Abstract

We analyze the optical (or microwave) tunneling properties of electromagnetic waves passing through thin films presenting a specific index profile that provides a cutoff frequency when the films are used below this frequency. We show that, contrary to the usual case of a square index profile, where tunneling is accompanied by a strong attenuation of the wave due to reflection, such films present the possibility of reflectionless tunneling, where the incoming intensity is totally transmitted.

© 2006 Optical Society of America

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References

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  1. E. H. Hauge and J. A. Stovneng, Rev. Mod. Phys. 61, 917 (1989).
    [Crossref]
  2. R. Y. Chiao and A. M. Steinberg, in Progress in Optics, Vol. 37, E.Wolf, ed. (Elsevier North-Holland, 1997), p. 345.
    [Crossref]
  3. V. S. Olkhovsky, E. Recami, and J. Jakiel, Phys. Rep. 398, 133 (2004).
    [Crossref]
  4. F. de Fornel, Evanescent waves from Newtonian Optics to Atomic Optics, Vol. 73 of Springer Series in Optical Sciences (Springer-Verlag, 2001).
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    [Crossref]
  6. A. Enders and G. Nimtz, Phys. Rev. E 48, 632 (1993).
    [Crossref]
  7. T. E. Hartman, J. Appl. Phys. 33, 3427 (1962).
    [Crossref]
  8. V. S. Olkhovsky and E. Recami, Phys. Rep. 214, 339 (1992).
    [Crossref]
  9. B. Lee and W. Lee, J. Opt. Soc. Am. B 14, 777 (1997).
    [Crossref]
  10. C.-F. Li and Q. Wang, J. Opt. Soc. Am. B 18, 1174 (2001).
    [Crossref]
  11. V. Laude and P. Tournois, J. Opt. Soc. Am. B 16, 194 (1999).
    [Crossref]
  12. A. Haibel, G. Nimtz, and A. A. Stahlhofen, Phys. Rev. E 63, 047601 (2001).
    [Crossref]
  13. A. Pablo, L. Barbero, H. E. Fernandez-Figueroa, and E. Recami, Phys. Rev. E 62, 8628 (2000).
    [Crossref]
  14. A. Ranfagni, P. Fabeni, G. Pazzi, and D. Mugnai, Phys. Rev. E 48, 1453 (1993).
    [Crossref]
  15. A. Shvartsburg, G. Petite, and P. Hecquet, J. Opt. Soc. Am. A 17, 2267 (2000).
    [Crossref]
  16. A. Shvartsburg and G. Petite, Eur. Phys. J. D 36, 111 (2005).
    [Crossref]
  17. V. S. Olkhovsky, E. Recami, and G. Salesi, Europhys. Lett. 57, 879 (2002).
    [Crossref]
  18. V. S. Olkhovski, E. Recami, and A. K. Zaichenko, Europhys. Lett. 70, 712 (2005).
    [Crossref]
  19. Y. Aharonov, N. Erez, and B. Reznik, Phys. Rev. A 65, 052124 (2002).
    [Crossref]
  20. S. Longhi, P. Laporta, M. Belmonte, and E. Recami, Phys. Rev. E 65, 046610 (2002).
    [Crossref]

2005 (2)

A. Shvartsburg and G. Petite, Eur. Phys. J. D 36, 111 (2005).
[Crossref]

V. S. Olkhovski, E. Recami, and A. K. Zaichenko, Europhys. Lett. 70, 712 (2005).
[Crossref]

2004 (1)

V. S. Olkhovsky, E. Recami, and J. Jakiel, Phys. Rep. 398, 133 (2004).
[Crossref]

2002 (3)

Y. Aharonov, N. Erez, and B. Reznik, Phys. Rev. A 65, 052124 (2002).
[Crossref]

S. Longhi, P. Laporta, M. Belmonte, and E. Recami, Phys. Rev. E 65, 046610 (2002).
[Crossref]

V. S. Olkhovsky, E. Recami, and G. Salesi, Europhys. Lett. 57, 879 (2002).
[Crossref]

2001 (2)

A. Haibel, G. Nimtz, and A. A. Stahlhofen, Phys. Rev. E 63, 047601 (2001).
[Crossref]

C.-F. Li and Q. Wang, J. Opt. Soc. Am. B 18, 1174 (2001).
[Crossref]

