Abstract

We investigate the phenomena of negative refraction and backward wave in pseudochiral mediums, with illustrations of Gaussian beams. Due to symmetry breaking intrinsic in pseudochiral mediums, there exist two elliptically polarized eigenwaves with different wave vectors. As the chirality parameter increases from zero, the two waves begin to split from each other. For a wave incident from vacuum onto a pseudochiral medium, negative refraction may occur for the right-handed wave, whereas backward wave may appear for the left-handed wave. These features are illustrated with Gaussian beams based on Fourier integral formulations for the incident, reflected, and transmitted waves. Negative refraction and backward wave are manifest, respectively, on the energy flow in space and wavefront movement in time.

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  1. J. A. Kong, “Theorems of bianisotropic media,” Proc. IEEE60, 1036–1046 (1972).
    [CrossRef]
  2. A. Serdyukov, I. Semchenko, S. Tretyakov, and A. Sihvola, Electromagnetics of Bi-anisotropic Materials: Theory and Applications (Gordon and Breach, 2001).
  3. S. A. Tretyakov, A. H. Sihvola, A. A. Sochava, and C. R. Simovski, “Magnetoelectric interactions in bi-anisotropic media,” J. Electromagn. Waves Appl.12, 481–497 (1998).
    [CrossRef]
  4. M. M. I. Saadoun and N. Engheta, “A reciprocal phase shifter using novel pseudochiral or s medium,” Microwave and Optical Technology Letters5, 184–188 (1992).
    [CrossRef]
  5. S. A. Matos, C. R. Paiva, and A. M. Barbosa, “Surface and proper leaky-modes in a lossless grounded pseudochiral omega slab,” Microw. Opt. Technol. Lett.50, 814–818 (2008).
    [CrossRef]
  6. W. S. Weiglhofer and A. Lakhtakia, Introduction to Complex Mediums for Optics and Electromagnetics (SPIE, 2003).
    [CrossRef]
  7. P. A. Belov, “Backward waves and negative refraction in uniaxial dielectrics with negative dielectric permittivity along the anisotropy axis,” Microw. Opt. Technol. Lett.37, 259–263 (2003).
    [CrossRef]
  8. L. Yonghua, W. Pei, Y. Peijun, X. Jianping, and M. Hai, “Negative refraction at the interface of uniaxial anisotropic media,” Opt. Comm.246, 429–435 (2005).
    [CrossRef]
  9. H. Chen, S. Xu, and J. Li, “Negative reflection of waves at planar interfaces associated with a uniaxial medium,” Opt. Lett.34, 3283–3285 (2009).
    [CrossRef] [PubMed]
  10. J. B. Pendry, “A chiral route to negative refraction,” Science306, 1353–1355 (2004).
    [CrossRef] [PubMed]
  11. 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]
  12. S. Tretyakov, A. Sihvola, and L. Jylha, “Backward-wave regime and negative refraction in chiral composites,” Photonics Nanostruct.3, 107–115 (2005).
    [CrossRef]
  13. Q. Cheng and T. J. Cui, “Negative refractions in uniaxially anisotropic chiral media,” Phys. Rev. B73, 113104 (2006).
    [CrossRef]
  14. S. A. Tretyakov, C. R. Simovski, and M. Hudlicka, “Bianisotropic route to the realization and matching of backward-wave metamaterial slabs,” Phys. Rev. B75, 153104 (2007).
    [CrossRef]
  15. B. R. Horowitz and T. Tamir, “Lateral Displacement of a light beam at a dielectric interface,” J. Opt. Soc. Am.61, 586–594 (1971).
    [CrossRef]

2009

2008

S. A. Matos, C. R. Paiva, and A. M. Barbosa, “Surface and proper leaky-modes in a lossless grounded pseudochiral omega slab,” Microw. Opt. Technol. Lett.50, 814–818 (2008).
[CrossRef]

2007

S. A. Tretyakov, C. R. Simovski, and M. Hudlicka, “Bianisotropic route to the realization and matching of backward-wave metamaterial slabs,” Phys. Rev. B75, 153104 (2007).
[CrossRef]

2006

Q. Cheng and T. J. Cui, “Negative refractions in uniaxially anisotropic chiral media,” Phys. Rev. B73, 113104 (2006).
[CrossRef]

2005

L. Yonghua, W. Pei, Y. Peijun, X. Jianping, and M. Hai, “Negative refraction at the interface of uniaxial anisotropic media,” Opt. Comm.246, 429–435 (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]

