Abstract

Design and realization of polarization splitting devices present several common challenges. Unwanted reflections from boundaries of the device and material anisotropy are among the major ones. We present a transformation electromagnetics-based method to design non-magnetic homogeneous polarization splitters that are reflectionless and have minimum anisotropy. This is accomplished by utilizing an area-preserving linear transformation with proper reflectionless conditions at the input and the output boundaries of the device. The condition of minimum anisotropy is determined analytically. This is done for the first time, to the best of our knowledge. The proposed devices enhance the performance of the optical systems by providing ideal transmission. The realizability of the device is also improved by minimization of the anisotropy. Several polarization splitters are designed which create an arbitrary deflection angle or lateral shift between TE and TM polarizations. In addition, the effective medium theory is employed to realize one of the designs by using equivalent dielectric layers. In order to verify the proposed methodology, the designed devices are simulated by the commercial software COMSOL Multiphysics.

© 2017 Optical Society of America

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    [Crossref]
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    [Crossref]
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2017 (1)

H. Wang, Y. Deng, B. Zheng, R. Li, Y. Jiang, S. Dehdashti, Z. Xu, and H. Chen, “Panoramic lens designed with transformation optics,” Sci. Rep. 7, 40083 (2017).
[Crossref]

2016 (3)

C. Qian, R. Li, Y. Jiang, B. Zheng, H. Wang, Z. Xu, and H. Chen, “Transient response of a signal through a dispersive invisibility cloak,” Opt. Lett. 41, 4911–4914 (2016).
[Crossref]

B. Zheng, H. A. Madni, R. Hao, X. Zhang, X. Liu, E. Li, and H. Chen, “Concealing arbitrary objects remotely with multi-folded transformation optics,” Light Sci. Appl. 5, e16177 (2016).
[Crossref]

G. Gurkan and G. Anthony, “A physical explanation for the all-angle reflectionless property of transformation optics designs,” J. Opt. 18, 044020 (2016).
[Crossref]

2015 (4)

W. Yicheng, H. Chengdong, W. Yuzhuo, L. Xuan, and Z. Jing, “Controlling the wave propagation through the medium designed by linear coordinate transformation,” Eur. J. Phys. 36, 015006 (2015).

S. Xu, H. Xu, H. Gao, Y. Jiang, F. Yu, J. D. Joannopoulos, M. Soljačić, H. Chen, H. Sun, and B. Zhang, “Broadband surface-wave transformation cloak,” Proc. Natl. Acad. Sci. USA 112, 7635–7638 (2015).
[Crossref]

N. Atefeh and S.-S. Mehrdad, “Design of an optical spatial interferometer with transformation optics,” J. Opt. 17, 105103 (2015).
[Crossref]

Y. Yang, H. Chen, F. Yu, E. Li, and H. Chen, “A full-parameter, broadband, homogeneous, and compact waveguide coupler designed with transformation optics,” IEEE Antennas Wireless Propag. Lett. 14, 634–637 (2015).
[Crossref]

2014 (2)

T. Han and Z. Wu, “Electromagnetic wave rotators with homogeneous, nonmagnetic, and isotropic materials,” Opt. Lett. 39, 3698–3701 (2014).
[Crossref]

J. Cao, L. Zhang, S. Yan, and X. Sun, “Reflectionless design of optical elements using impedance-tunable transformation optics,” Appl. Phys. Lett. 104, 191102 (2014).
[Crossref]

2013 (1)

L. Huang, X. Chen, B. Ni, G. Li, X. Wang, Z. Li, and W. Lu, “A general transformation for compact waveguide coupler by using homogeneous media,” Photonics Nanostruct. Fundam. Appl. 11, 115–122 (2013).
[Crossref]

2012 (2)

2011 (4)

T. Han, C.-W. Qiu, J.-W. Dong, X. Tang, and S. Zouhdi, “Homogeneous and isotropic bends to tunnel waves through multiple different/equal waveguides along arbitrary directions,” Opt. Express 19, 13020–13030 (2011).
[Crossref]

T. Han, C.-W. Qiu, and X. Tang, “Adaptive waveguide bends with homogeneous, nonmagnetic, and isotropic materials,” Opt. Lett. 36, 181–183 (2011).
[Crossref]

J. Zhou, M. Li, L. Xie, and D. Liu, “Design of a new kind of polarization splitter based on transformation optics,” Optik 122, 1672–1675 (2011).
[Crossref]

G. X. Yu, W. X. Jiang, and T. J. Cui, “Beam deflection and splitting using transformation optics,” Central Eur. J. Phys. 9, 183–188 (2011).
[Crossref]

2009 (2)

D.-H. Kwon and D. H. Werner, “Flat focusing lens designs having minimized reflection based on coordinate transformation techniques,” Opt. Express 17, 7807–7817 (2009).
[Crossref]

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[Crossref]

2008 (6)

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101, 203901 (2008).
[Crossref]

