Abstract

Backward waves can propagate in a chiral medium with material parameters satisfying certain conditions. A slab of such a chiral medium with both the refractive index and impedance matched to those of the air can be used as a perfect lens. The focusing by a slab of chiral medium with mismatched refractive index and impedance is studied numerically.

© 2005 Optical Society of America

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References

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  1. V.G. Veselago, “The electrodynamics of substances with simultaneously negative values of permittivity and permeability,” Sov. Phys. Usp. 10, 509–514 (1968).
    [Crossref]
  2. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
    [Crossref] [PubMed]
  3. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite Medium with Simultaneously Negative Permeability and Permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
    [Crossref] [PubMed]
  4. J. B. Pendry, “A Chiral Route to Negative Refraction,” Science 306, 1353–1355 (2004).
    [Crossref] [PubMed]
  5. 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).
  6. S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, “A metamaterial with extreme properties: The chiral nihility,” in Progress in Electromagnetics Research Symposium 2003, (Honolulu, Hawaii, USA, 2003), pp. 468.
  7. S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, “Waves and energy in chiral nihility,” J. Electromagn. Waves Appl. 17, 695–706 (2003).
    [Crossref]
  8. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1999).
  9. S. He, “A time-harmonic Green functions technique and wave propagation in a stratified nonreciprocal chiral slab with multiple discontinuities,” J. Math. Phys. 33, 4103–4110 (1992).
    [Crossref]

2004 (1)

J. B. Pendry, “A Chiral Route to Negative Refraction,” Science 306, 1353–1355 (2004).
[Crossref] [PubMed]

2003 (1)

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, “Waves and energy in chiral nihility,” J. Electromagn. Waves Appl. 17, 695–706 (2003).
[Crossref]

2000 (2)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite Medium with Simultaneously Negative Permeability and Permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

1992 (1)

S. He, “A time-harmonic Green functions technique and wave propagation in a stratified nonreciprocal chiral slab with multiple discontinuities,” J. Math. Phys. 33, 4103–4110 (1992).
[Crossref]

1968 (1)

V.G. Veselago, “The electrodynamics of substances with simultaneously negative values of permittivity and permeability,” Sov. Phys. Usp. 10, 509–514 (1968).
[Crossref]

He, S.

S. He, “A time-harmonic Green functions technique and wave propagation in a stratified nonreciprocal chiral slab with multiple discontinuities,” J. Math. Phys. 33, 4103–4110 (1992).
[Crossref]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1999).

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, Boston, 1994).

Maslovski, S.

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, “Waves and energy in chiral nihility,” J. Electromagn. Waves Appl. 17, 695–706 (2003).
[Crossref]

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, “A metamaterial with extreme properties: The chiral nihility,” in Progress in Electromagnetics Research Symposium 2003, (Honolulu, Hawaii, USA, 2003), pp. 468.

Nefedov, I.

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, “Waves and energy in chiral nihility,” J. Electromagn. Waves Appl. 17, 695–706 (2003).
[Crossref]

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, “A metamaterial with extreme properties: The chiral nihility,” in Progress in Electromagnetics Research Symposium 2003, (Honolulu, Hawaii, USA, 2003), pp. 468.

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite Medium with Simultaneously Negative Permeability and Permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite Medium with Simultaneously Negative Permeability and Permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

Pendry, J. B.

J. B. Pendry, “A Chiral Route to Negative Refraction,” Science 306, 1353–1355 (2004).
[Crossref] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref] [PubMed]

Schultz, S.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite Medium with Simultaneously Negative Permeability and Permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

Sihvola, A.

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, “Waves and energy in chiral nihility,” J. Electromagn. Waves Appl. 17, 695–706 (2003).
[Crossref]

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, “A metamaterial with extreme properties: The chiral nihility,” in Progress in Electromagnetics Research Symposium 2003, (Honolulu, Hawaii, USA, 2003), pp. 468.

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, Boston, 1994).

Simovski, C.

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, “Waves and energy in chiral nihility,” J. Electromagn. Waves Appl. 17, 695–706 (2003).
[Crossref]

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, “A metamaterial with extreme properties: The chiral nihility,” in Progress in Electromagnetics Research Symposium 2003, (Honolulu, Hawaii, USA, 2003), pp. 468.

Smith, D. R.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite Medium with Simultaneously Negative Permeability and Permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

Tretyakov, S.

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, “Waves and energy in chiral nihility,” J. Electromagn. Waves Appl. 17, 695–706 (2003).
[Crossref]

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, “A metamaterial with extreme properties: The chiral nihility,” in Progress in Electromagnetics Research Symposium 2003, (Honolulu, Hawaii, USA, 2003), pp. 468.

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, Boston, 1994).

Veselago, V.G.

V.G. Veselago, “The electrodynamics of substances with simultaneously negative values of permittivity and permeability,” Sov. Phys. Usp. 10, 509–514 (1968).
[Crossref]

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite Medium with Simultaneously Negative Permeability and Permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

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, Boston, 1994).

