Abstract

A body-of-revolution finite-difference time-domain (BOR-FDTD) method was developed and employed to rigorously analyze axisymmetric transformation optics (TO) lenses. The novelty of the proposed BOR-FDTD technique is that analytical expressions were derived and presented to introduce obliquely incident plane waves into the total-field/scattered-field formulation, allowing for accurate simulation of BOR objects in layered media illuminated by obliquely incident waves. The accuracy of the proposed method was verified by comparing numerical results with analytical solutions. The developed code was further utilized to study the imaging properties of a cylindrical TO Luneburg lens on a substrate, demonstrating the desired focusing of light onto a flat plane.

© 2012 Optical Society of America

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References

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  1. J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
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  3. J. Li and J. B. Pendry, Phys. Rev. Lett. 101, 203901 (2008).
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    [CrossRef]
  5. H. F. Ma and T. J. Cui, Nat. Commun. 1, 124 (2010).
    [CrossRef]
  6. J. Hunt, T. Tyler, S. Dhar, Y. J. Tsai, P. Bowen, S. Larouche, N. M. Jokerst, and D. R. Smith, Opt. Express 20, 1706 (2012).
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  7. M. G. Andreasen, IEEE Trans. Antennas Propag. 13, 303 (1965).
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  10. A. Taflove, and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, 2005).
  11. J. A. Kong, Electromagnetic Wave Theory (Wiley-Interscience, 1986).
  12. R. K. Luneburg, Mathematical Theory of Optics (Brown University, 1944).

2012

2010

D.-H. Kwon and D. H. Werner, IEEE Antennas Propag. Mag. 52, 24 (2010).
[CrossRef]

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

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

2009

J. Hoffmann, C. Hafner, P. Leidenberger, J. Hesselbarth, and S. Burger, Proc. SPIE 7390, 73900J (2009).
[CrossRef]

2008

J. Li and J. B. Pendry, Phys. Rev. Lett. 101, 203901 (2008).
[CrossRef]

2006

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

2001

1965

M. G. Andreasen, IEEE Trans. Antennas Propag. 13, 303 (1965).
[CrossRef]

Andreasen, M. G.

M. G. Andreasen, IEEE Trans. Antennas Propag. 13, 303 (1965).
[CrossRef]

Bowen, P.

Burger, S.

J. Hoffmann, C. Hafner, P. Leidenberger, J. Hesselbarth, and S. Burger, Proc. SPIE 7390, 73900J (2009).
[CrossRef]

Cui, T. J.

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

Dhar, S.

Hafner, C.

J. Hoffmann, C. Hafner, P. Leidenberger, J. Hesselbarth, and S. Burger, Proc. SPIE 7390, 73900J (2009).
[CrossRef]

Hagness, S. C.

A. Taflove, and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, 2005).

Hesselbarth, J.

J. Hoffmann, C. Hafner, P. Leidenberger, J. Hesselbarth, and S. Burger, Proc. SPIE 7390, 73900J (2009).
[CrossRef]

Hoffmann, J.

J. Hoffmann, C. Hafner, P. Leidenberger, J. Hesselbarth, and S. Burger, Proc. SPIE 7390, 73900J (2009).
[CrossRef]

Hunt, J.

Jokerst, N. M.

Kong, J. A.

J. A. Kong, Electromagnetic Wave Theory (Wiley-Interscience, 1986).

Kundtz, N.

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

Kwon, D.-H.

D.-H. Kwon and D. H. Werner, IEEE Antennas Propag. Mag. 52, 24 (2010).
[CrossRef]

Larouche, S.

Leidenberger, P.

J. Hoffmann, C. Hafner, P. Leidenberger, J. Hesselbarth, and S. Burger, Proc. SPIE 7390, 73900J (2009).
[CrossRef]

Li, J.

J. Li and J. B. Pendry, Phys. Rev. Lett. 101, 203901 (2008).
[CrossRef]

Luneburg, R. K.

