Abstract

We propose what we believe is a novel method to design waveguide bends for metallic waveguides with arbitrary bending angles. The proposed method is based on a new theoretical branch from transformation optics that is referred as to optic surface transformation. Compared with waveguide bends designed by traditional transformation optics, the design process of our method can be made in a graphical way that is very simple and convenient. To realize any waveguide bend designed by the method proposed in this study, one needs only one homogeneous material, i.e., an optic-null medium (even if the bending angles are different for various cases). After some reductions, we find that the optic-null media here can be approximately realized by some anisotropic zero refractive index materials. 2D numerical simulations verify the performance of the designed waveguide bends. The design principle can be extended to the 3D case.

© 2018 Optical Society of America

Full Article  |  PDF Article
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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2017 (1)

F. Sun, B. Zheng, H. Chen, W. Jiang, S. Guo, Y. Liu, Y. Ma, and S. He, “Transformation optics: from classic theory and applications to its new branches,” Laser Photon. Rev. 11, 1700034 (2017).
[Crossref]

2016 (2)

F. Sun and S. He, “Optic-null space medium for cover-up cloaking without any negative refraction index materials,” Sci. Rep. 6, 29280 (2016).
[Crossref]

F. Sun and S. He, “Overlapping illusions by transformation optics without any negative refraction material,” Sci. Rep. 6, 19130 (2016).
[Crossref]

2015 (3)

F. Sun and S. He, “Optical surface transformation: changing the optical surface by homogeneous optic-null medium at will,” Sci. Rep. 5, 16032 (2015).
[Crossref]

F. Sun and S. He, “Homogenous optic-null medium performs as optical surface transformation,” Prog. Electromagn. Res. 151, 169–173 (2015).
[Crossref]

M. M. Sadeghi, S. Li, L. Xu, B. Hou, and H. Chen, “Transformation optics with Fabry–Pérot resonances,” Sci. Rep. 5, 8680 (2015).
[Crossref]

2014 (1)

J. Luo and Y. Lai, “Anisotropic zero-index waveguide with arbitrary shapes,” Sci. Rep. 4, 5875 (2014).
[Crossref]

2013 (6)

H. Xu, H. Sun, and B. Zhang, “Waveguide design and application with transformation optics,” Sci. China Inf. Sci. 56, 1–11 (2013).
[Crossref]

J. S. Mei, Q. Wu, and K. Zhang, “Design of electromagnetic refractor and waveguide bends using complementary medium,” Physica B 426, 150–154 (2013).
[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,” Photon. Nanostr. Fundam. Appl. 11, 115–122 (2013).
[Crossref]

Y. Wang, D. H. Zhang, J. Wang, F. Qin, D. Li, and Z. Xu, “Design of sharp bends with transformation plasmonics,” Appl. Phys. A 112, 549–553 (2013).
[Crossref]

F. Sun, Y. G. Ma, X. Ge, and S. He, “Super-thin Mikaelian’s lens of small index as a beam compressor with an extremely high compression ratio,” Opt. Express 21, 7328–7336 (2013).
[Crossref]

Q. He, S. Xiao, X. Li, and L. Zhou, “Optic-null medium: realization and applications,” Opt. Express 21, 28948–28959 (2013).
[Crossref]

2012 (6)

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]

H. F. Ma, J. H. Shi, B. G. Cai, and T. J. Cui, “Total transmission and super reflection realized by anisotropic zero-index materials,” New J. Phys. 14, 123010 (2012).
[Crossref]

S. Xu, X. Cheng, S. Xi, R. Zhang, H. O. Moser, Z. Shen, Y. Xu, Z. Huang, X. Zhang, F. Yu, B. Zhang, and H. Chen, “Experimental demonstration of a free-space cylindrical cloak without superluminal propagation,” Phys. Rev. Lett. 109, 223903 (2012).
[Crossref]

T. Han, W. Ding, C. Qiu, and X. Tang, “All-dielectric tapered waveguide bender with homogeneous loading, arbitrary bending and simplified geometry,” J. Electromagn. Waves 26, 729–736 (2012).
[Crossref]