D.-H. Kwon and D. H. Werner, “Polarization splitter and polarization rotator designs based on transformation optics,” Opt. Express 16, 18731–18738 (2008).
[Crossref]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6, 87–95 (2008).
[Crossref]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100, 063903 (2008).
[Crossref]

K. Do-Hoon and H. W. Douglas, “Transformation optical designs for wave collimators, flat lenses and right-angle bends,” New J. Phys. 10, 115023 (2008).
[Crossref]

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16, 11555–11567 (2008).
[Crossref]

2007 (2)

H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90, 241105 (2007).
[Crossref]

W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91, 111105 (2007).
[Crossref]

2006 (3)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[Crossref]

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
[Crossref]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[Crossref]

2005 (2)

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[Crossref]

W. Yan, Z. Xuejun, and Y. Jinkui, “Reflection and refraction of light at the interface of a uniaxial bicrystal,” Europhys. Lett. 72, 830–836 (2005).
[Crossref]

2004 (1)

Z. Liu, Z. Lin, and S. T. Chui, “Negative refraction and omnidirectional total transmission at a planar interface associated with a uniaxial medium,” Phys. Rev. B 69, 115402 (2004).
[Crossref]

Anthony, G.

G. Gurkan and G. Anthony, “A physical explanation for the all-angle reflectionless property of transformation optics designs,” J. Opt. 18, 044020 (2016).
[Crossref]

Atefeh, N.

N. Atefeh and S.-S. Mehrdad, “Design of an optical spatial interferometer with transformation optics,” J. Opt. 17, 105103 (2015).
[Crossref]

Bai, J.

Barbastathis, G.

Bhatia, A. B.

E. W. Max Born, A. B. Bhatia, P. C. Clemmow, D. Gabor, A. R. Stokes, A. M. Taylor, P. A. Wayman, and W. L. Wilcock, “Optics of crystals,” in Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999), pp. 837–841, Chap. 15.

Cai, W.

W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91, 111105 (2007).
[Crossref]

Cao, J.

J. Cao, L. Zhang, S. Yan, and X. Sun, “Reflectionless design of optical elements using impedance-tunable transformation optics,” Appl. Phys. Lett. 104, 191102 (2014).
[Crossref]

Chan, C. T.

H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90, 241105 (2007).
[Crossref]

Chen, H.

H. Wang, Y. Deng, B. Zheng, R. Li, Y. Jiang, S. Dehdashti, Z. Xu, and H. Chen, “Panoramic lens designed with transformation optics,” Sci. Rep. 7, 40083 (2017).
[Crossref]

B. Zheng, H. A. Madni, R. Hao, X. Zhang, X. Liu, E. Li, and H. Chen, “Concealing arbitrary objects remotely with multi-folded transformation optics,” Light Sci. Appl. 5, e16177 (2016).
[Crossref]

C. Qian, R. Li, Y. Jiang, B. Zheng, H. Wang, Z. Xu, and H. Chen, “Transient response of a signal through a dispersive invisibility cloak,” Opt. Lett. 41, 4911–4914 (2016).
[Crossref]

S. Xu, H. Xu, H. Gao, Y. Jiang, F. Yu, J. D. Joannopoulos, M. Soljačić, H. Chen, H. Sun, and B. Zhang, “Broadband surface-wave transformation cloak,” Proc. Natl. Acad. Sci. USA 112, 7635–7638 (2015).
[Crossref]

Y. Yang, H. Chen, F. Yu, E. Li, and H. Chen, “A full-parameter, broadband, homogeneous, and compact waveguide coupler designed with transformation optics,” IEEE Antennas Wireless Propag. Lett. 14, 634–637 (2015).
[Crossref]

Y. Yang, H. Chen, F. Yu, E. Li, and H. Chen, “A full-parameter, broadband, homogeneous, and compact waveguide coupler designed with transformation optics,” IEEE Antennas Wireless Propag. Lett. 14, 634–637 (2015).
[Crossref]

H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90, 241105 (2007).
[Crossref]

Chen, X.

L. Huang, X. Chen, B. Ni, G. Li, X. Wang, Z. Li, and W. Lu, “A general transformation for compact waveguide coupler by using homogeneous media,” Photonics Nanostruct. Fundam. Appl. 11, 115–122 (2013).
[Crossref]

Chengdong, H.

W. Yicheng, H. Chengdong, W. Yuzhuo, L. Xuan, and Z. Jing, “Controlling the wave propagation through the medium designed by linear coordinate transformation,” Eur. J. Phys. 36, 015006 (2015).

Chettiar, U. K.

W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91, 111105 (2007).
[Crossref]

Chin, J. Y.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[Crossref]

Chui, S. T.

Z. Liu, Z. Lin, and S. T. Chui, “Negative refraction and omnidirectional total transmission at a planar interface associated with a uniaxial medium,” Phys. Rev. B 69, 115402 (2004).
[Crossref]

Clemmow, P. C.

E. W. Max Born, A. B. Bhatia, P. C. Clemmow, D. Gabor, A. R. Stokes, A. M. Taylor, P. A. Wayman, and W. L. Wilcock, “Optics of crystals,” in Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999), pp. 837–841, Chap. 15.

