Abstract

We show that a nonlinear metal-dielectric layered slab of subwavelength thickness and very small average dielectric permittivity displays optical multistable behavior at arbitrary low optical intensities. This is due to the fact that, in the presence of the small linear permittivity, one of the multiple electromagnetic slab states exists no matter how small is the transmitted optical intensity. We prove that multiple states at ultra-low optical intensities can be reached only by simultaneously operating on the incident optical intensity and incidence angle. By performing full wave simulations, we prove that the predicted phenomenology is feasible and very robust.

© 2011 Optical Society of America

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  1. A. Szoke, V. Daneu, J. Goldhar, and N. A. Kurnit, "Bistable optical element and its applications," Appl. Phys. Lett. 15, 376 (1969).
    [CrossRef]
  2. E. Abraham, and S. D. Smith, "Optical bistability and related devices," Rep. Prog. Phys. 45, 815 (1982).
    [CrossRef]
  3. J. E. Sipe, and R. W. Boyd, "Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model," Phys. Rev. A 46, 1614 (1992).
    [CrossRef] [PubMed]
  4. N. N. Lepeshkin, A. Schweinsberg, G. Piredda, R. S. Bennink, and R. W. Boyd, "Enhanced nonlinear optical response of one-dimensional metal-dielectric photonic crystals," Phys. Rev. Lett. 93, 123902 (2004).
    [CrossRef] [PubMed]
  5. A. Husakou, and J. Herrmann, "Steplike transmission of light through a metal-dielectric multilayer structure due to an intensity-dependent sign of the effective dielectric constant," Phys. Rev. Lett. 99, 127402 (2007).
    [CrossRef] [PubMed]
  6. J. Chen, P. Wang, X. Wang, Y. Lu, and R. Zheng, "Optical bistability enhanced by highly localized bulk plasmon polariton modes in subwavelength metal-nonlinear dielectric multilayer structure," Appl. Phys. Lett. 94, 081117 (2009).
    [CrossRef]
  7. R. K. Hickernell, and D. Sarid, "Optical bistability using prism-coupled, long-range surface plasmons," J. Opt. Soc. Am. B 3, 1059 (1986).
    [CrossRef]
  8. A. Ciattoni, C. Rizza, and E. Palange, "Extreme nonlinear electrodynamics in metamaterials with very small linear dielectric permittivity," Phys. Rev. A 81, 043839 (2010).
    [CrossRef]
  9. A. Ciattoni, C. Rizza, and E. Palange, "Transmissivity directional hysteresis of a nonlinear metamaterial slab with very small linear permittivity," Opt. Lett. 35, 2130 (2010).
    [CrossRef] [PubMed]
  10. It is worth noting that, in the considered situation, the longitudinal component Az is not due to surface waves (which here are not excited) since, as explained in Sec. 2, the strong values of Az belonging to the lower sheet of the surface in Fig. 2(c) arises from the impact of the nonlinearity on the boundary matching conditions at z = 0 and z = L.
  11. COMSOL, www.comsol.com.
  12. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, San Diego, 1998).
  13. G. Yang, D. Guan, W. Wang, W. Wu, and Z. Chen, "The inherent optical nonlinearities of thin silver films," Opt. Mater. 25, 439 (2004).
    [CrossRef]
  14. W. Cai, and V. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, Dordrecht, 2010).
  15. Y. Fu, L. Thylén, and H. Agrenm, "A Lossless Negative Dielectric Constant from Quantum Dot Exciton Polaritons," Nano Lett. 8, 1551 (2008).
    [CrossRef] [PubMed]

2010 (2)

A. Ciattoni, C. Rizza, and E. Palange, "Extreme nonlinear electrodynamics in metamaterials with very small linear dielectric permittivity," Phys. Rev. A 81, 043839 (2010).
[CrossRef]

A. Ciattoni, C. Rizza, and E. Palange, "Transmissivity directional hysteresis of a nonlinear metamaterial slab with very small linear permittivity," Opt. Lett. 35, 2130 (2010).
[CrossRef] [PubMed]

2009 (1)

J. Chen, P. Wang, X. Wang, Y. Lu, and R. Zheng, "Optical bistability enhanced by highly localized bulk plasmon polariton modes in subwavelength metal-nonlinear dielectric multilayer structure," Appl. Phys. Lett. 94, 081117 (2009).
[CrossRef]

2008 (1)

Y. Fu, L. Thylén, and H. Agrenm, "A Lossless Negative Dielectric Constant from Quantum Dot Exciton Polaritons," Nano Lett. 8, 1551 (2008).
[CrossRef] [PubMed]