J. Luo, P. Xu, H. Chen, B. Hou, L. Gao, and Y. Lai, “Realizing almost perfect bending waveguides with anisotropic epsilon-near-zero metamaterials,” Appl. Phys. Lett. 100, 221903 (2012).
[Crossref]

H. F. Ma, J. H. Shi, W. X. Jiang, and T. J. Cui, “Experimental realization of bending waveguide using anisotropic zero-index materials,” Appl. Phys. Lett. 101, 253513 (2012).
[Crossref]

2011 (5)

A. V. Kildishev and V. M. Shalaev, “Transformation optics and metamaterials,” Phys. Usp. 54, 53–63 (2011).
[Crossref]

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10, 582–586 (2011).
[Crossref]

H. Chen, L. Huang, X. Cheng, and H. Wang, “Magnetic properties of metamaterial composed of closed rings,” Prog. Electromagn. Res. 115, 317–326 (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]

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]

2010 (1)

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9, 387–396 (2010).
[Crossref]

2009 (2)

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

N. I. Landy and W. J. Padilla, “Guiding light with conformal transformations,” Opt. Express 17, 14872–14879 (2009).
[Crossref]

2008 (5)

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100, 033903 (2008).
[Crossref]

R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100, 023903 (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, 251111 (2008).
[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 78, 066607 (2008).
[Crossref]

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

2007 (1)

2006 (3)

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]

M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using e-near-zero materials,” Phys. Rev. Lett. 97, 157403 (2006).
[Crossref]

2005 (1)

G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87, 131102 (2005).
[Crossref]

1998 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys. Condens. Matter 10, 4785–4809 (1998).
[Crossref]

1996 (1)

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[Crossref]

1986 (1)

Alù, A.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100, 033903 (2008).
[Crossref]

Barbastathis, G.

Cai, B. G.

H. F. Ma, J. H. Shi, B. G. Cai, and T. J. Cui, “Total transmission and super reflection realized by anisotropic zero-index materials,” New J. Phys. 14, 123010 (2012).
[Crossref]

Chan, C. T.

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10, 582–586 (2011).
[Crossref]

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9, 387–396 (2010).
[Crossref]

Chen, H.

F. Sun, B. Zheng, H. Chen, W. Jiang, S. Guo, Y. Liu, Y. Ma, and S. He, “Transformation optics: from classic theory and applications to its new branches,” Laser Photon. Rev. 11, 1700034 (2017).
[Crossref]

M. M. Sadeghi, S. Li, L. Xu, B. Hou, and H. Chen, “Transformation optics with Fabry–Pérot resonances,” Sci. Rep. 5, 8680 (2015).
[Crossref]

J. Luo, P. Xu, H. Chen, B. Hou, L. Gao, and Y. Lai, “Realizing almost perfect bending waveguides with anisotropic epsilon-near-zero metamaterials,” Appl. Phys. Lett. 100, 221903 (2012).
[Crossref]

S. Xu, X. Cheng, S. Xi, R. Zhang, H. O. Moser, Z. Shen, Y. Xu, Z. Huang, X. Zhang, F. Yu, B. Zhang, and H. Chen, “Experimental demonstration of a free-space cylindrical cloak without superluminal propagation,” Phys. Rev. Lett. 109, 223903 (2012).
[Crossref]

H. Chen, L. Huang, X. Cheng, and H. Wang, “Magnetic properties of metamaterial composed of closed rings,” Prog. Electromagn. Res. 115, 317–326 (2011).
[Crossref]

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9, 387–396 (2010).
[Crossref]

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

Chen, J. C.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[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,” Photon. Nanostr. Fundam. Appl. 11, 115–122 (2013).
[Crossref]

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 78, 066607 (2008).
[Crossref]

R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100, 023903 (2008).
[Crossref]

Cheng, X.

