Abstract

In this paper, we discuss the existence of an electromagnetic mode propagating in a thin dielectric film deposited on a metallic film at the particular frequency such that the dielectric permittivity vanishes. We discuss the remarkable properties of this mode in terms of extreme subwavelength mode confinment and its potential applications. We also discuss the link between this mode, the IR absorption peak on a thin dielectric film known as Berreman effect and the surface phonon polariton mode at the air/dielectric interface. Finally, we establish a connection with the polarization shift occuring in quantum wells.

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References

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  1. H. Raether, Surface Plasmons (Springer Verlag, 1988).
  2. K. Holst and H. Raether, “The influence of thin surface films on the plasma resonance emission,” Opt. Commun.2, 312–316 (1970).
    [CrossRef]
  3. N. W. Ascroft and N. D. Mermin, Solid State Physics (Harcourt College Publishers, Berlin, 1976).
  4. K. L. Kliewer and R. Fuchs, “Optical modes of vibration in an ionic crystal slab including retardation. II. Radiative Region,” Phys. Rev.150, 573–588 (1966).
    [CrossRef]
  5. D. W. Berreman, “Infrared absorption at longitudinal optic frequency in cubic crystal films,” Phys. Rev.130, 2193–2198 (1963).
    [CrossRef]
  6. R. Ruppin and R. Englman, “Optical phonons of small crystals,” Rep. Progr. Phys.33, 149–196 (1970).
    [CrossRef]
  7. F. Proix and M. Balkanski, “Infrared measurements on CdS thin films deposited on aluminium,” Phys. Status Solidi b32, 119–126 (1969).
    [CrossRef]
  8. E. A. Vinogradov, G. N. Zizhin, and V. I. Yudson, Surface Polaritons, Ed. V. M. Agranovich and D. L. Mills, (North Holland, 1982).
  9. M. Schubert, Infrared Ellipsometry on Semiconductor Layer Structures (Springer, 2004).
  10. M. G. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett.97, 157403, (2006).
    [CrossRef] [PubMed]
  11. A. Al, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B75, 155410, (2007).
    [CrossRef]
  12. U. Fano, “The theory of anomalous diffraction gratings and of quasi-stationnary waves on metallic surfaces (Sommerfeld’s waves)”, J. Opt. Soc. Am.31, 213 (1941).
    [CrossRef]
  13. A. Archambault, T. V. Teperik, F. Marquier, and JJ. Greffet, “Surface plasmon Fourier optics,” Phys. Rev. B79, 195414 (2009).
  14. R. W. Alexander, G. S. Kovener, and R. J. Bell, “Dispersion curves for surface electromagnetic waves with damping,” Phys. Rev. Lett.32, 154–157 (1974).
    [CrossRef]
  15. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1985).
  16. M. Zaluzny, “Influence of the depolarization effect on the nonlinear intersubband absorption spectra of quantum wells,” Phys. Rev. B47, 3995–3998 (1993).
    [CrossRef]

2007 (1)

A. Al, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B75, 155410, (2007).
[CrossRef]

2006 (1)

M. G. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett.97, 157403, (2006).
[CrossRef] [PubMed]

1993 (1)

M. Zaluzny, “Influence of the depolarization effect on the nonlinear intersubband absorption spectra of quantum wells,” Phys. Rev. B47, 3995–3998 (1993).
[CrossRef]

1974 (1)

R. W. Alexander, G. S. Kovener, and R. J. Bell, “Dispersion curves for surface electromagnetic waves with damping,” Phys. Rev. Lett.32, 154–157 (1974).
[CrossRef]

1970 (2)

K. Holst and H. Raether, “The influence of thin surface films on the plasma resonance emission,” Opt. Commun.2, 312–316 (1970).
[CrossRef]

R. Ruppin and R. Englman, “Optical phonons of small crystals,” Rep. Progr. Phys.33, 149–196 (1970).
[CrossRef]

1969 (1)

F. Proix and M. Balkanski, “Infrared measurements on CdS thin films deposited on aluminium,” Phys. Status Solidi b32, 119–126 (1969).
[CrossRef]

1966 (1)

K. L. Kliewer and R. Fuchs, “Optical modes of vibration in an ionic crystal slab including retardation. II. Radiative Region,” Phys. Rev.150, 573–588 (1966).
[CrossRef]

1963 (1)

D. W. Berreman, “Infrared absorption at longitudinal optic frequency in cubic crystal films,” Phys. Rev.130, 2193–2198 (1963).
[CrossRef]

1954 (1)

A. Archambault, T. V. Teperik, F. Marquier, and JJ. Greffet, “Surface plasmon Fourier optics,” Phys. Rev. B79, 195414 (2009).

1941 (1)

Al, A.

