Abstract

The propagation of electromagnetic plane waves in an isotropic chiral medium is characterized, and a special interest is shown in chiral nihility and the effects of chirality on energy transmission. In particular, the wave impedance is matched to that of free space. Moreover, the refractive index n is also matched in impedance to that of free space when an appropriate value of the chirality is chosen. A “chiral nihility” medium is explored in which both the permittivity and the permeability tend to zero. Some specific case studies of chiral nihility are presented, and Brewster angles are found to cover an extremely wide range. The E-field distributions in these different cases where the chiral slab is placed in free space are analyzed by using the appropriate constitutive relations. It is shown from numerical calculations that one can obtain some critical characteristics of the effects of chirality on energy transmission and reflection, such as transparency and power tunneling.

© 2008 Optical Society of America

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    [CrossRef]
  4. C. W. Qiu, H. Y. Yao, S. Zouhdi, L. W. Li, and M. S. Leong, "On the constitutive relations of G-chiral media and the possibility to realize negative-index media," Microwave Opt. Technol. Lett. 48, 2534-2538 (2006).
    [CrossRef]
  5. H. Y. Yao, L. W. Li, C. W. Qiu, Q. Wu, and Z. N. Chen, "Properties of electromagnetic waves in a multilayered cylinder filled with double negative and positive materials," Radio Sci. 42, 2006RS003509 (2006).
  6. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  7. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
    [CrossRef]
  8. R. A. Shelby, D. R. Smith, and S. Schult, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
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2007

C. W. Qiu, H. Y. Yao, L. W. Li, S. Zouhdi, and T. S. Yeo, "Routes to left-handed materials by magnetoelectric couplings," Phys. Rev. B 75, 245214 (2007).
[CrossRef]

C. W. Qiu, H. Y. Yao, L. W. Li, S. Zouhdi, and T. S. Yeo, "Backward waves in magnetoelectrically chiral media: propagation, impedance and negative refraction," Phys. Rev. B 75, 155120 (2007).
[CrossRef]

2006

C. W. Qiu, L. W. Li, H. Y. Yao, and S. Zouhdi, "Properties of Faraday chiral media: green dyadics and negative refraction," Phys. Rev. B 74, 115110 (2006).
[CrossRef]

Q. Cheng and T. J. Cui, "Reflection and refraction properties of plane waves on the interface of uniaxially anisotropic chiral media," J. Opt. Soc. Am. A 23, 3203-3207 (2006).
[CrossRef]

G. Fedorov, S. I. Maslovski, A. V. Dorofeenko, A. P. Vinogradov, I. A. Ryzhikov, and S. A. Tretyakov, "Sub-wavelength imaging: resolution enhancement using metal wire gratings," Phys. Rev. B 73, 035409 (2006).
[CrossRef]

C. W. Qiu, H. Y. Yao, S. Zouhdi, L. W. Li, and M. S. Leong, "On the constitutive relations of G-chiral media and the possibility to realize negative-index media," Microwave Opt. Technol. Lett. 48, 2534-2538 (2006).
[CrossRef]

H. Y. Yao, L. W. Li, C. W. Qiu, Q. Wu, and Z. N. Chen, "Properties of electromagnetic waves in a multilayered cylinder filled with double negative and positive materials," Radio Sci. 42, 2006RS003509 (2006).

2005

N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, "Nanofabricated media with negative permeability at visible frequencies," Nature 438, 335-338 (2005).
[CrossRef] [PubMed]

S. Tretyakov, A. Sihvola, and L. Jylhä, "Backward-wave regime and negative refraction in chiral composites," Photonics Nanostruct. Fundam. Appl. 3, 107-115 (2005).
[CrossRef]

2004

2003

F. A. Pinheiro and B. A. van Tiggelen, "Light transport in chiral and magnetochiral random media," J. Opt. Soc. Am. A 20, 99-105 (2003).
[CrossRef]

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]

2001

R. A. Shelby, D. R. Smith, and S. Schult, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

2000

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

1999

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

1996

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic meso structures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

W. S. Weiglhofer and A. Lakhtakia, "Causality and natural optical activity (chirality)," J. Opt. Soc. Am. A 13, 385-386 (1996).
[CrossRef]

1994

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

S. Zouhdi, "Étude des milieux chiraux aux fréquences micro-ondes. Calcul des paraméters constitutifs. Application aux motifs chiraux plans," Thèse de Doctorat (l'Université Pierre et Marie Curie, 1994).

