Abstract

We propose a novel optical transformation to design homogeneous isotropic bends connecting multiple waveguides of different cross sections which can ideally tunnel the wave along any directions through multiple waveguides. First, the general expressions of homogeneous and anisotropic parameters in the bend region are derived. Second, the anisotropic material can be replaced by only two kinds of isotropic materials and they can be easily arranged in planarly stratified configuration. Finally, an arbitrary bender with homogeneous and isotropic materials is constructed, which can bend electromagnetic wave to any desired directions. To achieve the utmost aim, an advanced method is proposed to design nonmagnetic, isotropic and homogeneous bends that can bend waves along arbitrary directions. More importantly, all of the proposed bender has compact shape due to all flat boundaries, while the wave can still be perfectly tunneled without mode distortion. Numerical results validate these functionalities, which make the bend much easier in fabrication and application.

© 2011 OSA

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  4. H. Y. Chen, B. Hou, S. Y. Chen, X. Y. Ao, W. J. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. 102(18), 183903 (2009).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  19. A. Novitsky, C. W. Qiu, and S. Zouhdi, “Transformation-based spherical cloaks designed by an implicit transformation-independent method: theory and optimization,” N. J. Phys. 11(11), 113001 (2009).
    [CrossRef]

2010

2009

C. W. Qiu, L. Hu, X. F. Xu, and Y. J. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(4), 047602 (2009).
[CrossRef] [PubMed]

A. Novitsky, C. W. Qiu, and S. Zouhdi, “Transformation-based spherical cloaks designed by an implicit transformation-independent method: theory and optimization,” N. J. Phys. 11(11), 113001 (2009).
[CrossRef]

B. Vasić, G. Isic, R. Gajic, and K. Hingerl, “Coordinate transformation based design of confined metamaterial structures,” Phys. Rev. B 79(8), 085103 (2009).
[CrossRef]

X. J. Wu, Z. F. Lin, H. Y. Chen, and C. T. Chan, “Transformation optical design of a bending waveguide by use of isotropic materials,” Appl. Opt. 48(31), G101–G105 (2009).
[CrossRef] [PubMed]

Z. L. Mei and T. J. Cui, “Arbitrary bending of electromagnetic waves using isotropic materials,” J. Appl. Phys. 105(10), 104913 (2009).
[CrossRef]

Y. Lai, H. Y. Chen, Z. Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102(9), 093901 (2009).
[CrossRef] [PubMed]

H. Y. Chen, B. Hou, S. Y. Chen, X. Y. Ao, W. J. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. 102(18), 183903 (2009).
[CrossRef] [PubMed]

2008

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,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[CrossRef]

M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B 77(3), 035122 (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(15), 11555–11567 (2008).
[CrossRef] [PubMed]

W. X. Jiang, T. J. Cui, X. Y. Zhou, X. M. Yang, and Q. Cheng, “Arbitrary bending of electromagnetic waves using realizable inhomogeneous and anisotropic materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(6), 066607 (2008).
[CrossRef] [PubMed]

J. T. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bend waveguides,” J. Appl. Phys. 104(1), 014502 (2008).
[CrossRef]

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93(25), 251111 (2008).
[CrossRef]

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[CrossRef] [PubMed]

2006

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

2000

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

Ao, X. Y.

H. Y. Chen, B. Hou, S. Y. Chen, X. Y. Ao, W. J. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. 102(18), 183903 (2009).
[CrossRef] [PubMed]

Burokur, S. N.

Chan, C. T.

X. J. Wu, Z. F. Lin, H. Y. Chen, and C. T. Chan, “Transformation optical design of a bending waveguide by use of isotropic materials,” Appl. Opt. 48(31), G101–G105 (2009).
[CrossRef] [PubMed]

H. Y. Chen, B. Hou, S. Y. Chen, X. Y. Ao, W. J. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. 102(18), 183903 (2009).
[CrossRef] [PubMed]

Y. Lai, H. Y. Chen, Z. Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102(9), 093901 (2009).
[CrossRef] [PubMed]

Chen, H.

