Abstract

A rigorous analysis of the contra-directional coupling between a left-handed waveguide and a right-handed waveguide shows that such a structure supports twin modes with complex (conjugate) propagation constants. Using evanescent coupling or a source inside one of the waveguides, the twin modes can be excited. In this case, light rotates inside the lamellar structure forming an exotic mode : the light wheel. The structure can finally be seen as a new type of cavity and can be used for beam reshaping.

© 2007 Optical Society of America

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  1. V.G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Usp. Fiz. Nauk. 92, 517 (1967).
  2. R.A. Shelby, D.R. Smith, and S. Shultz, "Experimental verification of a negative index of refraction," Science 292, 77 (2001).
    [CrossRef]
  3. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966 (2000).
    [CrossRef]
  4. J.B. Pendry, D. Schuring, and D.R. Smith, "Controlling electromagnetic fields," Science 312, 1780 (2006).
    [CrossRef]
  5. P.R. Berman, "Goos-Hanchen shift in negatively refractive media," Phys. Rev. E 66, 067603 (2002).
    [CrossRef]
  6. A. Lakhtakia, "On plane wave remittances and goos-hanchen shifts of planar slabs with negative real permittivity and permeability," Electromagnetics 23, 71 (2003).
    [CrossRef]
  7. I.V. Shadrivov, A.A. Sukhorukov, and Y.S. Kivshar, "Guided modes in negative-refractive-index waveguides," Phys. Rev. E 67, 057602 (2003).
    [CrossRef]
  8. L.G. Wang and S.Y. Zhu, "Large negative lateral shifts from the kretschman-raether configuration with lefthanded materials," Appl. Phys. Lett. 87, 221102 (2005).
    [CrossRef]
  9. A. Moreau and D. Felbacq, "Comment on ’large negative lateral shifts from the kretschman-raether configuration with left-handed materials’," Appl. Phys. Lett. 90, 066102 (2007).
    [CrossRef]
  10. A. Alu and N. Engheta, in Negative-Refraction Metamaterials, edited by G.V. eleftheriades and K.G. Balmain (Wiley, New York, 2005).
  11. R. Islam, F. Elek and G.V. Eleftheriades, "A coupled-line metamaterial coupler having co-directional phase but contra-directional power flow," IEEE Electron. Lett. 40, 315-317 (2004).
    [CrossRef]
  12. Y. Wang, R. Islam and G.V. Eleftheriades, "An ultra-short contra-directional coupler utilizing surface plasmon-polaritons at optical frequencies," Opt. Express 14, 7279-7290 (2006).
    [CrossRef]
  13. N.M. Litchinitser, I.R. Gabitov, A.I. Mainmistov, "Optical bistability in a nonlinear optical coupler with a negative index channel," Phys. Rev. Lett. 99, 113902 (2007).
    [CrossRef]
  14. I.V. Shadrivov, A.A. Sukhorukov, and Y.S. Kivshar, "Beam shaping by a periodic structure with negative refraction," Appl. Phys. Lett. 82, 3820 (2003).
    [CrossRef]
  15. I.V. Shadrivov, A.A. Sukhorukov, and Y.S. Kivshar, "Complete band gaps in one-dimensional left-handed periodic structures," Phys. Rev. Lett. 95, 193903 (2005).
    [CrossRef]

2007 (2)

A. Moreau and D. Felbacq, "Comment on ’large negative lateral shifts from the kretschman-raether configuration with left-handed materials’," Appl. Phys. Lett. 90, 066102 (2007).
[CrossRef]

N.M. Litchinitser, I.R. Gabitov, A.I. Mainmistov, "Optical bistability in a nonlinear optical coupler with a negative index channel," Phys. Rev. Lett. 99, 113902 (2007).
[CrossRef]

2006 (2)

2005 (2)

L.G. Wang and S.Y. Zhu, "Large negative lateral shifts from the kretschman-raether configuration with lefthanded materials," Appl. Phys. Lett. 87, 221102 (2005).
[CrossRef]

I.V. Shadrivov, A.A. Sukhorukov, and Y.S. Kivshar, "Complete band gaps in one-dimensional left-handed periodic structures," Phys. Rev. Lett. 95, 193903 (2005).
[CrossRef]

2004 (1)

R. Islam, F. Elek and G.V. Eleftheriades, "A coupled-line metamaterial coupler having co-directional phase but contra-directional power flow," IEEE Electron. Lett. 40, 315-317 (2004).
[CrossRef]

2003 (3)

I.V. Shadrivov, A.A. Sukhorukov, and Y.S. Kivshar, "Beam shaping by a periodic structure with negative refraction," Appl. Phys. Lett. 82, 3820 (2003).
[CrossRef]

A. Lakhtakia, "On plane wave remittances and goos-hanchen shifts of planar slabs with negative real permittivity and permeability," Electromagnetics 23, 71 (2003).
[CrossRef]

I.V. Shadrivov, A.A. Sukhorukov, and Y.S. Kivshar, "Guided modes in negative-refractive-index waveguides," Phys. Rev. E 67, 057602 (2003).
[CrossRef]

2002 (1)

P.R. Berman, "Goos-Hanchen shift in negatively refractive media," Phys. Rev. E 66, 067603 (2002).
[CrossRef]

2001 (1)

R.A. Shelby, D.R. Smith, and S. Shultz, "Experimental verification of a negative index of refraction," Science 292, 77 (2001).
[CrossRef]

2000 (1)

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef]

1967 (1)

V.G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Usp. Fiz. Nauk. 92, 517 (1967).