S. Xu, X. Cheng, S. Xi, R. Zhang, H. O. Moser, Z. Shen, Y. Xu, Z. Huang, X. Zhang, F. Yu, B. Zhang, and H. Chen, “Experimental demonstration of a free-space cylindrical cloak without superluminal propagation,” Phys. Rev. Lett. 109, 223903 (2012).
[Crossref]

H. Chen, L. Huang, X. Cheng, and H. Wang, “Magnetic properties of metamaterial composed of closed rings,” Prog. Electromagn. Res. 115, 317–326 (2011).
[Crossref]

Cui, T. J.

H. F. Ma, J. H. Shi, W. X. Jiang, and T. J. Cui, “Experimental realization of bending waveguide using anisotropic zero-index materials,” Appl. Phys. Lett. 101, 253513 (2012).
[Crossref]

H. F. Ma, J. H. Shi, B. G. Cai, and T. J. Cui, “Total transmission and super reflection realized by anisotropic zero-index materials,” New J. Phys. 14, 123010 (2012).
[Crossref]

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

R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100, 023903 (2008).
[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 78, 066607 (2008).
[Crossref]

Cummer, S. A.

R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100, 023903 (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]

Ding, W.

T. Han, W. Ding, C. Qiu, and X. Tang, “All-dielectric tapered waveguide bender with homogeneous loading, arbitrary bending and simplified geometry,” J. Electromagn. Waves 26, 729–736 (2012).
[Crossref]

Dong, J. W.

Edwards, B.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100, 033903 (2008).
[Crossref]

Engheta, N.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100, 033903 (2008).
[Crossref]

M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using e-near-zero materials,” Phys. Rev. Lett. 97, 157403 (2006).
[Crossref]

Fan, S.

G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87, 131102 (2005).
[Crossref]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[Crossref]

Gao, L.

J. Luo, P. Xu, H. Chen, B. Hou, L. Gao, and Y. Lai, “Realizing almost perfect bending waveguides with anisotropic epsilon-near-zero metamaterials,” Appl. Phys. Lett. 100, 221903 (2012).
[Crossref]

Ge, X.

Guo, S.

F. Sun, B. Zheng, H. Chen, W. Jiang, S. Guo, Y. Liu, Y. Ma, and S. He, “Transformation optics: from classic theory and applications to its new branches,” Laser Photon. Rev. 11, 1700034 (2017).
[Crossref]

Han, T.

Hand, T.

R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100, 023903 (2008).
[Crossref]

Hang, Z. H.

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10, 582–586 (2011).
[Crossref]

He, Q.

He, S.

F. Sun, B. Zheng, H. Chen, W. Jiang, S. Guo, Y. Liu, Y. Ma, and S. He, “Transformation optics: from classic theory and applications to its new branches,” Laser Photon. Rev. 11, 1700034 (2017).
[Crossref]

F. Sun and S. He, “Overlapping illusions by transformation optics without any negative refraction material,” Sci. Rep. 6, 19130 (2016).
[Crossref]

F. Sun and S. He, “Optic-null space medium for cover-up cloaking without any negative refraction index materials,” Sci. Rep. 6, 29280 (2016).
[Crossref]

F. Sun and S. He, “Homogenous optic-null medium performs as optical surface transformation,” Prog. Electromagn. Res. 151, 169–173 (2015).
[Crossref]

F. Sun and S. He, “Optical surface transformation: changing the optical surface by homogeneous optic-null medium at will,” Sci. Rep. 5, 16032 (2015).
[Crossref]

F. Sun, Y. G. Ma, X. Ge, and S. He, “Super-thin Mikaelian’s lens of small index as a beam compressor with an extremely high compression ratio,” Opt. Express 21, 7328–7336 (2013).
[Crossref]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys. Condens. Matter 10, 4785–4809 (1998).
[Crossref]

Hou, B.

