Abstract

We have investigated the reflection and refraction properties of plane waves incident from free space into a uniaxially anisotropic chiral medium, where the chirality appears only in one direction and the host medium can be either an isotropic dielectric or an anisotropic electric plasma. We show that the reflection and refraction properties are closely related to the dispersion relation of the chiral medium and that negative phase refractions and/or negative group refractions may occur. We further demonstrate that the two eigenwaves within the uniaxially anisotropic chiral medium behave differently with respect to the incident angle, and in some cases only one of them can be supported and transmitted. We have studied the critical angle and Brewster’s angle with some special properties. We have also discussed the potential application of the uniaxially anisotropic chiral medium for the polarization beam splitter. Numerical results are given to validate our analysis.

© 2006 Optical Society of America

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References

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  1. D. L. Jaggard, A. R. Mickelson, and C. H. Papas, "On electromagnetic waves in chiral media," Appl. Phys. 18, 211-216 (1979).
    [CrossRef]
  2. K. F. Lindman, "Über eine durch ein isotropes System von Spiralförmigen Resonatoren erzeugte Rotationspolarisation der elektromagnetischen Wellen," Ann. Phys. (Leipzig) 63, 621-644 (1920).
    [CrossRef]
  3. I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-Isotropic Media (Artech House, 1994).
  4. J. B. Pendry, "Negative refraction," Contemp. Phys. 45, 191-202 (2004).
    [CrossRef]
  5. S. A. Ramakrishna, "Physics of negative refraction index materials," Rep. Prog. Phys. 68, 449-521 (2005).
    [CrossRef]
  6. J. B. Pendry, "A chiral route to negative refraction," Science 306, 1353-1355 (2004).
    [CrossRef] [PubMed]
  7. Y. Jin and S. He, "Focusing by a slab of chiral medium," Opt. Express 13, 4974-4979 (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. H. C. Chen, Theory of Electromagnetic Waves (McGraw-Hill, 1983).
  10. J. A. Kong, Theory of Electromagnetic Waves (Wiley, 1975).
  11. V. Mocella, P. Dardano, L. Moretti, and I. Rendina, "A polarizing beam splitter using negative refraction of photonic crystals," Opt. Express 13, 7699-7707 (2005).
    [CrossRef] [PubMed]

2006 (1)

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

2005 (3)

2004 (2)

J. B. Pendry, "A chiral route to negative refraction," Science 306, 1353-1355 (2004).
[CrossRef] [PubMed]

J. B. Pendry, "Negative refraction," Contemp. Phys. 45, 191-202 (2004).
[CrossRef]

1979 (1)

D. L. Jaggard, A. R. Mickelson, and C. H. Papas, "On electromagnetic waves in chiral media," Appl. Phys. 18, 211-216 (1979).
[CrossRef]

1920 (1)

K. F. Lindman, "Über eine durch ein isotropes System von Spiralförmigen Resonatoren erzeugte Rotationspolarisation der elektromagnetischen Wellen," Ann. Phys. (Leipzig) 63, 621-644 (1920).
[CrossRef]

Chen, H. C.

H. C. Chen, Theory of Electromagnetic Waves (McGraw-Hill, 1983).

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]

Dardano, P.

He, S.

Jaggard, D. L.

D. L. Jaggard, A. R. Mickelson, and C. H. Papas, "On electromagnetic waves in chiral media," Appl. Phys. 18, 211-216 (1979).
[CrossRef]

Jin, Y.

Kong, J. A.

J. A. Kong, Theory of Electromagnetic Waves (Wiley, 1975).

Lindell, I. V.

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

Lindman, K. F.

K. F. Lindman, "Über eine durch ein isotropes System von Spiralförmigen Resonatoren erzeugte Rotationspolarisation der elektromagnetischen Wellen," Ann. Phys. (Leipzig) 63, 621-644 (1920).
[CrossRef]

Mickelson, A. R.

D. L. Jaggard, A. R. Mickelson, and C. H. Papas, "On electromagnetic waves in chiral media," Appl. Phys. 18, 211-216 (1979).
[CrossRef]

Mocella, V.

Moretti, L.

Papas, C. H.

D. L. Jaggard, A. R. Mickelson, and C. H. Papas, "On electromagnetic waves in chiral media," Appl. Phys. 18, 211-216 (1979).
[CrossRef]

Pendry, J. B.

J. B. Pendry, "A chiral route to negative refraction," Science 306, 1353-1355 (2004).
[CrossRef] [PubMed]

J. B. Pendry, "Negative refraction," Contemp. Phys. 45, 191-202 (2004).
[CrossRef]

Ramakrishna, S. A.

S. A. Ramakrishna, "Physics of negative refraction index materials," Rep. Prog. Phys. 68, 449-521 (2005).
[CrossRef]

Rendina, I.

Sihvola, A. H.

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

Tretyakov, S. A.

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

Viitanen, A. J.

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

Ann. Phys. (1)

K. F. Lindman, "Über eine durch ein isotropes System von Spiralförmigen Resonatoren erzeugte Rotationspolarisation der elektromagnetischen Wellen," Ann. Phys. (Leipzig) 63, 621-644 (1920).
[CrossRef]

Appl. Phys. (1)

D. L. Jaggard, A. R. Mickelson, and C. H. Papas, "On electromagnetic waves in chiral media," Appl. Phys. 18, 211-216 (1979).
[CrossRef]

Contemp. Phys. (1)

J. B. Pendry, "Negative refraction," Contemp. Phys. 45, 191-202 (2004).
[CrossRef]

Opt. Express (2)

Phys. Rev. B (1)

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

Rep. Prog. Phys. (1)

S. A. Ramakrishna, "Physics of negative refraction index materials," Rep. Prog. Phys. 68, 449-521 (2005).
[CrossRef]

Science (1)

J. B. Pendry, "A chiral route to negative refraction," Science 306, 1353-1355 (2004).
[CrossRef] [PubMed]

Other (3)

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

H. C. Chen, Theory of Electromagnetic Waves (McGraw-Hill, 1983).

J. A. Kong, Theory of Electromagnetic Waves (Wiley, 1975).

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Figures (4)

Fig. 1
Fig. 1

Plane-wave reflection and refraction at the interface of free space and the uniaxially anisotropic chiral medium (UACM).