A. Al, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B75, 155410, (2007).
[CrossRef]

Alexander, R. W.

R. W. Alexander, G. S. Kovener, and R. J. Bell, “Dispersion curves for surface electromagnetic waves with damping,” Phys. Rev. Lett.32, 154–157 (1974).
[CrossRef]

Archambault, A.

A. Archambault, T. V. Teperik, F. Marquier, and JJ. Greffet, “Surface plasmon Fourier optics,” Phys. Rev. B79, 195414 (2009).

Ascroft, N. W.

N. W. Ascroft and N. D. Mermin, Solid State Physics (Harcourt College Publishers, Berlin, 1976).

Balkanski, M.

F. Proix and M. Balkanski, “Infrared measurements on CdS thin films deposited on aluminium,” Phys. Status Solidi b32, 119–126 (1969).
[CrossRef]

Bell, R. J.

R. W. Alexander, G. S. Kovener, and R. J. Bell, “Dispersion curves for surface electromagnetic waves with damping,” Phys. Rev. Lett.32, 154–157 (1974).
[CrossRef]

Berreman, D. W.

D. W. Berreman, “Infrared absorption at longitudinal optic frequency in cubic crystal films,” Phys. Rev.130, 2193–2198 (1963).
[CrossRef]

Engheta, N.

A. Al, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B75, 155410, (2007).
[CrossRef]

M. G. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett.97, 157403, (2006).
[CrossRef] [PubMed]

Englman, R.

R. Ruppin and R. Englman, “Optical phonons of small crystals,” Rep. Progr. Phys.33, 149–196 (1970).
[CrossRef]

Fano, U.

Fuchs, R.

K. L. Kliewer and R. Fuchs, “Optical modes of vibration in an ionic crystal slab including retardation. II. Radiative Region,” Phys. Rev.150, 573–588 (1966).
[CrossRef]

Greffet, JJ.

A. Archambault, T. V. Teperik, F. Marquier, and JJ. Greffet, “Surface plasmon Fourier optics,” Phys. Rev. B79, 195414 (2009).

Holst, K.

K. Holst and H. Raether, “The influence of thin surface films on the plasma resonance emission,” Opt. Commun.2, 312–316 (1970).
[CrossRef]

Kliewer, K. L.

K. L. Kliewer and R. Fuchs, “Optical modes of vibration in an ionic crystal slab including retardation. II. Radiative Region,” Phys. Rev.150, 573–588 (1966).
[CrossRef]

Kovener, G. S.

R. W. Alexander, G. S. Kovener, and R. J. Bell, “Dispersion curves for surface electromagnetic waves with damping,” Phys. Rev. Lett.32, 154–157 (1974).
[CrossRef]

Marquier, F.

A. Archambault, T. V. Teperik, F. Marquier, and JJ. Greffet, “Surface plasmon Fourier optics,” Phys. Rev. B79, 195414 (2009).

Mermin, N. D.

N. W. Ascroft and N. D. Mermin, Solid State Physics (Harcourt College Publishers, Berlin, 1976).

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1985).

Proix, F.

F. Proix and M. Balkanski, “Infrared measurements on CdS thin films deposited on aluminium,” Phys. Status Solidi b32, 119–126 (1969).
[CrossRef]

Raether, H.

K. Holst and H. Raether, “The influence of thin surface films on the plasma resonance emission,” Opt. Commun.2, 312–316 (1970).
[CrossRef]

H. Raether, Surface Plasmons (Springer Verlag, 1988).

Ruppin, R.

R. Ruppin and R. Englman, “Optical phonons of small crystals,” Rep. Progr. Phys.33, 149–196 (1970).
[CrossRef]

Salandrino, A.

A. Al, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B75, 155410, (2007).
[CrossRef]

Schubert, M.

M. Schubert, Infrared Ellipsometry on Semiconductor Layer Structures (Springer, 2004).

Silveirinha, M. G.

A. Al, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B75, 155410, (2007).
[CrossRef]

M. G. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett.97, 157403, (2006).
[CrossRef] [PubMed]

Teperik, T. V.

A. Archambault, T. V. Teperik, F. Marquier, and JJ. Greffet, “Surface plasmon Fourier optics,” Phys. Rev. B79, 195414 (2009).

Vinogradov, E. A.

E. A. Vinogradov, G. N. Zizhin, and V. I. Yudson, Surface Polaritons, Ed. V. M. Agranovich and D. L. Mills, (North Holland, 1982).

Yudson, V. I.

E. A. Vinogradov, G. N. Zizhin, and V. I. Yudson, Surface Polaritons, Ed. V. M. Agranovich and D. L. Mills, (North Holland, 1982).

Zaluzny, M.