M. M. Sadeghi, S. Li, L. Xu, B. Hou, and H. Chen, “Transformation optics with Fabry–Pérot resonances,” Sci. Rep. 5, 8680 (2015).
[Crossref]

J. Luo, P. Xu, H. Chen, B. Hou, L. Gao, and Y. Lai, “Realizing almost perfect bending waveguides with anisotropic epsilon-near-zero metamaterials,” Appl. Phys. Lett. 100, 221903 (2012).
[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,” Photon. Nanostr. Fundam. Appl. 11, 115–122 (2013).
[Crossref]

H. Chen, L. Huang, X. Cheng, and H. Wang, “Magnetic properties of metamaterial composed of closed rings,” Prog. Electromagn. Res. 115, 317–326 (2011).
[Crossref]

Huang, X.

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10, 582–586 (2011).
[Crossref]

Huang, Z.

S. Xu, X. Cheng, S. Xi, R. Zhang, H. O. Moser, Z. Shen, Y. Xu, Z. Huang, X. Zhang, F. Yu, B. Zhang, and H. Chen, “Experimental demonstration of a free-space cylindrical cloak without superluminal propagation,” Phys. Rev. Lett. 109, 223903 (2012).
[Crossref]

Huangfu, J.

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

Jiang, W.

F. Sun, B. Zheng, H. Chen, W. Jiang, S. Guo, Y. Liu, Y. Ma, and S. He, “Transformation optics: from classic theory and applications to its new branches,” Laser Photon. Rev. 11, 1700034 (2017).
[Crossref]

Jiang, W. X.

H. F. Ma, J. H. Shi, W. X. Jiang, and T. J. Cui, “Experimental realization of bending waveguide using anisotropic zero-index materials,” Appl. Phys. Lett. 101, 253513 (2012).
[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 78, 066607 (2008).
[Crossref]

Joannopoulos, J. D.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[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]

Kawakami, S.

Kildishev, A. V.

A. V. Kildishev and V. M. Shalaev, “Transformation optics and metamaterials,” Phys. Usp. 54, 53–63 (2011).
[Crossref]

Kong, F.

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

Kong, J. A.

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

Kurland, I.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[Crossref]

Kwon, D. H.

Lai, Y.

J. Luo and Y. Lai, “Anisotropic zero-index waveguide with arbitrary shapes,” Sci. Rep. 4, 5875 (2014).
[Crossref]

J. Luo, P. Xu, H. Chen, B. Hou, L. Gao, and Y. Lai, “Realizing almost perfect bending waveguides with anisotropic epsilon-near-zero metamaterials,” Appl. Phys. Lett. 100, 221903 (2012).
[Crossref]

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10, 582–586 (2011).
[Crossref]

Landy, N. I.

Li, D.

Y. Wang, D. H. Zhang, J. Wang, F. Qin, D. Li, and Z. Xu, “Design of sharp bends with transformation plasmonics,” Appl. Phys. A 112, 549–553 (2013).
[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,” Photon. Nanostr. Fundam. Appl. 11, 115–122 (2013).
[Crossref]

Li, S.

M. M. Sadeghi, S. Li, L. Xu, B. Hou, and H. Chen, “Transformation optics with Fabry–Pérot resonances,” Sci. Rep. 5, 8680 (2015).
[Crossref]

Li, X.

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,” Photon. Nanostr. Fundam. Appl. 11, 115–122 (2013).
[Crossref]

Liu, R.

R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100, 023903 (2008).
[Crossref]

Liu, Y.

F. Sun, B. Zheng, H. Chen, W. Jiang, S. Guo, Y. Liu, Y. Ma, and S. He, “Transformation optics: from classic theory and applications to its new branches,” Laser Photon. Rev. 11, 1700034 (2017).
[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,” Photon. Nanostr. Fundam. Appl. 11, 115–122 (2013).
[Crossref]

Luo, J.

J. Luo and Y. Lai, “Anisotropic zero-index waveguide with arbitrary shapes,” Sci. Rep. 4, 5875 (2014).
[Crossref]

J. Luo, P. Xu, H. Chen, B. Hou, L. Gao, and Y. Lai, “Realizing almost perfect bending waveguides with anisotropic epsilon-near-zero metamaterials,” Appl. Phys. Lett. 100, 221903 (2012).
[Crossref]

Ma, H. F.

