Abstract

The possibility of making an optically large (many wavelengths in diameter) object appear invisible has been a subject of many recent studies. Exact invisibility scenarios for large (relative to the wavelength) objects involve (meta)materials with superluminal phase velocity [refractive index (RI) less than unity] and/or magnetic response. We introduce a new approximation applicable to certain device geometries in the eikonal limit: piecewise-uniform scaling of the RI. This transformation preserves the ray trajectories but leads to a uniform phase delay. We show how to take advantage of phase delays to achieve a limited (directional and wavelength-dependent) form of invisibility that does not require loss-ridden (meta)materials with superluminal phase velocities.

© 2012 Optical Society of America

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  1. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
    [CrossRef]
  2. J. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
    [CrossRef]
  3. Y. Urzhumov, W. Chen, C. Bingham, W. Padilla, and D. R. Smith, Phys. Rev. B 85, 054430 (2012).
    [CrossRef]
  4. D. Huang, Y. Urzhumov, D. R. Smith, K. H. Teo, and J. Zhang, Phys. Rev. B 111, 064902 (2012).
    [CrossRef]
  5. H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, Nature 444, 597 (2006).
    [CrossRef]
  6. A. K. Sarychev and V. M. Shalaev, Electrodynamics of Metamaterials (World Scientific, 2007).
  7. A. Alu and N. Engheta, Phys. Rev. Lett. 100, 113901(2008).
    [CrossRef]
  8. S. Tretyakov, P. Alitalo, O. Luukkonen, and C. Simovski, Phys. Rev. Lett. 103, 103905 (2009).
    [CrossRef]
  9. W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, Appl. Phys. Lett. 91, 111105 (2007).
    [CrossRef]
  10. Y. A. Urzhumov, F. Ghezzo, J. Hunt, and D. R. Smith, New J. Phys. 12, 073014 (2010).
    [CrossRef]
  11. Y. A. Urzhumov, N. B. Kundtz, D. R. Smith, and J. B. Pendry, J. Opt. 13, 024002 (2011).
    [CrossRef]
  12. Y. Urzhumov, N. Landy, and D. R. Smith, J. Appl. Phys. 111, 053105 (2012).
    [CrossRef]
  13. U. Leonhardt, Science 312, 1777 (2006).
    [CrossRef]
  14. B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, Phys. Rev. Lett. 106, 033901 (2011).
    [CrossRef]
  15. N. I. Landy, N. Kundtz, and D. R. Smith, Phys. Rev. Lett. 105, 193902 (2010).
    [CrossRef]
  16. Y. A. Urzhumov and D. R. Smith, Phys. Rev. Lett. 105, 163901 (2010).
    [CrossRef]
  17. L. J. Boya and R. Murray, Phys. Rev. A 50, 4397 (1994).
    [CrossRef]

2012 (3)

Y. Urzhumov, W. Chen, C. Bingham, W. Padilla, and D. R. Smith, Phys. Rev. B 85, 054430 (2012).
[CrossRef]

D. Huang, Y. Urzhumov, D. R. Smith, K. H. Teo, and J. Zhang, Phys. Rev. B 111, 064902 (2012).
[CrossRef]

Y. Urzhumov, N. Landy, and D. R. Smith, J. Appl. Phys. 111, 053105 (2012).
[CrossRef]

2011 (2)

Y. A. Urzhumov, N. B. Kundtz, D. R. Smith, and J. B. Pendry, J. Opt. 13, 024002 (2011).
[CrossRef]

B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, Phys. Rev. Lett. 106, 033901 (2011).
[CrossRef]

2010 (3)

N. I. Landy, N. Kundtz, and D. R. Smith, Phys. Rev. Lett. 105, 193902 (2010).
[CrossRef]

Y. A. Urzhumov and D. R. Smith, Phys. Rev. Lett. 105, 163901 (2010).
[CrossRef]

Y. A. Urzhumov, F. Ghezzo, J. Hunt, and D. R. Smith, New J. Phys. 12, 073014 (2010).
[CrossRef]

2009 (1)

S. Tretyakov, P. Alitalo, O. Luukkonen, and C. Simovski, Phys. Rev. Lett. 103, 103905 (2009).
[CrossRef]

2008 (1)

A. Alu and N. Engheta, Phys. Rev. Lett. 100, 113901(2008).
[CrossRef]

2007 (1)

W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, Appl. Phys. Lett. 91, 111105 (2007).
[CrossRef]

2006 (4)

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, Nature 444, 597 (2006).
[CrossRef]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef]

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

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

1994 (1)

L. J. Boya and R. Murray, Phys. Rev. A 50, 4397 (1994).
[CrossRef]

Alitalo, P.