A. Lakhtakia, Beltrami Fields in Chiral Media, Vol. 2 of World Scientific Series in Contemporary Chemical Physics (World Scientific, 1994).
[CrossRef]

1988

1986

1968

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ϵ and μ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

1941

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

1930

M. Born, Optik (Springer-Verlag, 1930).

Bassiri, S.

Born, M.

M. Born, Optik (Springer-Verlag, 1930).

Chen, Z. N.

H. Y. Yao, L. W. Li, C. W. Qiu, Q. Wu, and Z. N. Chen, "Properties of electromagnetic waves in a multilayered cylinder filled with double negative and positive materials," Radio Sci. 42, 2006RS003509 (2006).

Cheng, Q.

Cui, T. J.

Dorofeenko, A. V.

G. Fedorov, S. I. Maslovski, A. V. Dorofeenko, A. P. Vinogradov, I. A. Ryzhikov, and S. A. Tretyakov, "Sub-wavelength imaging: resolution enhancement using metal wire gratings," Phys. Rev. B 73, 035409 (2006).
[CrossRef]

Engheta, N.

Fedorov, G.

G. Fedorov, S. I. Maslovski, A. V. Dorofeenko, A. P. Vinogradov, I. A. Ryzhikov, and S. A. Tretyakov, "Sub-wavelength imaging: resolution enhancement using metal wire gratings," Phys. Rev. B 73, 035409 (2006).
[CrossRef]

Firsov, A. A.

N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, "Nanofabricated media with negative permeability at visible frequencies," Nature 438, 335-338 (2005).
[CrossRef] [PubMed]

Geim, A. K.

N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, "Nanofabricated media with negative permeability at visible frequencies," Nature 438, 335-338 (2005).
[CrossRef] [PubMed]

Gleeson, H. F.

N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, "Nanofabricated media with negative permeability at visible frequencies," Nature 438, 335-338 (2005).
[CrossRef] [PubMed]

Grigorenko, N.

N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, "Nanofabricated media with negative permeability at visible frequencies," Nature 438, 335-338 (2005).
[CrossRef] [PubMed]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic meso structures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Jaggard, D. L.

Jylhä, L.

S. Tretyakov, A. Sihvola, and L. Jylhä, "Backward-wave regime and negative refraction in chiral composites," Photonics Nanostruct. Fundam. Appl. 3, 107-115 (2005).
[CrossRef]

Khrushchev, I. Y.

N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, "Nanofabricated media with negative permeability at visible frequencies," Nature 438, 335-338 (2005).
[CrossRef] [PubMed]

Lakhtakia, A.

W. S. Weiglhofer and A. Lakhtakia, "Causality and natural optical activity (chirality)," J. Opt. Soc. Am. A 13, 385-386 (1996).
[CrossRef]

A. Lakhtakia, Beltrami Fields in Chiral Media, Vol. 2 of World Scientific Series in Contemporary Chemical Physics (World Scientific, 1994).
[CrossRef]

Leong, M. S.

C. W. Qiu, H. Y. Yao, S. Zouhdi, L. W. Li, and M. S. Leong, "On the constitutive relations of G-chiral media and the possibility to realize negative-index media," Microwave Opt. Technol. Lett. 48, 2534-2538 (2006).
[CrossRef]

Li, L. W.