2000 (2)

A. Pablo, L. Barbero, H. E. Fernandez-Figueroa, and E. Recami, Phys. Rev. E 62, 8628 (2000).
[Crossref]

A. Shvartsburg, G. Petite, and P. Hecquet, J. Opt. Soc. Am. A 17, 2267 (2000).
[Crossref]

1999 (1)

1997 (1)

1993 (2)

A. Ranfagni, P. Fabeni, G. Pazzi, and D. Mugnai, Phys. Rev. E 48, 1453 (1993).
[Crossref]

A. Enders and G. Nimtz, Phys. Rev. E 48, 632 (1993).
[Crossref]

1992 (2)

A. Enders and G. Nimtz, J. Phys. I 2, 1963 (1992).
[Crossref]

V. S. Olkhovsky and E. Recami, Phys. Rep. 214, 339 (1992).
[Crossref]

1989 (1)

E. H. Hauge and J. A. Stovneng, Rev. Mod. Phys. 61, 917 (1989).
[Crossref]

1962 (1)

T. E. Hartman, J. Appl. Phys. 33, 3427 (1962).
[Crossref]

Aharonov, Y.

Y. Aharonov, N. Erez, and B. Reznik, Phys. Rev. A 65, 052124 (2002).
[Crossref]

Barbero, L.

A. Pablo, L. Barbero, H. E. Fernandez-Figueroa, and E. Recami, Phys. Rev. E 62, 8628 (2000).
[Crossref]

Belmonte, M.

S. Longhi, P. Laporta, M. Belmonte, and E. Recami, Phys. Rev. E 65, 046610 (2002).
[Crossref]

Chiao, R. Y.

R. Y. Chiao and A. M. Steinberg, in Progress in Optics, Vol. 37, E.Wolf, ed. (Elsevier North-Holland, 1997), p. 345.
[Crossref]

de Fornel, F.

F. de Fornel, Evanescent waves from Newtonian Optics to Atomic Optics, Vol. 73 of Springer Series in Optical Sciences (Springer-Verlag, 2001).

Enders, A.

A. Enders and G. Nimtz, Phys. Rev. E 48, 632 (1993).
[Crossref]

A. Enders and G. Nimtz, J. Phys. I 2, 1963 (1992).
[Crossref]

Erez, N.

Y. Aharonov, N. Erez, and B. Reznik, Phys. Rev. A 65, 052124 (2002).
[Crossref]

Fabeni, P.

A. Ranfagni, P. Fabeni, G. Pazzi, and D. Mugnai, Phys. Rev. E 48, 1453 (1993).
[Crossref]

Fernandez-Figueroa, H. E.

A. Pablo, L. Barbero, H. E. Fernandez-Figueroa, and E. Recami, Phys. Rev. E 62, 8628 (2000).
[Crossref]

Haibel, A.

A. Haibel, G. Nimtz, and A. A. Stahlhofen, Phys. Rev. E 63, 047601 (2001).
[Crossref]

Hartman, T. E.

T. E. Hartman, J. Appl. Phys. 33, 3427 (1962).
[Crossref]

Hauge, E. H.

E. H. Hauge and J. A. Stovneng, Rev. Mod. Phys. 61, 917 (1989).
[Crossref]

Hecquet, P.

Jakiel, J.

V. S. Olkhovsky, E. Recami, and J. Jakiel, Phys. Rep. 398, 133 (2004).
[Crossref]

Laporta, P.

S. Longhi, P. Laporta, M. Belmonte, and E. Recami, Phys. Rev. E 65, 046610 (2002).
[Crossref]

Laude, V.

Lee, B.

Lee, W.

Li, C.-F.

Longhi, S.

S. Longhi, P. Laporta, M. Belmonte, and E. Recami, Phys. Rev. E 65, 046610 (2002).
[Crossref]

Mugnai, D.

A. Ranfagni, P. Fabeni, G. Pazzi, and D. Mugnai, Phys. Rev. E 48, 1453 (1993).
[Crossref]

Nimtz, G.