Cui, T. J.

Z. L. Mei, Y. L. Xu, J. Bai, and T. J. Cui, “Nonmagnetic electromagnetic transparent wall realized by a metal-dielectric multilayer structure,” Opt. Express 20, 16955–16967 (2012).
[Crossref]

G. X. Yu, W. X. Jiang, and T. J. Cui, “Beam deflection and splitting using transformation optics,” Central Eur. J. Phys. 9, 183–188 (2011).
[Crossref]

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[Crossref]

Cummer, S. A.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6, 87–95 (2008).
[Crossref]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100, 063903 (2008).
[Crossref]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[Crossref]

Dehdashti, S.

H. Wang, Y. Deng, B. Zheng, R. Li, Y. Jiang, S. Dehdashti, Z. Xu, and H. Chen, “Panoramic lens designed with transformation optics,” Sci. Rep. 7, 40083 (2017).
[Crossref]

Deng, Y.

H. Wang, Y. Deng, B. Zheng, R. Li, Y. Jiang, S. Dehdashti, Z. Xu, and H. Chen, “Panoramic lens designed with transformation optics,” Sci. Rep. 7, 40083 (2017).
[Crossref]

Do-Hoon, K.

K. Do-Hoon and H. W. Douglas, “Transformation optical designs for wave collimators, flat lenses and right-angle bends,” New J. Phys. 10, 115023 (2008).
[Crossref]

Dong, J.-W.

Douglas, H. W.

K. Do-Hoon and H. W. Douglas, “Transformation optical designs for wave collimators, flat lenses and right-angle bends,” New J. Phys. 10, 115023 (2008).
[Crossref]

Economou, E. N.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[Crossref]

Gabor, D.

E. W. Max Born, A. B. Bhatia, P. C. Clemmow, D. Gabor, A. R. Stokes, A. M. Taylor, P. A. Wayman, and W. L. Wilcock, “Optics of crystals,” in Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999), pp. 837–841, Chap. 15.

Gao, H.

S. Xu, H. Xu, H. Gao, Y. Jiang, F. Yu, J. D. Joannopoulos, M. Soljačić, H. Chen, H. Sun, and B. Zhang, “Broadband surface-wave transformation cloak,” Proc. Natl. Acad. Sci. USA 112, 7635–7638 (2015).
[Crossref]

Gurkan, G.

G. Gurkan and G. Anthony, “A physical explanation for the all-angle reflectionless property of transformation optics designs,” J. Opt. 18, 044020 (2016).
[Crossref]

Han, T.

Hao, R.

B. Zheng, H. A. Madni, R. Hao, X. Zhang, X. Liu, E. Li, and H. Chen, “Concealing arbitrary objects remotely with multi-folded transformation optics,” Light Sci. Appl. 5, e16177 (2016).
[Crossref]

Huang, L.

L. Huang, X. Chen, B. Ni, G. Li, X. Wang, Z. Li, and W. Lu, “A general transformation for compact waveguide coupler by using homogeneous media,” Photonics Nanostruct. Fundam. Appl. 11, 115–122 (2013).
[Crossref]

Ji, C.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[Crossref]

Jiang, W. X.

G. X. Yu, W. X. Jiang, and T. J. Cui, “Beam deflection and splitting using transformation optics,” Central Eur. J. Phys. 9, 183–188 (2011).
[Crossref]

Jiang, Y.

H. Wang, Y. Deng, B. Zheng, R. Li, Y. Jiang, S. Dehdashti, Z. Xu, and H. Chen, “Panoramic lens designed with transformation optics,” Sci. Rep. 7, 40083 (2017).
[Crossref]

C. Qian, R. Li, Y. Jiang, B. Zheng, H. Wang, Z. Xu, and H. Chen, “Transient response of a signal through a dispersive invisibility cloak,” Opt. Lett. 41, 4911–4914 (2016).
[Crossref]

S. Xu, H. Xu, H. Gao, Y. Jiang, F. Yu, J. D. Joannopoulos, M. Soljačić, H. Chen, H. Sun, and B. Zhang, “Broadband surface-wave transformation cloak,” Proc. Natl. Acad. Sci. USA 112, 7635–7638 (2015).
[Crossref]

Jing, Z.

W. Yicheng, H. Chengdong, W. Yuzhuo, L. Xuan, and Z. Jing, “Controlling the wave propagation through the medium designed by linear coordinate transformation,” Eur. J. Phys. 36, 015006 (2015).

Jinkui, Y.

W. Yan, Z. Xuejun, and Y. Jinkui, “Reflection and refraction of light at the interface of a uniaxial bicrystal,” Europhys. Lett. 72, 830–836 (2005).
[Crossref]

Joannopoulos, J. D.

S. Xu, H. Xu, H. Gao, Y. Jiang, F. Yu, J. D. Joannopoulos, M. Soljačić, H. Chen, H. Sun, and B. Zhang, “Broadband surface-wave transformation cloak,” Proc. Natl. Acad. Sci. USA 112, 7635–7638 (2015).
[Crossref]

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[Crossref]

Kafesaki, M.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[Crossref]

Kildishev, A. V.

