Abstract

We study the no reflection condition for a planar boundary between vacuum and an isotropic chiral medium. In general chiral media, elliptically polarized waves incident at a particular angle satisfy the no reflection condition. When the wave impedance and wavenumber of the chiral medium are equal to the corresponding parameters of vacuum, one of the circularly polarized waves is transmitted to the medium without reflection or refraction for all angles of incidence. We propose a circular polarizing beam splitter as a simple application of the no reflection effect.

© 2008 Optical Society of America

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    [CrossRef] [PubMed]

2008

2007

J. Kastel, M. Fleischhauer, S. F. Yelin, and R. L. Walsworth, "Tunable Negative Refraction without Absorption via Electromagnetically Induced Chirality," Phys. Rev. Lett. 99, 073602 (2007).
[CrossRef] [PubMed]

W. Shu, Z. Ren, H. Luo, and F. Li, "Brewster angle for anisotropic materials from the extinction theorem," Appl. Phys. A 87, 297-303 (2007).
[CrossRef]

2006

T. Tanaka, A. Ishikawa, and S. Kawata, "Unattenuated light transmission through the interface between two materials with different indices of refraction using magnetic metamaterials," Phys. Rev. B 73, 125423 (2006).
[CrossRef]

X.-L. Xu, B.-G. Quan, C.-Z. Gu, and L. Wang, "Bianisotropic response of microfabricated metamaterials in the terahertz region," J. Opt. Soc. Am. B 23, 1174-1180 (2006).
[CrossRef]

Y. Tamayama, T. Nakanishi, K. Sugiyama, and M. Kitano, "Observation of Brewster’s effect for transverseelectric electromagnetic waves in metamaterials: Experiment and theory," Phys. Rev. B 73, 193104 (2006).
[CrossRef]

2005

C. Fu, Z. M. Zhang, and P. N. First, "Brewster angle with a negative-index material," Appl. Opt. 44, 3716-3724 (2005).
[CrossRef] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, "Magnetic Metamaterials at Telecommunication and Visible Frequencies," Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

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]

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]

V. A. Sautenkov, Y. V. Rostovtsev, H. Chen, P. Hsu, G. S. Agarwal, and M. O. Scully, "Electromagnetically Induced Magnetochiral Anisotropy in a Resonant Medium" Phys. Rev. Lett. 94, 233601 (2005).
[CrossRef] [PubMed]

T. M. Grzegorczyk, Z. M. Thomas, and J. A. Kong, "Inversion of critical angle and Brewster angle in anisotropic left-handed metamaterials," Appl. Phys. Lett. 86, 251909 (2005).
[CrossRef]

2003

R. M. A. Azzam and A. De, "Circular polarization beam splitter that uses frustrated total internal reflection by an embedded symmetric achiral multilayer coating," Opt. Lett. 28, 355-357 (2003).
[CrossRef] [PubMed]

R. Marques, F. Mesa, J. Martel, and F. Medina, "Comparative Analysis of Edge- and Broadside-Coupled Split Ring Resonators for Metamaterial Design—Theory and Experiments," IEEE Trans. Antennas Propag. 51, 2572-2581 (2003).
[CrossRef]

T. A. Leskova, A. A. Maradudin, and I. Simonsen, "Coherent Scattering of an Electromagnetic Wave From, and its Transmission Through, a Slab of a Left-Handed Medium with a Randomly Rough Illuminated Surface," Proc. SPIE 5189, 22-35 (2003).
[CrossRef]

2001

1999

A. Lakhtakia, "Cross-refractive chiral media and constitutive contrasts," Microwave Opt. Technol. Lett. 20, 337-339 (1999).
[CrossRef]

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]

1998

S. F. Mahmoud and S. Tariq, "Gaussian beam splitting by a chiral prism," J. Electromagnet. Wave. 12, 73-83 (1998).
[CrossRef]

1996

S. A. Tretyakov, F. Mariotte, C. R. Simovski, T. G. Kharina, and J.-P. Heliot, "Analytical Antenna Model for Chiral Scatterers: Comparison with Numerical and Experimental Data," IEEE Trans. Antennas Propag. 44, 1006-1014 (1996).
[CrossRef]

1995

J. Futterman, "Magnetic Brewster angle," Am. J. Phys. 63, 471 (1995).
[CrossRef]

1992

A. Lakhtakia, "General schema for the Brewster conditions," Optik (Stuttgart) 90, 184-186 (1992).

1989

A. Lakhtakia, "Would Brewster recognize today’s Brewster angle?" Opt. News 15, 14-18 (1989).
[CrossRef]

1988

1986

1983

1980

W. T. Doyle, "Graphical approach to Fresnel’s equations for reflection and refraction of light," Am. J. Phys. 48, 643-647 (1980).
[CrossRef]

Adachi, J.