S. Tretyakov, A. Sihvola, and L. Jylha, “Backward-wave regime and negative refraction in chiral composites,” Photonics Nanostruct.3, 107–115 (2005).
[CrossRef]

2004

J. B. Pendry, “A chiral route to negative refraction,” Science306, 1353–1355 (2004).
[CrossRef] [PubMed]

2003

P. A. Belov, “Backward waves and negative refraction in uniaxial dielectrics with negative dielectric permittivity along the anisotropy axis,” Microw. Opt. Technol. Lett.37, 259–263 (2003).
[CrossRef]

1998

S. A. Tretyakov, A. H. Sihvola, A. A. Sochava, and C. R. Simovski, “Magnetoelectric interactions in bi-anisotropic media,” J. Electromagn. Waves Appl.12, 481–497 (1998).
[CrossRef]

1992

M. M. I. Saadoun and N. Engheta, “A reciprocal phase shifter using novel pseudochiral or s medium,” Microwave and Optical Technology Letters5, 184–188 (1992).
[CrossRef]

1972

J. A. Kong, “Theorems of bianisotropic media,” Proc. IEEE60, 1036–1046 (1972).
[CrossRef]

1971

Barbosa, A. M.

S. A. Matos, C. R. Paiva, and A. M. Barbosa, “Surface and proper leaky-modes in a lossless grounded pseudochiral omega slab,” Microw. Opt. Technol. Lett.50, 814–818 (2008).
[CrossRef]

Belov, P. A.

P. A. Belov, “Backward waves and negative refraction in uniaxial dielectrics with negative dielectric permittivity along the anisotropy axis,” Microw. Opt. Technol. Lett.37, 259–263 (2003).
[CrossRef]

Chen, H.

Cheng, Q.

Q. Cheng and T. J. Cui, “Negative refractions in uniaxially anisotropic chiral media,” Phys. Rev. B73, 113104 (2006).
[CrossRef]

Cui, T. J.

Q. Cheng and T. J. Cui, “Negative refractions in uniaxially anisotropic chiral media,” Phys. Rev. B73, 113104 (2006).
[CrossRef]

Engheta, N.

M. M. I. Saadoun and N. Engheta, “A reciprocal phase shifter using novel pseudochiral or s medium,” Microwave and Optical Technology Letters5, 184–188 (1992).
[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]

Hai, M.

L. Yonghua, W. Pei, Y. Peijun, X. Jianping, and M. Hai, “Negative refraction at the interface of uniaxial anisotropic media,” Opt. Comm.246, 429–435 (2005).
[CrossRef]

Horowitz, B. R.

Hudlicka, M.

S. A. Tretyakov, C. R. Simovski, and M. Hudlicka, “Bianisotropic route to the realization and matching of backward-wave metamaterial slabs,” Phys. Rev. B75, 153104 (2007).
[CrossRef]

Jianping, X.

L. Yonghua, W. Pei, Y. Peijun, X. Jianping, and M. Hai, “Negative refraction at the interface of uniaxial anisotropic media,” Opt. Comm.246, 429–435 (2005).
[CrossRef]

Jylha, L.

S. Tretyakov, A. Sihvola, and L. Jylha, “Backward-wave regime and negative refraction in chiral composites,” Photonics Nanostruct.3, 107–115 (2005).
[CrossRef]

Kong, J. A.

J. A. Kong, “Theorems of bianisotropic media,” Proc. IEEE60, 1036–1046 (1972).
[CrossRef]

Lakhtakia, A.

W. S. Weiglhofer and A. Lakhtakia, Introduction to Complex Mediums for Optics and Electromagnetics (SPIE, 2003).
[CrossRef]

Li, J.

Matos, S. A.

S. A. Matos, C. R. Paiva, and A. M. Barbosa, “Surface and proper leaky-modes in a lossless grounded pseudochiral omega slab,” Microw. Opt. Technol. Lett.50, 814–818 (2008).
[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]

Paiva, C. R.

S. A. Matos, C. R. Paiva, and A. M. Barbosa, “Surface and proper leaky-modes in a lossless grounded pseudochiral omega slab,” Microw. Opt. Technol. Lett.50, 814–818 (2008).
[CrossRef]

Pei, W.

L. Yonghua, W. Pei, Y. Peijun, X. Jianping, and M. Hai, “Negative refraction at the interface of uniaxial anisotropic media,” Opt. Comm.246, 429–435 (2005).
[CrossRef]

Peijun, Y.