M. Zaluzny, “Influence of the depolarization effect on the nonlinear intersubband absorption spectra of quantum wells,” Phys. Rev. B47, 3995–3998 (1993).
[CrossRef]

Zizhin, G. N.

E. A. Vinogradov, G. N. Zizhin, and V. I. Yudson, Surface Polaritons, Ed. V. M. Agranovich and D. L. Mills, (North Holland, 1982).

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

K. Holst and H. Raether, “The influence of thin surface films on the plasma resonance emission,” Opt. Commun.2, 312–316 (1970).
[CrossRef]

Phys. Rev. (2)

K. L. Kliewer and R. Fuchs, “Optical modes of vibration in an ionic crystal slab including retardation. II. Radiative Region,” Phys. Rev.150, 573–588 (1966).
[CrossRef]

D. W. Berreman, “Infrared absorption at longitudinal optic frequency in cubic crystal films,” Phys. Rev.130, 2193–2198 (1963).
[CrossRef]

Phys. Rev. B (3)

M. Zaluzny, “Influence of the depolarization effect on the nonlinear intersubband absorption spectra of quantum wells,” Phys. Rev. B47, 3995–3998 (1993).
[CrossRef]

A. Al, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B75, 155410, (2007).
[CrossRef]

A. Archambault, T. V. Teperik, F. Marquier, and JJ. Greffet, “Surface plasmon Fourier optics,” Phys. Rev. B79, 195414 (2009).

Phys. Rev. Lett. (2)

R. W. Alexander, G. S. Kovener, and R. J. Bell, “Dispersion curves for surface electromagnetic waves with damping,” Phys. Rev. Lett.32, 154–157 (1974).
[CrossRef]

M. G. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett.97, 157403, (2006).
[CrossRef] [PubMed]

Phys. Status Solidi b (1)

F. Proix and M. Balkanski, “Infrared measurements on CdS thin films deposited on aluminium,” Phys. Status Solidi b32, 119–126 (1969).
[CrossRef]

Rep. Progr. Phys. (1)

R. Ruppin and R. Englman, “Optical phonons of small crystals,” Rep. Progr. Phys.33, 149–196 (1970).
[CrossRef]

Other (5)

N. W. Ascroft and N. D. Mermin, Solid State Physics (Harcourt College Publishers, Berlin, 1976).

E. A. Vinogradov, G. N. Zizhin, and V. I. Yudson, Surface Polaritons, Ed. V. M. Agranovich and D. L. Mills, (North Holland, 1982).

M. Schubert, Infrared Ellipsometry on Semiconductor Layer Structures (Springer, 2004).

H. Raether, Surface Plasmons (Springer Verlag, 1988).

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1985).

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Figures (5)

Fig. 1
Fig. 1

Sketch of the geometry. A SiO2 film is deposited onto a gold substrate. The thickness of this film is denoted by d. In the next figures, the upper medium is air (ε1 = 1).

Fig. 2
Fig. 2

Dispersion relation for three different film thicknesses. Point A corresponds to the Berreman leaky mode, Point B corresponds to the ENZ mode, Point C corresponds to the surface phonon polariton mode. The oblique thin line is the light line ω = cK. The two horizontal lines correspond to Re[ε2(ω)] = 0 (close to ENZ) and Re[ε2(ω)] = −1, which is the asymptot of the plane-interface surface-phonon-polariton dispersion relation.

Fig. 3
Fig. 3

Structure of the fields |H|2 and |Ez|2 (arbitrary units) for the Berreman mode (point A in Fig. 3), the ENZ mode (B), the surface phonon polariton mode (C). The layers are characterized by the same colors as Fig. 1.

Fig. 4
Fig. 4

ENZ enhancement factor

Fig. 5
Fig. 5

Relative error (δ) between the approximate and exact solutions of the dispersion relation in logarithmic scale as a function of K for different thicknesses of the film. The inset presents the dispersion relation of Fig. 2, on which first order iterative solutions have been added (circles).

Equations (5)

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( 1 + ε 1 k z , 1 ε 3 k z , 3 ) = i tan ( k z , 2 d ) ( ε 2 k z , 3 ε 3 k z , 2 + ε 1 k z , 2 ε 2 k z , 1 )
ε ( ω ) = ε ω 2 ω L 2 + i ω Γ ω 2 ω T 2 + i ω Γ ,
( ε 1 + ε 2 ) ( 1 ε 3 + 1 ε 2 ) = 0 ,
ω = ω ENZ + K | | 2 ( ω L 2 ω T 2 ) [ A ( ω , K | | ) K | | 2 ] [ ω + ω L 2 / ω ENZ ] ,
A ( ω , K | | ) = i ε d [ k z , 1 ε 1 + k z , 3 ε 3 i d ( ω 2 c 2 + ε 2 k z , 1 ε 1 k z , 3 ε 3 ) ] .

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