Abstract

We investigate the refraction and propagation properties of electromagnetic waves which are incident from free space to a biaxially anisotropic chiral medium. Such a chiral medium can be realized by putting chiral elements pointing to two directions into a host medium. When the host medium is a normally isotropic dielectric, no negative refraction and/or backward waves are supported for the propagating eigenwaves in the chiral medium. When the host medium changes to an anisotropic dielectric or an electric plasma, however, negative refractions and backward waves can be realized separately or even simultaneously if we choose the medium parameters properly. Numerical simulations validate our theoretical analysis.

© 2006 Optical Society of America

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References

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  1. I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic waves in Chiral and Bi-Isotropic Media (Artech House, Boston, 1994).
  2. J. B. Pendry, "A chiral route to negative refraction," Science 306, 1353 (2004).
    [CrossRef] [PubMed]
  3. S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, "Waves and energy in chiral nihility," J. Electromagn. Waves Appl. 17, 695 (2003).
    [CrossRef]
  4. T. G. Mackay and A. Lakhtakia, "Plane waves with negative phase velocity in Faraday chiral mediums," Phys. Rev. E 69, 026602 (2004).
    [CrossRef]
  5. Y. Jin and S. He, "Focusing by a slab of chiral medium," Opt. Express 13, 4974 (2005).
    [CrossRef] [PubMed]
  6. S. Tretyakov, A. Sihvola, and L. Jylha, "Backward-wave regime and negative refraction in chiral composites," Photonics Nanostruct. Fundam. Appl. 3, 107 (2005).
    [CrossRef]
  7. C. Monzon and D. W. Forester, "Negative refraction and focusing of circularly polarized waves in optically active media," Phys. Rev. Lett. 95, 123904 (2005).
    [CrossRef] [PubMed]
  8. Q. Cheng and T. J. Cui, "Negative refractions in uniaxially anisotropic chiral media," Phys. Rev. B 73, 113104 (2006).
    [CrossRef]
  9. T. G. Mackay and A. Lakhtakia, "Negative phase velocity in a material with simultaneous mirror-conjugated and racemic chirality characteristics," New J. Phys. 7, 165 (2005).
    [CrossRef]
  10. J. L. Tsalamengas, "Interaction of electromagnetic waves with general bianisotropic slabs," IEEE Trans. Microwave Theory Tech. 40, 1870 (1992).
    [CrossRef]

2006

Q. Cheng and T. J. Cui, "Negative refractions in uniaxially anisotropic chiral media," Phys. Rev. B 73, 113104 (2006).
[CrossRef]

2005

T. G. Mackay and A. Lakhtakia, "Negative phase velocity in a material with simultaneous mirror-conjugated and racemic chirality characteristics," New J. Phys. 7, 165 (2005).
[CrossRef]

Y. Jin and S. He, "Focusing by a slab of chiral medium," Opt. Express 13, 4974 (2005).
[CrossRef] [PubMed]

S. Tretyakov, A. Sihvola, and L. Jylha, "Backward-wave regime and negative refraction in chiral composites," Photonics Nanostruct. Fundam. Appl. 3, 107 (2005).
[CrossRef]

C. Monzon and D. W. Forester, "Negative refraction and focusing of circularly polarized waves in optically active media," Phys. Rev. Lett. 95, 123904 (2005).
[CrossRef] [PubMed]

2004

J. B. Pendry, "A chiral route to negative refraction," Science 306, 1353 (2004).
[CrossRef] [PubMed]

T. G. Mackay and A. Lakhtakia, "Plane waves with negative phase velocity in Faraday chiral mediums," Phys. Rev. E 69, 026602 (2004).
[CrossRef]

2003

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, "Waves and energy in chiral nihility," J. Electromagn. Waves Appl. 17, 695 (2003).
[CrossRef]

1992

J. L. Tsalamengas, "Interaction of electromagnetic waves with general bianisotropic slabs," IEEE Trans. Microwave Theory Tech. 40, 1870 (1992).
[CrossRef]

Cheng, Q.

