Abstract

When a plane wave is incident from an isotropic medium into a uniaxial transparent medium so that the ordinary wave propagates in the direction of the optical axis, the extraordinary wave will also propagate in the same direction and with the same refractive index. We will show that this is not the case when the second medium is a uniaxial absorbing material. In this work, we will state a clear and precise interpretation of the meaning of propagation in the direction of the optical axis in the case of uniaxial absorbing media. Assuming that the ordinary wave is refracted in the direction of the optical axis we will analyze the refraction of the extraordinary wave and we will compare it with the case of transparent media. The necessary conditions to have both ordinary and extraordinary waves refracted in the direction of the optical axis will be obtained.

© 2013 Optical Society of America

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References

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    [CrossRef]
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  3. A. V. Kozlov, V. G. Mozhaev, and A. V. Zyryanova, “Waveguide effect under ‘antiguiding’ conditions in graded anisotropic media,” J. Phys. Condens. Matter 22, 075401 (2010).
    [CrossRef]
  4. M. Sluijter, A. Herzog, D. K. de Boer, M. Krijn, and H. P. Urbach, “Ray-tracing simulations of liquid-crystal gradient-index lenses for three-dimensional displays,” J. Opt. Soc. Am. B 26, 2035–2043 (2009).
    [CrossRef]
  5. J. M. Cabrera, F. Agulló, and F. J. López, Optica Electromagnética Vol. 2 (Addison-Wesley Iberoamericana Eapañola S.A, 2000).
  6. M. Born and E. Wolf, Principles of Optics7th ed. (Cambridge University, 2002).
  7. L. I. Perez and C. E. Vanney, “Non-absorbing isotropic-uniaxial interfaces: refraction in ordinary and extraordinary total reflection,” J. Mod. Opt. 52, 1981–2000 (2005).
    [CrossRef]
  8. P. Adamson, “Reflection equivalence of inhomogeneous and uniaxilly anisotropic dielectric films with optical axis normal to the film surface,” J. Opt. 13, 095703 (2011).
    [CrossRef]
  9. S. Khorasani, “Generalized conditions for the existence of optical axes,” J. Opt. A 3, 144–145 (2001).
    [CrossRef]
  10. H. Guo, X. Weng, G. Sui, X. Dong, X. Gao, and S. Zhuang, “Propagation of an arbitrary incident light in a uniaxially planar slab,” Opt. Commun 284, 5509–5512 (2011).
    [CrossRef]
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    [CrossRef]
  13. M. Sluijter, D. K. de Boer, and H. P. Urbach, “Ray-optics analysis of inhomogeneous biaxially anisotropic media,” J. Opt. Soc. Am. A 26, 317–329 (2009).
    [CrossRef]
  14. M. C. Simon, K. V. Gottschalk, and J. M. Simon, “The coincidence of ordinary and extraordinary rays in unaxial birefringent crystal,” J. Mod. Opt. 55, 959–974 (2008).
    [CrossRef]
  15. H. Wu, C. Zhang, and X. Bai, “A complete description of polarization and transmission of nonnormal incident rays in a uniaxial birefringent plate with arbitrary optic axis,” Opt. Commun. 283, 4129–4134 (2010).
    [CrossRef]
  16. Y. Wang, L. Liang, H. Xin, and L. Wu, “Complex ray tracing in uniaxial absorbing media,” J. Opt. Soc. Am. A 25, 653–657 (2008).
    [CrossRef]
  17. C. Alberdi, S. Alfonso, M. Berrogui, J. M. Diñeiro, C. Sáenz, and B. Hernandez, “Field and Poynting vectors of homogeneous waves in uniaxial and absorbing dielectric media,” J. Mod. Opt. 49, 1553–1566 (2002).
    [CrossRef]
  18. S. Alfonso, C. Alberdi, J. M. Diñeiro, M. Berrogui, B. Hernandez, and C. Sáenz, “Complex unitary vectors for the direction of propagation and for the polarization of electromagnetic waves in absorbing isotropic media,” J. Opt. Soc. Am. A 21, 1776–1784 (2004).
    [CrossRef]
  19. C. Alberdi, S. Alfonso, J. M. Diñeiro, B. Hernández, and C. Sáenz, “Interface between transparent isotropic and uniaxial absorbing dielectric media: equations for ray tracing and for the direction of propagation,” J. Opt. Soc. Am. A 25, 2476–2488 (2008).
    [CrossRef]
  20. M. Berek, “Das problem der quantitativen Mikroskopie der Erzmineralien und seine Lösung,” Z. Kristallogr. 76, 396–430 (1931).
  21. J. M. Diñeiro, M. Berrogui, S. Alfonso, C. Alberdi, B. Hernandez, and C. Sáenz, “Complex unitary vectors for the direction of propagation and for the polarization of electromagnetic waves in uniaxial and absorbing dielectric media,” J. Opt. Soc. Am. A 24, 1767–1775 (2007).
    [CrossRef]
  22. N. L. Dmitruk and A. V. Korovin, “Electromagnetic wave refraction on the interface of absorptive and transparent isotropic media and non-resonant excitation of surface waves,” Opt. Commun. 284, 4254–4258 (2011).
    [CrossRef]
  23. W. Q. Zhang and F. Yang, “Negative refraction at various crystal interfaces,” Opt. Commun. 281, 3081–3086 (2008).
    [CrossRef]
  24. Y.-J. Jen, A. Lakhtakia, C.-W. Yu, and C.-T. Lin, “Negative refraction in a uniaxial absorbent dielectric material,” Eur. J. Phys. 30, 1381–1390 (2009).
    [CrossRef]
  25. P. Hillion, “Electromagnetic wave reflection from right- and left-handed anisotropic materials,” Phys. Scr. 80, 065015 (2009).
    [CrossRef]
  26. S. Alfonso, J. M. Diñeiro, C. Alberdi, B. Hernández, and C. Sáenz, “Influence of absorption on the anomalous negative refraction in right-handed uniaxial absorbing dielectric media,” J. Opt. Soc. Am. A 27, 1938–1945 (2010).
    [CrossRef]