J. T. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bend waveguides,” J. Appl. Phys. 104(1), 014502 (2008).
[CrossRef]

Chen, H. Y.

H. Y. Chen, B. Hou, S. Y. Chen, X. Y. Ao, W. J. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. 102(18), 183903 (2009).
[CrossRef] [PubMed]

Y. Lai, H. Y. Chen, Z. Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102(9), 093901 (2009).
[CrossRef] [PubMed]

X. J. Wu, Z. F. Lin, H. Y. Chen, and C. T. Chan, “Transformation optical design of a bending waveguide by use of isotropic materials,” Appl. Opt. 48(31), G101–G105 (2009).
[CrossRef] [PubMed]

Chen, L. X.

W. Q. Ding, D. H. Tang, Y. Liu, L. X. Chen, and X. D. Sun, “Arbitrary waveguide bends using isotropic and homogeneous metamaterial,” Appl. Phys. Lett. 96(4), 041102 (2010).
[CrossRef]

Chen, S. Y.

H. Y. Chen, B. Hou, S. Y. Chen, X. Y. Ao, W. J. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. 102(18), 183903 (2009).
[CrossRef] [PubMed]

Cheng, Q.

W. X. Jiang, T. J. Cui, X. Y. Zhou, X. M. Yang, and Q. Cheng, “Arbitrary bending of electromagnetic waves using realizable inhomogeneous and anisotropic materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(6), 066607 (2008).
[CrossRef] [PubMed]

Cui, T. J.

Z. L. Mei and T. J. Cui, “Arbitrary bending of electromagnetic waves using isotropic materials,” J. Appl. Phys. 105(10), 104913 (2009).
[CrossRef]

W. X. Jiang, T. J. Cui, X. Y. Zhou, X. M. Yang, and Q. Cheng, “Arbitrary bending of electromagnetic waves using realizable inhomogeneous and anisotropic materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(6), 066607 (2008).
[CrossRef] [PubMed]

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,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[CrossRef]

de Lustrac, A.

Ding, W. Q.

W. Q. Ding, D. H. Tang, Y. Liu, L. X. Chen, and X. D. Sun, “Arbitrary waveguide bends using isotropic and homogeneous metamaterial,” Appl. Phys. Lett. 96(4), 041102 (2010).
[CrossRef]

Feng, Y. J.

C. W. Qiu, L. Hu, X. F. Xu, and Y. J. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(4), 047602 (2009).
[CrossRef] [PubMed]

Gajic, R.

B. Vasić, G. Isic, R. Gajic, and K. Hingerl, “Coordinate transformation based design of confined metamaterial structures,” Phys. Rev. B 79(8), 085103 (2009).
[CrossRef]

Hingerl, K.

B. Vasić, G. Isic, R. Gajic, and K. Hingerl, “Coordinate transformation based design of confined metamaterial structures,” Phys. Rev. B 79(8), 085103 (2009).
[CrossRef]

Hou, B.

H. Y. Chen, B. Hou, S. Y. Chen, X. Y. Ao, W. J. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. 102(18), 183903 (2009).
[CrossRef] [PubMed]

Hu, L.

C. W. Qiu, L. Hu, X. F. Xu, and Y. J. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(4), 047602 (2009).
[CrossRef] [PubMed]

Huangfu, J. T.

J. T. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bend waveguides,” J. Appl. Phys. 104(1), 014502 (2008).
[CrossRef]

Isic, G.

B. Vasić, G. Isic, R. Gajic, and K. Hingerl, “Coordinate transformation based design of confined metamaterial structures,” Phys. Rev. B 79(8), 085103 (2009).
[CrossRef]

Jiang, W. X.

W. X. Jiang, T. J. Cui, X. Y. Zhou, X. M. Yang, and Q. Cheng, “Arbitrary bending of electromagnetic waves using realizable inhomogeneous and anisotropic materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(6), 066607 (2008).
[CrossRef] [PubMed]

Kong, F.

J. T. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bend waveguides,” J. Appl. Phys. 104(1), 014502 (2008).
[CrossRef]

Kong, J. A.

