Abstract

We propose a method for adaptive waveguide bends using homogeneous, nonmagnetic, and isotropic materials, which simplifies the parameters of the bends to the utmost extent. The proposed bend has an adaptive and compact shape because of all the flat boundaries. The nonmagnetic property is realized by selecting OB/OC=0.5. Only two nonmagnetic isotropic dielectrics are needed throughout, and the transmission is not sensitive to nonmagnetic isotropic dielectrics. Results validate and illustrate these functionalities, which make the bend much easier to fabricate and apply, owing to its simple parameters, compact shape, and versatility in connecting different waveguides.

© 2011 Optical Society of America

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2010 (1)

2009 (4)

C. W. Qiu, L. Hu, X. F. Xu, and Y. J. Feng, Phys. Rev. E 79, 047602 (2009).
[CrossRef]

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, Science 323, 366 (2009).
[CrossRef] [PubMed]

B. Vasic, G. Isic, R. Gajic, and K. Hingerl, Phys. Rev. B 79, 085103 (2009).
[CrossRef]

X. J. Wu, Z. F. Lin, H. Y. Chen, and C. T. Chan, Appl. Opt. 48, G101 (2009).
[CrossRef] [PubMed]

2008 (5)

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

W. X. Jiang, T. J. Cui, X. Y. Zhou, X. M. Yang, and Q. Cheng, Phys. Rev. E 78, 066607 (2008).
[CrossRef]

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, J. Appl. Phys. 104, 014502 (2008).
[CrossRef]

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, Appl. Phys. Lett. 93, 251111 (2008).
[CrossRef]

A. V. Kildishev and V. M. Shalaev, Opt. Lett. 33, 43 (2008).
[CrossRef]

2006 (2)

U. Leonhardt, Science 312, 1777 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

2005 (1)

G. Veronis and S. Fan, Appl. Phys. Lett. 87, 131102 (2005).
[CrossRef]

1998 (1)

1996 (1)

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Chan, C. T.

Chen, H.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, J. Appl. Phys. 104, 014502 (2008).
[CrossRef]

Chen, H. Y.

Chen, J. C.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Cheng, Q.

W. X. Jiang, T. J. Cui, X. Y. Zhou, X. M. Yang, and Q. Cheng, Phys. Rev. E 78, 066607 (2008).
[CrossRef]

Chin, J. Y.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, Science 323, 366 (2009).
[CrossRef] [PubMed]

Cui, T. J.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, Science 323, 366 (2009).
[CrossRef] [PubMed]

W. X. Jiang, T. J. Cui, X. Y. Zhou, X. M. Yang, and Q. Cheng, Phys. Rev. E 78, 066607 (2008).
[CrossRef]

Cummer, S. A.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

Fan, S.

G. Veronis and S. Fan, Appl. Phys. Lett. 87, 131102 (2005).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Feng, Y. J.

C. W. Qiu, L. Hu, X. F. Xu, and Y. J. Feng, Phys. Rev. E 79, 047602 (2009).
[CrossRef]

Gajic, R.

B. Vasic, G. Isic, R. Gajic, and K. Hingerl, Phys. Rev. B 79, 085103 (2009).
[CrossRef]

Han, T. C.

Hingerl, K.

B. Vasic, G. Isic, R. Gajic, and K. Hingerl, Phys. Rev. B 79, 085103 (2009).
[CrossRef]

Hsu, J.-M.

Hu, L.

C. W. Qiu, L. Hu, X. F. Xu, and Y. J. Feng, Phys. Rev. E 79, 047602 (2009).
[CrossRef]

Huangfu, J.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, J. Appl. Phys. 104, 014502 (2008).
[CrossRef]

Isic, G.

B. Vasic, G. Isic, R. Gajic, and K. Hingerl, Phys. Rev. B 79, 085103 (2009).
[CrossRef]

Ji, C.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, Science 323, 366 (2009).
[CrossRef] [PubMed]

Jiang, W. X.

W. X. Jiang, T. J. Cui, X. Y. Zhou, X. M. Yang, and Q. Cheng, 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, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Kildishev, A. V.

Kong, F.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, J. Appl. Phys. 104, 014502 (2008).
[CrossRef]

Kong, J. A.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, 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, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Lee, T.

Leonhardt, U.

U. Leonhardt, Science 312, 1777 (2006).
[CrossRef] [PubMed]

Lin, Z. F.

Liu, R.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, Science 323, 366 (2009).
[CrossRef] [PubMed]

Mekis, A.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Mock, J. J.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, Science 323, 366 (2009).
[CrossRef] [PubMed]

Pendry, J. B.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, Appl. Phys. Lett. 93, 251111 (2008).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

Qiu, C. W.

