Abstract

When a guided mode is excited in a dielectric slab coupled to a backward surface wave at the interface between a dielectric and a left-handed medium, light is confined in the structure: this is a light wheel. Complex plane analysis of the dispersion relation and coupled-mode formalism give deep insight into the physics of this phenomenon (lateral confinement and the presence of a dark zone).

© 2010 Optical Society of America

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References

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2010 (1)

F. Krayzel, R. Pollès, A. Moreau, M. Mihailovic, and G. Granet, J. Europ. Opt. Soc. Rap. Public. 5, 10025 (2010).
[CrossRef]

2009 (1)

2007 (1)

2004 (1)

I. V. Shadrivov, A. A. Sukhorukov, Y. S. Kivshar, A. A. Zharov, A. D. Boardman, and P. Egan, Phys. Rev. E 69, 016617 (2004).
[CrossRef]

2003 (1)

S. A. Darmanyan, M. Neviere, and A. A. Zakhidov, Opt. Commun. 225, 233 (2003).
[CrossRef]

1994 (1)

1973 (1)

A. Yariv, IEEE J. Quantum Electron. 9, 919 (1973).
[CrossRef]

1970 (1)

1954 (1)

J. R. Pierce, J. Appl. Phys. 25, 179 (1954).
[CrossRef]

Boardman, A. D.

I. V. Shadrivov, A. A. Sukhorukov, Y. S. Kivshar, A. A. Zharov, A. D. Boardman, and P. Egan, Phys. Rev. E 69, 016617 (2004).
[CrossRef]

Darmanyan, S. A.

S. A. Darmanyan, M. Neviere, and A. A. Zakhidov, Opt. Commun. 225, 233 (2003).
[CrossRef]

Egan, P.

I. V. Shadrivov, A. A. Sukhorukov, Y. S. Kivshar, A. A. Zharov, A. D. Boardman, and P. Egan, Phys. Rev. E 69, 016617 (2004).
[CrossRef]

Granet, G.

F. Krayzel, R. Pollès, A. Moreau, M. Mihailovic, and G. Granet, J. Europ. Opt. Soc. Rap. Public. 5, 10025 (2010).
[CrossRef]

P. H. Tichit, A. Moreau, and G. Granet, Opt. Express 15, 14961 (2007).
[CrossRef] [PubMed]

He, S.

Huang, W-P.

Jin, Y.

Kivshar, Y. S.

I. V. Shadrivov, A. A. Sukhorukov, Y. S. Kivshar, A. A. Zharov, A. D. Boardman, and P. Egan, Phys. Rev. E 69, 016617 (2004).
[CrossRef]

Krayzel, F.

F. Krayzel, R. Pollès, A. Moreau, M. Mihailovic, and G. Granet, J. Europ. Opt. Soc. Rap. Public. 5, 10025 (2010).
[CrossRef]

Mihailovic, M.

F. Krayzel, R. Pollès, A. Moreau, M. Mihailovic, and G. Granet, J. Europ. Opt. Soc. Rap. Public. 5, 10025 (2010).
[CrossRef]

Moreau, A.

F. Krayzel, R. Pollès, A. Moreau, M. Mihailovic, and G. Granet, J. Europ. Opt. Soc. Rap. Public. 5, 10025 (2010).
[CrossRef]

P. H. Tichit, A. Moreau, and G. Granet, Opt. Express 15, 14961 (2007).
[CrossRef] [PubMed]

Neviere, M.

S. A. Darmanyan, M. Neviere, and A. A. Zakhidov, Opt. Commun. 225, 233 (2003).
[CrossRef]

Pierce, J. R.

J. R. Pierce, J. Appl. Phys. 25, 179 (1954).
[CrossRef]

Pollès, R.

F. Krayzel, R. Pollès, A. Moreau, M. Mihailovic, and G. Granet, J. Europ. Opt. Soc. Rap. Public. 5, 10025 (2010).
[CrossRef]

Shadrivov, I. V.

I. V. Shadrivov, A. A. Sukhorukov, Y. S. Kivshar, A. A. Zharov, A. D. Boardman, and P. Egan, Phys. Rev. E 69, 016617 (2004).
[CrossRef]

Sukhorukov, A. A.

