrossRef]

A. K. Popov and V. M. Shalaev, Opt. Lett. 31, 2169 (2006).
[CrossRef] [PubMed]

Sarychev, A. K.

Scalora, M.

G. D'Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Phys. Rev. Lett. 93, 213902 (2004).
[CrossRef] [PubMed]

Shadrivov, I. V.

A. A. Zharov, N. A. Zharova, I. V. Shadrivov, and Yu. S. Kivshar, Appl. Phys. Lett. 87, 091104 (2005).
[CrossRef]

M. W. Feise, I. V. Shadrivov, and Yu. S. Kivshar, Phys. Rev. E 71, 037602 (2005).
[CrossRef]

Shalaev, V. M.

Shen, Y. R.

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, Phys. Rev. B 69, 165112 (2004).
[CrossRef]

Soukoulis, C. M.

Wegener, M.

Winful, H.

Yuan, H.

Zakhidov, A. A.

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, Phys. Rev. B 69, 165112 (2004).
[CrossRef]

Zhang, S.

S. Zhang, W. Fan, C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. Brueck, Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

Zhang, Y.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, Nature 438, 335 (2005).
[CrossRef] [PubMed]

Zharov, A. A.

A. A. Zharov, N. A. Zharova, I. V. Shadrivov, and Yu. S. Kivshar, Appl. Phys. Lett. 87, 091104 (2005).
[CrossRef]

Zharova, N. A.

A. A. Zharov, N. A. Zharova, I. V. Shadrivov, and Yu. S. Kivshar, Appl. Phys. Lett. 87, 091104 (2005).
[CrossRef]

Appl. Phys. B (1)

A. K. Popov and V. M. Shalaev, Appl. Phys. B 84, 131 (2006).
[CrossRef]

Appl. Phys. Lett. (1)

A. A. Zharov, N. A. Zharova, I. V. Shadrivov, and Yu. S. Kivshar, Appl. Phys. Lett. 87, 091104 (2005).
[CrossRef]

Nature (1)

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, Nature 438, 335 (2005).
[CrossRef] [PubMed]

Opt. Lett. (4)

Phys. Rev. B (1)

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, Phys. Rev. B 69, 165112 (2004).
[CrossRef]

Phys. Rev. E (1)

M. W. Feise, I. V. Shadrivov, and Yu. S. Kivshar, Phys. Rev. E 71, 037602 (2005).
[CrossRef]

Phys. Rev. Lett. (2)

S. Zhang, W. Fan, C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. Brueck, Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

G. D'Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Phys. Rev. Lett. 93, 213902 (2004).
[CrossRef] [PubMed]

Solid State Commun. (1)

A. L. Efros and A. L. Pokrovsky, Solid State Commun. 129, 643 (2004).
[CrossRef]

Other (1)

H. M. Gibbs, Optical Bistability (Academic, 1985).

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Figures (4)

Fig. 1
Fig. 1

Schematic of the layered structure under investigation. E in is the incident field, E r is the reflected field, and E t is the transmitted field.

Fig. 2
Fig. 2

(a) Linear transmission coefficient versus the angle of incidence for a single layer 1 (solid curve), the transmission coefficient for a combination of layer 1 and a NIM thin film (dashed curve), and the transmission coefficient for a combination of layer 1 and a PIM thin film (dotted–dashed curve). (b) Transmission coefficient versus the input flux corresponding to the three configurations in (a).

Fig. 3
Fig. 3

Comparison of the transmission coefficient versus the input flux for the case of fixed dielectric permittivity in the (a) NIM and (b) PIM layers and varying magnetic permeability, and for the case of fixed refractive index in the (c) NIM and (d) PIM layers and varying both magnetic permeability and dielectric permittivity. Vertical straight lines indicate the maximum bistability threshold in the PIM case.

Fig. 4
Fig. 4

Transmission coefficient versus the input flux for the layered structure shown in Fig. 1 when the light enters from the left [curve (1)] and when the light enters from the right [curve (2)]. Curves (3) and (4) correspond to the case of the PIM thin layer.

Equations (1)

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d 2 E d ζ 2 + p 2 E + μ L ε N L ( E 2 ) E = 0 ,

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