C. W. Qiu, H. Y. Yao, L. W. Li, S. Zouhdi, and T. S. Yeo, "Routes to left-handed materials by magnetoelectric couplings," Phys. Rev. B 75, 245214 (2007).
[CrossRef]

C. W. Qiu, H. Y. Yao, L. W. Li, S. Zouhdi, and T. S. Yeo, "Backward waves in magnetoelectrically chiral media: propagation, impedance and negative refraction," Phys. Rev. B 75, 155120 (2007).
[CrossRef]

C. W. Qiu, L. W. Li, H. Y. Yao, and S. Zouhdi, "Properties of Faraday chiral media: green dyadics and negative refraction," Phys. Rev. B 74, 115110 (2006).
[CrossRef]

C. W. Qiu, H. Y. Yao, S. Zouhdi, L. W. Li, and M. S. Leong, "On the constitutive relations of G-chiral media and the possibility to realize negative-index media," Microwave Opt. Technol. Lett. 48, 2534-2538 (2006).
[CrossRef]

H. Y. Yao, L. W. Li, C. W. Qiu, Q. Wu, and Z. N. Chen, "Properties of electromagnetic waves in a multilayered cylinder filled with double negative and positive materials," Radio Sci. 42, 2006RS003509 (2006).

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).

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]

Maslovski, S. I.

G. Fedorov, S. I. Maslovski, A. V. Dorofeenko, A. P. Vinogradov, I. A. Ryzhikov, and S. A. Tretyakov, "Sub-wavelength imaging: resolution enhancement using metal wire gratings," Phys. Rev. B 73, 035409 (2006).
[CrossRef]

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]

Papas, C. H.

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]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic meso structures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Petrovic, J.

N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, "Nanofabricated media with negative permeability at visible frequencies," Nature 438, 335-338 (2005).
[CrossRef] [PubMed]

Pinheiro, F. A.

Qiu, C. W.

C. W. Qiu, H. Y. Yao, L. W. Li, S. Zouhdi, and T. S. Yeo, "Backward waves in magnetoelectrically chiral media: propagation, impedance and negative refraction," Phys. Rev. B 75, 155120 (2007).
[CrossRef]

C. W. Qiu, H. Y. Yao, L. W. Li, S. Zouhdi, and T. S. Yeo, "Routes to left-handed materials by magnetoelectric couplings," Phys. Rev. B 75, 245214 (2007).
[CrossRef]

H. Y. Yao, L. W. Li, C. W. Qiu, Q. Wu, and Z. N. Chen, "Properties of electromagnetic waves in a multilayered cylinder filled with double negative and positive materials," Radio Sci. 42, 2006RS003509 (2006).

C. W. Qiu, H. Y. Yao, S. Zouhdi, L. W. Li, and M. S. Leong, "On the constitutive relations of G-chiral media and the possibility to realize negative-index media," Microwave Opt. Technol. Lett. 48, 2534-2538 (2006).
[CrossRef]

C. W. Qiu, L. W. Li, H. Y. Yao, and S. Zouhdi, "Properties of Faraday chiral media: green dyadics and negative refraction," Phys. Rev. B 74, 115110 (2006).
[CrossRef]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Ryzhikov, I. A.

G. Fedorov, S. I. Maslovski, A. V. Dorofeenko, A. P. Vinogradov, I. A. Ryzhikov, and S. A. Tretyakov, "Sub-wavelength imaging: resolution enhancement using metal wire gratings," Phys. Rev. B 73, 035409 (2006).
[CrossRef]

Schult, S.

R. A. Shelby, D. R. Smith, and S. Schult, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schult, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Sihvola, A.

S. Tretyakov, A. Sihvola, and L. Jylhä, "Backward-wave regime and negative refraction in chiral composites," Photonics Nanostruct. Fundam. Appl. 3, 107-115 (2005).
[CrossRef]

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

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).

Silverman, M. P.

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]

Smith, D. R.

R. A. Shelby, D. R. Smith, and S. Schult, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Sohn, R. B.

M. P. Silverman and R. B. Sohn, "Effects of circular birefringence on light propagation and reflection," Am. J. Phys. 54, 69-76 (1986).
[CrossRef]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic meso structures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

Tretyakov, S.

S. Tretyakov, A. Sihvola, and L. Jylhä, "Backward-wave regime and negative refraction in chiral composites," Photonics Nanostruct. Fundam. Appl. 3, 107-115 (2005).
[CrossRef]

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

Tretyakov, S. A.

G. Fedorov, S. I. Maslovski, A. V. Dorofeenko, A. P. Vinogradov, I. A. Ryzhikov, and S. A. Tretyakov, "Sub-wavelength imaging: resolution enhancement using metal wire gratings," Phys. Rev. B 73, 035409 (2006).
[CrossRef]

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

van Tiggelen, B. A.