J. T. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bend waveguides,” J. Appl. Phys. 104(1), 014502 (2008).
[CrossRef]

Lai, Y.

Y. Lai, H. Y. Chen, Z. Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102(9), 093901 (2009).
[CrossRef] [PubMed]

Li, J.

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[CrossRef] [PubMed]

Li, L. W.

Lin, Z. F.

Liu, Y.

W. Q. Ding, D. H. Tang, Y. Liu, L. X. Chen, and X. D. Sun, “Arbitrary waveguide bends using isotropic and homogeneous metamaterial,” Appl. Phys. Lett. 96(4), 041102 (2010).
[CrossRef]

Mei, Z. L.

Z. L. Mei and T. J. Cui, “Arbitrary bending of electromagnetic waves using isotropic materials,” J. Appl. Phys. 105(10), 104913 (2009).
[CrossRef]

Meng, F. Y.

Novitsky, A.

A. Novitsky, C. W. Qiu, and S. Zouhdi, “Transformation-based spherical cloaks designed by an implicit transformation-independent method: theory and optimization,” N. J. Phys. 11(11), 113001 (2009).
[CrossRef]

Pendry, J. B.

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93(25), 251111 (2008).
[CrossRef]

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[CrossRef] [PubMed]

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(15), 11555–11567 (2008).
[CrossRef] [PubMed]

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,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

Psaltis, D.

M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B 77(3), 035122 (2008).
[CrossRef]

Qiu, C. W.

A. Novitsky, C. W. Qiu, and S. Zouhdi, “Transformation-based spherical cloaks designed by an implicit transformation-independent method: theory and optimization,” N. J. Phys. 11(11), 113001 (2009).
[CrossRef]

C. W. Qiu, L. Hu, X. F. Xu, and Y. J. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(4), 047602 (2009).
[CrossRef] [PubMed]

Rahm, M.

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93(25), 251111 (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(15), 11555–11567 (2008).
[CrossRef] [PubMed]

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,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[CrossRef]

Ran, L.

J. T. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bend waveguides,” J. Appl. Phys. 104(1), 014502 (2008).
[CrossRef]

Roberts, D. A.

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93(25), 251111 (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(15), 11555–11567 (2008).
[CrossRef] [PubMed]

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,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[CrossRef]

Schurig, D.

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,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

Smith, D. R.

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,” Photon. Nanostruct. Fundam. Appl. 6(1), 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(15), 11555–11567 (2008).
[CrossRef] [PubMed]

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93(25), 251111 (2008).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

Sun, X. D.

W. Q. Ding, D. H. Tang, Y. Liu, L. X. Chen, and X. D. Sun, “Arbitrary waveguide bends using isotropic and homogeneous metamaterial,” Appl. Phys. Lett. 96(4), 041102 (2010).
[CrossRef]

Tang, D. H.

W. Q. Ding, D. H. Tang, Y. Liu, L. X. Chen, and X. D. Sun, “Arbitrary waveguide bends using isotropic and homogeneous metamaterial,” Appl. Phys. Lett. 96(4), 041102 (2010).
[CrossRef]

Tichit, P. H.

Tsang, M.

M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B 77(3), 035122 (2008).
[CrossRef]

Vasic, B.

B. Vasić, G. Isic, R. Gajic, and K. Hingerl, “Coordinate transformation based design of confined metamaterial structures,” Phys. Rev. B 79(8), 085103 (2009).
[CrossRef]

Wang, D.

J. T. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bend waveguides,” J. Appl. Phys. 104(1), 014502 (2008).
[CrossRef]

Wen, W. J.

H. Y. Chen, B. Hou, S. Y. Chen, X. Y. Ao, W. J. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. 102(18), 183903 (2009).
[CrossRef] [PubMed]

Wu, B.-I.

J. T. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bend waveguides,” J. Appl. Phys. 104(1), 014502 (2008).
[CrossRef]

Wu, Q.

Wu, X. J.

Xi, S.