2011 (3)

P. Adamson, “Reflection equivalence of inhomogeneous and uniaxilly anisotropic dielectric films with optical axis normal to the film surface,” J. Opt. 13, 095703 (2011).
[CrossRef]

H. Guo, X. Weng, G. Sui, X. Dong, X. Gao, and S. Zhuang, “Propagation of an arbitrary incident light in a uniaxially planar slab,” Opt. Commun 284, 5509–5512 (2011).
[CrossRef]

N. L. Dmitruk and A. V. Korovin, “Electromagnetic wave refraction on the interface of absorptive and transparent isotropic media and non-resonant excitation of surface waves,” Opt. Commun. 284, 4254–4258 (2011).
[CrossRef]

2010 (3)

S. Alfonso, J. M. Diñeiro, C. Alberdi, B. Hernández, and C. Sáenz, “Influence of absorption on the anomalous negative refraction in right-handed uniaxial absorbing dielectric media,” J. Opt. Soc. Am. A 27, 1938–1945 (2010).
[CrossRef]

A. V. Kozlov, V. G. Mozhaev, and A. V. Zyryanova, “Waveguide effect under ‘antiguiding’ conditions in graded anisotropic media,” J. Phys. Condens. Matter 22, 075401 (2010).
[CrossRef]

H. Wu, C. Zhang, and X. Bai, “A complete description of polarization and transmission of nonnormal incident rays in a uniaxial birefringent plate with arbitrary optic axis,” Opt. Commun. 283, 4129–4134 (2010).
[CrossRef]

2009 (4)

M. Sluijter, D. K. de Boer, and H. P. Urbach, “Ray-optics analysis of inhomogeneous biaxially anisotropic media,” J. Opt. Soc. Am. A 26, 317–329 (2009).
[CrossRef]

M. Sluijter, A. Herzog, D. K. de Boer, M. Krijn, and H. P. Urbach, “Ray-tracing simulations of liquid-crystal gradient-index lenses for three-dimensional displays,” J. Opt. Soc. Am. B 26, 2035–2043 (2009).
[CrossRef]

Y.-J. Jen, A. Lakhtakia, C.-W. Yu, and C.-T. Lin, “Negative refraction in a uniaxial absorbent dielectric material,” Eur. J. Phys. 30, 1381–1390 (2009).
[CrossRef]