L. Yonghua, W. Pei, Y. Peijun, X. Jianping, and M. Hai, “Negative refraction at the interface of uniaxial anisotropic media,” Opt. Comm.246, 429–435 (2005).
[CrossRef]

Pendry, J. B.

J. B. Pendry, “A chiral route to negative refraction,” Science306, 1353–1355 (2004).
[CrossRef] [PubMed]

Saadoun, M. M. I.

M. M. I. Saadoun and N. Engheta, “A reciprocal phase shifter using novel pseudochiral or s medium,” Microwave and Optical Technology Letters5, 184–188 (1992).
[CrossRef]

Semchenko, I.

A. Serdyukov, I. Semchenko, S. Tretyakov, and A. Sihvola, Electromagnetics of Bi-anisotropic Materials: Theory and Applications (Gordon and Breach, 2001).

Serdyukov, A.

A. Serdyukov, I. Semchenko, S. Tretyakov, and A. Sihvola, Electromagnetics of Bi-anisotropic Materials: Theory and Applications (Gordon and Breach, 2001).

Sihvola, A.

S. Tretyakov, A. Sihvola, and L. Jylha, “Backward-wave regime and negative refraction in chiral composites,” Photonics Nanostruct.3, 107–115 (2005).
[CrossRef]

A. Serdyukov, I. Semchenko, S. Tretyakov, and A. Sihvola, Electromagnetics of Bi-anisotropic Materials: Theory and Applications (Gordon and Breach, 2001).

Sihvola, A. H.

S. A. Tretyakov, A. H. Sihvola, A. A. Sochava, and C. R. Simovski, “Magnetoelectric interactions in bi-anisotropic media,” J. Electromagn. Waves Appl.12, 481–497 (1998).
[CrossRef]

Simovski, C. R.

S. A. Tretyakov, C. R. Simovski, and M. Hudlicka, “Bianisotropic route to the realization and matching of backward-wave metamaterial slabs,” Phys. Rev. B75, 153104 (2007).
[CrossRef]

S. A. Tretyakov, A. H. Sihvola, A. A. Sochava, and C. R. Simovski, “Magnetoelectric interactions in bi-anisotropic media,” J. Electromagn. Waves Appl.12, 481–497 (1998).
[CrossRef]

Sochava, A. A.

S. A. Tretyakov, A. H. Sihvola, A. A. Sochava, and C. R. Simovski, “Magnetoelectric interactions in bi-anisotropic media,” J. Electromagn. Waves Appl.12, 481–497 (1998).
[CrossRef]

Tamir, T.

Tretyakov, S.

S. Tretyakov, A. Sihvola, and L. Jylha, “Backward-wave regime and negative refraction in chiral composites,” Photonics Nanostruct.3, 107–115 (2005).
[CrossRef]

A. Serdyukov, I. Semchenko, S. Tretyakov, and A. Sihvola, Electromagnetics of Bi-anisotropic Materials: Theory and Applications (Gordon and Breach, 2001).

Tretyakov, S. A.

S. A. Tretyakov, C. R. Simovski, and M. Hudlicka, “Bianisotropic route to the realization and matching of backward-wave metamaterial slabs,” Phys. Rev. B75, 153104 (2007).
[CrossRef]

S. A. Tretyakov, A. H. Sihvola, A. A. Sochava, and C. R. Simovski, “Magnetoelectric interactions in bi-anisotropic media,” J. Electromagn. Waves Appl.12, 481–497 (1998).
[CrossRef]

Weiglhofer, W. S.

W. S. Weiglhofer and A. Lakhtakia, Introduction to Complex Mediums for Optics and Electromagnetics (SPIE, 2003).
[CrossRef]

Xu, S.

Yonghua, L.

L. Yonghua, W. Pei, Y. Peijun, X. Jianping, and M. Hai, “Negative refraction at the interface of uniaxial anisotropic media,” Opt. Comm.246, 429–435 (2005).
[CrossRef]

J. Electromagn. Waves Appl.

S. A. Tretyakov, A. H. Sihvola, A. A. Sochava, and C. R. Simovski, “Magnetoelectric interactions in bi-anisotropic media,” J. Electromagn. Waves Appl.12, 481–497 (1998).
[CrossRef]

J. Opt. Soc. Am.

Microw. Opt. Technol. Lett.