2007 (1)

A. Husakou, and J. Herrmann, "Steplike transmission of light through a metal-dielectric multilayer structure due to an intensity-dependent sign of the effective dielectric constant," Phys. Rev. Lett. 99, 127402 (2007).
[CrossRef] [PubMed]

2004 (2)

G. Yang, D. Guan, W. Wang, W. Wu, and Z. Chen, "The inherent optical nonlinearities of thin silver films," Opt. Mater. 25, 439 (2004).
[CrossRef]

N. N. Lepeshkin, A. Schweinsberg, G. Piredda, R. S. Bennink, and R. W. Boyd, "Enhanced nonlinear optical response of one-dimensional metal-dielectric photonic crystals," Phys. Rev. Lett. 93, 123902 (2004).
[CrossRef] [PubMed]

1992 (1)

J. E. Sipe, and R. W. Boyd, "Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model," Phys. Rev. A 46, 1614 (1992).
[CrossRef] [PubMed]

1986 (1)

1982 (1)

E. Abraham, and S. D. Smith, "Optical bistability and related devices," Rep. Prog. Phys. 45, 815 (1982).
[CrossRef]

1969 (1)

A. Szoke, V. Daneu, J. Goldhar, and N. A. Kurnit, "Bistable optical element and its applications," Appl. Phys. Lett. 15, 376 (1969).
[CrossRef]

Abraham, E.

E. Abraham, and S. D. Smith, "Optical bistability and related devices," Rep. Prog. Phys. 45, 815 (1982).
[CrossRef]

Agrenm, H.

Y. Fu, L. Thylén, and H. Agrenm, "A Lossless Negative Dielectric Constant from Quantum Dot Exciton Polaritons," Nano Lett. 8, 1551 (2008).
[CrossRef] [PubMed]

Bennink, R. S.

N. N. Lepeshkin, A. Schweinsberg, G. Piredda, R. S. Bennink, and R. W. Boyd, "Enhanced nonlinear optical response of one-dimensional metal-dielectric photonic crystals," Phys. Rev. Lett. 93, 123902 (2004).
[CrossRef] [PubMed]

Boyd, R. W.

N. N. Lepeshkin, A. Schweinsberg, G. Piredda, R. S. Bennink, and R. W. Boyd, "Enhanced nonlinear optical response of one-dimensional metal-dielectric photonic crystals," Phys. Rev. Lett. 93, 123902 (2004).
[CrossRef] [PubMed]

J. E. Sipe, and R. W. Boyd, "Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model," Phys. Rev. A 46, 1614 (1992).
[CrossRef] [PubMed]

Chen, J.

J. Chen, P. Wang, X. Wang, Y. Lu, and R. Zheng, "Optical bistability enhanced by highly localized bulk plasmon polariton modes in subwavelength metal-nonlinear dielectric multilayer structure," Appl. Phys. Lett. 94, 081117 (2009).
[CrossRef]

Chen, Z.

G. Yang, D. Guan, W. Wang, W. Wu, and Z. Chen, "The inherent optical nonlinearities of thin silver films," Opt. Mater. 25, 439 (2004).
[CrossRef]

Ciattoni, A.

A. Ciattoni, C. Rizza, and E. Palange, "Extreme nonlinear electrodynamics in metamaterials with very small linear dielectric permittivity," Phys. Rev. A 81, 043839 (2010).
[CrossRef]

A. Ciattoni, C. Rizza, and E. Palange, "Transmissivity directional hysteresis of a nonlinear metamaterial slab with very small linear permittivity," Opt. Lett. 35, 2130 (2010).
[CrossRef] [PubMed]

Daneu, V.

A. Szoke, V. Daneu, J. Goldhar, and N. A. Kurnit, "Bistable optical element and its applications," Appl. Phys. Lett. 15, 376 (1969).
[CrossRef]

Fu, Y.

Y. Fu, L. Thylén, and H. Agrenm, "A Lossless Negative Dielectric Constant from Quantum Dot Exciton Polaritons," Nano Lett. 8, 1551 (2008).
[CrossRef] [PubMed]

Goldhar, J.

A. Szoke, V. Daneu, J. Goldhar, and N. A. Kurnit, "Bistable optical element and its applications," Appl. Phys. Lett. 15, 376 (1969).
[CrossRef]

Guan, D.

G. Yang, D. Guan, W. Wang, W. Wu, and Z. Chen, "The inherent optical nonlinearities of thin silver films," Opt. Mater. 25, 439 (2004).
[CrossRef]

Herrmann, J.