P. Hillion, “Electromagnetic wave reflection from right- and left-handed anisotropic materials,” Phys. Scr. 80, 065015 (2009).
[CrossRef]

2008 (4)

W. Q. Zhang and F. Yang, “Negative refraction at various crystal interfaces,” Opt. Commun. 281, 3081–3086 (2008).
[CrossRef]

M. C. Simon, K. V. Gottschalk, and J. M. Simon, “The coincidence of ordinary and extraordinary rays in unaxial birefringent crystal,” J. Mod. Opt. 55, 959–974 (2008).
[CrossRef]

Y. Wang, L. Liang, H. Xin, and L. Wu, “Complex ray tracing in uniaxial absorbing media,” J. Opt. Soc. Am. A 25, 653–657 (2008).
[CrossRef]

C. Alberdi, S. Alfonso, J. M. Diñeiro, B. Hernández, and C. Sáenz, “Interface between transparent isotropic and uniaxial absorbing dielectric media: equations for ray tracing and for the direction of propagation,” J. Opt. Soc. Am. A 25, 2476–2488 (2008).
[CrossRef]

2007 (3)

2005 (1)

L. I. Perez and C. E. Vanney, “Non-absorbing isotropic-uniaxial interfaces: refraction in ordinary and extraordinary total reflection,” J. Mod. Opt. 52, 1981–2000 (2005).
[CrossRef]

2004 (1)

2002 (1)

C. Alberdi, S. Alfonso, M. Berrogui, J. M. Diñeiro, C. Sáenz, and B. Hernandez, “Field and Poynting vectors of homogeneous waves in uniaxial and absorbing dielectric media,” J. Mod. Opt. 49, 1553–1566 (2002).
[CrossRef]

2001 (1)

S. Khorasani, “Generalized conditions for the existence of optical axes,” J. Opt. A 3, 144–145 (2001).
[CrossRef]

1999 (1)

1997 (1)

J. M. Diñeiro, S. Alfonso, C. Alberdi, and M. Berrogui, “Statistical parameters of the indicating surface of natural reflectance for biaxial transparent media,” J. Mod. Opt. 44, 1661–1670 (1997).
[CrossRef]

1931 (1)

M. Berek, “Das problem der quantitativen Mikroskopie der Erzmineralien und seine Lösung,” Z. Kristallogr. 76, 396–430 (1931).

Adamson, P.

P. Adamson, “Reflection equivalence of inhomogeneous and uniaxilly anisotropic dielectric films with optical axis normal to the film surface,” J. Opt. 13, 095703 (2011).
[CrossRef]

Agulló, F.

J. M. Cabrera, F. Agulló, and F. J. López, Optica Electromagnética Vol. 2 (Addison-Wesley Iberoamericana Eapañola S.A, 2000).

Alberdi, C.

S. Alfonso, J. M. Diñeiro, C. Alberdi, B. Hernández, and C. Sáenz, “Influence of absorption on the anomalous negative refraction in right-handed uniaxial absorbing dielectric media,” J. Opt. Soc. Am. A 27, 1938–1945 (2010).
[CrossRef]

C. Alberdi, S. Alfonso, J. M. Diñeiro, B. Hernández, and C. Sáenz, “Interface between transparent isotropic and uniaxial absorbing dielectric media: equations for ray tracing and for the direction of propagation,” J. Opt. Soc. Am. A 25, 2476–2488 (2008).
[CrossRef]

J. M. Diñeiro, M. Berrogui, S. Alfonso, C. Alberdi, B. Hernandez, and C. Sáenz, “Complex unitary vectors for the direction of propagation and for the polarization of electromagnetic waves in uniaxial and absorbing dielectric media,” J. Opt. Soc. Am. A 24, 1767–1775 (2007).
[CrossRef]

S. Alfonso, C. Alberdi, J. M. Diñeiro, M. Berrogui, B. Hernandez, and C. Sáenz, “Complex unitary vectors for the direction of propagation and for the polarization of electromagnetic waves in absorbing isotropic media,” J. Opt. Soc. Am. A 21, 1776–1784 (2004).
[CrossRef]

C. Alberdi, S. Alfonso, M. Berrogui, J. M. Diñeiro, C. Sáenz, and B. Hernandez, “Field and Poynting vectors of homogeneous waves in uniaxial and absorbing dielectric media,” J. Mod. Opt. 49, 1553–1566 (2002).
[CrossRef]

J. M. Diñeiro, S. Alfonso, C. Alberdi, and M. Berrogui, “Statistical parameters of the indicating surface of natural reflectance for biaxial transparent media,” J. Mod. Opt. 44, 1661–1670 (1997).
[CrossRef]

Alfonso, S.

