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 OSA

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References

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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,” App. 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. Thyln, 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,” App. Phys. Lett. 94, 081117 (2009).
[Crossref]

2008 (1)

Y. Fu, L. Thyln, 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. Thyln, 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]

Cai, W.

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

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,” App. 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. Thyln, 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,” App. Phys. Lett. 94, 081117 (2009).
[Crossref]

Palange, E.

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]

Palik, E. D.

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

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, “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]

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]

Shalaev, V.

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

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]

Thyln, L.

Y. Fu, L. Thyln, 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,” App. 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,” App. 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,” App. Phys. Lett. 94, 081117 (2009).
[Crossref]

App. Phys. Lett. (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,” App. Phys. Lett. 94, 081117 (2009).
[Crossref]

Appl. Phys. Lett. (1)

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

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

Nano Lett. (1)

Y. Fu, L. Thyln, 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 (1)

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]

Phys. Rev. Lett. (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]

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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