A. Haibel, G. Nimtz, and A. A. Stahlhofen, Phys. Rev. E 63, 047601 (2001).
[Crossref]

A. Enders and G. Nimtz, Phys. Rev. E 48, 632 (1993).
[Crossref]

A. Enders and G. Nimtz, J. Phys. I 2, 1963 (1992).
[Crossref]

Olkhovski, V. S.

V. S. Olkhovski, E. Recami, and A. K. Zaichenko, Europhys. Lett. 70, 712 (2005).
[Crossref]

Olkhovsky, V. S.

V. S. Olkhovsky, E. Recami, and J. Jakiel, Phys. Rep. 398, 133 (2004).
[Crossref]

V. S. Olkhovsky, E. Recami, and G. Salesi, Europhys. Lett. 57, 879 (2002).
[Crossref]

V. S. Olkhovsky and E. Recami, Phys. Rep. 214, 339 (1992).
[Crossref]

Pablo, A.

A. Pablo, L. Barbero, H. E. Fernandez-Figueroa, and E. Recami, Phys. Rev. E 62, 8628 (2000).
[Crossref]

Pazzi, G.

A. Ranfagni, P. Fabeni, G. Pazzi, and D. Mugnai, Phys. Rev. E 48, 1453 (1993).
[Crossref]

Petite, G.

Ranfagni, A.

A. Ranfagni, P. Fabeni, G. Pazzi, and D. Mugnai, Phys. Rev. E 48, 1453 (1993).
[Crossref]

Recami, E.

V. S. Olkhovski, E. Recami, and A. K. Zaichenko, Europhys. Lett. 70, 712 (2005).
[Crossref]

V. S. Olkhovsky, E. Recami, and J. Jakiel, Phys. Rep. 398, 133 (2004).
[Crossref]

V. S. Olkhovsky, E. Recami, and G. Salesi, Europhys. Lett. 57, 879 (2002).
[Crossref]

S. Longhi, P. Laporta, M. Belmonte, and E. Recami, Phys. Rev. E 65, 046610 (2002).
[Crossref]

A. Pablo, L. Barbero, H. E. Fernandez-Figueroa, and E. Recami, Phys. Rev. E 62, 8628 (2000).
[Crossref]

V. S. Olkhovsky and E. Recami, Phys. Rep. 214, 339 (1992).
[Crossref]

Reznik, B.

Y. Aharonov, N. Erez, and B. Reznik, Phys. Rev. A 65, 052124 (2002).
[Crossref]

Salesi, G.

V. S. Olkhovsky, E. Recami, and G. Salesi, Europhys. Lett. 57, 879 (2002).
[Crossref]

Shvartsburg, A.

Stahlhofen, A. A.

A. Haibel, G. Nimtz, and A. A. Stahlhofen, Phys. Rev. E 63, 047601 (2001).
[Crossref]

Steinberg, A. M.

R. Y. Chiao and A. M. Steinberg, in Progress in Optics, Vol. 37, E.Wolf, ed. (Elsevier North-Holland, 1997), p. 345.
[Crossref]

Stovneng, J. A.

E. H. Hauge and J. A. Stovneng, Rev. Mod. Phys. 61, 917 (1989).
[Crossref]

Tournois, P.

Wang, Q.

Zaichenko, A. K.

V. S. Olkhovski, E. Recami, and A. K. Zaichenko, Europhys. Lett. 70, 712 (2005).
[Crossref]

Eur. Phys. J. D (1)

A. Shvartsburg and G. Petite, Eur. Phys. J. D 36, 111 (2005).
[Crossref]

Europhys. Lett. (2)

V. S. Olkhovsky, E. Recami, and G. Salesi, Europhys. Lett. 57, 879 (2002).
[Crossref]

V. S. Olkhovski, E. Recami, and A. K. Zaichenko, Europhys. Lett. 70, 712 (2005).
[Crossref]

J. Appl. Phys. (1)

T. E. Hartman, J. Appl. Phys. 33, 3427 (1962).
[Crossref]

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

J. Opt. Soc. Am. B (3)

J. Phys. I (1)

A. Enders and G. Nimtz, J. Phys. I 2, 1963 (1992).
[Crossref]

Phys. Rep. (2)