S. Tretyakov, P. Alitalo, O. Luukkonen, and C. Simovski, Phys. Rev. Lett. 103, 103905 (2009).
[CrossRef]

Alu, A.

A. Alu and N. Engheta, Phys. Rev. Lett. 100, 113901(2008).
[CrossRef]

Averitt, R. D.

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, Nature 444, 597 (2006).
[CrossRef]

Barbastathis, G.

B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, Phys. Rev. Lett. 106, 033901 (2011).
[CrossRef]

Bingham, C.

Y. Urzhumov, W. Chen, C. Bingham, W. Padilla, and D. R. Smith, Phys. Rev. B 85, 054430 (2012).
[CrossRef]

Boya, L. J.

L. J. Boya and R. Murray, Phys. Rev. A 50, 4397 (1994).
[CrossRef]

Cai, W.

W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, Appl. Phys. Lett. 91, 111105 (2007).
[CrossRef]

Chen, H.-T.

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, Nature 444, 597 (2006).
[CrossRef]

Chen, W.

Y. Urzhumov, W. Chen, C. Bingham, W. Padilla, and D. R. Smith, Phys. Rev. B 85, 054430 (2012).
[CrossRef]

Chettiar, U. K.

W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, Appl. Phys. Lett. 91, 111105 (2007).
[CrossRef]

Cummer, S. A.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef]

Engheta, N.

A. Alu and N. Engheta, Phys. Rev. Lett. 100, 113901(2008).
[CrossRef]

Ghezzo, F.

Y. A. Urzhumov, F. Ghezzo, J. Hunt, and D. R. Smith, New J. Phys. 12, 073014 (2010).
[CrossRef]

Gossard, A. C.

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, Nature 444, 597 (2006).
[CrossRef]

Huang, D.

D. Huang, Y. Urzhumov, D. R. Smith, K. H. Teo, and J. Zhang, Phys. Rev. B 111, 064902 (2012).
[CrossRef]

Hunt, J.

Y. A. Urzhumov, F. Ghezzo, J. Hunt, and D. R. Smith, New J. Phys. 12, 073014 (2010).
[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, Science 314, 977 (2006).
[CrossRef]

Kildishev, A. V.

W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, Appl. Phys. Lett. 91, 111105 (2007).
[CrossRef]

Kundtz, N.

N. I. Landy, N. Kundtz, and D. R. Smith, Phys. Rev. Lett. 105, 193902 (2010).
[CrossRef]

Kundtz, N. B.

Y. A. Urzhumov, N. B. Kundtz, D. R. Smith, and J. B. Pendry, J. Opt. 13, 024002 (2011).
[CrossRef]

Landy, N.

Y. Urzhumov, N. Landy, and D. R. Smith, J. Appl. Phys. 111, 053105 (2012).
[CrossRef]

Landy, N. I.

N. I. Landy, N. Kundtz, and D. R. Smith, Phys. Rev. Lett. 105, 193902 (2010).
[CrossRef]

Leonhardt, U.

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

Liu, X.

B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, Phys. Rev. Lett. 106, 033901 (2011).
[CrossRef]

Luo, Y.

B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, Phys. Rev. Lett. 106, 033901 (2011).
[CrossRef]

Luukkonen, O.

S. Tretyakov, P. Alitalo, O. Luukkonen, and C. Simovski, Phys. Rev. Lett. 103, 103905 (2009).
[CrossRef]

Milton, G. W.

W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, Appl. Phys. Lett. 91, 111105 (2007).
[CrossRef]

Mock, J. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef]

Murray, R.

L. J. Boya and R. Murray, Phys. Rev. A 50, 4397 (1994).
[CrossRef]

Padilla, W.

Y. Urzhumov, W. Chen, C. Bingham, W. Padilla, and D. R. Smith, Phys. Rev. B 85, 054430 (2012).
[CrossRef]

Padilla, W. J.

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, Nature 444, 597 (2006).
[CrossRef]

Pendry, J.

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

Pendry, J. B.

Y. A. Urzhumov, N. B. Kundtz, D. R. Smith, and J. B. Pendry, J. Opt. 13, 024002 (2011).
[CrossRef]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef]

Sarychev, A. K.

A. K. Sarychev and V. M. Shalaev, Electrodynamics of Metamaterials (World Scientific, 2007).

Schurig, D.

