Abstract

We investigate theoretically the optical response of bulk samples and thin films of the MAX phase materials, accounting for their large electrical anisotropy. We reveal the unusual behavior of the reflection and transmission spectra as a function of the incidence angle and predict the effect of the inverse total internal reflection. We also investigate the behavior of the surface plasmon modes in bulk samples and thin films and analyze the difference between MAX materials and conventional metals.

© 2011 Optical Society of America

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  1. P. Eklund, M. Beckers, U. Jansson, H. Hogberg, and L. Hultman, Thin Solid Films 518, 1851 (2010).
    [CrossRef]
  2. L. Toth, Transition Metal Carbides and Nitrides(Academic, 1971).
  3. M. W. Barsoum and T. El-Raghy, Am. Sci. 89, 337 (2001).
    [CrossRef]
  4. M. W. Barsoum, Prog. Solid State Chem. 28, 201 (2000).
    [CrossRef]
  5. N. Haddad, E. Garcia-Caurel, L. Hultman, M. W. Barsoum, and G. Hug, J. Appl. Phys. 104, 023531 (2008).
    [CrossRef]
  6. S. Li, R. Ahuja, M. W. Barsoum, P. Jena, and B. Johansson, Appl. Phys. Lett. 92, 221907 (2008).
    [CrossRef]
  7. J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, Rep. Prog. Phys. 70, 1 (2007).
    [CrossRef]
  8. S. I. Bozhevolnyi, Plasmonic Nanoguides and Circuits (Pan Stanford, 2008).
    [CrossRef]
  9. M. W. Barsoum, M. Ali, and T. El-Raghy, Metall. Mater. Trans. A 31, 1857 (2000).
    [CrossRef]
  10. E. N. Economou, Phys. Rev. 182, 539 (1969).
    [CrossRef]
  11. S. Brand, R. A. Abram, and M. A. Kaliteevski, Phys. Rev. B 75, 035102 (2007).
    [CrossRef]

2010 (1)

P. Eklund, M. Beckers, U. Jansson, H. Hogberg, and L. Hultman, Thin Solid Films 518, 1851 (2010).
[CrossRef]

2008 (2)

N. Haddad, E. Garcia-Caurel, L. Hultman, M. W. Barsoum, and G. Hug, J. Appl. Phys. 104, 023531 (2008).
[CrossRef]

S. Li, R. Ahuja, M. W. Barsoum, P. Jena, and B. Johansson, Appl. Phys. Lett. 92, 221907 (2008).
[CrossRef]

2007 (2)

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, Rep. Prog. Phys. 70, 1 (2007).
[CrossRef]

S. Brand, R. A. Abram, and M. A. Kaliteevski, Phys. Rev. B 75, 035102 (2007).
[CrossRef]

2001 (1)

M. W. Barsoum and T. El-Raghy, Am. Sci. 89, 337 (2001).
[CrossRef]

2000 (2)

M. W. Barsoum, Prog. Solid State Chem. 28, 201 (2000).
[CrossRef]

M. W. Barsoum, M. Ali, and T. El-Raghy, Metall. Mater. Trans. A 31, 1857 (2000).
[CrossRef]

1969 (1)

E. N. Economou, Phys. Rev. 182, 539 (1969).
[CrossRef]

Abram, R. A.

S. Brand, R. A. Abram, and M. A. Kaliteevski, Phys. Rev. B 75, 035102 (2007).
[CrossRef]

Ahuja, R.

S. Li, R. Ahuja, M. W. Barsoum, P. Jena, and B. Johansson, Appl. Phys. Lett. 92, 221907 (2008).
[CrossRef]

Ali, M.

M. W. Barsoum, M. Ali, and T. El-Raghy, Metall. Mater. Trans. A 31, 1857 (2000).
[CrossRef]

Barsoum, M. W.