Q. Cheng and T. J. Cui, "Negative refractions in uniaxially anisotropic chiral media," Phys. Rev. B 73, 113104 (2006).
[CrossRef]

Cui, T. J.

Q. Cheng and T. J. Cui, "Negative refractions in uniaxially anisotropic chiral media," Phys. Rev. B 73, 113104 (2006).
[CrossRef]

Forester, D. W.

C. Monzon and D. W. Forester, "Negative refraction and focusing of circularly polarized waves in optically active media," Phys. Rev. Lett. 95, 123904 (2005).
[CrossRef] [PubMed]

He, S.

Jin, Y.

Jylha, L.

S. Tretyakov, A. Sihvola, and L. Jylha, "Backward-wave regime and negative refraction in chiral composites," Photonics Nanostruct. Fundam. Appl. 3, 107 (2005).
[CrossRef]

Lakhtakia, A.

T. G. Mackay and A. Lakhtakia, "Negative phase velocity in a material with simultaneous mirror-conjugated and racemic chirality characteristics," New J. Phys. 7, 165 (2005).
[CrossRef]

T. G. Mackay and A. Lakhtakia, "Plane waves with negative phase velocity in Faraday chiral mediums," Phys. Rev. E 69, 026602 (2004).
[CrossRef]

Mackay, T. G.

T. G. Mackay and A. Lakhtakia, "Negative phase velocity in a material with simultaneous mirror-conjugated and racemic chirality characteristics," New J. Phys. 7, 165 (2005).
[CrossRef]

T. G. Mackay and A. Lakhtakia, "Plane waves with negative phase velocity in Faraday chiral mediums," Phys. Rev. E 69, 026602 (2004).
[CrossRef]

Maslovski, S.

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, "Waves and energy in chiral nihility," J. Electromagn. Waves Appl. 17, 695 (2003).
[CrossRef]

Monzon, C.

C. Monzon and D. W. Forester, "Negative refraction and focusing of circularly polarized waves in optically active media," Phys. Rev. Lett. 95, 123904 (2005).
[CrossRef] [PubMed]

Nefedov, I.

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, "Waves and energy in chiral nihility," J. Electromagn. Waves Appl. 17, 695 (2003).
[CrossRef]

Pendry, J. B.

J. B. Pendry, "A chiral route to negative refraction," Science 306, 1353 (2004).
[CrossRef] [PubMed]

Sihvola, A.

S. Tretyakov, A. Sihvola, and L. Jylha, "Backward-wave regime and negative refraction in chiral composites," Photonics Nanostruct. Fundam. Appl. 3, 107 (2005).
[CrossRef]

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, "Waves and energy in chiral nihility," J. Electromagn. Waves Appl. 17, 695 (2003).
[CrossRef]

Simovski, C.

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, "Waves and energy in chiral nihility," J. Electromagn. Waves Appl. 17, 695 (2003).
[CrossRef]

Tretyakov, S.

S. Tretyakov, A. Sihvola, and L. Jylha, "Backward-wave regime and negative refraction in chiral composites," Photonics Nanostruct. Fundam. Appl. 3, 107 (2005).
[CrossRef]

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, "Waves and energy in chiral nihility," J. Electromagn. Waves Appl. 17, 695 (2003).
[CrossRef]

Tsalamengas, J. L.

J. L. Tsalamengas, "Interaction of electromagnetic waves with general bianisotropic slabs," IEEE Trans. Microwave Theory Tech. 40, 1870 (1992).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

J. L. Tsalamengas, "Interaction of electromagnetic waves with general bianisotropic slabs," IEEE Trans. Microwave Theory Tech. 40, 1870 (1992).
[CrossRef]

J. Electromagn. Waves Appl.

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, "Waves and energy in chiral nihility," J. Electromagn. Waves Appl. 17, 695 (2003).
[CrossRef]

New J. Phys.