S. A. Matos, C. R. Paiva, and A. M. Barbosa, “Surface and proper leaky-modes in a lossless grounded pseudochiral omega slab,” Microw. Opt. Technol. Lett.50, 814–818 (2008).
[CrossRef]

P. A. Belov, “Backward waves and negative refraction in uniaxial dielectrics with negative dielectric permittivity along the anisotropy axis,” Microw. Opt. Technol. Lett.37, 259–263 (2003).
[CrossRef]

Microwave and Optical Technology Letters

M. M. I. Saadoun and N. Engheta, “A reciprocal phase shifter using novel pseudochiral or s medium,” Microwave and Optical Technology Letters5, 184–188 (1992).
[CrossRef]

Opt. Comm.

L. Yonghua, W. Pei, Y. Peijun, X. Jianping, and M. Hai, “Negative refraction at the interface of uniaxial anisotropic media,” Opt. Comm.246, 429–435 (2005).
[CrossRef]

Opt. Lett.

Photonics Nanostruct.

S. Tretyakov, A. Sihvola, and L. Jylha, “Backward-wave regime and negative refraction in chiral composites,” Photonics Nanostruct.3, 107–115 (2005).
[CrossRef]

Phys. Rev. B

Q. Cheng and T. J. Cui, “Negative refractions in uniaxially anisotropic chiral media,” Phys. Rev. B73, 113104 (2006).
[CrossRef]

S. A. Tretyakov, C. R. Simovski, and M. Hudlicka, “Bianisotropic route to the realization and matching of backward-wave metamaterial slabs,” Phys. Rev. B75, 153104 (2007).
[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]

Proc. IEEE

J. A. Kong, “Theorems of bianisotropic media,” Proc. IEEE60, 1036–1046 (1972).
[CrossRef]

Science

J. B. Pendry, “A chiral route to negative refraction,” Science306, 1353–1355 (2004).
[CrossRef] [PubMed]

Other

W. S. Weiglhofer and A. Lakhtakia, Introduction to Complex Mediums for Optics and Electromagnetics (SPIE, 2003).
[CrossRef]

A. Serdyukov, I. Semchenko, S. Tretyakov, and A. Sihvola, Electromagnetics of Bi-anisotropic Materials: Theory and Applications (Gordon and Breach, 2001).

Supplementary Material (1)

» Media 1: MOV (403 KB)     

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of the wave vectors and Poynting vectors for a Gaussian beam incident from vacuum (z < 0) onto a pseudochiral medium (z > 0) characterized by ε, μ, and γ, where (a) θ < θNR, θ < θBW and (b) θBW< θ < θNR.

Fig. 2
Fig. 2

Power intensities for a p-polarized (TM) Gaussian beam incident from vacuum at θ = 20° onto a pseudochiral medium with εr = 2, μr = 1, and (a) γ = 0.2 (b) γ = 0.8. The intensities are normalized to have a maximum value of unity. White solid line denotes the interface. Black dashed lines indicate the beam centers.

Fig. 3
Fig. 3

Power intensities for a (a) RCP and (b) LCP Gaussian beam incident from vacuum at θ = 20° onto a pseudochiral medium with the same material parameters as in Fig. 2(b).

Fig. 4
Fig. 4

(a) Power intensities for a p-polarized Gaussian beam incident from vacuum at θ = 0° onto the pseudochiral medium with εr = 1, μr = 1, and γ̃ = 0.6. (b) Effect of the chirality parameter γ̃ on the angles of Poynting vectors for REP and LEP waves.

Fig. 5
Fig. 5

Electric field (Ey) for a s-polarized Gaussian beam incident from vacuum at θ = 25° onto a pseudochiral medium with εr = 1, μr = 1, and γ̃ = 0.95 ( Media 1).

Equations (45)