Fig. 2
Fig. 2

Refraction angle for the p + wave (dashed curve), and p wave (solid curve), where μ t = μ z = μ 0 ; (a) ϵ t = ϵ z = 2 ϵ 0 , κ = 1.1 ; (b) ϵ t = ϵ z = 2 ϵ 0 , κ = 1.8 ; (c) ϵ t = 2 ϵ 0 , ϵ z = ϵ 0 , κ = 0.5 ; (d) ϵ t = 0.2 ϵ 0 , ϵ z = ϵ 0 , κ = 1.3 .

Fig. 3
Fig. 3

Distributions of the eigenvalues for the reflection matrix λ 1 (dashed curve) and λ 2 (solid curve), where μ t = μ z = μ 0 ; (a) ϵ t = ϵ z = 2 ϵ 0 , κ = 0.5 ; (b) ϵ t = ϵ z = 2 ϵ 0 , κ = 0.9 ; (c) ϵ t = 0.2 ϵ 0 , ϵ z = ϵ 0 , κ = 0.3 ; (d) ϵ t = 0.2 ϵ 0 , ϵ z = ϵ 0 , κ = 1.3 .

Fig. 4
Fig. 4

(a) Transmission coefficients for p + and p waves, (b) refraction angles of the energy velocities for p + and p waves. Here, ϵ t = 3 ϵ 0 , ϵ z = ϵ 0 , μ t = μ z = μ 0 , κ = 0.2 .

Equations (29)

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D ¯ = [ ϵ t I ̿ + ϵ z z ̂ z ̂ ] E ¯ + i κ ϵ 0 μ 0 z ̂ z ̂ H ¯ ,
B ¯ = [ μ t I ̿ t + μ z z ̂ z ̂ ] H ¯ i κ ϵ 0 μ 0 z ̂ z ̂ E ¯ ,
k ± = k t cos 2 θ t ± + sin 2 θ t ± ρ ± ,
ρ ± = 1 2 [ ϵ z ϵ t + μ z μ t ± ( ϵ z ϵ z μ z μ t ) 2 + 4 κ 2 ϵ 0 μ 0 ϵ t μ t ] .
k y 2 ρ ± + ( k 1 z ± ) 2 = k t 2 .
k ¯ i × z ̂ = k ¯ r × z ̂ = k ¯ ± × z ̂ .
E ¯ 0 i = A x ̂ + A ( k ¯ i × x ̂ ) ,
E ¯ 0 r = B x ̂ + B ( k ¯ r × x ̂ ) ,
E ¯ 1 t = C + e ¯ + + C e ¯ ,
( B B ) = [ R 11 R 12 R 21 R 22 ] ( A A ) ,
( C + C ) = [ T 11 T 12 T 21 T 22 ] ( A A ) ,
R 11 = ( S 11 Γ 22 S 12 Γ 21 ) ( Γ 11 Γ 22 Γ 12 Γ 21 ) ,
R 12 = ( S 12 Γ 11 S 11 Γ 12 ) ( Γ 11 Γ 22 Γ 12 Γ 21 ) ,
R 21 = ( S 21 Γ 22 S 22 Γ 21 ) ( Γ 11 Γ 22 Γ 12 Γ 21 ) ,
R 22 = ( S 22 Γ 11 S 21 Γ 12 ) ( Γ 11 Γ 22 Γ 12 Γ 21 ) ,
T 11 = Γ 22 ( Γ 11 Γ 22 Γ 12 Γ 21 ) ,
T 12 = Γ 12 ( Γ 11 Γ 22 Γ 12 Γ 21 ) ,
T 21 = Γ 21 ( Γ 11 Γ 22 Γ 12 Γ 21 ) ,
T 22 = Γ 11 ( Γ 11 Γ 22 Γ 12 Γ 21 ) ,
Γ 11 = i ω μ t β + ( k i cos θ i + k 1 z + ) 2 k i k 1 z + cos θ i ,
Γ 12 = i ω μ t β ( k i cos θ i + k 1 z ) 2 k i k 1 z cos θ i ,
Γ 21 = ( ϵ 0 k 1 z + + ϵ t k i cos θ i ) 2 ϵ 0 k 1 z + cos θ i ,
Γ 22 = ( ϵ 0 k 1 z + ϵ t k i cos θ i ) 2 ϵ 0 k 1 z cos θ i ,
S 11 = i ω μ t β + ( k i cos θ i k 1 z + ) 2 k i k 1 z + cos θ i ,
S 12 = i ω μ t β ( k i cos θ i k 1 z ) 2 k i k 1 z cos θ i ,
S 21 = ( ϵ 0 k 1 z + ϵ t k i cos θ i ) 2 ϵ 0 k 1 z + cos θ i ,
S 22 = ( ϵ 0 k 1 z ϵ t k i cos θ i ) 2 ϵ 0 k 1 z cos θ i ,
sin 2 θ t ± = s ρ ± ( ( s + 1 ) ρ ± s ) ,
sin 2 θ t = s ρ ( ( s 1 ) ρ + s ) ,

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