H. F. Ma, J. H. Shi, W. X. Jiang, and T. J. Cui, “Experimental realization of bending waveguide using anisotropic zero-index materials,” Appl. Phys. Lett. 101, 253513 (2012).
[Crossref]

H. F. Ma, J. H. Shi, B. G. Cai, and T. J. Cui, “Total transmission and super reflection realized by anisotropic zero-index materials,” New J. Phys. 14, 123010 (2012).
[Crossref]

Ma, Y.

F. Sun, B. Zheng, H. Chen, W. Jiang, S. Guo, Y. Liu, Y. Ma, and S. He, “Transformation optics: from classic theory and applications to its new branches,” Laser Photon. Rev. 11, 1700034 (2017).
[Crossref]

Ma, Y. G.

Mei, J. S.

J. S. Mei, Q. Wu, and K. Zhang, “Design of electromagnetic refractor and waveguide bends using complementary medium,” Physica B 426, 150–154 (2013).
[Crossref]

Mei, Z. L.

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

Mekis, A.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[Crossref]

Mock, J. J.

R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100, 023903 (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]

Moser, H. O.

S. Xu, X. Cheng, S. Xi, R. Zhang, H. O. Moser, Z. Shen, Y. Xu, Z. Huang, X. Zhang, F. Yu, B. Zhang, and H. Chen, “Experimental demonstration of a free-space cylindrical cloak without superluminal propagation,” Phys. Rev. Lett. 109, 223903 (2012).
[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,” Photon. Nanostr. Fundam. Appl. 11, 115–122 (2013).
[Crossref]

Padilla, W. J.

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, 251111 (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. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys. Condens. Matter 10, 4785–4809 (1998).
[Crossref]

Qin, F.

Y. Wang, D. H. Zhang, J. Wang, F. Qin, D. Li, and Z. Xu, “Design of sharp bends with transformation plasmonics,” Appl. Phys. A 112, 549–553 (2013).
[Crossref]

Qiu, C.

T. Han, W. Ding, C. Qiu, and X. Tang, “All-dielectric tapered waveguide bender with homogeneous loading, arbitrary bending and simplified geometry,” J. Electromagn. Waves 26, 729–736 (2012).
[Crossref]

Qiu, C. W.

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, 251111 (2008).
[Crossref]

Ran, L.

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

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys. Condens. Matter 10, 4785–4809 (1998).
[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, 251111 (2008).
[Crossref]

Sadeghi, M. M.

M. M. Sadeghi, S. Li, L. Xu, B. Hou, and H. Chen, “Transformation optics with Fabry–Pérot resonances,” Sci. Rep. 5, 8680 (2015).
[Crossref]

Schurig, D.

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.

A. V. Kildishev and V. M. Shalaev, “Transformation optics and metamaterials,” Phys. Usp. 54, 53–63 (2011).
[Crossref]

Shen, Z.

S. Xu, X. Cheng, S. Xi, R. Zhang, H. O. Moser, Z. Shen, Y. Xu, Z. Huang, X. Zhang, F. Yu, B. Zhang, and H. Chen, “Experimental demonstration of a free-space cylindrical cloak without superluminal propagation,” Phys. Rev. Lett. 109, 223903 (2012).
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Sheng, P.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9, 387–396 (2010).
[Crossref]

Shi, J. H.

H. F. Ma, J. H. Shi, W. X. Jiang, and T. J. Cui, “Experimental realization of bending waveguide using anisotropic zero-index materials,” Appl. Phys. Lett. 101, 253513 (2012).
[Crossref]

H. F. Ma, J. H. Shi, B. G. Cai, and T. J. Cui, “Total transmission and super reflection realized by anisotropic zero-index materials,” New J. Phys. 14, 123010 (2012).
[Crossref]

Shiina, T.

Shiraishi, K.