Agarwal, G. S.

V. A. Sautenkov, Y. V. Rostovtsev, H. Chen, P. Hsu, G. S. Agarwal, and M. O. Scully, "Electromagnetically Induced Magnetochiral Anisotropy in a Resonant Medium" Phys. Rev. Lett. 94, 233601 (2005).
[CrossRef] [PubMed]

Azzam, R. M. A.

Bassiri, S.

Burger, S.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, "Magnetic Metamaterials at Telecommunication and Visible Frequencies," Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Burokur, N.

Cerqua, K. A.

Chen, H.

V. A. Sautenkov, Y. V. Rostovtsev, H. Chen, P. Hsu, G. S. Agarwal, and M. O. Scully, "Electromagnetically Induced Magnetochiral Anisotropy in a Resonant Medium" Phys. Rev. Lett. 94, 233601 (2005).
[CrossRef] [PubMed]

Davis, J. A.

De, A.

Doyle, W. T.

W. T. Doyle, "Graphical approach to Fresnel’s equations for reflection and refraction of light," Am. J. Phys. 48, 643-647 (1980).
[CrossRef]

Engheta, N.

Enkrich, C.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, "Magnetic Metamaterials at Telecommunication and Visible Frequencies," Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Fernandez-Pousa, C. R.

Firsov, A. 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]

First, P. N.

Fleischhauer, M.

J. Kastel, M. Fleischhauer, S. F. Yelin, and R. L. Walsworth, "Tunable Negative Refraction without Absorption via Electromagnetically Induced Chirality," Phys. Rev. Lett. 99, 073602 (2007).
[CrossRef] [PubMed]

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]

Fu, C.

Futterman, J.

J. Futterman, "Magnetic Brewster angle," Am. J. Phys. 63, 471 (1995).
[CrossRef]

Geim, A. K.

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]

Gleeson, H. F.

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]

Grigorenko, A. N.

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]

Grzegorczyk, T. M.

T. M. Grzegorczyk, Z. M. Thomas, and J. A. Kong, "Inversion of critical angle and Brewster angle in anisotropic left-handed metamaterials," Appl. Phys. Lett. 86, 251909 (2005).
[CrossRef]

Gu, C.-Z.

Guardalben, M. J.

Heliot, J.-P.

S. A. Tretyakov, F. Mariotte, C. R. Simovski, T. G. Kharina, and J.-P. Heliot, "Analytical Antenna Model for Chiral Scatterers: Comparison with Numerical and Experimental Data," IEEE Trans. Antennas Propag. 44, 1006-1014 (1996).
[CrossRef]

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]

Hsu, P.

V. A. Sautenkov, Y. V. Rostovtsev, H. Chen, P. Hsu, G. S. Agarwal, and M. O. Scully, "Electromagnetically Induced Magnetochiral Anisotropy in a Resonant Medium" Phys. Rev. Lett. 94, 233601 (2005).
[CrossRef] [PubMed]

Ishikawa, A.

T. Tanaka, A. Ishikawa, and S. Kawata, "Unattenuated light transmission through the interface between two materials with different indices of refraction using magnetic metamaterials," Phys. Rev. B 73, 125423 (2006).
[CrossRef]

Jacobs, S. D.

Kastel, J.

J. Kastel, M. Fleischhauer, S. F. Yelin, and R. L. Walsworth, "Tunable Negative Refraction without Absorption via Electromagnetically Induced Chirality," Phys. Rev. Lett. 99, 073602 (2007).
[CrossRef] [PubMed]

Kawata, S.

T. Tanaka, A. Ishikawa, and S. Kawata, "Unattenuated light transmission through the interface between two materials with different indices of refraction using magnetic metamaterials," Phys. Rev. B 73, 125423 (2006).
[CrossRef]

Kharina, T. G.