I. V. Shadrivov, A. A. Sukhorukov, Y. S. Kivshar, A. A. Zharov, A. D. Boardman, and P. Egan, Phys. Rev. E 69, 016617 (2004).
[CrossRef]

Tichit, P. H.

Ulrich, R.

Yariv, A.

A. Yariv, IEEE J. Quantum Electron. 9, 919 (1973).
[CrossRef]

Ye, Y. Q.

Zakhidov, A. A.

S. A. Darmanyan, M. Neviere, and A. A. Zakhidov, Opt. Commun. 225, 233 (2003).
[CrossRef]

Zharov, A. A.

I. V. Shadrivov, A. A. Sukhorukov, Y. S. Kivshar, A. A. Zharov, A. D. Boardman, and P. Egan, Phys. Rev. E 69, 016617 (2004).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. Yariv, IEEE J. Quantum Electron. 9, 919 (1973).
[CrossRef]

J. Appl. Phys. (1)

J. R. Pierce, J. Appl. Phys. 25, 179 (1954).
[CrossRef]

J. Europ. Opt. Soc. Rap. Public. (1)

F. Krayzel, R. Pollès, A. Moreau, M. Mihailovic, and G. Granet, J. Europ. Opt. Soc. Rap. Public. 5, 10025 (2010).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt. Commun. (1)

S. A. Darmanyan, M. Neviere, and A. A. Zakhidov, Opt. Commun. 225, 233 (2003).
[CrossRef]

Opt. Express (2)

Phys. Rev. E (1)

I. V. Shadrivov, A. A. Sukhorukov, Y. S. Kivshar, A. A. Zharov, A. D. Boardman, and P. Egan, Phys. Rev. E 69, 016617 (2004).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Dielectric slab waveguide and the LHM interface separated by a distance h 1 and surrounded by a medium characterized by ε 1 and μ 1 .

Fig. 2
Fig. 2

Solutions of the dispersion relation in the α complex plane, for different values of h 1 in wavelength, the distance between the dielectric waveguide and the LHM surface. Inset, zoom in the region around α 0 .

Fig. 3
Fig. 3

Modulus of the field represented in a domain 100 λ large, 5 λ high. The distance between the dielectric slab and the LHM interface is h 1 = 0.8 λ . (a) The punctual source, placed in the dielectric waveguide, excites two contrapropagative light wheels. (b) The light wheel is excited by a an incident Gaussian beam (angle, 33.9 ° ; waist, 10 λ ) in a prism ( ε = 5 , μ = 1 ). White arrows indicate the propagation direction of light. These images are obtained using the numerical method described in [9].

Fig. 4
Fig. 4

Modulus of the field in the middle of the dielectric waveguide (blue curve) and | A ( x ) | the modulus of the theoretical amplitude of the mode a (uppermost, red curve). Parameters of the structure and the beam are as in Fig. 3. S 0 is chosen arbitrarily.

Equations (10)

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α 2 = k 0 2 μ 1 ε 1 X ( X Y ) ( X 2 1 ) ,
1 < X < 1 / Y
h 2 = 2 γ 2 arctan ( ε 2 κ 1 ε 1 γ 2 ) ,
x 2 [ exp ( 2 j γ 2 h 2 ) + X 2 ] [ exp ( 2 κ 1 h 1 ) + X 3 ] [ exp ( 2 j γ 2 h 2 ) X 2 ] [ exp ( 2 κ 1 h 1 ) X 3 ] = 1 ,
d A d x = κ * B ,
d B d x = κ A ,
A 1 ( x ) = H ( x ) exp ( | κ | x ) H ( x ) exp ( | κ | x ) ,
B 1 ( x ) = exp ( i π 2 ) [ H ( x ) exp ( | κ | x ) + H ( x ) exp ( | κ | x ) ] ,
A ( x ) = S 0 π 2 exp ( κ 2 w 2 4 ) [ exp ( | κ | x ) erfc ( x w + | κ | w 2 ) exp ( | κ | x ) erfc ( x w + | κ | w 2 ) ] ,
B ( x ) = S 0 π 2 exp ( κ 2 w 2 4 i π 2 ) [ exp ( | κ | x ) erfc ( x w + | κ | w 2 ) + exp ( κ x ) erfc ( x w + | κ | w 2 ) ] ,

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