S. Alfonso, J. M. Diñeiro, C. Alberdi, B. Hernández, and C. Sáenz, “Influence of absorption on the anomalous negative refraction in right-handed uniaxial absorbing dielectric media,” J. Opt. Soc. Am. A 27, 1938–1945 (2010).
[CrossRef]

C. Alberdi, S. Alfonso, J. M. Diñeiro, B. Hernández, and C. Sáenz, “Interface between transparent isotropic and uniaxial absorbing dielectric media: equations for ray tracing and for the direction of propagation,” J. Opt. Soc. Am. A 25, 2476–2488 (2008).
[CrossRef]

J. M. Diñeiro, M. Berrogui, S. Alfonso, C. Alberdi, B. Hernandez, and C. Sáenz, “Complex unitary vectors for the direction of propagation and for the polarization of electromagnetic waves in uniaxial and absorbing dielectric media,” J. Opt. Soc. Am. A 24, 1767–1775 (2007).
[CrossRef]

S. Alfonso, C. Alberdi, J. M. Diñeiro, M. Berrogui, B. Hernandez, and C. Sáenz, “Complex unitary vectors for the direction of propagation and for the polarization of electromagnetic waves in absorbing isotropic media,” J. Opt. Soc. Am. A 21, 1776–1784 (2004).
[CrossRef]

C. Alberdi, S. Alfonso, M. Berrogui, J. M. Diñeiro, C. Sáenz, and B. Hernandez, “Field and Poynting vectors of homogeneous waves in uniaxial and absorbing dielectric media,” J. Mod. Opt. 49, 1553–1566 (2002).
[CrossRef]

J. M. Diñeiro, S. Alfonso, C. Alberdi, and M. Berrogui, “Statistical parameters of the indicating surface of natural reflectance for biaxial transparent media,” J. Mod. Opt. 44, 1661–1670 (1997).
[CrossRef]

Bai, X.

H. Wu, C. Zhang, and X. Bai, “A complete description of polarization and transmission of nonnormal incident rays in a uniaxial birefringent plate with arbitrary optic axis,” Opt. Commun. 283, 4129–4134 (2010).
[CrossRef]

Berek, M.

M. Berek, “Das problem der quantitativen Mikroskopie der Erzmineralien und seine Lösung,” Z. Kristallogr. 76, 396–430 (1931).

Berrogui, M.

J. M. Diñeiro, M. Berrogui, S. Alfonso, C. Alberdi, B. Hernandez, and C. Sáenz, “Complex unitary vectors for the direction of propagation and for the polarization of electromagnetic waves in uniaxial and absorbing dielectric media,” J. Opt. Soc. Am. A 24, 1767–1775 (2007).
[CrossRef]

S. Alfonso, C. Alberdi, J. M. Diñeiro, M. Berrogui, B. Hernandez, and C. Sáenz, “Complex unitary vectors for the direction of propagation and for the polarization of electromagnetic waves in absorbing isotropic media,” J. Opt. Soc. Am. A 21, 1776–1784 (2004).
[CrossRef]

C. Alberdi, S. Alfonso, M. Berrogui, J. M. Diñeiro, C. Sáenz, and B. Hernandez, “Field and Poynting vectors of homogeneous waves in uniaxial and absorbing dielectric media,” J. Mod. Opt. 49, 1553–1566 (2002).
[CrossRef]

J. M. Diñeiro, S. Alfonso, C. Alberdi, and M. Berrogui, “Statistical parameters of the indicating surface of natural reflectance for biaxial transparent media,” J. Mod. Opt. 44, 1661–1670 (1997).
[CrossRef]

Bingham, R.

Born, M.

M. Born and E. Wolf, Principles of Optics7th ed. (Cambridge University, 2002).

Cabrera, J. M.