Veselago, V. G.

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ϵ and μ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

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).

Vinogradov, A. P.

G. Fedorov, S. I. Maslovski, A. V. Dorofeenko, A. P. Vinogradov, I. A. Ryzhikov, and S. A. Tretyakov, "Sub-wavelength imaging: resolution enhancement using metal wire gratings," Phys. Rev. B 73, 035409 (2006).
[CrossRef]

Weiglhofer, W. S.

Wu, Q.

H. Y. Yao, L. W. Li, C. W. Qiu, Q. Wu, and Z. N. Chen, "Properties of electromagnetic waves in a multilayered cylinder filled with double negative and positive materials," Radio Sci. 42, 2006RS003509 (2006).

Wu, T. X.

Yang, X.

Yao, H. Y.

C. W. Qiu, H. Y. Yao, L. W. Li, S. Zouhdi, and T. S. Yeo, "Backward waves in magnetoelectrically chiral media: propagation, impedance and negative refraction," Phys. Rev. B 75, 155120 (2007).
[CrossRef]

C. W. Qiu, H. Y. Yao, L. W. Li, S. Zouhdi, and T. S. Yeo, "Routes to left-handed materials by magnetoelectric couplings," Phys. Rev. B 75, 245214 (2007).
[CrossRef]

H. Y. Yao, L. W. Li, C. W. Qiu, Q. Wu, and Z. N. Chen, "Properties of electromagnetic waves in a multilayered cylinder filled with double negative and positive materials," Radio Sci. 42, 2006RS003509 (2006).

C. W. Qiu, H. Y. Yao, S. Zouhdi, L. W. Li, and M. S. Leong, "On the constitutive relations of G-chiral media and the possibility to realize negative-index media," Microwave Opt. Technol. Lett. 48, 2534-2538 (2006).
[CrossRef]

C. W. Qiu, L. W. Li, H. Y. Yao, and S. Zouhdi, "Properties of Faraday chiral media: green dyadics and negative refraction," Phys. Rev. B 74, 115110 (2006).
[CrossRef]

Yeo, T. S.

C. W. Qiu, H. Y. Yao, L. W. Li, S. Zouhdi, and T. S. Yeo, "Routes to left-handed materials by magnetoelectric couplings," Phys. Rev. B 75, 245214 (2007).
[CrossRef]

C. W. Qiu, H. Y. Yao, L. W. Li, S. Zouhdi, and T. S. Yeo, "Backward waves in magnetoelectrically chiral media: propagation, impedance and negative refraction," Phys. Rev. B 75, 155120 (2007).
[CrossRef]

Youngs, I.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic meso structures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Zhang, Y.

N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, "Nanofabricated media with negative permeability at visible frequencies," Nature 438, 335-338 (2005).
[CrossRef] [PubMed]

Zouhdi, S.

C. W. Qiu, H. Y. Yao, L. W. Li, S. Zouhdi, and T. S. Yeo, "Routes to left-handed materials by magnetoelectric couplings," Phys. Rev. B 75, 245214 (2007).
[CrossRef]

C. W. Qiu, H. Y. Yao, L. W. Li, S. Zouhdi, and T. S. Yeo, "Backward waves in magnetoelectrically chiral media: propagation, impedance and negative refraction," Phys. Rev. B 75, 155120 (2007).
[CrossRef]

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Figures (12)

Fig. 1
Fig. 1

Orientation of the wave vectors at an oblique incidence on a dielectric–chiral interface. The subscripts ∥ and ⊥, respectively, stand for parallel and perpendicular with respect to the plane of incidence.

Fig. 2
Fig. 2

Reflected power as a function of the incidence with unit permeability, the same chirality, but different permittivity. μ 1 = μ = 1 , κ = 0.25 . (a) ϵ 1 = 1 , ϵ = 4 ; (b) ϵ 1 = 4 , ϵ = 1 .