J. T. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bend waveguides,” J. Appl. Phys. 104(1), 014502 (2008).
[CrossRef]

Xu, X. F.

C. W. Qiu, L. Hu, X. F. Xu, and Y. J. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(4), 047602 (2009).
[CrossRef] [PubMed]

Yang, X. M.

W. X. Jiang, T. J. Cui, X. Y. Zhou, X. M. Yang, and Q. Cheng, “Arbitrary bending of electromagnetic waves using realizable inhomogeneous and anisotropic materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(6), 066607 (2008).
[CrossRef] [PubMed]

Zhang, J.

J. T. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bend waveguides,” J. Appl. Phys. 104(1), 014502 (2008).
[CrossRef]

Zhang, K.

Zhang, Z. Q.

Y. Lai, H. Y. Chen, Z. Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102(9), 093901 (2009).
[CrossRef] [PubMed]

Zhou, X. Y.

W. X. Jiang, T. J. Cui, X. Y. Zhou, X. M. Yang, and Q. Cheng, “Arbitrary bending of electromagnetic waves using realizable inhomogeneous and anisotropic materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(6), 066607 (2008).
[CrossRef] [PubMed]

Zouhdi, S.

A. Novitsky, C. W. Qiu, and S. Zouhdi, “Transformation-based spherical cloaks designed by an implicit transformation-independent method: theory and optimization,” N. J. Phys. 11(11), 113001 (2009).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93(25), 251111 (2008).
[CrossRef]

W. Q. Ding, D. H. Tang, Y. Liu, L. X. Chen, and X. D. Sun, “Arbitrary waveguide bends using isotropic and homogeneous metamaterial,” Appl. Phys. Lett. 96(4), 041102 (2010).
[CrossRef]

J. Appl. Phys.

Z. L. Mei and T. J. Cui, “Arbitrary bending of electromagnetic waves using isotropic materials,” J. Appl. Phys. 105(10), 104913 (2009).
[CrossRef]

J. T. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bend waveguides,” J. Appl. Phys. 104(1), 014502 (2008).
[CrossRef]

N. J. Phys.

A. Novitsky, C. W. Qiu, and S. Zouhdi, “Transformation-based spherical cloaks designed by an implicit transformation-independent method: theory and optimization,” N. J. Phys. 11(11), 113001 (2009).
[CrossRef]

Opt. Express

Photon. Nanostruct. Fundam. Appl.

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,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[CrossRef]

Phys. Rev. B

M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B 77(3), 035122 (2008).
[CrossRef]

B. Vasić, G. Isic, R. Gajic, and K. Hingerl, “Coordinate transformation based design of confined metamaterial structures,” Phys. Rev. B 79(8), 085103 (2009).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

C. W. Qiu, L. Hu, X. F. Xu, and Y. J. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(4), 047602 (2009).
[CrossRef] [PubMed]

W. X. Jiang, T. J. Cui, X. Y. Zhou, X. M. Yang, and Q. Cheng, “Arbitrary bending of electromagnetic waves using realizable inhomogeneous and anisotropic materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(6), 066607 (2008).
[CrossRef] [PubMed]

Phys. Rev. Lett.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[CrossRef] [PubMed]

Y. Lai, H. Y. Chen, Z. Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102(9), 093901 (2009).
[CrossRef] [PubMed]

H. Y. Chen, B. Hou, S. Y. Chen, X. Y. Ao, W. J. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. 102(18), 183903 (2009).
[CrossRef] [PubMed]

Science

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

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Figures (8)

Fig. 1
Fig. 1

(Color online). (a) The schematic illustration of the design of a homogeneous waveguide bend. (b) The layered structure includes two kinds of materials ε i A and ε i B (i = I, II), which is used to fill the bending region to construct the isotropic bend with all PEC (perfect electric conductor) boundaries.

Fig. 2
Fig. 2

(Color online). The magnetic field distribution of the designed bend using homogeneous materials for a = 10 cm, with or without anisotropy. (a) a vacuum bend. (b) ideal anisotropic transformation media filled-bend. (c) layered isotropic bend with θ I = 137 and θ II = 122 . (d) The average power outflow at port 2. (e) The electric field distribution of the dominant mode TE10 in the extruded bend with 0.04 m thickness along z direction.