J. M. Cabrera, F. Agulló, and F. J. López, Optica Electromagnética Vol. 2 (Addison-Wesley Iberoamericana Eapañola S.A, 2000).

Cojocaru, E.

de Boer, D. K.

Diñeiro, J. M.

S. Alfonso, J. M. Diñeiro, C. Alberdi, B. Hernández, and C. Sáenz, “Influence of absorption on the anomalous negative refraction in right-handed uniaxial absorbing dielectric media,” J. Opt. Soc. Am. A 27, 1938–1945 (2010).
[CrossRef]

C. Alberdi, S. Alfonso, J. M. Diñeiro, B. Hernández, and C. Sáenz, “Interface between transparent isotropic and uniaxial absorbing dielectric media: equations for ray tracing and for the direction of propagation,” J. Opt. Soc. Am. A 25, 2476–2488 (2008).
[CrossRef]

J. M. Diñeiro, M. Berrogui, S. Alfonso, C. Alberdi, B. Hernandez, and C. Sáenz, “Complex unitary vectors for the direction of propagation and for the polarization of electromagnetic waves in uniaxial and absorbing dielectric media,” J. Opt. Soc. Am. A 24, 1767–1775 (2007).
[CrossRef]

S. Alfonso, C. Alberdi, J. M. Diñeiro, M. Berrogui, B. Hernandez, and C. Sáenz, “Complex unitary vectors for the direction of propagation and for the polarization of electromagnetic waves in absorbing isotropic media,” J. Opt. Soc. Am. A 21, 1776–1784 (2004).
[CrossRef]

C. Alberdi, S. Alfonso, M. Berrogui, J. M. Diñeiro, C. Sáenz, and B. Hernandez, “Field and Poynting vectors of homogeneous waves in uniaxial and absorbing dielectric media,” J. Mod. Opt. 49, 1553–1566 (2002).
[CrossRef]

J. M. Diñeiro, S. Alfonso, C. Alberdi, and M. Berrogui, “Statistical parameters of the indicating surface of natural reflectance for biaxial transparent media,” J. Mod. Opt. 44, 1661–1670 (1997).
[CrossRef]

Dmitruk, N. L.

N. L. Dmitruk and A. V. Korovin, “Electromagnetic wave refraction on the interface of absorptive and transparent isotropic media and non-resonant excitation of surface waves,” Opt. Commun. 284, 4254–4258 (2011).
[CrossRef]

Dong, X.

H. Guo, X. Weng, G. Sui, X. Dong, X. Gao, and S. Zhuang, “Propagation of an arbitrary incident light in a uniaxially planar slab,” Opt. Commun 284, 5509–5512 (2011).
[CrossRef]

Gao, X.

H. Guo, X. Weng, G. Sui, X. Dong, X. Gao, and S. Zhuang, “Propagation of an arbitrary incident light in a uniaxially planar slab,” Opt. Commun 284, 5509–5512 (2011).
[CrossRef]

Gottschalk, K. V.

M. C. Simon, K. V. Gottschalk, and J. M. Simon, “The coincidence of ordinary and extraordinary rays in unaxial birefringent crystal,” J. Mod. Opt. 55, 959–974 (2008).
[CrossRef]

Guo, H.

H. Guo, X. Weng, G. Sui, X. Dong, X. Gao, and S. Zhuang, “Propagation of an arbitrary incident light in a uniaxially planar slab,” Opt. Commun 284, 5509–5512 (2011).
[CrossRef]

Hernandez, B.

Hernández, B.

Herzog, A.

Hillion, P.

P. Hillion, “Electromagnetic wave reflection from right- and left-handed anisotropic materials,” Phys. Scr. 80, 065015 (2009).
[CrossRef]

Jen, Y.-J.

Y.-J. Jen, A. Lakhtakia, C.-W. Yu, and C.-T. Lin, “Negative refraction in a uniaxial absorbent dielectric material,” Eur. J. Phys. 30, 1381–1390 (2009).
[CrossRef]

Jenkins, C.

Khorasani, S.

S. Khorasani, “Generalized conditions for the existence of optical axes,” J. Opt. A 3, 144–145 (2001).
[CrossRef]

Korovin, A. V.