Berman, P.R.

P.R. Berman, "Goos-Hanchen shift in negatively refractive media," Phys. Rev. E 66, 067603 (2002).
[CrossRef]

Eleftheriades, G.V.

Y. Wang, R. Islam and G.V. Eleftheriades, "An ultra-short contra-directional coupler utilizing surface plasmon-polaritons at optical frequencies," Opt. Express 14, 7279-7290 (2006).
[CrossRef]

R. Islam, F. Elek and G.V. Eleftheriades, "A coupled-line metamaterial coupler having co-directional phase but contra-directional power flow," IEEE Electron. Lett. 40, 315-317 (2004).
[CrossRef]

Elek, F.

R. Islam, F. Elek and G.V. Eleftheriades, "A coupled-line metamaterial coupler having co-directional phase but contra-directional power flow," IEEE Electron. Lett. 40, 315-317 (2004).
[CrossRef]

Felbacq, D.

A. Moreau and D. Felbacq, "Comment on ’large negative lateral shifts from the kretschman-raether configuration with left-handed materials’," Appl. Phys. Lett. 90, 066102 (2007).
[CrossRef]

Gabitov, I.R.

N.M. Litchinitser, I.R. Gabitov, A.I. Mainmistov, "Optical bistability in a nonlinear optical coupler with a negative index channel," Phys. Rev. Lett. 99, 113902 (2007).
[CrossRef]

Islam, R.

Y. Wang, R. Islam and G.V. Eleftheriades, "An ultra-short contra-directional coupler utilizing surface plasmon-polaritons at optical frequencies," Opt. Express 14, 7279-7290 (2006).
[CrossRef]

R. Islam, F. Elek and G.V. Eleftheriades, "A coupled-line metamaterial coupler having co-directional phase but contra-directional power flow," IEEE Electron. Lett. 40, 315-317 (2004).
[CrossRef]

Kivshar, Y.S.

I.V. Shadrivov, A.A. Sukhorukov, and Y.S. Kivshar, "Complete band gaps in one-dimensional left-handed periodic structures," Phys. Rev. Lett. 95, 193903 (2005).
[CrossRef]

I.V. Shadrivov, A.A. Sukhorukov, and Y.S. Kivshar, "Guided modes in negative-refractive-index waveguides," Phys. Rev. E 67, 057602 (2003).
[CrossRef]

I.V. Shadrivov, A.A. Sukhorukov, and Y.S. Kivshar, "Beam shaping by a periodic structure with negative refraction," Appl. Phys. Lett. 82, 3820 (2003).
[CrossRef]

Lakhtakia, A.

A. Lakhtakia, "On plane wave remittances and goos-hanchen shifts of planar slabs with negative real permittivity and permeability," Electromagnetics 23, 71 (2003).
[CrossRef]

Litchinitser, N.M.

N.M. Litchinitser, I.R. Gabitov, A.I. Mainmistov, "Optical bistability in a nonlinear optical coupler with a negative index channel," Phys. Rev. Lett. 99, 113902 (2007).
[CrossRef]

Mainmistov, A.I.

N.M. Litchinitser, I.R. Gabitov, A.I. Mainmistov, "Optical bistability in a nonlinear optical coupler with a negative index channel," Phys. Rev. Lett. 99, 113902 (2007).
[CrossRef]

Moreau, A.

A. Moreau and D. Felbacq, "Comment on ’large negative lateral shifts from the kretschman-raether configuration with left-handed materials’," Appl. Phys. Lett. 90, 066102 (2007).
[CrossRef]

Pendry, J. B.

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef]

Pendry, J.B.

J.B. Pendry, D. Schuring, and D.R. Smith, "Controlling electromagnetic fields," Science 312, 1780 (2006).
[CrossRef]

Schuring, D.

J.B. Pendry, D. Schuring, and D.R. Smith, "Controlling electromagnetic fields," Science 312, 1780 (2006).
[CrossRef]

Shadrivov, I.V.

I.V. Shadrivov, A.A. Sukhorukov, and Y.S. Kivshar, "Complete band gaps in one-dimensional left-handed periodic structures," Phys. Rev. Lett. 95, 193903 (2005).
[CrossRef]

I.V. Shadrivov, A.A. Sukhorukov, and Y.S. Kivshar, "Guided modes in negative-refractive-index waveguides," Phys. Rev. E 67, 057602 (2003).
[CrossRef]

I.V. Shadrivov, A.A. Sukhorukov, and Y.S. Kivshar, "Beam shaping by a periodic structure with negative refraction," Appl. Phys. Lett. 82, 3820 (2003).
[CrossRef]

Shelby, R.A.