T. G. Mackay and A. Lakhtakia, "Negative phase velocity in a material with simultaneous mirror-conjugated and racemic chirality characteristics," New J. Phys. 7, 165 (2005).
[CrossRef]

Opt. Express

Photonics Nanostruct. Fundam. Appl.

S. Tretyakov, A. Sihvola, and L. Jylha, "Backward-wave regime and negative refraction in chiral composites," Photonics Nanostruct. Fundam. Appl. 3, 107 (2005).
[CrossRef]

Phys. Rev. B

Q. Cheng and T. J. Cui, "Negative refractions in uniaxially anisotropic chiral media," Phys. Rev. B 73, 113104 (2006).
[CrossRef]

Phys. Rev. E

T. G. Mackay and A. Lakhtakia, "Plane waves with negative phase velocity in Faraday chiral mediums," Phys. Rev. E 69, 026602 (2004).
[CrossRef]

Phys. Rev. Lett.

C. Monzon and D. W. Forester, "Negative refraction and focusing of circularly polarized waves in optically active media," Phys. Rev. Lett. 95, 123904 (2005).
[CrossRef] [PubMed]

Science

J. B. Pendry, "A chiral route to negative refraction," Science 306, 1353 (2004).
[CrossRef] [PubMed]

Other

I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic waves in Chiral and Bi-Isotropic Media (Artech House, Boston, 1994).

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Figures (7)

Fig. 1.
Fig. 1.

A plane wave incident from free space to a biaxially anisotropic chiral medium.

Fig. 2.
Fig. 2.

Refractions of phase and energy flow for p + and p - waves on the interface of free space and the biaxially chiral medium. (a) κ < ε t ε 0 . (b) κ > ε t ε 0 .

Fig. 3.
Fig. 3.

The refraction and propagation properties of eigenwaves in the biaxially chiral medium with respect to incident angles, where ε t =ε z =2ε 0 and µ t =µ z =µ 0. (a) α(γ) for κ=0.2, (b) α(τ)·L(k 1z ) for κ=0.2, (c) α(γ) for κ=1.5, (d) α(τ)·L(k 1z ) for κ=1.5.

Fig. 4.
Fig. 4.

The refraction and propagation properties of eigenwaves in the biaxially chiral medium with respect to incident angles, where ε t =8ε 0, ε z =2ε 0, and µ t =µ z =µ 0. (a) α(γ) for κ=0.3, (b) α(τ)·L(k 1z ) for κ=0.3, (c) α(γ) for κ=1.5, (d) α(τ)·L(k 1z ) for κ=1.5.

Fig. 5.
Fig. 5.

The refraction and propagation properties of eigenwaves in the biaxially chiral medium with respect to incident angles, where ε t =-2ε 0, ε z =ε 0, and µ t =µ z =µ 0. (a) α(γ) for κ=0.3, (b) α(τ)·L(k 1z ) for κ=0.3, (c) α(γ) for κ=1.5, (d) α(τ)·L(k 1z ) for κ=1.5.

Fig. 6.
Fig. 6.

The refraction and propagation properties of eigenwaves in the biaxially chiral medium with respect to incident angles, where ε t =2ε 0, ε z =-ε 0, and µ t =µ z =µ 0. (a) α(γ) for κ=0.3, (b) α(τ)·L(k 1z ) for κ=0.3, (c) α(γ) for κ=0.8, (d) α(τ)·L(k 1z ) for κ=0.8.

Fig. 7.
Fig. 7.

The refraction and propagation properties of eigenwaves in the biaxially chiral medium with respect to incident angles, where ε t =2ε 0, ε z =-ε 0, and µ t =2µ 0, µ z =µ 0. (a) α(γ) for κ=0.3, (b) α(τ)·L(k 1z ) for κ=0.3, (c) α(γ) for κ=0.8, (d) α(τ)·L(k 1z ) for κ=0.8.