N. L. Dmitruk and A. V. Korovin, “Electromagnetic wave refraction on the interface of absorptive and transparent isotropic media and non-resonant excitation of surface waves,” Opt. Commun. 284, 4254–4258 (2011).
[CrossRef]

Kozlov, A. V.

A. V. Kozlov, V. G. Mozhaev, and A. V. Zyryanova, “Waveguide effect under ‘antiguiding’ conditions in graded anisotropic media,” J. Phys. Condens. Matter 22, 075401 (2010).
[CrossRef]

Krijn, M.

Lakhtakia, A.

Y.-J. Jen, A. Lakhtakia, C.-W. Yu, and C.-T. Lin, “Negative refraction in a uniaxial absorbent dielectric material,” Eur. J. Phys. 30, 1381–1390 (2009).
[CrossRef]

Li, F.

H. Luo, Z. Ren, W. Shu, and F. Li, “Construct a polarizing beam splitter by an anisotropic metamaterial slab,” Appl. Phys. B 87, 283–287 (2007).
[CrossRef]

Liang, L.

Lin, C.-T.

Y.-J. Jen, A. Lakhtakia, C.-W. Yu, and C.-T. Lin, “Negative refraction in a uniaxial absorbent dielectric material,” Eur. J. Phys. 30, 1381–1390 (2009).
[CrossRef]

López, F. J.

J. M. Cabrera, F. Agulló, and F. J. López, Optica Electromagnética Vol. 2 (Addison-Wesley Iberoamericana Eapañola S.A, 2000).

Love, G. D.

Luo, H.

H. Luo, Z. Ren, W. Shu, and F. Li, “Construct a polarizing beam splitter by an anisotropic metamaterial slab,” Appl. Phys. B 87, 283–287 (2007).
[CrossRef]

Moore, K.

Mozhaev, V. G.

A. V. Kozlov, V. G. Mozhaev, and A. V. Zyryanova, “Waveguide effect under ‘antiguiding’ conditions in graded anisotropic media,” J. Phys. Condens. Matter 22, 075401 (2010).
[CrossRef]

Perez, L. I.

L. I. Perez and C. E. Vanney, “Non-absorbing isotropic-uniaxial interfaces: refraction in ordinary and extraordinary total reflection,” J. Mod. Opt. 52, 1981–2000 (2005).
[CrossRef]

Ren, Z.

H. Luo, Z. Ren, W. Shu, and F. Li, “Construct a polarizing beam splitter by an anisotropic metamaterial slab,” Appl. Phys. B 87, 283–287 (2007).
[CrossRef]

Sáenz, C.

Shu, W.

H. Luo, Z. Ren, W. Shu, and F. Li, “Construct a polarizing beam splitter by an anisotropic metamaterial slab,” Appl. Phys. B 87, 283–287 (2007).
[CrossRef]

Simon, J. M.

M. C. Simon, K. V. Gottschalk, and J. M. Simon, “The coincidence of ordinary and extraordinary rays in unaxial birefringent crystal,” J. Mod. Opt. 55, 959–974 (2008).
[CrossRef]

Simon, M. C.

M. C. Simon, K. V. Gottschalk, and J. M. Simon, “The coincidence of ordinary and extraordinary rays in unaxial birefringent crystal,” J. Mod. Opt. 55, 959–974 (2008).
[CrossRef]

Sluijter, M.

Sui, G.

H. Guo, X. Weng, G. Sui, X. Dong, X. Gao, and S. Zhuang, “Propagation of an arbitrary incident light in a uniaxially planar slab,” Opt. Commun 284, 5509–5512 (2011).
[CrossRef]

Urbach, H. P.

Vanney, C. E.

L. I. Perez and C. E. Vanney, “Non-absorbing isotropic-uniaxial interfaces: refraction in ordinary and extraordinary total reflection,” J. Mod. Opt. 52, 1981–2000 (2005).
[CrossRef]

Wang, Y.

Weng, X.

H. Guo, X. Weng, G. Sui, X. Dong, X. Gao, and S. Zhuang, “Propagation of an arbitrary incident light in a uniaxially planar slab,” Opt. Commun 284, 5509–5512 (2011).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics7th ed. (Cambridge University, 2002).

Wu, H.

