Abstract

Transformation electromagnetics has opened possibilities for designing antenna structures. Using an analytical approach, we demonstrate here how directive antenna radiation can be achieved from an omnidirectional source behind a diffuse surface. This diffuse surface has been obtained by an optical transformation of a Luneburg lens. Two different transformation approaches have been proposed (polynomial and sinusoidal), and for both cases, the resulting material properties have been simplified to ease the fabrication by using all-dielectric media. Therefore, the proposed design has no upper boundary to the operational frequency. Directive radiation has been achieved from thin diffuse structures, which demonstrates promising future possibilities for this technique.

© 2013 Optical Society of America

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References

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2012

2011

2010

W. Tang, Y. Hao, and F. Medina, Opt. Express 18, 16946 (2010).
[CrossRef]

H.-F. Ma and T.-J. Cui, Nat. Commun. 1, 124 (2010).
[CrossRef]

D. Bao, K. Z. Rajab, W. Tang, and Y. Hao, Appl. Phys. Lett. 97, 134105 (2010).
[CrossRef]

N. Kundtz and D. R. Smith, Nat. Mater. 9, 129 (2010).
[CrossRef]

2009

Q. Cheng, H.-F. Ma, and T.-J. Cui, Appl. Phys. Lett. 95, 181901 (2009).
[CrossRef]

D. A. Roberts, N. Kundtz, and D. R. Smith, Opt. Express 17, 16535 (2009).
[CrossRef]

2008

2007

F. Kong, B.-I. Wu, J. A. Kong, J. Huangfu, S. Xi, and H. Chen, Appl. Phys. Lett. 91, 253509 (2007).
[CrossRef]

2006

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

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

1954

A. S. Gutman, J. Appl. Phys. 25, 855 (1954).
[CrossRef]

Argyropoulos, C.

Bao, D.

D. Bao, K. Z. Rajab, W. Tang, and Y. Hao, Appl. Phys. Lett. 97, 134105 (2010).
[CrossRef]

Chen, H.

F. Kong, B.-I. Wu, J. A. Kong, J. Huangfu, S. Xi, and H. Chen, Appl. Phys. Lett. 91, 253509 (2007).
[CrossRef]

Cheng, Q.

Q. Cheng, H.-F. Ma, and T.-J. Cui, Appl. Phys. Lett. 95, 181901 (2009).
[CrossRef]

Cui, T.-J.

H.-F. Ma and T.-J. Cui, Nat. Commun. 1, 124 (2010).
[CrossRef]

Q. Cheng, H.-F. Ma, and T.-J. Cui, Appl. Phys. Lett. 95, 181901 (2009).
[CrossRef]

Demetriadou, A.

Gutman, A. S.

A. S. Gutman, J. Appl. Phys. 25, 855 (1954).
[CrossRef]

Hao, Y.

Huangfu, J.

F. Kong, B.-I. Wu, J. A. Kong, J. Huangfu, S. Xi, and H. Chen, Appl. Phys. Lett. 91, 253509 (2007).
[CrossRef]

Kong, F.

F. Kong, B.-I. Wu, J. A. Kong, J. Huangfu, S. Xi, and H. Chen, Appl. Phys. Lett. 91, 253509 (2007).
[CrossRef]

Kong, J. A.

F. Kong, B.-I. Wu, J. A. Kong, J. Huangfu, S. Xi, and H. Chen, Appl. Phys. Lett. 91, 253509 (2007).
[CrossRef]

Kundtz, N.

Leonhardt, U.

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

Luneburg, R.

R. Luneburg, Mathematical Theory of Optics (Brown University, 1944).

Ma, H.-F.

H.-F. Ma and T.-J. Cui, Nat. Commun. 1, 124 (2010).
[CrossRef]

Q. Cheng, H.-F. Ma, and T.-J. Cui, Appl. Phys. Lett. 95, 181901 (2009).
[CrossRef]

Medina, F.

Mittra, R.

Y. Hao and R. Mittra, FDTD Modeling of Metamaterials: Theory and Applications (Artech House, 2008).

Pendry, J. B.

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

Quevedo-Teruel, O.

Rajab, K. Z.