Equations (38)

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D ¯ = [ ε t I ̿ t + ε z z ̂ z ̂ ] · E ¯ + i κ ε 0 μ 0 ( y ̂ y ̂ + z ̂ z ̂ ) · H ¯ ,
B ¯ = [ μ t I ̿ t + μ z z ̂ z ̂ ] · H ¯ i κ ε 0 μ 0 ( y ̂ y ̂ + z ̂ z ̂ ) · E ¯ ,
z [ E ¯ t H ¯ t ] = i ω M ̿ · [ E ¯ t H ¯ t ] ,
E ¯ t = [ E x E y ] , H ¯ t = [ H x H y ] ,
M ̿ = [ 0 α 0 μ t p α 0 μ t + p μ z 0 0 ε t 0 α ε t p ε z 0 p α 0 ] ,
k 1 z = ω λ ,
k 1 z 2 = ω 2 ( ε t μ t + p ζ ± f )
ζ = κ 2 ε 0 μ 0 1 2 ε t μ z 1 2 ε z μ t ,
f = 1 2 a p 2 + b p + c ,
p = k y 2 ω 2 ( ε z μ z κ 2 ε 0 μ 0 ) ,
a = ( ε t μ z ε z μ t ) 2 + 4 κ 2 ε 0 μ 0 q ,
b = 4 κ 2 ε 0 μ 0 ( 2 ε t μ t ε z μ t ε t μ z ) ,
c = 4 κ 2 ε 0 μ 0 ε t μ t .
k 1 z 2 ε t + k y 2 ε z = ω 2 μ t ,
k 1 z 2 μ t + k y 2 μ z = ω 2 ε t ,
E ¯ = A e ¯ ± , H ¯ = A h ¯ ± ,
e ¯ ± = x ̂ 1 p α ( μ t p μ z + λ σ ) + y ̂ σ + z ̂ s k y p ( μ t + λ σ ) ,
h ¯ ± = x ̂ y ̂ 1 α ( λ + ε t σ ) z ̂ s k y [ ε z p α ( μ t p μ z + λ σ ) α ] ,
s = 1 ( ω ( ε z μ 0 κ 2 ε 0 μ 0 ) ) ,
σ = λ m ( ( p + 1 ) μ t p μ z ) ,
m = λ 2 p κ 2 ε 0 μ 0 + p ε t μ 0 .
S y = s k y [ ε z p 2 κ 2 ε 0 μ 0 ( μ t p μ z + λ σ ) 2 + 1 p ( 2 μ t p μ z + 2 λ σ ) ] A 2 ,
S 1 z = [ 1 p α 2 ( μ t p μ z + λ σ ) ( λ + ε t σ ) σ ] A 2 .
e ¯ ± = x ̂ i μ 0 ξ 1 p κ ε 0 μ 0 y ̂ λ m μ 0 + z ̂ s p k y μ 0 ξ 2 ,
h ¯ ± = x ̂ + y ̂ i λ κ ε 0 μ 0 ξ 3 z ̂ s k y ξ 4 ,
ξ 1 = 1 p λ 2 m ,
ξ 2 = ξ 1 + p ,
ξ 3 = 1 ε t μ 0 m ,
ξ 4 = i ε z μ 0 ξ 1 ( p κ ε 0 μ 0 ) i κ ε 0 μ 0 .
S y = k y μ 0 γ A 2 ,
S 1 z = k 1 z τ ( ω κ 2 ε 0 ) A 2 ,
γ = s [ ε z κ 2 ε 0 ( 1 g m ) 2 ( 1 2 g m ) ] ,
τ = ( 1 g m ) ( 1 1 m ε t μ 0 ) + 1 m κ 2 ε 0 μ 0 ,
g = ε t μ 0 κ 2 ε 0 μ 0 .
k y 2 + k 1 z 2 = ω 2 μ 0 ( ε t ± κ ε 0 ε t ) ,
S y = 2 k y ω ( ε t ± κ ε 0 ε t ) A 2 ,
S 1 z = 2 k 1 z ω ( ε t ± κ ε 0 ε t ) A 2 .
α ( h ) = { 0 , Re ( h ) = 0 , 1 , Re ( h ) > 0 , 1 , Re ( h ) < 0 ,

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