H. Wu, C. Zhang, and X. Bai, “A complete description of polarization and transmission of nonnormal incident rays in a uniaxial birefringent plate with arbitrary optic axis,” Opt. Commun. 283, 4129–4134 (2010).
[CrossRef]

Wu, L.

Xin, H.

Yang, F.

W. Q. Zhang and F. Yang, “Negative refraction at various crystal interfaces,” Opt. Commun. 281, 3081–3086 (2008).
[CrossRef]

Yu, C.-W.

Y.-J. Jen, A. Lakhtakia, C.-W. Yu, and C.-T. Lin, “Negative refraction in a uniaxial absorbent dielectric material,” Eur. J. Phys. 30, 1381–1390 (2009).
[CrossRef]

Zhang, C.

H. Wu, C. Zhang, and X. Bai, “A complete description of polarization and transmission of nonnormal incident rays in a uniaxial birefringent plate with arbitrary optic axis,” Opt. Commun. 283, 4129–4134 (2010).
[CrossRef]

Zhang, W. Q.

W. Q. Zhang and F. Yang, “Negative refraction at various crystal interfaces,” Opt. Commun. 281, 3081–3086 (2008).
[CrossRef]

Zhuang, S.

H. Guo, X. Weng, G. Sui, X. Dong, X. Gao, and S. Zhuang, “Propagation of an arbitrary incident light in a uniaxially planar slab,” Opt. Commun 284, 5509–5512 (2011).
[CrossRef]

Zyryanova, A. V.

A. V. Kozlov, V. G. Mozhaev, and A. V. Zyryanova, “Waveguide effect under ‘antiguiding’ conditions in graded anisotropic media,” J. Phys. Condens. Matter 22, 075401 (2010).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

H. Luo, Z. Ren, W. Shu, and F. Li, “Construct a polarizing beam splitter by an anisotropic metamaterial slab,” Appl. Phys. B 87, 283–287 (2007).
[CrossRef]

Eur. J. Phys. (1)

Y.-J. Jen, A. Lakhtakia, C.-W. Yu, and C.-T. Lin, “Negative refraction in a uniaxial absorbent dielectric material,” Eur. J. Phys. 30, 1381–1390 (2009).
[CrossRef]

J. Mod. Opt. (4)

L. I. Perez and C. E. Vanney, “Non-absorbing isotropic-uniaxial interfaces: refraction in ordinary and extraordinary total reflection,” J. Mod. Opt. 52, 1981–2000 (2005).
[CrossRef]

J. M. Diñeiro, S. Alfonso, C. Alberdi, and M. Berrogui, “Statistical parameters of the indicating surface of natural reflectance for biaxial transparent media,” J. Mod. Opt. 44, 1661–1670 (1997).
[CrossRef]

M. C. Simon, K. V. Gottschalk, and J. M. Simon, “The coincidence of ordinary and extraordinary rays in unaxial birefringent crystal,” J. Mod. Opt. 55, 959–974 (2008).
[CrossRef]

C. Alberdi, S. Alfonso, M. Berrogui, J. M. Diñeiro, C. Sáenz, and B. Hernandez, “Field and Poynting vectors of homogeneous waves in uniaxial and absorbing dielectric media,” J. Mod. Opt. 49, 1553–1566 (2002).
[CrossRef]

J. Opt. (1)

P. Adamson, “Reflection equivalence of inhomogeneous and uniaxilly anisotropic dielectric films with optical axis normal to the film surface,” J. Opt. 13, 095703 (2011).
[CrossRef]

J. Opt. A (1)

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H. Guo, X. Weng, G. Sui, X. Dong, X. Gao, and S. Zhuang, “Propagation of an arbitrary incident light in a uniaxially planar slab,” Opt. Commun 284, 5509–5512 (2011).
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Figures (6)

Fig. 1.
Fig. 1.

Plane wave falls with an angle of incidence αo from an isotropic medium with index no to a uniaxial absorbing medium with indices n˜ω and n˜ε. XmYmZm is the coordinate system of the medium, XYZ the coordinate system of principal axes, and XπYπZπ is defined so that YπZπ is the plane of incidence π.

Fig. 2.
Fig. 2.

k/k0-surfaces for the refraction in positive uniaxial media (nε>nω) with the optical axis contained in the plane of incidence and an ordinary wave refracted in the direction of the optical axis.

