Abstract

We investigate the basic features of wave propagation in pseudochiral media characterized by symmetric magneto-electric tensors with zero diagonal elements. The wave propagation is described by two dispersion relations with elliptically polarized eigenwaves. For a linearly polarized wave incident from vacuum onto a pseudochiral medium, the transmitted waves are elliptically polarized, whereas the reflected wave remains to be linearly polarized. A generalized form of Fresnel equations for reflection and transmission coefficients is derived for pseudochiral media, which includes the chirality as an additional parameter. Brewster’s angles that correspond to zero reflection from the interface are also studied.

© 2013 Optical Society of America

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References

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  1. J. A. Kong, “Theorems of bianisotropic media,” Proc. IEEE 60, 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, “Magneto–electric 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 Ω medium,” Microwave Opt. Technol. Lett. 5, 184–188 (1992).
    [CrossRef]
  5. C. R. Simovski, S. A. Tretyakov, A. A. Sochava, B. Sauviac, F. Mariotte, and T. G. Kharina, “Antenna model for conductive omega particles,” J. Electromagn. Waves Appl. 11, 1509–1530 (1997).
    [CrossRef]
  6. S. A. Matos, C. R. Paiva, and A. M. Barbosa, “Surface and proper leaky-modes in a lossless grounded pseudochiral omega slab,” Microwave Opt. Technol. Lett. 50, 814–818 (2008).
    [CrossRef]
  7. C. R. Simovski and S. He, “Frequency range and explicit expressions for negative permittivity and permeability for an isotropic medium formed by a lattice of perfectly conducting particles,” Phys. Lett. A 311, 254–263 (2003).
    [CrossRef]
  8. S. A. Tretyakov, C. R. Simovski, and M. Hudlicka, “Bianisotropic route to the realization and matching of backward-wave metamaterial slabs,” Phys. Rev. B 75, 153104 (2007).
    [CrossRef]
  9. W. S. Weiglhofer and A. Lakhtakia, Introduction to Complex Mediums for Optics and Electromagnetics (SPIE, 2003).
  10. P. A. Belov, “Backward waves and negative refraction in uniaxial dielectrics with negative dielectric permittivity along the anisotropy axis,” Microwave Opt. Technol. Lett. 37, 259–263 (2003).
    [CrossRef]
  11. L. Yonghua, W. Pei, Y. Peijun, X. Jianping, and M. Hai, “Negative refraction at the interface of uniaxial anisotropic media,” Opt. Commun. 246, 429–435 (2005).
    [CrossRef]
  12. 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]
  13. J. B. Pendry, “A chiral route to negative refraction,” Science 306, 1353–1355 (2004).
    [CrossRef]
  14. 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]
  15. S. Tretyakov, A. Sihvola, and L. Jylha, “Backward-wave regime and negative refraction in chiral composites,” Photon. Nanostr. Fundam. Applic. 3, 107–115 (2005).
    [CrossRef]
  16. Q. Cheng and T. J. Cui, “Negative refractions in uniaxially anisotropic chiral media,” Phys. Rev. B 73, 113104 (2006).
    [CrossRef]

2009 (1)

2008 (1)

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

2007 (1)

S. A. Tretyakov, C. R. Simovski, and M. Hudlicka, “Bianisotropic route to the realization and matching of backward-wave metamaterial slabs,” Phys. Rev. B 75, 153104 (2007).
[CrossRef]

2006 (1)

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

2005 (3)

L. Yonghua, W. Pei, Y. Peijun, X. Jianping, and M. Hai, “Negative refraction at the interface of uniaxial anisotropic media,” Opt. Commun. 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]

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

2004 (1)

J. B. Pendry, “A chiral route to negative refraction,” Science 306, 1353–1355 (2004).
[CrossRef]

2003 (2)

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

C. R. Simovski and S. He, “Frequency range and explicit expressions for negative permittivity and permeability for an isotropic medium formed by a lattice of perfectly conducting particles,” Phys. Lett. A 311, 254–263 (2003).
[CrossRef]

1998 (1)

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

1997 (1)