W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91, 111105 (2007).
[Crossref]

Koschny, T.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[Crossref]

Kwon, D.-H.

Leonhardt, U.

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
[Crossref]

Li, E.

B. Zheng, H. A. Madni, R. Hao, X. Zhang, X. Liu, E. Li, and H. Chen, “Concealing arbitrary objects remotely with multi-folded transformation optics,” Light Sci. Appl. 5, e16177 (2016).
[Crossref]

Y. Yang, H. Chen, F. Yu, E. Li, and H. Chen, “A full-parameter, broadband, homogeneous, and compact waveguide coupler designed with transformation optics,” IEEE Antennas Wireless Propag. Lett. 14, 634–637 (2015).
[Crossref]

Li, G.

L. Huang, X. Chen, B. Ni, G. Li, X. Wang, Z. Li, and W. Lu, “A general transformation for compact waveguide coupler by using homogeneous media,” Photonics Nanostruct. Fundam. Appl. 11, 115–122 (2013).
[Crossref]

Li, J.

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101, 203901 (2008).
[Crossref]

Li, M.

J. Zhou, M. Li, L. Xie, and D. Liu, “Design of a new kind of polarization splitter based on transformation optics,” Optik 122, 1672–1675 (2011).
[Crossref]

Li, R.

H. Wang, Y. Deng, B. Zheng, R. Li, Y. Jiang, S. Dehdashti, Z. Xu, and H. Chen, “Panoramic lens designed with transformation optics,” Sci. Rep. 7, 40083 (2017).
[Crossref]

C. Qian, R. Li, Y. Jiang, B. Zheng, H. Wang, Z. Xu, and H. Chen, “Transient response of a signal through a dispersive invisibility cloak,” Opt. Lett. 41, 4911–4914 (2016).
[Crossref]

Li, Z.

L. Huang, X. Chen, B. Ni, G. Li, X. Wang, Z. Li, and W. Lu, “A general transformation for compact waveguide coupler by using homogeneous media,” Photonics Nanostruct. Fundam. Appl. 11, 115–122 (2013).
[Crossref]

Lin, Z.

Z. Liu, Z. Lin, and S. T. Chui, “Negative refraction and omnidirectional total transmission at a planar interface associated with a uniaxial medium,” Phys. Rev. B 69, 115402 (2004).
[Crossref]

Liu, D.

J. Zhou, M. Li, L. Xie, and D. Liu, “Design of a new kind of polarization splitter based on transformation optics,” Optik 122, 1672–1675 (2011).
[Crossref]

Liu, R.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[Crossref]

Liu, X.

B. Zheng, H. A. Madni, R. Hao, X. Zhang, X. Liu, E. Li, and H. Chen, “Concealing arbitrary objects remotely with multi-folded transformation optics,” Light Sci. Appl. 5, e16177 (2016).
[Crossref]

Liu, Z.

Z. Liu, Z. Lin, and S. T. Chui, “Negative refraction and omnidirectional total transmission at a planar interface associated with a uniaxial medium,” Phys. Rev. B 69, 115402 (2004).
[Crossref]

Lu, W.

L. Huang, X. Chen, B. Ni, G. Li, X. Wang, Z. Li, and W. Lu, “A general transformation for compact waveguide coupler by using homogeneous media,” Photonics Nanostruct. Fundam. Appl. 11, 115–122 (2013).
[Crossref]

Madni, H. A.

B. Zheng, H. A. Madni, R. Hao, X. Zhang, X. Liu, E. Li, and H. Chen, “Concealing arbitrary objects remotely with multi-folded transformation optics,” Light Sci. Appl. 5, e16177 (2016).
[Crossref]

Max Born, E. W.

E. W. Max Born, A. B. Bhatia, P. C. Clemmow, D. Gabor, A. R. Stokes, A. M. Taylor, P. A. Wayman, and W. L. Wilcock, “Optics of crystals,” in Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999), pp. 837–841, Chap. 15.

Mehrdad, S.-S.

N. Atefeh and S.-S. Mehrdad, “Design of an optical spatial interferometer with transformation optics,” J. Opt. 17, 105103 (2015).
[Crossref]

Mei, Z. L.

Milton, G. W.

W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91, 111105 (2007).
[Crossref]

Min, Q.

Y. Wei, Y. Min, and Q. Min, “Necessary and sufficient conditions for reflectionless transformation media in an isotropic and homogenous background,” arXiv:0806.3231 (2008).

Min, Y.

Y. Wei, Y. Min, and Q. Min, “Necessary and sufficient conditions for reflectionless transformation media in an isotropic and homogenous background,” arXiv:0806.3231 (2008).

Mock, J. J.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[Crossref]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[Crossref]

Ni, B.