S. A. Tretyakov, F. Mariotte, C. R. Simovski, T. G. Kharina, and J.-P. Heliot, "Analytical Antenna Model for Chiral Scatterers: Comparison with Numerical and Experimental Data," IEEE Trans. Antennas Propag. 44, 1006-1014 (1996).
[CrossRef]

Khrushchev, I. Y.

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]

Kim, S. Y.

Kitano, M.

Y. Tamayama, T. Nakanishi, K. Sugiyama, and M. Kitano, "Observation of Brewster’s effect for transverseelectric electromagnetic waves in metamaterials: Experiment and theory," Phys. Rev. B 73, 193104 (2006).
[CrossRef]

Kong, J. A.

T. M. Grzegorczyk, Z. M. Thomas, and J. A. Kong, "Inversion of critical angle and Brewster angle in anisotropic left-handed metamaterials," Appl. Phys. Lett. 86, 251909 (2005).
[CrossRef]

Koschny, Th.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, "Magnetic Metamaterials at Telecommunication and Visible Frequencies," Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Lakhtakia, A.

A. Lakhtakia, "Cross-refractive chiral media and constitutive contrasts," Microwave Opt. Technol. Lett. 20, 337-339 (1999).
[CrossRef]

A. Lakhtakia, "General schema for the Brewster conditions," Optik (Stuttgart) 90, 184-186 (1992).

A. Lakhtakia, "Would Brewster recognize today’s Brewster angle?" Opt. News 15, 14-18 (1989).
[CrossRef]

Leskova, T. A.

T. A. Leskova, A. A. Maradudin, and I. Simonsen, "Coherent Scattering of an Electromagnetic Wave From, and its Transmission Through, a Slab of a Left-Handed Medium with a Randomly Rough Illuminated Surface," Proc. SPIE 5189, 22-35 (2003).
[CrossRef]

Li, F.

W. Shu, Z. Ren, H. Luo, and F. Li, "Brewster angle for anisotropic materials from the extinction theorem," Appl. Phys. A 87, 297-303 (2007).
[CrossRef]

Li, L.-W.

Linden, S.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, "Magnetic Metamaterials at Telecommunication and Visible Frequencies," Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Luo, H.

W. Shu, Z. Ren, H. Luo, and F. Li, "Brewster angle for anisotropic materials from the extinction theorem," Appl. Phys. A 87, 297-303 (2007).
[CrossRef]

Mahmoud, S. F.

S. F. Mahmoud and S. Tariq, "Gaussian beam splitting by a chiral prism," J. Electromagnet. Wave. 12, 73-83 (1998).
[CrossRef]

Maradudin, A. A.

T. A. Leskova, A. A. Maradudin, and I. Simonsen, "Coherent Scattering of an Electromagnetic Wave From, and its Transmission Through, a Slab of a Left-Handed Medium with a Randomly Rough Illuminated Surface," Proc. SPIE 5189, 22-35 (2003).
[CrossRef]

Mariotte, F.

S. A. Tretyakov, F. Mariotte, C. R. Simovski, T. G. Kharina, and J.-P. Heliot, "Analytical Antenna Model for Chiral Scatterers: Comparison with Numerical and Experimental Data," IEEE Trans. Antennas Propag. 44, 1006-1014 (1996).
[CrossRef]

Marques, R.

R. Marques, F. Mesa, J. Martel, and F. Medina, "Comparative Analysis of Edge- and Broadside-Coupled Split Ring Resonators for Metamaterial Design—Theory and Experiments," IEEE Trans. Antennas Propag. 51, 2572-2581 (2003).
[CrossRef]

Marshall, K. L.

Martel, J.

R. Marques, F. Mesa, J. Martel, and F. Medina, "Comparative Analysis of Edge- and Broadside-Coupled Split Ring Resonators for Metamaterial Design—Theory and Experiments," IEEE Trans. Antennas Propag. 51, 2572-2581 (2003).
[CrossRef]

Medina, F.

R. Marques, F. Mesa, J. Martel, and F. Medina, "Comparative Analysis of Edge- and Broadside-Coupled Split Ring Resonators for Metamaterial Design—Theory and Experiments," IEEE Trans. Antennas Propag. 51, 2572-2581 (2003).
[CrossRef]

Mesa, F.