S. Li, R. Ahuja, M. W. Barsoum, P. Jena, and B. Johansson, Appl. Phys. Lett. 92, 221907 (2008).
[CrossRef]

N. Haddad, E. Garcia-Caurel, L. Hultman, M. W. Barsoum, and G. Hug, J. Appl. Phys. 104, 023531 (2008).
[CrossRef]

M. W. Barsoum and T. El-Raghy, Am. Sci. 89, 337 (2001).
[CrossRef]

M. W. Barsoum, Prog. Solid State Chem. 28, 201 (2000).
[CrossRef]

M. W. Barsoum, M. Ali, and T. El-Raghy, Metall. Mater. Trans. A 31, 1857 (2000).
[CrossRef]

Beckers, M.

P. Eklund, M. Beckers, U. Jansson, H. Hogberg, and L. Hultman, Thin Solid Films 518, 1851 (2010).
[CrossRef]

Bozhevolnyi, S. I.

S. I. Bozhevolnyi, Plasmonic Nanoguides and Circuits (Pan Stanford, 2008).
[CrossRef]

Brand, S.

S. Brand, R. A. Abram, and M. A. Kaliteevski, Phys. Rev. B 75, 035102 (2007).
[CrossRef]

Chulkov, E. V.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, Rep. Prog. Phys. 70, 1 (2007).
[CrossRef]

Echenique, P. M.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, Rep. Prog. Phys. 70, 1 (2007).
[CrossRef]

Economou, E. N.

E. N. Economou, Phys. Rev. 182, 539 (1969).
[CrossRef]

Eklund, P.

P. Eklund, M. Beckers, U. Jansson, H. Hogberg, and L. Hultman, Thin Solid Films 518, 1851 (2010).
[CrossRef]

El-Raghy, T.

M. W. Barsoum and T. El-Raghy, Am. Sci. 89, 337 (2001).
[CrossRef]

M. W. Barsoum, M. Ali, and T. El-Raghy, Metall. Mater. Trans. A 31, 1857 (2000).
[CrossRef]

Garcia-Caurel, E.

N. Haddad, E. Garcia-Caurel, L. Hultman, M. W. Barsoum, and G. Hug, J. Appl. Phys. 104, 023531 (2008).
[CrossRef]

Haddad, N.

N. Haddad, E. Garcia-Caurel, L. Hultman, M. W. Barsoum, and G. Hug, J. Appl. Phys. 104, 023531 (2008).
[CrossRef]

Hogberg, H.

P. Eklund, M. Beckers, U. Jansson, H. Hogberg, and L. Hultman, Thin Solid Films 518, 1851 (2010).
[CrossRef]

Hug, G.

N. Haddad, E. Garcia-Caurel, L. Hultman, M. W. Barsoum, and G. Hug, J. Appl. Phys. 104, 023531 (2008).
[CrossRef]

Hultman, L.

P. Eklund, M. Beckers, U. Jansson, H. Hogberg, and L. Hultman, Thin Solid Films 518, 1851 (2010).
[CrossRef]

N. Haddad, E. Garcia-Caurel, L. Hultman, M. W. Barsoum, and G. Hug, J. Appl. Phys. 104, 023531 (2008).
[CrossRef]

Jansson, U.

P. Eklund, M. Beckers, U. Jansson, H. Hogberg, and L. Hultman, Thin Solid Films 518, 1851 (2010).
[CrossRef]

Jena, P.

S. Li, R. Ahuja, M. W. Barsoum, P. Jena, and B. Johansson, Appl. Phys. Lett. 92, 221907 (2008).
[CrossRef]

Johansson, B.

S. Li, R. Ahuja, M. W. Barsoum, P. Jena, and B. Johansson, Appl. Phys. Lett. 92, 221907 (2008).
[CrossRef]

Kaliteevski, M. A.

S. Brand, R. A. Abram, and M. A. Kaliteevski, Phys. Rev. B 75, 035102 (2007).
[CrossRef]

Li, S.

S. Li, R. Ahuja, M. W. Barsoum, P. Jena, and B. Johansson, Appl. Phys. Lett. 92, 221907 (2008).
[CrossRef]

Pitarke, J. M.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, Rep. Prog. Phys. 70, 1 (2007).
[CrossRef]

Silkin, V. M.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, Rep. Prog. Phys. 70, 1 (2007).
[CrossRef]

Toth, L.