T. C. Han and C. W. Qiu, Opt. Express 18, 13038 (2010).
[CrossRef] [PubMed]

C. W. Qiu, L. Hu, X. F. Xu, and Y. J. Feng, Phys. Rev. E 79, 047602 (2009).
[CrossRef]

Rahm, M.

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, Appl. Phys. Lett. 93, 251111 (2008).
[CrossRef]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

Ran, L.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, J. Appl. Phys. 104, 014502 (2008).
[CrossRef]

Roberts, D. A.

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, Appl. Phys. Lett. 93, 251111 (2008).
[CrossRef]

Schurig, D.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

Shalaev, V. M.

Smith, D. R.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, Science 323, 366 (2009).
[CrossRef] [PubMed]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, Appl. Phys. Lett. 93, 251111 (2008).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

Vasic, B.

B. Vasic, G. Isic, R. Gajic, and K. Hingerl, Phys. Rev. B 79, 085103 (2009).
[CrossRef]

Veronis, G.

G. Veronis and S. Fan, Appl. Phys. Lett. 87, 131102 (2005).
[CrossRef]

Villeneuve, P. R.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Wang, D.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, J. Appl. Phys. 104, 014502 (2008).
[CrossRef]

Wu, B.-I.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, J. Appl. Phys. 104, 014502 (2008).
[CrossRef]

Wu, X. J.

Xi, S.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, J. Appl. Phys. 104, 014502 (2008).
[CrossRef]

Xu, X. F.

C. W. Qiu, L. Hu, X. F. Xu, and Y. J. Feng, Phys. Rev. E 79, 047602 (2009).
[CrossRef]

Yang, X. M.

W. X. Jiang, T. J. Cui, X. Y. Zhou, X. M. Yang, and Q. Cheng, Phys. Rev. E 78, 066607 (2008).
[CrossRef]

Zhang, J.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, J. Appl. Phys. 104, 014502 (2008).
[CrossRef]

Zhou, X. Y.

W. X. Jiang, T. J. Cui, X. Y. Zhou, X. M. Yang, and Q. Cheng, Phys. Rev. E 78, 066607 (2008).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (2)

G. Veronis and S. Fan, Appl. Phys. Lett. 87, 131102 (2005).
[CrossRef]

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, Appl. Phys. Lett. 93, 251111 (2008).
[CrossRef]

J. Appl. Phys. (1)

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, J. Appl. Phys. 104, 014502 (2008).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (1)

B. Vasic, G. Isic, R. Gajic, and K. Hingerl, Phys. Rev. B 79, 085103 (2009).
[CrossRef]

Phys. Rev. E (2)

W. X. Jiang, T. J. Cui, X. Y. Zhou, X. M. Yang, and Q. Cheng, Phys. Rev. E 78, 066607 (2008).
[CrossRef]

C. W. Qiu, L. Hu, X. F. Xu, and Y. J. Feng, Phys. Rev. E 79, 047602 (2009).
[CrossRef]

Phys. Rev. Lett. (2)

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

Science (3)

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, Science 323, 366 (2009).
[CrossRef] [PubMed]

U. Leonhardt, Science 312, 1777 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Schematic illustration of coordinate transformation in the design of advanced waveguide bends: (a) bend connecting two waveguides of different widths and (b) bend connecting two waveguides with nonmagnetic materials.

Fig. 2
Fig. 2

Snapshots of the total electric fields for Fig. 1a when a = 10 cm and b = 2 cm : (a) field distribution without transformation materials in bending region and (b) field distribution with homogeneous transformation materials in the bend.

Fig. 3
Fig. 3

Magnetic field distribution of the bend designed using homogeneous and nonmagnetic materials for a = 10 cm , with or without anisotropy: (a) vacuum bend, (b) ideal anisotropic transformation media filled in the bend, (c) layered isotropic dielectrics filled in the bend and θ 0 = 58 ° , and (d) average power outflow at port 2.

Fig. 4
Fig. 4

(a) Average power outflow at port 2 when isotropic medium B ε B is with the loss tangent of 0.001, 0.01, and 0.1 at O B / O C = 0.5 to comply with the nonmagnetic condition. (b) Parameters of two isotropic media versus O B / O C .

Equations (2)

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

x = a 11 x + b 11 y + c 11 , y = a 12 x + b 12 y + c 12 , z = z ,
x = a 21 x + b 21 y + c 21 , y = a 22 x + b 22 y + c 22 , z = z ,

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