Silveirinha, M.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100, 033903 (2008).
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M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using e-near-zero materials,” Phys. Rev. Lett. 97, 157403 (2006).
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Smith, D. R.

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, 251111 (2008).
[Crossref]

R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100, 023903 (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]

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]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys. Condens. Matter 10, 4785–4809 (1998).
[Crossref]

Sun, F.

F. Sun, B. Zheng, H. Chen, W. Jiang, S. Guo, Y. Liu, Y. Ma, and S. He, “Transformation optics: from classic theory and applications to its new branches,” Laser Photon. Rev. 11, 1700034 (2017).
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F. Sun and S. He, “Overlapping illusions by transformation optics without any negative refraction material,” Sci. Rep. 6, 19130 (2016).
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F. Sun and S. He, “Optic-null space medium for cover-up cloaking without any negative refraction index materials,” Sci. Rep. 6, 29280 (2016).
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F. Sun and S. He, “Homogenous optic-null medium performs as optical surface transformation,” Prog. Electromagn. Res. 151, 169–173 (2015).
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F. Sun and S. He, “Optical surface transformation: changing the optical surface by homogeneous optic-null medium at will,” Sci. Rep. 5, 16032 (2015).
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F. Sun, Y. G. Ma, X. Ge, and S. He, “Super-thin Mikaelian’s lens of small index as a beam compressor with an extremely high compression ratio,” Opt. Express 21, 7328–7336 (2013).
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Sun, H.

Tang, X.

Veronis, G.

G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87, 131102 (2005).
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A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[Crossref]

Wang, D.

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

Wang, H.

H. Chen, L. Huang, X. Cheng, and H. Wang, “Magnetic properties of metamaterial composed of closed rings,” Prog. Electromagn. Res. 115, 317–326 (2011).
[Crossref]

Wang, J.

Y. Wang, D. H. Zhang, J. Wang, F. Qin, D. Li, and Z. Xu, “Design of sharp bends with transformation plasmonics,” Appl. Phys. A 112, 549–553 (2013).
[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,” Photon. Nanostr. Fundam. Appl. 11, 115–122 (2013).
[Crossref]

Wang, Y.

Y. Wang, D. H. Zhang, J. Wang, F. Qin, D. Li, and Z. Xu, “Design of sharp bends with transformation plasmonics,” Appl. Phys. A 112, 549–553 (2013).
[Crossref]

Werner, D. H.

Wu, B.

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

Wu, Q.

J. S. Mei, Q. Wu, and K. Zhang, “Design of electromagnetic refractor and waveguide bends using complementary medium,” Physica B 426, 150–154 (2013).
[Crossref]

Xi, S.

S. Xu, X. Cheng, S. Xi, R. Zhang, H. O. Moser, Z. Shen, Y. Xu, Z. Huang, X. Zhang, F. Yu, B. Zhang, and H. Chen, “Experimental demonstration of a free-space cylindrical cloak without superluminal propagation,” Phys. Rev. Lett. 109, 223903 (2012).
[Crossref]

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

Xiao, S.

Xu, H.

Xu, L.

M. M. Sadeghi, S. Li, L. Xu, B. Hou, and H. Chen, “Transformation optics with Fabry–Pérot resonances,” Sci. Rep. 5, 8680 (2015).
[Crossref]

Xu, P.

J. Luo, P. Xu, H. Chen, B. Hou, L. Gao, and Y. Lai, “Realizing almost perfect bending waveguides with anisotropic epsilon-near-zero metamaterials,” Appl. Phys. Lett. 100, 221903 (2012).
[Crossref]

Xu, S.

S. Xu, X. Cheng, S. Xi, R. Zhang, H. O. Moser, Z. Shen, Y. Xu, Z. Huang, X. Zhang, F. Yu, B. Zhang, and H. Chen, “Experimental demonstration of a free-space cylindrical cloak without superluminal propagation,” Phys. Rev. Lett. 109, 223903 (2012).
[Crossref]

Xu, Y.