L. Huang, X. Chen, B. Ni, G. Li, X. Wang, Z. Li, and W. Lu, “A general transformation for compact waveguide coupler by using homogeneous media,” Photonics Nanostruct. Fundam. Appl. 11, 115–122 (2013).
[Crossref]

Pendry, J. B.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6, 87–95 (2008).
[Crossref]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100, 063903 (2008).
[Crossref]

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16, 11555–11567 (2008).
[Crossref]

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101, 203901 (2008).
[Crossref]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[Crossref]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[Crossref]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[Crossref]

Qian, C.

Qiu, C.-W.

Rahm, M.

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16, 11555–11567 (2008).
[Crossref]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100, 063903 (2008).
[Crossref]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6, 87–95 (2008).
[Crossref]

Roberts, D. A.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6, 87–95 (2008).
[Crossref]

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16, 11555–11567 (2008).
[Crossref]

Schurig, D.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100, 063903 (2008).
[Crossref]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6, 87–95 (2008).
[Crossref]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[Crossref]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[Crossref]

Shalaev, V. M.

W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91, 111105 (2007).
[Crossref]

Smith, D. R.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[Crossref]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6, 87–95 (2008).
[Crossref]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100, 063903 (2008).
[Crossref]

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16, 11555–11567 (2008).
[Crossref]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[Crossref]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[Crossref]

Soljacic, M.

S. Xu, H. Xu, H. Gao, Y. Jiang, F. Yu, J. D. Joannopoulos, M. Soljačić, H. Chen, H. Sun, and B. Zhang, “Broadband surface-wave transformation cloak,” Proc. Natl. Acad. Sci. USA 112, 7635–7638 (2015).
[Crossref]

Soukoulis, C. M.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[Crossref]

Starr, A. F.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[Crossref]

Stokes, A. R.

E. W. Max Born, A. B. Bhatia, P. C. Clemmow, D. Gabor, A. R. Stokes, A. M. Taylor, P. A. Wayman, and W. L. Wilcock, “Optics of crystals,” in Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999), pp. 837–841, Chap. 15.

Sun, H.

S. Xu, H. Xu, H. Gao, Y. Jiang, F. Yu, J. D. Joannopoulos, M. Soljačić, H. Chen, H. Sun, and B. Zhang, “Broadband surface-wave transformation cloak,” Proc. Natl. Acad. Sci. USA 112, 7635–7638 (2015).
[Crossref]

H. Xu, B. Zhang, T. Yu, G. Barbastathis, and H. Sun, “Dielectric waveguide bending adapter with ideal transmission: practical design strategy of area-preserving affine transformation optics,” J. Opt. Soc. Am. B 29, 1287–1290 (2012).
[Crossref]

Sun, X.

J. Cao, L. Zhang, S. Yan, and X. Sun, “Reflectionless design of optical elements using impedance-tunable transformation optics,” Appl. Phys. Lett. 104, 191102 (2014).
[Crossref]

Tang, X.

Taylor, A. M.

E. W. Max Born, A. B. Bhatia, P. C. Clemmow, D. Gabor, A. R. Stokes, A. M. Taylor, P. A. Wayman, and W. L. Wilcock, “Optics of crystals,” in Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999), pp. 837–841, Chap. 15.

Wang, H.

H. Wang, Y. Deng, B. Zheng, R. Li, Y. Jiang, S. Dehdashti, Z. Xu, and H. Chen, “Panoramic lens designed with transformation optics,” Sci. Rep. 7, 40083 (2017).
[Crossref]

C. Qian, R. Li, Y. Jiang, B. Zheng, H. Wang, Z. Xu, and H. Chen, “Transient response of a signal through a dispersive invisibility cloak,” Opt. Lett. 41, 4911–4914 (2016).
[Crossref]

Wang, X.

L. Huang, X. Chen, B. Ni, G. Li, X. Wang, Z. Li, and W. Lu, “A general transformation for compact waveguide coupler by using homogeneous media,” Photonics Nanostruct. Fundam. Appl. 11, 115–122 (2013).
[Crossref]

Wayman, P. A.

E. W. Max Born, A. B. Bhatia, P. C. Clemmow, D. Gabor, A. R. Stokes, A. M. Taylor, P. A. Wayman, and W. L. Wilcock, “Optics of crystals,” in Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999), pp. 837–841, Chap. 15.

Wei, Y.

Y. Wei, Y. Min, and Q. Min, “Necessary and sufficient conditions for reflectionless transformation media in an isotropic and homogenous background,” arXiv:0806.3231 (2008).

Werner, D. H.

Wilcock, W. L.

E. W. Max Born, A. B. Bhatia, P. C. Clemmow, D. Gabor, A. R. Stokes, A. M. Taylor, P. A. Wayman, and W. L. Wilcock, “Optics of crystals,” in Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999), pp. 837–841, Chap. 15.

Wu, Z.

Xie, L.

J. Zhou, M. Li, L. Xie, and D. Liu, “Design of a new kind of polarization splitter based on transformation optics,” Optik 122, 1672–1675 (2011).
[Crossref]

Xu, H.