Fig. 3.
Fig. 3.

k/k0-surfaces for the refraction in negative uniaxial media (nε<nω) with the optical axis contained in the plane of incidence and an ordinary wave refracted in the direction of the optical axis.

Fig. 4.
Fig. 4.

(a) Angle α1 of the direction of phase propagation of the extraordinary wave plotted as a function of the orientation γ of the optical axis for various different absorbing uniaxial media. (b) Detailed view of the region γ>30° of Fig. 4(a).

Fig. 5.
Fig. 5.

Angle α1 of the direction of phase propagation of the extraordinary wave plotted as a function of kε in the particular case γ=20°, nω=1.6, and nε=1.4 for different values of kω (2, 1, 0.5, and 0.2).

Fig. 6.
Fig. 6.

Angle α1 of the direction of phase propagation of the extraordinary wave plotted as a function of kε in the particular case γ=20° and nω=nε=1.4 for different values of kω (2, 1, 0.5, and 0.2).

Equations (39)

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sx21nx21n2+sy21ny21n2+sz21nz21n2=0.
1n12=1sz2nε2+sz2nω2,
1n22=1nω2.
nosinαo=nωsinγ.
nosinαo=n1sinα1.
F˜=Fu˜Fexp[iω(tn˜cr·s˜)]exp(iθF)=Fu˜Fexp[ωcnr·(χsRsI)]exp[iω(tncr·(sR+χsI))]exp(iθF)=Fu˜Fexp(iθF)AtPr,
so=(sinαo,0,cosαo),
sr=(sinαo,0,cosαo),
s˜1,2=[non˜1,2sinαo,0,(1non˜1,22sin2αo)1/2],
1n˜12=1s˜1z2n˜ε2+s˜1z2n˜ε2,
1n˜22=1n˜ω2,
s˜1x=cosγs˜1xmsinγs˜1zm=0,
s˜1z=sinγs˜1xm+cosγs˜1zm=0.
s˜1=(sinγ,0,cosγ).
sinα0=nωnosinγ.
(sR+χsI)2x=0=cosγ(sR+χsI)2xmsinγ(sR+χsI)2zm,
(sR+χsI)2y=(sR+χsI)2ym=0,
(sR+χsI)2z=sinγ(sR+χsI)2xm+cosγ(sR+χsI)2zm.
s2Ixm=χωs2Rxm.
nosoxm=nω(s2Rxm+χωs2Ixm),
s2R2s2I2=1,
s2R·s2I=0.
(1χω2)no2soxm2nω2(1+χω2)2+s2Rzm2s2Izm2=1,
χωno2soxm2nω2(1+χω2)2+s2Rzms2Izm,
nosoxmnωtgγ=s2Rzm+χωs2Izm.
soxm2=2nω2χω2tg2γn021[(χω21)[(1+χω2)2+4χω2tg2γ]1/2].
soxm=nωsinγno1χω2+Aω2,
Aω=(1+χω2)2+4χω2tg2γ.
so=(soxm,0,1soxm2)
soxm=nωnosinγ,
M˜1s˜1z4+M˜2s˜1z2+M˜3=0,
M˜1=[1+(1n˜ω21n˜ε2)no2(soxm2cos2γ)]2+no4sin22γsoxm4(1n˜ω21n˜ε2)2,
M˜2=2[1+(1n˜ω21n˜ε2)no2(soxm2cos2γ)][cos2γno2n˜ε2(soxm2cos2γ)]no2soxm2sin22γ(1n˜ω21n˜ε2)(12n02soxm2nε2),
M˜3=[cos2γn02nε2(soxm2cos2γ)]2no2soxm2sin22γnε2(1no2soxm2nε2).
sinα1=nosinαosI12|n˜1|2+n12.
soxm=nωsinγno1χω2+Aω2=n1sinγno1χ12+A12.
n1=T(T2+2k12)2(2k1tg2γ)+T2+2k12,
T=nω1χω2(1+χω2)2+(2χω2tgγ)2.
nω=1.6,nε=1.4,kω=3andkε=2.8476nω=1.6,nε=1.4,kω=1andkε=1.0576nω=1.6,nε=1.4,kω=2andkε=1.9345.

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