S. Xu, X. Cheng, S. Xi, R. Zhang, H. O. Moser, Z. Shen, Y. Xu, Z. Huang, X. Zhang, F. Yu, B. Zhang, and H. Chen, “Experimental demonstration of a free-space cylindrical cloak without superluminal propagation,” Phys. Rev. Lett. 109, 223903 (2012).
[Crossref]

Xu, Z.

Y. Wang, D. H. Zhang, J. Wang, F. Qin, D. Li, and Z. Xu, “Design of sharp bends with transformation plasmonics,” Appl. Phys. A 112, 549–553 (2013).
[Crossref]

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 78, 066607 (2008).
[Crossref]

Young, M. E.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100, 033903 (2008).
[Crossref]

Yu, F.

S. Xu, X. Cheng, S. Xi, R. Zhang, H. O. Moser, Z. Shen, Y. Xu, Z. Huang, X. Zhang, F. Yu, B. Zhang, and H. Chen, “Experimental demonstration of a free-space cylindrical cloak without superluminal propagation,” Phys. Rev. Lett. 109, 223903 (2012).
[Crossref]

Yu, T.

Zhang, B.

H. Xu, H. Sun, and B. Zhang, “Waveguide design and application with transformation optics,” Sci. China Inf. Sci. 56, 1–11 (2013).
[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]

S. Xu, X. Cheng, S. Xi, R. Zhang, H. O. Moser, Z. Shen, Y. Xu, Z. Huang, X. Zhang, F. Yu, B. Zhang, and H. Chen, “Experimental demonstration of a free-space cylindrical cloak without superluminal propagation,” Phys. Rev. Lett. 109, 223903 (2012).
[Crossref]

Zhang, D. H.

Y. Wang, D. H. Zhang, J. Wang, F. Qin, D. Li, and Z. Xu, “Design of sharp bends with transformation plasmonics,” Appl. Phys. A 112, 549–553 (2013).
[Crossref]

Zhang, J.

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

Zhang, K.

J. S. Mei, Q. Wu, and K. Zhang, “Design of electromagnetic refractor and waveguide bends using complementary medium,” Physica B 426, 150–154 (2013).
[Crossref]

Zhang, R.

S. Xu, X. Cheng, S. Xi, R. Zhang, H. O. Moser, Z. Shen, Y. Xu, Z. Huang, X. Zhang, F. Yu, B. Zhang, and H. Chen, “Experimental demonstration of a free-space cylindrical cloak without superluminal propagation,” Phys. Rev. Lett. 109, 223903 (2012).
[Crossref]

Zhang, X.

S. Xu, X. Cheng, S. Xi, R. Zhang, H. O. Moser, Z. Shen, Y. Xu, Z. Huang, X. Zhang, F. Yu, B. Zhang, and H. Chen, “Experimental demonstration of a free-space cylindrical cloak without superluminal propagation,” Phys. Rev. Lett. 109, 223903 (2012).
[Crossref]

Zheng, B.

F. Sun, B. Zheng, H. Chen, W. Jiang, S. Guo, Y. Liu, Y. Ma, and S. He, “Transformation optics: from classic theory and applications to its new branches,” Laser Photon. Rev. 11, 1700034 (2017).
[Crossref]

Zheng, H.

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10, 582–586 (2011).
[Crossref]

Zhou, L.

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 78, 066607 (2008).
[Crossref]

Zouhdi, S.

Appl. Phys. A (1)

Y. Wang, D. H. Zhang, J. Wang, F. Qin, D. Li, and Z. Xu, “Design of sharp bends with transformation plasmonics,” Appl. Phys. A 112, 549–553 (2013).
[Crossref]

Appl. Phys. Lett. (4)

G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87, 131102 (2005).
[Crossref]

J. Luo, P. Xu, H. Chen, B. Hou, L. Gao, and Y. Lai, “Realizing almost perfect bending waveguides with anisotropic epsilon-near-zero metamaterials,” Appl. Phys. Lett. 100, 221903 (2012).
[Crossref]