J. Electromagn. Waves Appl. (1)

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, “Waves and energy in chiral nihility,” J. Electromagn. Waves Appl. 17, 695–706 (2003).
[Crossref]

J. Math. Phys. (1)

S. He, “A time-harmonic Green functions technique and wave propagation in a stratified nonreciprocal chiral slab with multiple discontinuities,” J. Math. Phys. 33, 4103–4110 (1992).
[Crossref]

Phys. Rev. Lett. (2)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite Medium with Simultaneously Negative Permeability and Permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

Science (1)

J. B. Pendry, “A Chiral Route to Negative Refraction,” Science 306, 1353–1355 (2004).
[Crossref] [PubMed]

Sov. Phys. Usp. (1)

V.G. Veselago, “The electrodynamics of substances with simultaneously negative values of permittivity and permeability,” Sov. Phys. Usp. 10, 509–514 (1968).
[Crossref]

Other (3)

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1999).

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).

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, “A metamaterial with extreme properties: The chiral nihility,” in Progress in Electromagnetics Research Symposium 2003, (Honolulu, Hawaii, USA, 2003), pp. 468.

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Figures (2)

Fig. 1.
Fig. 1.

Configuration for the focusing of a chiral slab for an object in air. Superscripts “+” and “-” of the electric field spectra indicate the left-and right-going wave streams, respectively.

Fig. 2.
Fig. 2.

The normalized electric field intensity distribution on the right side of a chiral slab. (a) and (c): A case with a small mismatch in the refractive index (the parameters are chosen as ε=ε 0, µ=µ 0, κ=1.975, d 0=0.5λ 0 and d 1=λ 0); (b) and (d): The case with a large mismatch in both the refractive index and the impedance (the parameters are chosen as ε=0.1ε 0, μ = μ 0 , κ = 2 μ ε μ 0 ε 0 , d 0=0.5λ 0 and d 1=0.3λ 0). The left circularly polarized plane wave components in the incident field (generated by a unit current line source) are removed for (a) and (b), but kept for (c) and (d). The electric field intensity distribution in the white box in (c) is renormalized for the reduced area and shown in the inset.

Equations (11)

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D = ε E + i κ μ 0 ε 0 , H , B = μ H i κ μ 0 ε 0 E ,
k × E = ω B , k × H = ω D .
[ k 2 ω 2 ( μ ε κ 2 μ 0 ε 0 ) ] 2 = ( 2 ω κ μ 0 ε 0 k ) 2 = 0 ,
{ E x = ( i k y k ± ) E z , E y = ( i k x k ± ) E z , H x = [ k y ( ω μ ) k y κ μ 0 ε 0 ( μ k ± ) ] E z , H y = [ k x ( ω μ ) + k x κ μ 0 ε 0 ( μ k ± ) ] E z , H z = [ i k 2 ( ω μ k ± ) + i κ μ 0 ε 0 μ ] E z .
E obj ( r ) = d k 0 , y [ E 0 + + ( k 0 , y ) + E 0 + ( k 0 , y ) ] exp [ i ( k 0 , x + k 0 , y y ) ] ,
E img ( r ) = d k 0 , y [ E 2 + + ( k 0 , y ) + E 2 + ( k 0 , y ) ] exp [ i ( k 0 , x x + k 0 , y y ) ] ,
{ E 0 + , y + + E 0 , y + + E 0 + , y + E 0 , y = E 1 + , y + + E 1 , y + + E 1 + , y + E 1 , y , E 0 + , z + + E 0 , z + + E 0 + , z + E 0 , z = E 1 + , z + + E 1 , z + + E 1 + , z + E 1 , z , H 0 + , y + + H 0 , y + + H 0 + , y + H 0 , y = H 1 + , y + + H 1 , y + + H 1 + , y + H 1 , y , H 0 + , z + + H 0 , z + + H 0 + , z + H 0 , z = H 1 + , z + + H 1 , z + + H 1 + , z + H 1 , z , a E 1 + , y + + b E 1 , y + + c E 1 + , y + d E 1 , y = e ( E 2 + , y + + E 2 , y + ) , a E 1 + , z + + b E 1 , z + + c E 1 + , z + d E 1 , z = e ( E 2 + , z + + E 2 , z + ) , a H 1 + , y + + b H 1 , y + + c H 1 + , y + d H 1 , y = e ( H 2 + , y + + H 2 , y + ) , a H 1 + , z + + b H 1 , z + + c H 1 + , z + d H 1 , z = e ( H 2 + , z + + H 2 , z + ) ,
{ ( k 0 , x k 0 ) ( E 0 , z + E 0 , z ) = ( k 1 , x k ) ( E 1 , z + E 1 , z ) , E 0 , z + + E 0 , z = E 1 , z + + E 1 , z , ( k 1 , x k ) [ exp ( i k 1 , x d 1 ) E 1 , z + exp ( i k 1 , x d 1 ) E 1 , z ] = ( k 0 , x k 0 ) exp ( i k 0 , x d 1 ) E 2 , z + , exp ( i k 1 , x d 1 ) E 1 , z + + exp ( i k 1 , x d 1 ) E 1 , z = exp ( i k 0 , x d 1 ) E 2 , z + .
E img ( 2 d 1 d 0 , y ) = dk 0 , y [ ( i k 0 , y k 0 ) e x + ( i k 0 , x k 0 ) e y + e z ] E 0 , z + exp [ i ( k 0 , x d 0 + k 0 , y y ) ]
= E obj ( d 0 , y ) ,
E lin, z ( r ) = ω 0 μ 0 8 π 1 k 0 , x exp { i [ k 0 , x ( x + d 0 ) + k 0 , y y ] } dk 0 , y ,

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