Fig. 3
Fig. 3

Reflected power as a function of the incidence with different cases of chiral nihility. κ = 0.5 . (a) ϵ 1 = μ 1 = 1 , ϵ = 4 × 10 5 , μ = 1 × 10 5 ; (b) ϵ 1 = μ 1 , ϵ = μ = 1 × 10 5 .

Fig. 4
Fig. 4

Reflected power as a function of the incidence with the same permittivity and permeability as in Fig. 3 but with a higher chirality. ϵ 1 = μ 1 = 1 , ϵ = 4 × 10 5 , μ = 1 × 10 5 , κ = 1 .

Fig. 5
Fig. 5

Reflected power as a function of the chirality for an oblique incidence at an angle of θ i n c = 45 ° . (a) ϵ 1 = μ 1 = 1 , ϵ = 4 , μ = 1 ; (b) ϵ 1 = 4 , μ 1 = 1 , ϵ = μ = 1 .

Fig. 6
Fig. 6

Reflected power as a function of the chirality for an oblique incidence at an angle of θ i n c = 45 ° in different cases of chiral nihility. ϵ 1 = μ 1 = 1 . (a) μ 1 = 1 × 10 5 ; (b) ϵ = μ = 1 × 10 5 .

Fig. 7
Fig. 7

(a) Chiral slab of thickness d placed in free space. The two interfaces with the chiral slab are situated at z = 0 and z = d . Regions 1 and 3 are considered to be vacuum, and region 2 is the chiral medium. (b) Illustration of negative refraction and subwavelength focusing by a chiral slab ( k 1 > 0 and k 2 < 0 ).

Fig. 8
Fig. 8

Indices of refraction and wave vectors in the chiral nihility slab versus the chirality.

Fig. 9
Fig. 9

Total transmitted power in vacuum on the right-hand side of the chiral nihility slab (region 3) for different values of ϵ r and μ r versus the angle of incidence θ i . (a) κ = 0 , (b) κ = 0.25 , (c) κ = 0.8 , (d) κ = 1 .

Fig. 10
Fig. 10

Electric field and transmitted power as a function of the z coordinate when a normally incident wave illuminates a slab of medium with ϵ r = μ r = 1 × 10 5 and κ = 0 .

Fig. 11
Fig. 11

Electric field and transmitted power as a function of the z coordinate when a normally incident wave illuminates a slab of medium with ϵ r = μ r = 1 × 10 5 and κ = 0.25 . (a) Magnitude of real parts and transmitted power. (b) Magnitude of imaginary parts.

Fig. 12
Fig. 12

Electric field as a function of the z coordinate when a normally incident wave illuminates a slab of medium with ϵ r = μ r = 1 × 10 5 and κ = 1 . (a) Magnitude of real parts and transmitted power. (b) Magnitude of imaginary parts.

Equations (16)

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D = ϵ r ϵ 0 E i κ ϵ 0 μ 0 H ,
B = μ r μ 0 H + i κ ϵ 0 μ 0 E .
× E = i ω B ,
× H = i ω D .
k 1 , 2 = k 0 ( μ r ϵ r ± κ ) ,
E 1 = E 01 ( e ̂ x + i e ̂ y ) exp ( i k 1 z ) ,
E 2 = E 02 ( e ̂ x i e ̂ y ) exp ( i k 2 z ) ,
n 1 , 2 = μ r ϵ r ± κ .
z ̂ × [ E i n c + E r ] = z ̂ × [ E 1 + E 2 ] ,
z ̂ × [ H i n c + H r ] = z ̂ × [ H 1 + H 2 ] .
θ 1 , 2 = sin 1 ( k i n c sin θ i n c k 1 , 2 ) ,
D = 1 1 ϵ B μ B γ 2 k 0 2 ( ϵ B E + i ϵ B μ B γ k 0 H ) ,
B = 1 1 ϵ B μ B γ 2 k 0 2 ( μ B H i ϵ B μ B γ k 0 E ) ,
ϵ = ϵ B 1 ϵ B μ B γ 2 k 0 2 ,
μ = μ B 1 ϵ B μ B γ 2 k 0 2 ,
κ = ϵ B μ B γ ω ( 1 ϵ B μ B γ 2 k 0 2 ) .

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