L. Toth, Transition Metal Carbides and Nitrides(Academic, 1971).

Am. Sci. (1)

M. W. Barsoum and T. El-Raghy, Am. Sci. 89, 337 (2001).
[CrossRef]

Appl. Phys. Lett. (1)

S. Li, R. Ahuja, M. W. Barsoum, P. Jena, and B. Johansson, Appl. Phys. Lett. 92, 221907 (2008).
[CrossRef]

J. Appl. Phys. (1)

N. Haddad, E. Garcia-Caurel, L. Hultman, M. W. Barsoum, and G. Hug, J. Appl. Phys. 104, 023531 (2008).
[CrossRef]

Metall. Mater. Trans. A (1)

M. W. Barsoum, M. Ali, and T. El-Raghy, Metall. Mater. Trans. A 31, 1857 (2000).
[CrossRef]

Phys. Rev. (1)

E. N. Economou, Phys. Rev. 182, 539 (1969).
[CrossRef]

Phys. Rev. B (1)

S. Brand, R. A. Abram, and M. A. Kaliteevski, Phys. Rev. B 75, 035102 (2007).
[CrossRef]

Prog. Solid State Chem. (1)

M. W. Barsoum, Prog. Solid State Chem. 28, 201 (2000).
[CrossRef]

Rep. Prog. Phys. (1)

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, Rep. Prog. Phys. 70, 1 (2007).
[CrossRef]

Thin Solid Films (1)

P. Eklund, M. Beckers, U. Jansson, H. Hogberg, and L. Hultman, Thin Solid Films 518, 1851 (2010).
[CrossRef]

Other (2)

L. Toth, Transition Metal Carbides and Nitrides(Academic, 1971).

S. I. Bozhevolnyi, Plasmonic Nanoguides and Circuits (Pan Stanford, 2008).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

(a) Sketch of the MAX phase crystal structure in the x z plane. The conductivity in the system is provided by A atoms and is greater in the x and y directions. (b) Geometry of the system for semi-infinite dielectric–MAX-phase interface for a TM-polarized beam. ε 2 denotes the isotropic dielectric constant of the media in contact with the MAX phase, while ε x y , ε z are components of dielectric tensor of the MAX phase.

Fig. 2
Fig. 2

(a) Reflectivity of the MAX phase semi-infinite crystal for two different values of the frequency ω. The red curve corresponds to the case ω p ( z ) < ω < ω p ( x y ) (without damping) and demonstrates the inverse total internal reflection, while the other solid curves show the influence of optical damping on the reflectivity spectrum. The blue dashed curve denotes the case of fully dielectric behavior and shows the effect of total internal reflection. (b) Attenuation length of the free electromagnetic wave in the MAX phase and metal for ω p z < ω < ω p ( x y ) (solid curves) and ω > ω p ( x y , z ) (dashed curves).

Fig. 3
Fig. 3

(a) Dispersion of SPP modes at the interfaces MAX-phase–vacuum (red solid) and metal–vacuum (purple short dashed). (b) Profiles of the SPP modes at the interfaces MAX-phase–vacuum (red solid) and metal–vacuum (purple dashed). (c) Decay length as a function of plasmon wave vector for MAX phase (red solid) and metal (purple dashed). (d) The dispersions of the symmetric and antisymmetric plasmonic modes in thin MAX phase film (solid) and metal (dashed) ( d = 25 nm ). Blue curves (solid and short dashed) correspond to the bulk surface plasmons.

Equations (8)

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ε = ( ε x y 0 0 0 ε x y 0 0 0 ε z ) ,
ε x y , z = 1 ω p ( x y , z ) 2 ω ( ω + i γ ) ,
n 1 e = ε 2 sin 2 ϕ ( 1 ε x y ε z ) + ε x y ,
q ( ω ) = ω c ε 2 ε z ( ω ) [ ε 2 ε x y ( ω ) ] ε 2 2 ε x y ( ω ) ε z ( ω ) ,
κ 1 = ε x y ε z ( ω ) [ q 2 ε z ω 2 c 2 ] ,
κ 2 = q 2 ε 2 ω 2 c 2 .
ε x y κ 1 + ε 2 κ 2 tanh ( κ 1 d / 2 ) = 0 ,
ε x y κ 1 + ε 2 κ 2 coth ( κ 1 d / 2 ) = 0 ,

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