S. Xu, H. Xu, H. Gao, Y. Jiang, F. Yu, J. D. Joannopoulos, M. Soljačić, H. Chen, H. Sun, and B. Zhang, “Broadband surface-wave transformation cloak,” Proc. Natl. Acad. Sci. USA 112, 7635–7638 (2015).
[Crossref]

H. Xu, B. Zhang, T. Yu, G. Barbastathis, and H. Sun, “Dielectric waveguide bending adapter with ideal transmission: practical design strategy of area-preserving affine transformation optics,” J. Opt. Soc. Am. B 29, 1287–1290 (2012).
[Crossref]

Xu, S.

S. Xu, H. Xu, H. Gao, Y. Jiang, F. Yu, J. D. Joannopoulos, M. Soljačić, H. Chen, H. Sun, and B. Zhang, “Broadband surface-wave transformation cloak,” Proc. Natl. Acad. Sci. USA 112, 7635–7638 (2015).
[Crossref]

Xu, Y. L.

Xu, Z.

H. Wang, Y. Deng, B. Zheng, R. Li, Y. Jiang, S. Dehdashti, Z. Xu, and H. Chen, “Panoramic lens designed with transformation optics,” Sci. Rep. 7, 40083 (2017).
[Crossref]

C. Qian, R. Li, Y. Jiang, B. Zheng, H. Wang, Z. Xu, and H. Chen, “Transient response of a signal through a dispersive invisibility cloak,” Opt. Lett. 41, 4911–4914 (2016).
[Crossref]

Xuan, L.

W. Yicheng, H. Chengdong, W. Yuzhuo, L. Xuan, and Z. Jing, “Controlling the wave propagation through the medium designed by linear coordinate transformation,” Eur. J. Phys. 36, 015006 (2015).

Xuejun, Z.

W. Yan, Z. Xuejun, and Y. Jinkui, “Reflection and refraction of light at the interface of a uniaxial bicrystal,” Europhys. Lett. 72, 830–836 (2005).
[Crossref]

Yan, S.

J. Cao, L. Zhang, S. Yan, and X. Sun, “Reflectionless design of optical elements using impedance-tunable transformation optics,” Appl. Phys. Lett. 104, 191102 (2014).
[Crossref]

Yan, W.

W. Yan, Z. Xuejun, and Y. Jinkui, “Reflection and refraction of light at the interface of a uniaxial bicrystal,” Europhys. Lett. 72, 830–836 (2005).
[Crossref]

Yang, Y.

Y. Yang, H. Chen, F. Yu, E. Li, and H. Chen, “A full-parameter, broadband, homogeneous, and compact waveguide coupler designed with transformation optics,” IEEE Antennas Wireless Propag. Lett. 14, 634–637 (2015).
[Crossref]

Yicheng, W.

W. Yicheng, H. Chengdong, W. Yuzhuo, L. Xuan, and Z. Jing, “Controlling the wave propagation through the medium designed by linear coordinate transformation,” Eur. J. Phys. 36, 015006 (2015).

Yu, F.

Y. Yang, H. Chen, F. Yu, E. Li, and H. Chen, “A full-parameter, broadband, homogeneous, and compact waveguide coupler designed with transformation optics,” IEEE Antennas Wireless Propag. Lett. 14, 634–637 (2015).
[Crossref]

S. Xu, H. Xu, H. Gao, Y. Jiang, F. Yu, J. D. Joannopoulos, M. Soljačić, H. Chen, H. Sun, and B. Zhang, “Broadband surface-wave transformation cloak,” Proc. Natl. Acad. Sci. USA 112, 7635–7638 (2015).
[Crossref]

Yu, G. X.

G. X. Yu, W. X. Jiang, and T. J. Cui, “Beam deflection and splitting using transformation optics,” Central Eur. J. Phys. 9, 183–188 (2011).
[Crossref]

Yu, T.

Yuzhuo, W.

W. Yicheng, H. Chengdong, W. Yuzhuo, L. Xuan, and Z. Jing, “Controlling the wave propagation through the medium designed by linear coordinate transformation,” Eur. J. Phys. 36, 015006 (2015).

Zhang, B.

S. Xu, H. Xu, H. Gao, Y. Jiang, F. Yu, J. D. Joannopoulos, M. Soljačić, H. Chen, H. Sun, and B. Zhang, “Broadband surface-wave transformation cloak,” Proc. Natl. Acad. Sci. USA 112, 7635–7638 (2015).
[Crossref]

H. Xu, B. Zhang, T. Yu, G. Barbastathis, and H. Sun, “Dielectric waveguide bending adapter with ideal transmission: practical design strategy of area-preserving affine transformation optics,” J. Opt. Soc. Am. B 29, 1287–1290 (2012).
[Crossref]

Zhang, L.

J. Cao, L. Zhang, S. Yan, and X. Sun, “Reflectionless design of optical elements using impedance-tunable transformation optics,” Appl. Phys. Lett. 104, 191102 (2014).
[Crossref]

Zhang, X.