D. Bao, K. Z. Rajab, W. Tang, and Y. Hao, Appl. Phys. Lett. 97, 134105 (2010).
[CrossRef]

Roberts, D. A.

Schurig, D.

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

Smith, D. R.

N. Kundtz and D. R. Smith, Nat. Mater. 9, 129 (2010).
[CrossRef]

D. A. Roberts, N. Kundtz, and D. R. Smith, Opt. Express 17, 16535 (2009).
[CrossRef]

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

Tang, W.

Wu, B.-I.

F. Kong, B.-I. Wu, J. A. Kong, J. Huangfu, S. Xi, and H. Chen, Appl. Phys. Lett. 91, 253509 (2007).
[CrossRef]

Xi, S.

F. Kong, B.-I. Wu, J. A. Kong, J. Huangfu, S. Xi, and H. Chen, Appl. Phys. Lett. 91, 253509 (2007).
[CrossRef]

Yang, R.

Zhao, Y.

Appl. Phys. Lett.

Q. Cheng, H.-F. Ma, and T.-J. Cui, Appl. Phys. Lett. 95, 181901 (2009).
[CrossRef]

D. Bao, K. Z. Rajab, W. Tang, and Y. Hao, Appl. Phys. Lett. 97, 134105 (2010).
[CrossRef]

F. Kong, B.-I. Wu, J. A. Kong, J. Huangfu, S. Xi, and H. Chen, Appl. Phys. Lett. 91, 253509 (2007).
[CrossRef]

J. Appl. Phys.

A. S. Gutman, J. Appl. Phys. 25, 855 (1954).
[CrossRef]

Nat. Commun.

H.-F. Ma and T.-J. Cui, Nat. Commun. 1, 124 (2010).
[CrossRef]

Nat. Mater.

N. Kundtz and D. R. Smith, Nat. Mater. 9, 129 (2010).
[CrossRef]

Opt. Express

Opt. Lett.

Science

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

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

Other

R. Luneburg, Mathematical Theory of Optics (Brown University, 1944).

Y. Hao and R. Mittra, FDTD Modeling of Metamaterials: Theory and Applications (Artech House, 2008).

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Figures (5)

Fig. 1.
Fig. 1.

Slim diffuse Luneburg lens (polynomial approach): (a) two-dimensional (2D) permittivity map following Eq. (6) when R=1.66λ with a=1/10, δ=4, and Ra=2R; (b) 2D permittivity map of Luneburg lens before transformation; and (c)–(f) normalized field distribution in the lens when it is fed at different positions with a normal line source.

Fig. 2.
Fig. 2.

Normalized field distribution for different feeding positions. This field was obtained at a distance of 8λ as it is indicated in Figs. 1(c)1(f) with a solid blue curve. The results for the original Luneburg lens before transformation are also represented (with dashed curves) for comparison.

Fig. 3.
Fig. 3.

Slim diffuse Luneburg lens (sinusoidal approach): (a) 2D permittivity map following Eq. (10) when R=1.66λ with a=10, δ=5, and Ra=R. (b)–(d) Normalized field distribution in the lens when it is fed at different positions with a normal line source.

Fig. 4.
Fig. 4.

Normalized field distribution for different feeding positions. This field was obtained at a distance of 8λ as it is indicated in Figs. 3(b)3(d) with a solid blue curve. The original Luneburg lens is plotted with a dashed curve, for comparison.

Fig. 5.
Fig. 5.

Normalized field distribution for different feeding positions and different operational frequencies for the case of polynomial transformation.

Equations (11)

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

ϵr=2(rR)2,
x=xRa+(a·y)3δ,
y=y,
ϵ=JϵJT|J|,
μ=JμJT|J|,
ϵr=ϵr(1δ(1+9a6y4)3a3y23a3y2δ),
ϵr=(2y2+(δx+Ra(a·y)3)2R2).
x=xRa+acos(2π·y/Ra)δ,
y=y.
ϵr=ϵr(1δ(1+4π2Ra2sin2(2πyRa))2πRasin(2πyRa)2πRasin(2πyRa)δ),
ϵr=(2y2+(δxRa+acos(2π·y/Ra))2R2).

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