C. R. Simovski, S. A. Tretyakov, A. A. Sochava, B. Sauviac, F. Mariotte, and T. G. Kharina, “Antenna model for conductive omega particles,” J. Electromagn. Waves Appl. 11, 1509–1530 (1997).
[CrossRef]

1992 (1)

M. M. I. Saadoun and N. Engheta, “A reciprocal phase shifter using novel pseudochiral or Ω medium,” Microwave Opt. Technol. Lett. 5, 184–188 (1992).
[CrossRef]

1972 (1)

J. A. Kong, “Theorems of bianisotropic media,” Proc. IEEE 60, 1036–1046 (1972).
[CrossRef]

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,” Microwave 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,” Microwave 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. 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]

Engheta, N.

M. M. I. Saadoun and N. Engheta, “A reciprocal phase shifter using novel pseudochiral or Ω medium,” Microwave Opt. Technol. Lett. 5, 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]

Hai, M.

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

He, S.

C. R. Simovski and S. He, “Frequency range and explicit expressions for negative permittivity and permeability for an isotropic medium formed by a lattice of perfectly conducting particles,” Phys. Lett. A 311, 254–263 (2003).
[CrossRef]

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. B 75, 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. Commun. 246, 429–435 (2005).
[CrossRef]

Jylha, L.

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

Kharina, T. G.

C. R. Simovski, S. A. Tretyakov, A. A. Sochava, B. Sauviac, F. Mariotte, and T. G. Kharina, “Antenna model for conductive omega particles,” J. Electromagn. Waves Appl. 11, 1509–1530 (1997).
[CrossRef]

Kong, J. A.

J. A. Kong, “Theorems of bianisotropic media,” Proc. IEEE 60, 1036–1046 (1972).
[CrossRef]

Lakhtakia, A.

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

Li, J.

Mariotte, F.

C. R. Simovski, S. A. Tretyakov, A. A. Sochava, B. Sauviac, F. Mariotte, and T. G. Kharina, “Antenna model for conductive omega particles,” J. Electromagn. Waves Appl. 11, 1509–1530 (1997).
[CrossRef]

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,” Microwave 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]

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,” Microwave 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. Commun. 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. Commun. 246, 429–435 (2005).
[CrossRef]

Pendry, J. B.

J. B. Pendry, “A chiral route to negative refraction,” Science 306, 1353–1355 (2004).
[CrossRef]

Saadoun, M. M. I.

M. M. I. Saadoun and N. Engheta, “A reciprocal phase shifter using novel pseudochiral or Ω medium,” Microwave Opt. Technol. Lett. 5, 184–188 (1992).
[CrossRef]

Sauviac, B.

C. R. Simovski, S. A. Tretyakov, A. A. Sochava, B. Sauviac, F. Mariotte, and T. G. Kharina, “Antenna model for conductive omega particles,” J. Electromagn. Waves Appl. 11, 1509–1530 (1997).
[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,” Photon. Nanostr. Fundam. Applic. 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, “Magneto–electric 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. B 75, 153104 (2007).
[CrossRef]

C. R. Simovski and S. He, “Frequency range and explicit expressions for negative permittivity and permeability for an isotropic medium formed by a lattice of perfectly conducting particles,” Phys. Lett. A 311, 254–263 (2003).
[CrossRef]

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

C. R. Simovski, S. A. Tretyakov, A. A. Sochava, B. Sauviac, F. Mariotte, and T. G. Kharina, “Antenna model for conductive omega particles,” J. Electromagn. Waves Appl. 11, 1509–1530 (1997).
[CrossRef]

Sochava, A. A.

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

C. R. Simovski, S. A. Tretyakov, A. A. Sochava, B. Sauviac, F. Mariotte, and T. G. Kharina, “Antenna model for conductive omega particles,” J. Electromagn. Waves Appl. 11, 1509–1530 (1997).
[CrossRef]

Tretyakov, S.