R. Marques, F. Mesa, J. Martel, and F. Medina, "Comparative Analysis of Edge- and Broadside-Coupled Split Ring Resonators for Metamaterial Design—Theory and Experiments," IEEE Trans. Antennas Propag. 51, 2572-2581 (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]

Moreno, I.

Nakanishi, T.

Y. Tamayama, T. Nakanishi, K. Sugiyama, and M. Kitano, "Observation of Brewster’s effect for transverseelectric electromagnetic waves in metamaterials: Experiment and theory," Phys. Rev. B 73, 193104 (2006).
[CrossRef]

Papas, C. H.

Pendry, J. B.

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]

Petrovic, J.

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]

Qiu, C.-W.

Quan, B.-G.

Ren, Z.

W. Shu, Z. Ren, H. Luo, and F. Li, "Brewster angle for anisotropic materials from the extinction theorem," Appl. Phys. A 87, 297-303 (2007).
[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]

Rostovtsev, Y. V.

V. A. Sautenkov, Y. V. Rostovtsev, H. Chen, P. Hsu, G. S. Agarwal, and M. O. Scully, "Electromagnetically Induced Magnetochiral Anisotropy in a Resonant Medium" Phys. Rev. Lett. 94, 233601 (2005).
[CrossRef] [PubMed]

Sautenkov, V. A.

V. A. Sautenkov, Y. V. Rostovtsev, H. Chen, P. Hsu, G. S. Agarwal, and M. O. Scully, "Electromagnetically Induced Magnetochiral Anisotropy in a Resonant Medium" Phys. Rev. Lett. 94, 233601 (2005).
[CrossRef] [PubMed]

Schmid, A.

Schmidt, F.

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[CrossRef]

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[CrossRef]

Phys. Rev. Lett.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, "Magnetic Metamaterials at Telecommunication and Visible Frequencies," Phys. Rev. Lett. 95, 203901 (2005).
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[CrossRef] [PubMed]

J. Kastel, M. Fleischhauer, S. F. Yelin, and R. L. Walsworth, "Tunable Negative Refraction without Absorption via Electromagnetically Induced Chirality," Phys. Rev. Lett. 99, 073602 (2007).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1.
Fig. 1.

Geometry of coordinate system. The incident, reflected, and transmitted waves are denoted by the subscripts i, r, and t, respectively. Region x<0 represents vacuum, and region x≥0 represents the chiral medium.

Fig. 2.
Fig. 2.

(a) Relation between µ r and ε r and (b) between µ r and ξr for no reflection conditions (invisible conditions). In the (µ rr) graph, the red and green lines represent the conditions for LCP and RCP waves, respectively.

Fig. 3.
Fig. 3.

Fig. 3. Results of two-dimensional FDTD analysis of the CPBS. Propagation of (a) LCP waves and (b) RCP waves. Straight and curved arrows represent the propagation direction and polarization direction, respectively. λ is the wavelength of the EM waves.

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

D = ε E i ξ B , H = μ 1 B i ξ E ,
E r = 1 Δ M R E i , M R = c u I + c 2 σ 2 + c 2 σ 3 ,
c u = 2 Z 0 Z c ( cos 2 θ cos θ + cos θ ) ,
c 2 = 2 Z 0 Z c cos θ ( cos θ + - cos θ ) ,
c 3 = ( Z c 2 Z 0 2 ) cos θ ( cos θ + + cos θ ) ,
Δ = ( Z c 2 + Z 0 2 ) cos θ ( cos θ + + cos θ ) + 2 Z 0 Z c ( cos 2 θ + cos θ + cos θ ) ,
σ 2 = [ 0 i i 0 ] , σ 3 = [ 1 0 0 1 ] .
M R = c u I + c φ σ φ ,
ε r = 2 1 μ r , ξ r = ( 1 1 μ r ) ,
E z y = i ω ( μ ± μ ξ Z c ) H x ,
E z x = i ω ( μ ± μ ξ Z c ) H y ,
H y x H x y = i ω [ ( ε + μ ξ 2 ) ± μ ξ Z c ] E z ,

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