Abstract

We investigate propagation of a transverse magnetic field through a nonlinear metamaterial slab of subwavelength thickness and with a very small and negative linear dielectric permittivity. We prove that, for a given input intensity, the output intensity is a multivalued function of the field incidence angle so that the transmissivity exhibits angular multistability and a pronounced directional hysteresis behavior. The predicted directional hysteresis is a consequence of the fact that the linear and nonlinear contributions to the overall dielectric response can be comparable so that the electromagnetic matching conditions at the output slab boundary allow more than one field configuration within the slab to be compatible with the transmitted field.

© 2010 Optical Society of America

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  1. W. Chen and D. L. Mills, Phys. Rev. B 35, 524 (1987).
    [CrossRef]
  2. E. Abrhaham and S. D. Smith, Rep. Prog. Phys. 45, 815 (1982).
    [CrossRef]
  3. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, Science 305, 788 (2004).
    [CrossRef] [PubMed]
  4. N. M. Litchinitser, I. R. Gabitov, and A. I. Maimistov, Phys. Rev. Lett. 99, 113902 (2007).
    [CrossRef] [PubMed]
  5. M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, Appl. Phys. Lett. 85, 1451 (2004).
    [CrossRef]
  6. R. S. Hegde and H. G. Winful, Opt. Lett. 30, 1852 (2005).
    [CrossRef] [PubMed]
  7. A. Husakou and J. Herrmann, Phys. Rev. Lett. 99, 127402 (2007).
    [CrossRef] [PubMed]
  8. A. Ciattoni, C. Rizza, and E. Palange, Phys. Rev. A 81, 043839 (2010).
  9. A. Ciattoni, C. Rizza, and E. Palange, Opt. Express 18, 11911 (2010).
    [CrossRef] [PubMed]
  10. S. A. Ramakrishna and J. B. Pendry, Phys. Rev. B 67, 201101(R) (2003).

2010 (1)

2007 (2)

N. M. Litchinitser, I. R. Gabitov, and A. I. Maimistov, Phys. Rev. Lett. 99, 113902 (2007).
[CrossRef] [PubMed]

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

2005 (1)

2004 (2)

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, Science 305, 788 (2004).
[CrossRef] [PubMed]

M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, Appl. Phys. Lett. 85, 1451 (2004).
[CrossRef]

2003 (1)

S. A. Ramakrishna and J. B. Pendry, Phys. Rev. B 67, 201101(R) (2003).

1987 (1)

W. Chen and D. L. Mills, Phys. Rev. B 35, 524 (1987).
[CrossRef]

1982 (1)

E. Abrhaham and S. D. Smith, Rep. Prog. Phys. 45, 815 (1982).
[CrossRef]

Abrhaham, E.

E. Abrhaham and S. D. Smith, Rep. Prog. Phys. 45, 815 (1982).
[CrossRef]

Chen, W.

W. Chen and D. L. Mills, Phys. Rev. B 35, 524 (1987).
[CrossRef]

Ciattoni, A.

A. Ciattoni, C. Rizza, and E. Palange, Opt. Express 18, 11911 (2010).
[CrossRef] [PubMed]

A. Ciattoni, C. Rizza, and E. Palange, Phys. Rev. A 81, 043839 (2010).

Feise, M. W.

M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, Appl. Phys. Lett. 85, 1451 (2004).
[CrossRef]

Gabitov, I. R.

N. M. Litchinitser, I. R. Gabitov, and A. I. Maimistov, Phys. Rev. Lett. 99, 113902 (2007).
[CrossRef] [PubMed]

Hegde, R. S.

Herrmann, J.

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

Husakou, A.

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

Kivshar, Y. S.

M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, Appl. Phys. Lett. 85, 1451 (2004).
[CrossRef]

Litchinitser, N. M.

N. M. Litchinitser, I. R. Gabitov, and A. I. Maimistov, Phys. Rev. Lett. 99, 113902 (2007).
[CrossRef] [PubMed]

Maimistov, A. I.