R.A. Shelby, D.R. Smith, and S. Shultz, "Experimental verification of a negative index of refraction," Science 292, 77 (2001).
[CrossRef]

Shultz, S.

R.A. Shelby, D.R. Smith, and S. Shultz, "Experimental verification of a negative index of refraction," Science 292, 77 (2001).
[CrossRef]

Smith, D.R.

J.B. Pendry, D. Schuring, and D.R. Smith, "Controlling electromagnetic fields," Science 312, 1780 (2006).
[CrossRef]

R.A. Shelby, D.R. Smith, and S. Shultz, "Experimental verification of a negative index of refraction," Science 292, 77 (2001).
[CrossRef]

Sukhorukov, A.A.

I.V. Shadrivov, A.A. Sukhorukov, and Y.S. Kivshar, "Complete band gaps in one-dimensional left-handed periodic structures," Phys. Rev. Lett. 95, 193903 (2005).
[CrossRef]

I.V. Shadrivov, A.A. Sukhorukov, and Y.S. Kivshar, "Guided modes in negative-refractive-index waveguides," Phys. Rev. E 67, 057602 (2003).
[CrossRef]

I.V. Shadrivov, A.A. Sukhorukov, and Y.S. Kivshar, "Beam shaping by a periodic structure with negative refraction," Appl. Phys. Lett. 82, 3820 (2003).
[CrossRef]

Veselago, V.G.

V.G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Usp. Fiz. Nauk. 92, 517 (1967).

Wang, L.G.

L.G. Wang and S.Y. Zhu, "Large negative lateral shifts from the kretschman-raether configuration with lefthanded materials," Appl. Phys. Lett. 87, 221102 (2005).
[CrossRef]

Wang, Y.

Zhu, S.Y.

L.G. Wang and S.Y. Zhu, "Large negative lateral shifts from the kretschman-raether configuration with lefthanded materials," Appl. Phys. Lett. 87, 221102 (2005).
[CrossRef]

Appl. Phys. Lett. (3)

L.G. Wang and S.Y. Zhu, "Large negative lateral shifts from the kretschman-raether configuration with lefthanded materials," Appl. Phys. Lett. 87, 221102 (2005).
[CrossRef]

A. Moreau and D. Felbacq, "Comment on ’large negative lateral shifts from the kretschman-raether configuration with left-handed materials’," Appl. Phys. Lett. 90, 066102 (2007).
[CrossRef]

I.V. Shadrivov, A.A. Sukhorukov, and Y.S. Kivshar, "Beam shaping by a periodic structure with negative refraction," Appl. Phys. Lett. 82, 3820 (2003).
[CrossRef]

Electromagnetics (1)

A. Lakhtakia, "On plane wave remittances and goos-hanchen shifts of planar slabs with negative real permittivity and permeability," Electromagnetics 23, 71 (2003).
[CrossRef]

IEEE Electron. Lett. (1)

R. Islam, F. Elek and G.V. Eleftheriades, "A coupled-line metamaterial coupler having co-directional phase but contra-directional power flow," IEEE Electron. Lett. 40, 315-317 (2004).
[CrossRef]

Opt. Express (1)

Phys. Rev. E (2)

P.R. Berman, "Goos-Hanchen shift in negatively refractive media," Phys. Rev. E 66, 067603 (2002).
[CrossRef]

I.V. Shadrivov, A.A. Sukhorukov, and Y.S. Kivshar, "Guided modes in negative-refractive-index waveguides," Phys. Rev. E 67, 057602 (2003).
[CrossRef]

Phys. Rev. Lett. (3)

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef]

N.M. Litchinitser, I.R. Gabitov, A.I. Mainmistov, "Optical bistability in a nonlinear optical coupler with a negative index channel," Phys. Rev. Lett. 99, 113902 (2007).
[CrossRef]

I.V. Shadrivov, A.A. Sukhorukov, and Y.S. Kivshar, "Complete band gaps in one-dimensional left-handed periodic structures," Phys. Rev. Lett. 95, 193903 (2005).
[CrossRef]

Science (2)

J.B. Pendry, D. Schuring, and D.R. Smith, "Controlling electromagnetic fields," Science 312, 1780 (2006).
[CrossRef]

R.A. Shelby, D.R. Smith, and S. Shultz, "Experimental verification of a negative index of refraction," Science 292, 77 (2001).
[CrossRef]

Usp. Fiz. Nauk. (1)

V.G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Usp. Fiz. Nauk. 92, 517 (1967).

Other (1)

A. Alu and N. Engheta, in Negative-Refraction Metamaterials, edited by G.V. eleftheriades and K.G. Balmain (Wiley, New York, 2005).

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