S. Tretyakov, A. Sihvola, and L. Jylha, “Backward-wave regime and negative refraction in chiral composites,” Photon. Nanostr. Fundam. Applic. 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. B 75, 153104 (2007).
[CrossRef]

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

C. R. Simovski, S. A. Tretyakov, A. A. Sochava, B. Sauviac, F. Mariotte, and T. G. Kharina, “Antenna model for conductive omega particles,” J. Electromagn. Waves Appl. 11, 1509–1530 (1997).
[CrossRef]

Weiglhofer, W. S.

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

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. Commun. 246, 429–435 (2005).
[CrossRef]

J. Electromagn. Waves Appl. (2)

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

C. R. Simovski, S. A. Tretyakov, A. A. Sochava, B. Sauviac, F. Mariotte, and T. G. Kharina, “Antenna model for conductive omega particles,” J. Electromagn. Waves Appl. 11, 1509–1530 (1997).
[CrossRef]

Microwave Opt. Technol. Lett. (3)

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

M. M. I. Saadoun and N. Engheta, “A reciprocal phase shifter using novel pseudochiral or Ω medium,” Microwave Opt. Technol. Lett. 5, 184–188 (1992).
[CrossRef]

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

Opt. Commun. (1)

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

Opt. Lett. (1)

Photon. Nanostr. Fundam. Applic. (1)

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

Phys. Lett. A (1)

C. R. Simovski and S. He, “Frequency range and explicit expressions for negative permittivity and permeability for an isotropic medium formed by a lattice of perfectly conducting particles,” Phys. Lett. A 311, 254–263 (2003).
[CrossRef]

Phys. Rev. B (2)

S. A. Tretyakov, C. R. Simovski, and M. Hudlicka, “Bianisotropic route to the realization and matching of backward-wave metamaterial slabs,” Phys. Rev. B 75, 153104 (2007).
[CrossRef]

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

Phys. Rev. Lett. (1)

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]

Proc. IEEE (1)

J. A. Kong, “Theorems of bianisotropic media,” Proc. IEEE 60, 1036–1046 (1972).
[CrossRef]

Science (1)

J. B. Pendry, “A chiral route to negative refraction,” Science 306, 1353–1355 (2004).
[CrossRef]

Other (2)

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

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

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Figures (7)

Fig. 1.
Fig. 1.

Equifrequency contours for the pseudochiral medium with εr=1, μr=1, and (a) γ˜=0.3, (b) γ˜=0.9. Black and gray lines are dispersion relations [Eq. (9)] with the plus and minus signs, respectively. Point A corresponds to the lower bound of kx for backward wave, and point B the upper bound of kx for negative refraction.

Fig. 2.
Fig. 2.

Angles of (a) wave vectors (θ±) and (b) Poynting vectors (ϕ±) with respect to the interface normal as functions of θ for a plane wave incident from vacuum onto a pseudochiral medium with εr=1, μr=1, and γ˜=0.5.

Fig. 3.
Fig. 3.

Schematic diagram of the wave vectors and Poynting vectors for a planar interface between vacuum (z<0) and a pseudochiral medium (z>0) with ε, μ, and γ, where (a) kx<γ˜h0, kx<ρh0 and (b) ρh0<kx<γ˜h0.

Fig. 4.
Fig. 4.

Reflection coefficients for a planar interface between vacuum and the pseudochiral medium with (a) εr=4, μr=1, γ˜=0.5 and (b) εr=0.5, μr=1, γ˜=0.8. Dots correspond to zero reflection, and the dashed line denotes the critical angle θc.

Fig. 5.
Fig. 5.

Transmission coefficients for a planar interface between vacuum and the pseudochiral medium with (a) εr=4, μr=1, γ˜=0.5 and (b) εr=4, μr=1, γ˜=0.8.

Fig. 6.
Fig. 6.

Effect of the chirality parameter γ˜ on the reflection and transmission coefficients at normal incidence (θ=0°) for a planar interface between vacuum and the pseudochiral medium with εr=4 and μr=1. The dashed curve represents the imaginary part.

Fig. 7.
Fig. 7.

Brewster’s angles for the pseudochiral medium with μr=1 for (a) p- and (b) s-polarized incidences. Dashed lines denote the boundaries between the allowed and forbidden regions for Brewster’s angles.