B. Zheng, H. A. Madni, R. Hao, X. Zhang, X. Liu, E. Li, and H. Chen, “Concealing arbitrary objects remotely with multi-folded transformation optics,” Light Sci. Appl. 5, e16177 (2016).
[Crossref]

Zheng, B.

H. Wang, Y. Deng, B. Zheng, R. Li, Y. Jiang, S. Dehdashti, Z. Xu, and H. Chen, “Panoramic lens designed with transformation optics,” Sci. Rep. 7, 40083 (2017).
[Crossref]

B. Zheng, H. A. Madni, R. Hao, X. Zhang, X. Liu, E. Li, and H. Chen, “Concealing arbitrary objects remotely with multi-folded transformation optics,” Light Sci. Appl. 5, e16177 (2016).
[Crossref]

C. Qian, R. Li, Y. Jiang, B. Zheng, H. Wang, Z. Xu, and H. Chen, “Transient response of a signal through a dispersive invisibility cloak,” Opt. Lett. 41, 4911–4914 (2016).
[Crossref]

Zhou, J.

J. Zhou, M. Li, L. Xie, and D. Liu, “Design of a new kind of polarization splitter based on transformation optics,” Optik 122, 1672–1675 (2011).
[Crossref]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[Crossref]

Zouhdi, S.

Appl. Phys. Lett. (3)

W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91, 111105 (2007).
[Crossref]

H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90, 241105 (2007).
[Crossref]

J. Cao, L. Zhang, S. Yan, and X. Sun, “Reflectionless design of optical elements using impedance-tunable transformation optics,” Appl. Phys. Lett. 104, 191102 (2014).
[Crossref]

Central Eur. J. Phys. (1)

G. X. Yu, W. X. Jiang, and T. J. Cui, “Beam deflection and splitting using transformation optics,” Central Eur. J. Phys. 9, 183–188 (2011).
[Crossref]

Eur. J. Phys. (1)

W. Yicheng, H. Chengdong, W. Yuzhuo, L. Xuan, and Z. Jing, “Controlling the wave propagation through the medium designed by linear coordinate transformation,” Eur. J. Phys. 36, 015006 (2015).

Europhys. Lett. (1)

W. Yan, Z. Xuejun, and Y. Jinkui, “Reflection and refraction of light at the interface of a uniaxial bicrystal,” Europhys. Lett. 72, 830–836 (2005).
[Crossref]

IEEE Antennas Wireless Propag. Lett. (1)

Y. Yang, H. Chen, F. Yu, E. Li, and H. Chen, “A full-parameter, broadband, homogeneous, and compact waveguide coupler designed with transformation optics,” IEEE Antennas Wireless Propag. Lett. 14, 634–637 (2015).
[Crossref]

J. Opt. (2)

N. Atefeh and S.-S. Mehrdad, “Design of an optical spatial interferometer with transformation optics,” J. Opt. 17, 105103 (2015).
[Crossref]

G. Gurkan and G. Anthony, “A physical explanation for the all-angle reflectionless property of transformation optics designs,” J. Opt. 18, 044020 (2016).
[Crossref]

J. Opt. Soc. Am. B (1)

Light Sci. Appl. (1)

B. Zheng, H. A. Madni, R. Hao, X. Zhang, X. Liu, E. Li, and H. Chen, “Concealing arbitrary objects remotely with multi-folded transformation optics,” Light Sci. Appl. 5, e16177 (2016).
[Crossref]

New J. Phys. (1)

K. Do-Hoon and H. W. Douglas, “Transformation optical designs for wave collimators, flat lenses and right-angle bends,” New J. Phys. 10, 115023 (2008).
[Crossref]

Opt. Express (5)

Opt. Lett. (3)

Optik (1)

J. Zhou, M. Li, L. Xie, and D. Liu, “Design of a new kind of polarization splitter based on transformation optics,” Optik 122, 1672–1675 (2011).
[Crossref]

Photonics Nanostruct. Fundam. Appl. (2)

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6, 87–95 (2008).
[Crossref]

L. Huang, X. Chen, B. Ni, G. Li, X. Wang, Z. Li, and W. Lu, “A general transformation for compact waveguide coupler by using homogeneous media,” Photonics Nanostruct. Fundam. Appl. 11, 115–122 (2013).
[Crossref]

Phys. Rev. B (1)

Z. Liu, Z. Lin, and S. T. Chui, “Negative refraction and omnidirectional total transmission at a planar interface associated with a uniaxial medium,” Phys. Rev. B 69, 115402 (2004).
[Crossref]

Phys. Rev. Lett. (3)

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101, 203901 (2008).
[Crossref]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[Crossref]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100, 063903 (2008).
[Crossref]

Proc. Natl. Acad. Sci. USA (1)

S. Xu, H. Xu, H. Gao, Y. Jiang, F. Yu, J. D. Joannopoulos, M. Soljačić, H. Chen, H. Sun, and B. Zhang, “Broadband surface-wave transformation cloak,” Proc. Natl. Acad. Sci. USA 112, 7635–7638 (2015).
[Crossref]

Sci. Rep. (1)

H. Wang, Y. Deng, B. Zheng, R. Li, Y. Jiang, S. Dehdashti, Z. Xu, and H. Chen, “Panoramic lens designed with transformation optics,” Sci. Rep. 7, 40083 (2017).
[Crossref]

Science (4)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[Crossref]

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
[Crossref]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[Crossref]

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[Crossref]

Other (2)

E. W. Max Born, A. B. Bhatia, P. C. Clemmow, D. Gabor, A. R. Stokes, A. M. Taylor, P. A. Wayman, and W. L. Wilcock, “Optics of crystals,” in Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999), pp. 837–841, Chap. 15.