Fig. 3
Fig. 3

(Color online). The magnetic field distribution of the bend designed using homogeneous materials for a = 10 cm and b = 2 cm, with or without anisotropy. (a) a vacuum bend. (b) ideal anisotropic transformation media filled in the bend. (c-e) Layered isotropic materials filled in the bend with θ I = 115 and θ II = 122 . (c) M = 10, (d) M = 20, and (e) M = 40. (f) The average power outflow at port 2.

Fig. 4
Fig. 4

(Color online). Normalized electric fields distribution inside the waveguide bends. Two waveguides of identical cross section with a = 10 cm: (a) bending angle 45 , (b) bending angle 135 . Two waveguides of different cross sections with a = 10 cm and b = 2 cm: (c) bending angle 45 , (d) bending angle 135 .

Fig. 5
Fig. 5

(Color online). Normalized electric fields distribution inside the waveguide bends with bending angle 180 . Two waveguides of equal width with a = 10 cm: (a) a vacuum bend. (b) transformation media filled in the bend. Two waveguides of different width with a = 10 cm and b = 2 cm: (c) a vacuum bend. (d) transformation media filled in the bend.

Fig. 6
Fig. 6

(Color online). A collar-shaped waveguide bending system with two 135 compact bends when a = 10 cm, b = 2 cm and θ 0 = 45 . Normalized electric field distribution of the system filled with (a) air; and (b) transformation materials. Normalized average power flow of the system filled with (c) air and (d) transformation materials. (e) Schematic diagram of designing an extremely compact bending structure in (a) by transforming triangles ABC and CBD to ABC' and C'BD', respectively. (f) The average outflow power at port 2 in (b).

Fig. 7
Fig. 7

(Color online). (a) The schematic illustration of coordinate transformation in the design of advanced nonmagnetic bend by transforming ABD and CBD to ABD’ and C’BD’, respectively. (b) The magnetic field distribution of a vacuum bend with a = 10 cm and θ = 60 . (c) The magnetic field distribution of the bend in (b) filled with nonmagnetic, homogeneous and anisotropic transformation material. (d) The magnetic field distribution of the bend in (b) filled with layered isotropic dielectric (M = 10) and θ 0 = 150 . The embedded figure in (d) illustrates the distribution of constitutive parameters in transformed region.

Fig. 8
Fig. 8

(Color online). An isotropic and nonmagnetic bending system with two 60 dielectric bends in Fig. 7(d) when a = 10 cm. Magnetic field distribution of the system filled with (a) air; and (b) transformation materials. The embedded figure in (b) illustrates the arrangement of constitutive parameters in transformed regions.

Equations (9)

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x = a 11 x + b 11 y + c 11 , y = a 12 x + b 12 y + c 12 , z = z
[ a 11 b 11 c 11 ] = [ x B y B 1 x C y C 1 x D y D 1 ] 1 [ x B x C x D ]     and     [ a 12 b 12 c 12 ] = [ x B y B 1 x C y C 1 x D y D 1 ] 1 [ y B y C y D ] .
ε I = μ I = Λ 1 · Λ 1 T / det ( Λ 1 )
x = a 21 x + b 21 y + c 21 , y = a 22 x + b 22 y + c 22 , z = z
[ a 21 b 21 c 21 ] = [ x A y A 1 x B y B 1 x D y D 1 ] 1 [ x A x B x D ' ]     and     [ a 22 b 22 c 22 ] = [ x A y A 1 x B y B 1 x D y D 1 ] 1 [ y A y B y D ' ] .
ε II = μ II = Λ 2 · Λ 2 T / det ( Λ 2 )
ε i = diag [ ζ i x , ζ i y ,     ζ i z ]
tan ( 2 θ i ) = 2 ε i x y / ( ε i x x ε i y y )
ε i A,   B = ζ i x ± ( ζ i x ) 2 ζ i x ζ i y

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