Equations (53)

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

D=ε̲E+ξ̲H,
B=μ̲H+ζ̲E,
×μ̲1×Eiω×(μ̲1ζ̲E)+iωξ̲μ̲1×Eω2(ε̲ξ̲μ̲1ζ̲)E=0,
×ε̲1×Hiωζ̲ε̲1×H+iω×(ε̲1ξ̲H)ω2(μ̲ζ̲ε̲1ξ̲)H=0,
M̲=(k×I̲+ωξ̲)μ̲1(k×I̲ωζ̲)+ω2ε̲,
N̲=(k×I̲ωζ̲)ε̲1(k×I̲+ωξ̲)+ω2μ̲,
ξ̲=[00iγ000iγ00],ζ̲=[00iγ000iγ00],
ε2μ2ρ4ω42εμρ2|k|2ω2+|k|44γ˜2kx2kz2=0,
ω=1ρεμ|k|2±2γ˜|kxkz|.
kz±=ρh02kx2±γ˜|kx|,
θBW=arcsin(ρh0k0)
E±=E0±(hzh0x^±iρy^hzh0σ±z^),
σ±=kxkz±(1γ˜2h02hz2)sign(kx)γ˜(1kx2hz2),
H±=μ̲1(1ωk×E±ζ̲E±)=iηE±,
S±=ρhzηh0(E0±)2(σ±x^+z^).
θNR=arcsin(γ˜h0k0)
Ei=Eip(cosθx^sinθz^)+Eisy^,
Er=Erp(cosθx^+sinθz^)+Ersy^,
Hi=Eipη0y^+Eisη0(cosθx^+sinθz^),
Hr=Erpη0y^+Ersη0(cosθx^+sinθz^),
Et±=Et±(hzh0x^±iρy^hzh0σ±z^),
Ht±=iηEt±(hzh0x^±iρy^hzh0σ±z^),
(Ei+Er)×z^=(Et++Et)×z^,
(Hi+Hr)×z^=(Ht++Ht)×z^.
[ErpErs]=[rpprpsrsprss][EipEis],
[Et+Et]=[t+pt+stpts][EipEis],
rpp=αρβα+ρβ,rps=0,rsp=0,rss=ραβρ+αβ,
t+p=1α+ρβ,t+s=iρ+αβ,tp=1α+ρβ,ts=iρ+αβ,
rpp=αβα+β,rps=0,rsp=0,rss=1αβ1+αβ,
t+p=1α+β,t+s=i1+αβ,tp=1α+β,ts=i1+αβ.
Iiσ=(Eiσ)22η0cosθ,
Irσ=12η0|rσσ|2(Eiσ)2cosθ,
Itσ=ρhzηh0(|t+σ|2+|tσ|2)(Eiσ)2.
Rσ=IrσIiσ=|rσσ|2,
Tσ=ItσIiσ=2ραβ(|t+σ|2+|tσ|2).
Rσ+Tσ=1,
Ei±=Ei±(cosθx^±iy^sinθz^),
Er±=Er±(cosθx^±iy^+sinθz^),
Hi±=iη0Ei±(cosθx^±iy^sinθz^),
Hr±=iη0Er±(cosθx^±iy^+sinθz^).
[Er+Er]=[r++r+r+r][Ei+Ei],
[Et+Et]=[t++t+t+t][Ei+Ei],
r++=r=ρα(1β2)(α+ρβ)(ρ+αβ),r+=r+=β(α2ρ2)(α+ρβ)(ρ+αβ),
t++=t=1α+ρβ+1ρ+αβ,t+=t+=1α+ρβ1ρ+αβ.
r+=r+=αρα+ρ,t++=t=2α+ρ.
Ii±=(Ei±)2η0cosθ.
Ir±=1η0(|r+±|2+|r±|2)(Ei±)2cosθ,
It±=ρhzηh0(|t+±|2+|t±|2)(Ei±)2.
R±=Ir±Ii±=|r+±|2+|r±|2,
T±=It±Ii±=ραβ(|t+±|2+|t±|2).
R±+T±=1.
sin2θB=μrρ2εr1εrρ2εr.
sin2θB=εrρ2μr1μrρ2μr.

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