Y. Wei, Y. Min, and Q. Min, “Necessary and sufficient conditions for reflectionless transformation media in an isotropic and homogenous background,” arXiv:0806.3231 (2008).

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Figures (10)

Fig. 1.
Fig. 1.

Virtual space (ABC) and physical space (ABC) triangles of the general reflectionless polarization splitter.

Fig. 2.
Fig. 2.

Virtual space (ABC) and physical space (ABC) triangles of the general non-magnetic polarization deflector.

Fig. 3.
Fig. 3.

Virtual space (ABC) and physical space (ABC) triangles of the minimum anisotropy deflector design.

Fig. 4.
Fig. 4.

Polarization splitter that provides lateral shift with minimum anisotropy.

Fig. 5.
Fig. 5.

Anisotropy factor of the non-magnetic designs versus β.

Fig. 6.
Fig. 6.

Polarization splitter with deflection angle of β=π/4  rad. (a) Normalized real part of Hz, (b) normalized real part of Ez, (c) normalized magnetic fields magnitude, (d) normalized Poynting vector magnitude along the two lines perpendicular to the propagation direction of the incident and the transmitted waves.

Fig. 7.
Fig. 7.

Non-magnetic polarization deflectors with minimum anisotropy. (a), (c), (e) Normalized real part of Hz; (b), (d), (f) normalized magnitude of Hz; (g), (h), (i) normalized Poynting vector magnitude along the two lines perpendicular to the propagation direction of the incident and the transmitted waves, for deflection angles of π/2, π/4 and π/2  rad, respectively.

Fig. 8.
Fig. 8.

Non-magnetic polarization splitters that provide lateral shift with minimum anisotropy. (a), (c) Normalized real part of Hz; (b), (d) normalized magnitude of Hz; (e), (f) normalized Poynting vector magnitude along the two lines perpendicular to the propagation direction of the incident and the transmitted waves, of the first case (W=D=2L) and the second case (2W=D=2L), respectively.

Fig. 9.
Fig. 9.

Dielectric constants of the layers versus the fill factor f for the π/4  rad deflector with minimum anisotropy.

Fig. 10.
Fig. 10.

Equivalent layered structure of the π/4  rad polarization deflector. (a) Normalized real part of Hz, (b) normalized magnitude of Hz, (c) normalized Poynting vector magnitude along the two lines perpendicular to the propagation direction of the incident and the transmitted waves.

Equations (14)

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ε=Jε0JT/det(J),μ=Jμ0JT/det(J),E=(JT)1E,H=(JT)1H.
x=ax+by+ey=cx+dy+fz=z}J=(ab0cd0001).
[abe]=[xAyA1xByB1xCyC1]1[xAxBxC],[cdf]=[xAyA1xByB1xCyC1]1[yAyByC],
J=(Q00P10001)εr=μr=(QP0P(P2+1)/Q0001/Q),Q=sin(α+β)/sinα,P=cos(α+β)/sinαcotα.
J=(Q00P1/Q0001)εr=(Q2PQ0PQP2+1/Q20001),μr=1,Q=sin(α+β)/sinα,P=cos(α+β)/sinαcosα/sin(α+β).
γ=(εrxx+εryy(εrxx+εryy)24εrxx+εryy+(εrxx+εryy)24)1/2.
εrxy=(Q2PQPQP2+1/Q2)εp1+εp2=P2+Q2+1/Q2,
(εp1+εp2)α=2csc(α)3csc(α+β)3sin(β)2sin(2α+β)=0α=π/2β/2,2(εp1+εp2)α2=csc(α)4csc(α+β)4sin(β)2×(4cos(2α)cos(2(α+β))2cos(2(2α+β)))>0.
εr=(12tan(β/2)02tan(β/2)1+4tan2(β/2)0001),μr=1.
εp1=ε1ε2/((1f)ε1+fε2),εp2=εp3=fε1+(1f)ε2,f=d1/(d1+d2),
εr=(10.8300.831.680002.24){εp1=0.45εp2=εp3=2.24φ=33.8°.
εrABC=(εrxxεrxy0εryxεryy0001).
εrABC=RεrABCRT,R=(cosθ0sinθ010sinθ0cosθ),εrABC=(εrxxεrxy0εryxεryy0001),
εrxxL=εrxxR,εrxxLεryyLεrxyLεryxL=εrxxRεryyRεrxyRεryxR.

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