A. Husakou, and J. Herrmann, "Steplike transmission of light through a metal-dielectric multilayer structure due to an intensity-dependent sign of the effective dielectric constant," Phys. Rev. Lett. 99, 127402 (2007).
[CrossRef] [PubMed]

Hickernell, R. K.

Husakou, A.

A. Husakou, and J. Herrmann, "Steplike transmission of light through a metal-dielectric multilayer structure due to an intensity-dependent sign of the effective dielectric constant," Phys. Rev. Lett. 99, 127402 (2007).
[CrossRef] [PubMed]

Kurnit, N. A.

A. Szoke, V. Daneu, J. Goldhar, and N. A. Kurnit, "Bistable optical element and its applications," Appl. Phys. Lett. 15, 376 (1969).
[CrossRef]

Lepeshkin, N. N.

N. N. Lepeshkin, A. Schweinsberg, G. Piredda, R. S. Bennink, and R. W. Boyd, "Enhanced nonlinear optical response of one-dimensional metal-dielectric photonic crystals," Phys. Rev. Lett. 93, 123902 (2004).
[CrossRef] [PubMed]

Lu, Y.

J. Chen, P. Wang, X. Wang, Y. Lu, and R. Zheng, "Optical bistability enhanced by highly localized bulk plasmon polariton modes in subwavelength metal-nonlinear dielectric multilayer structure," Appl. Phys. Lett. 94, 081117 (2009).
[CrossRef]

Palange, E.

A. Ciattoni, C. Rizza, and E. Palange, "Transmissivity directional hysteresis of a nonlinear metamaterial slab with very small linear permittivity," Opt. Lett. 35, 2130 (2010).
[CrossRef] [PubMed]

A. Ciattoni, C. Rizza, and E. Palange, "Extreme nonlinear electrodynamics in metamaterials with very small linear dielectric permittivity," Phys. Rev. A 81, 043839 (2010).
[CrossRef]

Piredda, G.

N. N. Lepeshkin, A. Schweinsberg, G. Piredda, R. S. Bennink, and R. W. Boyd, "Enhanced nonlinear optical response of one-dimensional metal-dielectric photonic crystals," Phys. Rev. Lett. 93, 123902 (2004).
[CrossRef] [PubMed]

Rizza, C.

A. Ciattoni, C. Rizza, and E. Palange, "Transmissivity directional hysteresis of a nonlinear metamaterial slab with very small linear permittivity," Opt. Lett. 35, 2130 (2010).
[CrossRef] [PubMed]

A. Ciattoni, C. Rizza, and E. Palange, "Extreme nonlinear electrodynamics in metamaterials with very small linear dielectric permittivity," Phys. Rev. A 81, 043839 (2010).
[CrossRef]

Sarid, D.

Schweinsberg, A.

N. N. Lepeshkin, A. Schweinsberg, G. Piredda, R. S. Bennink, and R. W. Boyd, "Enhanced nonlinear optical response of one-dimensional metal-dielectric photonic crystals," Phys. Rev. Lett. 93, 123902 (2004).
[CrossRef] [PubMed]

Sipe, J. E.

J. E. Sipe, and R. W. Boyd, "Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model," Phys. Rev. A 46, 1614 (1992).
[CrossRef] [PubMed]

Smith, S. D.

E. Abraham, and S. D. Smith, "Optical bistability and related devices," Rep. Prog. Phys. 45, 815 (1982).
[CrossRef]

Szoke, A.

A. Szoke, V. Daneu, J. Goldhar, and N. A. Kurnit, "Bistable optical element and its applications," Appl. Phys. Lett. 15, 376 (1969).
[CrossRef]

Thylén, L.

Y. Fu, L. Thylén, and H. Agrenm, "A Lossless Negative Dielectric Constant from Quantum Dot Exciton Polaritons," Nano Lett. 8, 1551 (2008).
[CrossRef] [PubMed]

Wang, P.

J. Chen, P. Wang, X. Wang, Y. Lu, and R. Zheng, "Optical bistability enhanced by highly localized bulk plasmon polariton modes in subwavelength metal-nonlinear dielectric multilayer structure," Appl. Phys. Lett. 94, 081117 (2009).
[CrossRef]

Wang, W.

G. Yang, D. Guan, W. Wang, W. Wu, and Z. Chen, "The inherent optical nonlinearities of thin silver films," Opt. Mater. 25, 439 (2004).
[CrossRef]

Wang, X.

J. Chen, P. Wang, X. Wang, Y. Lu, and R. Zheng, "Optical bistability enhanced by highly localized bulk plasmon polariton modes in subwavelength metal-nonlinear dielectric multilayer structure," Appl. Phys. Lett. 94, 081117 (2009).
[CrossRef]

Wu, W.