N. M. Litchinitser, I. R. Gabitov, and A. I. Maimistov, Phys. Rev. Lett. 99, 113902 (2007).
[CrossRef] [PubMed]

Mills, D. L.

W. Chen and D. L. Mills, Phys. Rev. B 35, 524 (1987).
[CrossRef]

Palange, E.

A. Ciattoni, C. Rizza, and E. Palange, Opt. Express 18, 11911 (2010).
[CrossRef] [PubMed]

A. Ciattoni, C. Rizza, and E. Palange, Phys. Rev. A 81, 043839 (2010).

Pendry, J. B.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, Science 305, 788 (2004).
[CrossRef] [PubMed]

S. A. Ramakrishna and J. B. Pendry, Phys. Rev. B 67, 201101(R) (2003).

Ramakrishna, S. A.

S. A. Ramakrishna and J. B. Pendry, Phys. Rev. B 67, 201101(R) (2003).

Rizza, C.

A. Ciattoni, C. Rizza, and E. Palange, Opt. Express 18, 11911 (2010).
[CrossRef] [PubMed]

A. Ciattoni, C. Rizza, and E. Palange, Phys. Rev. A 81, 043839 (2010).

Shadrivov, I. V.

M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, Appl. Phys. Lett. 85, 1451 (2004).
[CrossRef]

Smith, D. R.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, Science 305, 788 (2004).
[CrossRef] [PubMed]

Smith, S. D.

E. Abrhaham and S. D. Smith, Rep. Prog. Phys. 45, 815 (1982).
[CrossRef]

Wiltshire, M. C. K.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, Science 305, 788 (2004).
[CrossRef] [PubMed]

Winful, H. G.

Appl. Phys. Lett. (1)

M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, Appl. Phys. Lett. 85, 1451 (2004).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (1)

A. Ciattoni, C. Rizza, and E. Palange, Phys. Rev. A 81, 043839 (2010).

Phys. Rev. B (2)

S. A. Ramakrishna and J. B. Pendry, Phys. Rev. B 67, 201101(R) (2003).

W. Chen and D. L. Mills, Phys. Rev. B 35, 524 (1987).
[CrossRef]

Phys. Rev. Lett. (2)

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

N. M. Litchinitser, I. R. Gabitov, and A. I. Maimistov, Phys. Rev. Lett. 99, 113902 (2007).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

E. Abrhaham and S. D. Smith, Rep. Prog. Phys. 45, 815 (1982).
[CrossRef]

Science (1)

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, Science 305, 788 (2004).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

(a) Geometry of the metamaterial slab. (b) Geometry of the TM incident (i), reflected (r) and transmitted (t) plane waves together with the TM field within the slab.

Fig. 2
Fig. 2

Slab transmissivity T as a function of θ for | E i | = 10 6 | χ | 1 / 2 (dashed curve) and for | E i | = 5.3 · 10 4 | χ | 1 / 2 (solid curve), for a slab with ϵ = 0.001 and χ > 0 .

Fig. 3
Fig. 3

Surface | χ | 1 / 2 A z obtained by Eq. (3), in the case ϵ = 0.001 and χ > 0 .

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

D x = ϵ 0 { ϵ E x + χ [ ( | E x | 2 + | E z | 2 ) E x + 1 2 ( E x 2 + E z 2 ) E x * ] } , D z = ϵ 0 { ϵ E z + χ [ ( | E x | 2 + | E z | 2 ) E z + 1 2 ( E x 2 + E z 2 ) E z * ] } ,
d E x d z = i ( k 0 sin θ ) E z + i ω μ 0 H y , d H y d z = i ω D x , ( k 0 sin θ ) H y = ω D z ,
[ ϵ + 3 2 χ ( | E t | 2 cos 2 θ + A z 2 ) ] A z + | E t | sin θ = 0 ,

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