V. S. Olkhovsky and E. Recami, Phys. Rep. 214, 339 (1992).
[Crossref]

V. S. Olkhovsky, E. Recami, and J. Jakiel, Phys. Rep. 398, 133 (2004).
[Crossref]

Phys. Rev. A (1)

Y. Aharonov, N. Erez, and B. Reznik, Phys. Rev. A 65, 052124 (2002).
[Crossref]

Phys. Rev. E (5)

S. Longhi, P. Laporta, M. Belmonte, and E. Recami, Phys. Rev. E 65, 046610 (2002).
[Crossref]

A. Haibel, G. Nimtz, and A. A. Stahlhofen, Phys. Rev. E 63, 047601 (2001).
[Crossref]

A. Pablo, L. Barbero, H. E. Fernandez-Figueroa, and E. Recami, Phys. Rev. E 62, 8628 (2000).
[Crossref]

A. Ranfagni, P. Fabeni, G. Pazzi, and D. Mugnai, Phys. Rev. E 48, 1453 (1993).
[Crossref]

A. Enders and G. Nimtz, Phys. Rev. E 48, 632 (1993).
[Crossref]

Rev. Mod. Phys. (1)

E. H. Hauge and J. A. Stovneng, Rev. Mod. Phys. 61, 917 (1989).
[Crossref]

Other (2)

R. Y. Chiao and A. M. Steinberg, in Progress in Optics, Vol. 37, E.Wolf, ed. (Elsevier North-Holland, 1997), p. 345.
[Crossref]

F. de Fornel, Evanescent waves from Newtonian Optics to Atomic Optics, Vol. 73 of Springer Series in Optical Sciences (Springer-Verlag, 2001).

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Equations (22)

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E x = 1 c ψ t , H y = ψ z ,
2 ψ z 2 ε ( z ) c 2 2 ψ t 2 = 0 .
U ( z ) = ( 1 + z L 1 + z 2 L 2 ) 1 .
L 1 = d 4 y 2 , L 2 = d 2 y , y = U m 1 1 .
Ω = 2 c y 1 + y 2 n 0 d .
ψ 1 = A 1 U ( z ) [ exp ( p η ) + Q 1 exp ( p η ) ] ,
p = ω N c , N 2 = u 2 1 , u = Ω ω ,
η = L 2 1 + y 2 ln ( 1 + y + z 2 L 2 1 y z 2 L 2 ) , y ± = 1 + y 2 ± y .
ψ 2 = A 2 [ exp ( i k z ) + Q 2 exp ( i k z ) ] , k = ω n c .
R = ( 1 + i γ 2 i n 0 N 1 Q 1 1 + Q 1 ) ( 1 i γ 2 + i n 0 N 1 Q 1 1 + Q 1 ) 1 .
Q 1 = S 1 S 2 exp ( 2 p η 0 ) ,
S 1 = n 0 N + γ 2 + i M , S 2 = n 0 N γ 2 i M ,
M = n 1 Q 2 1 + Q 2 ,
γ = 2 y u n 0 1 + y 2 , η 0 = η ( d ) = L 2 1 + y 2 ln ( y + y ) .
Q 2 = n 1 n + 1 exp ( 2 i ω n D c ) .
M = n 1 i n t 1 n i t 1 , t 1 = tan ( ω n D c ) .
k D = s , s = 1 ; 2 ; 3 .
R = tanh ( p η 0 ) ( 1 + γ 2 4 + n 0 2 N 2 ) γ n 0 N tanh ( p η 0 ) ( 1 γ 2 4 n 0 2 N 2 ) + γ n 0 N + i [ 2 n 0 N γ tanh ( p η 0 ) ] .
R = tanh ( p d ) ( u 2 ) tanh ( p d ) ( 2 u 2 ) + 2 i N .
tanh ( m p η 0 ) = γ n 0 N 1 + γ 2 4 + n 0 2 N 2 .
tan ( ϕ t ) = γ 1 + n 0 2 N 2 γ 2 4 .
tanh ( m l x ) = 2 x y 1 + y 2 [ 1 n 0 2 + y 2 1 + y 2 + x 2 ( 1 1 n 0 2 ) ] 1 , l = ln ( y + y ) .

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