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D = ε _ E + ξ _ H ,
B = μ _ H + ζ _ E ,
ξ _ = [ 0 0 i γ 0 0 0 i γ 0 0 ] , ζ _ = [ 0 0 i γ 0 0 0 i γ 0 0 ] ,
ω = 1 ρ ε μ | k | 2 ± 2 γ ˜ | k x k z | .
k z ± = ρ h 0 2 k x 2 ± γ ˜ | k x | ,
E ± = E 0 ± ( h z h 0 , ± i ρ , h z h 0 σ ± ) , H ± = i η E ± ,
σ ± = k x k z ± ( 1 γ ˜ 2 h 0 2 h z 2 ) sign ( k x ) γ ˜ ( 1 k x 2 h z 2 ) .
S ± = ρ h z η h 0 ( E 0 ± ) 2 ( σ ± x ^ + z ^ ) .
θ ± = arccos ( k z ± k ± ) , ϕ ± = arctan ( σ ± ) .
θ NR = arcsin ( γ ˜ h 0 k 0 )
θ BW = arcsin ( ρ h 0 k 0 )
f ( x , z ) = ψ ( k x ) e ik x x + ik z z d k x ,
ψ ( k x ) = w 0 2 cos θ π exp [ w 0 2 4 cos 2 θ ( k x k 0 sin θ ) 2 ik x x 0 + ik z h ] ,
E i p , s = E 0 p , s e i p , s ψ ( k x ) e ik x x + ik z z d k x ,
H i p , s = E 0 p , s η 0 h i p , s ψ ( k x ) e ik x x + ik z z d k x ,
E r p , s = e r p , s R p , s ψ ( k x ) e ik x x ik z z d k x ,
H r p , s = 1 η 0 h r p , s R p , s ψ ( k x ) e ik x x ik z z d k x ,
E t ± = e t ± T ± ψ ( k x ) e ik x x + i k z ± z d k x ,
H t ± = 1 η h t ± T ± ψ ( k x ) e ik x x + i k z ± z d k x ,
E i ± = E 0 ± e i ± ( k x ) ψ ( k x ) e ik x x + ik z z d k x ,
H i ± = E 0 ± η 0 h i ± ψ ( k x ) e ik x x + ik z z d k x ,
E r ± = e r ± R ± ψ ( k x ) e ik x x ik z z d k x ,
H r ± = 1 η 0 h r ± R ± ψ ( k x ) e ik x x ik z z d k x ,
f ( x , z ) = IFT [ FT [ f 0 ( x ) ] ϕ ( k x ) e i q z z ] ,
f 0 ( x ) = exp [ ( x x 0 ) 2 cos 2 θ w 0 2 + ik 0 sin θ ( x x 0 ) + ik z h ]
FT [ f ( x ) ] = F ( k x ) 1 2 π f ( x ) e ik x x d x ,
IFT [ F ( k x ) ] = f ( x ) 1 2 π F ( k x ) e ik x x d k x ,
f ± ( x , z ) = ψ ( k x ) e ik x x + i k z ± z d k x .
f ± ( x , z ) = w 0 2 w { e ( x + γ ˜ z ) 2 w 2 [ 1 ± i erfi ( x + γ ˜ z w ) ] + e ( x γ ˜ z ) 2 w 2 [ 1 i erfi ( x γ ˜ z w ) ] } e i ρ h 0 z ,
× μ _ 1 × E i ω × ( μ _ 1 ζ _ E ) + i ω ξ _ μ _ 1 × E ω 2 ( ε _ ξ _ μ _ 1 ζ _ ) E = 0 ,
× ε _ 1 × H i ω ζ _ ε _ 1 × H + i ω × ( ε _ 1 ξ _ H ) ω 2 ( μ _ ζ _ ε _ 1 ξ _ ) H = 0 ,
M _ = ( k × I _ + ω ξ _ ) μ _ 1 ( k × I _ ω ζ _ ) + ω 2 ε _ ,
N _ = ( k × I _ ω ζ _ ) ε _ 1 ( k × I _ + ω ξ _ ) + ω 2 μ _ ,
ε 2 μ 2 ρ 4 ω 4 2 ε μ ρ 2 | k | 2 ω 2 + | k | 4 4 γ ˜ 2 k x 2 k z 2 = 0 ,
ω = 1 ρ ε μ | k | 2 ± 2 γ ˜ | k x k z | .
E ± = ( h z h 0 , ± i ρ , h z h 0 σ ± ) , H ± = i η E ± ,
σ ± = k x k z ± ( 1 γ ˜ 2 h 0 2 h z 2 ) sign ( k x ) γ ˜ ( 1 k x 2 h z 2 ) .
[ E r p E r s ] = [ r p p r p s r s p r s s ] [ E i p E i s ] ,
[ E t + E t ] = [ t + p t + s t p t s ] [ E i p E i s ] ,
r p p = α ρ β α + ρ β , r p s = 0 , r s p = 0 , r s s = ρ α B ρ + α β ,
t + p = + α + ρ β , t + s = i ρ + α β , t p = 1 α + ρ β , t s = i ρ + α β .
[ E r + E r ] = [ r + + r + r + r ] [ E i + E i ] ,
[ E t + E t ] = [ t + + t + t + t ] [ E i + E i ] ,
r + + = r = ρ α ( 1 β 2 ) ( α + ρ β ) ( ρ + α β ) , r + = r + = β ( α 2 ρ 2 ) ( α + ρ β ) ( ρ + α β ) ,
t + + = t = 1 α + ρ β + 1 ρ + α β , t + = t + = 1 α + ρ β 1 ρ + α β .

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