H. F. Ma, J. H. Shi, W. X. Jiang, and T. J. Cui, “Experimental realization of bending waveguide using anisotropic zero-index materials,” Appl. Phys. Lett. 101, 253513 (2012).
[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, 251111 (2008).
[Crossref]

J. Appl. Phys. (2)

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

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

J. Electromagn. Waves (1)

T. Han, W. Ding, C. Qiu, and X. Tang, “All-dielectric tapered waveguide bender with homogeneous loading, arbitrary bending and simplified geometry,” J. Electromagn. Waves 26, 729–736 (2012).
[Crossref]

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

J. Phys. Condens. Matter (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys. Condens. Matter 10, 4785–4809 (1998).
[Crossref]

Laser Photon. Rev. (1)

F. Sun, B. Zheng, H. Chen, W. Jiang, S. Guo, Y. Liu, Y. Ma, and S. He, “Transformation optics: from classic theory and applications to its new branches,” Laser Photon. Rev. 11, 1700034 (2017).
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Figures (6)

Fig. 1.
Fig. 1. Basic schematic diagram of the design of a waveguide bend using OST.
Fig. 2.
Fig. 2. 2D numerical simulation results by finite element method for TE polarization mode. (a)–(c) Normalized electric field distribution inside two waveguides and the waveguide bend designed with ONMs as the bending angle varies from 60 to 120 deg. The black arrows in the inserted subfigures indicate the main axes of the ONM of our waveguide bends. (d)–(f) Normalized absolute value of the electric field distribution corresponding to (a)–(c). (g)–(i) show the normalized electric field distribution without the bends as the bending angle changes.
Fig. 3.
Fig. 3. 2D numerical simulation results by finite element method for TE polarization mode. (a) and (b) plot the normalized electric field distributions inside two waveguides and the waveguide bend designed with ONMs when the bending angles are 180 and 360 deg. The black arrows in the inserted subfigures indicate the main axes of the ONMs. (c) and (d) plot the normalized absolute value of the electric field distribution for (a) and (b), respectively. (e) and (f) show the normalized electric field distribution without the bends when the bending angles are 180 and 360 deg.
Fig. 4.
Fig. 4. 2D numerical simulation results by finite element method for TE polarization mode. (a)–(c) Normalized electric field distributions inside two waveguides and the reduced waveguide bend using anisotropic, zero refractive index materials as the bending angle varies from 60 to 120 deg. (d)–(f) Normalized absolute value of the electric field distributions corresponding to (a)–(c).
Fig. 5.
Fig. 5. Normalized electric field distribution inside two waveguides and the waveguide bends designed with ONMs (the bending angle=60  deg) when the imaginary part of the relative permittivity is introduced as ϵ=0.001 (a) and ϵ=0.01 (b). (c) and (d) show the amplitude of the electric field in (a) and (b), respectively.
Fig. 6.
Fig. 6. Reflection feature of the reduced waveguide bends. (a) Relation between the reflection parameter S11 and the wavelength. We fix the size (width=0.4  m) and bending angle (90 deg) of the waveguide bend. (b) Gradual tapers are introduced before the bend in order to reduce the reflection. (c) Relation between the reflection parameter S11 and the taper’s expansion parameter d, when the working wavelength λ=0.4  m, bending angle (90 deg), and waveguide size (width=0.4  m) are fixed. Blue line and red line are for cases in which bends are filled by ONMs and free space, respectively.

Equations (7)

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{μx=1μy=Δ2ϵz=Δ2,Δ0.
{yEz=jωμxμ0HxxEz=jωμyμ0HyxHyyHx=jωϵzϵ0Ez.
x2Ezμy+y2Ezμx+k02ϵzEz=0.
x2EzC0μy+y2EzC0μx+k02ϵzC0Ez=0.
x2EzC0ϵzμy+y2EzC0ϵzμx+k021C0Ez=0.
{μxideal=1Δμyideal=Δϵzideal=Δ,Δ0.
{μx=C01Δμy=C0Δϵz=C0Δ.