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

Ma, H. F.

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

Pendry, J. B.

J. Li and J. B. Pendry, Phys. Rev. Lett. 101, 203901 (2008).
[CrossRef]

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

Prather, D. W.

Schurig, D.

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

Shi, S.

Smith, D. R.

J. Hunt, T. Tyler, S. Dhar, Y. J. Tsai, P. Bowen, S. Larouche, N. M. Jokerst, and D. R. Smith, Opt. Express 20, 1706 (2012).
[CrossRef]

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

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

Taflove, A.

A. Taflove, and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, 2005).

Tsai, Y. J.

Tyler, T.

Werner, D. H.

D.-H. Kwon and D. H. Werner, IEEE Antennas Propag. Mag. 52, 24 (2010).
[CrossRef]

IEEE Antennas Propag. Mag.

D.-H. Kwon and D. H. Werner, IEEE Antennas Propag. Mag. 52, 24 (2010).
[CrossRef]

IEEE Trans. Antennas Propag.

M. G. Andreasen, IEEE Trans. Antennas Propag. 13, 303 (1965).
[CrossRef]

J. Opt. Soc. Am. A

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

Phys. Rev. Lett.

J. Li and J. B. Pendry, Phys. Rev. Lett. 101, 203901 (2008).
[CrossRef]

Proc. SPIE

J. Hoffmann, C. Hafner, P. Leidenberger, J. Hesselbarth, and S. Burger, Proc. SPIE 7390, 73900J (2009).
[CrossRef]

Science

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

Other

A. Taflove, and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, 2005).

J. A. Kong, Electromagnetic Wave Theory (Wiley-Interscience, 1986).

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

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Figures (5)

Fig. 1.
Fig. 1.

(a) Cross section of the computational domain in the BOR-FDTD method and (b) a TM-polarized obliquely incident plane wave upon a dielectric half-space.

Fig. 2.
Fig. 2.

Dielectric constant profile in the XOZ plane for (a) the spherical shaped Luneburg lens, (b) planar flattened TO Luneburg GRIN lens in free space, and (c) with a substrate.

Fig. 3.
Fig. 3.

Imaging properties of a 3D conventional spherical Luneburg lens in free space.

Fig. 4.
Fig. 4.

Imaging properties of a 3D axisymmetric flat TO Luneburg lens in free space.

Fig. 5.
Fig. 5.

Imaging properties of a 3D axisymmetric flat TO Luneburg lens on a dielectric substrate.

Tables (1)

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Table 1. BOR-FDTD Method Versus COMSOL Software

Equations (16)

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EρU=E0cosθim=02cmF1(t,m)Jm(s)cos(mϕ),
EϕU=E0cosθim=02cmF1(t,m)B(s,m)sin(mϕ),
EzU=E0sinθim=02cmF2(t,m)Jm(s)cos(mϕ),
EρL=cosθtTTME0m=02cmF3(t,m)Jm(s)cos(mϕ),
EϕL=cosθtTTME0m=02cmF3(t,m)B(s,m)sin(mϕ),
EzL=sinθtTTME0m=02cmF4(t,m)Jm(s)cos(mϕ),
F1(t,m)=ejp1(t,m)RTMejq1(t,m),
F2(t,m)=ejp2(t,m)+RTMejq2(t,m),
F3(t,m)=ejg1(t,m),
F4(t,m)=ejg2(t,m)
p1(t,m)=ω(t+cosθiz/c)+0.5π(m1),
q1(t,m)=ω(tcosθiz/c)+0.5π(m1),
p2(t,m)=ω(t+cosθiz/c)+0.5πm
q2(t,m)=ω(tcosθiz/c)+0.5πm,
g1(t,m)=ω(tεtrsin2θiz/c)+0.5π(m1),
g2(t,m)=ω(tεtrsin2θiz/c)+0.5πm,

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