G. Yang, D. Guan, W. Wang, W. Wu, and Z. Chen, "The inherent optical nonlinearities of thin silver films," Opt. Mater. 25, 439 (2004).
[CrossRef]

Yang, G.

G. Yang, D. Guan, W. Wang, W. Wu, and Z. Chen, "The inherent optical nonlinearities of thin silver films," Opt. Mater. 25, 439 (2004).
[CrossRef]

Zheng, R.

J. Chen, P. Wang, X. Wang, Y. Lu, and R. Zheng, "Optical bistability enhanced by highly localized bulk plasmon polariton modes in subwavelength metal-nonlinear dielectric multilayer structure," Appl. Phys. Lett. 94, 081117 (2009).
[CrossRef]

Appl. Phys. Lett. (2)

A. Szoke, V. Daneu, J. Goldhar, and N. A. Kurnit, "Bistable optical element and its applications," Appl. Phys. Lett. 15, 376 (1969).
[CrossRef]

J. Chen, P. Wang, X. Wang, Y. Lu, and R. Zheng, "Optical bistability enhanced by highly localized bulk plasmon polariton modes in subwavelength metal-nonlinear dielectric multilayer structure," Appl. Phys. Lett. 94, 081117 (2009).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nano Lett. (1)

Y. Fu, L. Thylén, and H. Agrenm, "A Lossless Negative Dielectric Constant from Quantum Dot Exciton Polaritons," Nano Lett. 8, 1551 (2008).
[CrossRef] [PubMed]

Opt. Lett. (1)

Opt. Mater. (1)

G. Yang, D. Guan, W. Wang, W. Wu, and Z. Chen, "The inherent optical nonlinearities of thin silver films," Opt. Mater. 25, 439 (2004).
[CrossRef]

Phys. Rev. A (2)

A. Ciattoni, C. Rizza, and E. Palange, "Extreme nonlinear electrodynamics in metamaterials with very small linear dielectric permittivity," Phys. Rev. A 81, 043839 (2010).
[CrossRef]

J. E. Sipe, and R. W. Boyd, "Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model," Phys. Rev. A 46, 1614 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

N. N. Lepeshkin, A. Schweinsberg, G. Piredda, R. S. Bennink, and R. W. Boyd, "Enhanced nonlinear optical response of one-dimensional metal-dielectric photonic crystals," Phys. Rev. Lett. 93, 123902 (2004).
[CrossRef] [PubMed]

A. Husakou, and J. Herrmann, "Steplike transmission of light through a metal-dielectric multilayer structure due to an intensity-dependent sign of the effective dielectric constant," Phys. Rev. Lett. 99, 127402 (2007).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

E. Abraham, and S. D. Smith, "Optical bistability and related devices," Rep. Prog. Phys. 45, 815 (1982).
[CrossRef]

Other (4)

It is worth noting that, in the considered situation, the longitudinal component Az is not due to surface waves (which here are not excited) since, as explained in Sec. 2, the strong values of Az belonging to the lower sheet of the surface in Fig. 2(c) arises from the impact of the nonlinearity on the boundary matching conditions at z = 0 and z = L.

COMSOL, www.comsol.com.

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, San Diego, 1998).

W. Cai, and V. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, Dordrecht, 2010).

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Figures (3)

Fig. 1
Fig. 1

Geometry of the layered metal-dielectric slab and of the TM incident (i), reflected (r) and transmitted (t) plane waves.

Fig. 2
Fig. 2

Nonlinear slab transmissivity T (solid line) as a function of the normalized input field intensity Iin at the fixed incident angles θ = 0.028 rad (panel (a)) and θ = 0.170 rad (panel (b)). (c) Surface |χ|1/2Az and values of |χ|1/2Az (solid lines) corresponding to the transmissivities of panels (a) and (b). In the three panels, capital letters label some reference states. (d) Slab transmissivity T as a function of both the incident optical intensity Iin and incidence angle θ. Dashed lines represent the slab transmissivity of panels (a) and (b) and capital letters label the same reference states as in panels (a) and (b). In the inset the plane of independent parameters Iin and θ is reported together with the region at which slab multistability occurs (shaded region).

Fig. 3
Fig. 3

(a) Comparison between the slab transmissivities evaluated through full-wave simulations (dotted lines) and those of Fig. 2(b) (solid lines). (b) Semi-log plot of the maximum values, within the layered medium bulk, of the normalized squared field components as a function of the normalized input field amplitude obtained for the full-wave evaluation of the slab transmissivity reported in panel (a).

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