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

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef]

Shalaev, V. M.

W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, Appl. Phys. Lett. 91, 111105 (2007).
[CrossRef]

A. K. Sarychev and V. M. Shalaev, Electrodynamics of Metamaterials (World Scientific, 2007).

Simovski, C.

S. Tretyakov, P. Alitalo, O. Luukkonen, and C. Simovski, Phys. Rev. Lett. 103, 103905 (2009).
[CrossRef]

Smith, D. R.

Y. Urzhumov, N. Landy, and D. R. Smith, J. Appl. Phys. 111, 053105 (2012).
[CrossRef]

Y. Urzhumov, W. Chen, C. Bingham, W. Padilla, and D. R. Smith, Phys. Rev. B 85, 054430 (2012).
[CrossRef]

D. Huang, Y. Urzhumov, D. R. Smith, K. H. Teo, and J. Zhang, Phys. Rev. B 111, 064902 (2012).
[CrossRef]

Y. A. Urzhumov, N. B. Kundtz, D. R. Smith, and J. B. Pendry, J. Opt. 13, 024002 (2011).
[CrossRef]

N. I. Landy, N. Kundtz, and D. R. Smith, Phys. Rev. Lett. 105, 193902 (2010).
[CrossRef]

Y. A. Urzhumov, F. Ghezzo, J. Hunt, and D. R. Smith, New J. Phys. 12, 073014 (2010).
[CrossRef]

Y. A. Urzhumov and D. R. Smith, Phys. Rev. Lett. 105, 163901 (2010).
[CrossRef]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef]

J. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (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, Science 314, 977 (2006).
[CrossRef]

Taylor, A. J.

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, Nature 444, 597 (2006).
[CrossRef]

Teo, K. H.

D. Huang, Y. Urzhumov, D. R. Smith, K. H. Teo, and J. Zhang, Phys. Rev. B 111, 064902 (2012).
[CrossRef]

Tretyakov, S.

S. Tretyakov, P. Alitalo, O. Luukkonen, and C. Simovski, Phys. Rev. Lett. 103, 103905 (2009).
[CrossRef]

Urzhumov, Y.

Y. Urzhumov, N. Landy, and D. R. Smith, J. Appl. Phys. 111, 053105 (2012).
[CrossRef]

D. Huang, Y. Urzhumov, D. R. Smith, K. H. Teo, and J. Zhang, Phys. Rev. B 111, 064902 (2012).
[CrossRef]

Y. Urzhumov, W. Chen, C. Bingham, W. Padilla, and D. R. Smith, Phys. Rev. B 85, 054430 (2012).
[CrossRef]

Urzhumov, Y. A.

Y. A. Urzhumov, N. B. Kundtz, D. R. Smith, and J. B. Pendry, J. Opt. 13, 024002 (2011).
[CrossRef]

Y. A. Urzhumov, F. Ghezzo, J. Hunt, and D. R. Smith, New J. Phys. 12, 073014 (2010).
[CrossRef]

Y. A. Urzhumov and D. R. Smith, Phys. Rev. Lett. 105, 163901 (2010).
[CrossRef]

Zhang, B.

B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, Phys. Rev. Lett. 106, 033901 (2011).
[CrossRef]

Zhang, J.

D. Huang, Y. Urzhumov, D. R. Smith, K. H. Teo, and J. Zhang, Phys. Rev. B 111, 064902 (2012).
[CrossRef]

Zide, J. M. O.

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, Nature 444, 597 (2006).
[CrossRef]

Appl. Phys. Lett. (1)

W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, Appl. Phys. Lett. 91, 111105 (2007).
[CrossRef]

J. Appl. Phys. (1)

Y. Urzhumov, N. Landy, and D. R. Smith, J. Appl. Phys. 111, 053105 (2012).
[CrossRef]

J. Opt. (1)

Y. A. Urzhumov, N. B. Kundtz, D. R. Smith, and J. B. Pendry, J. Opt. 13, 024002 (2011).
[CrossRef]

Nature (1)

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, Nature 444, 597 (2006).
[CrossRef]

New J. Phys. (1)

Y. A. Urzhumov, F. Ghezzo, J. Hunt, and D. R. Smith, New J. Phys. 12, 073014 (2010).
[CrossRef]

Phys. Rev. A (1)

L. J. Boya and R. Murray, Phys. Rev. A 50, 4397 (1994).
[CrossRef]

Phys. Rev. B (2)

Y. Urzhumov, W. Chen, C. Bingham, W. Padilla, and D. R. Smith, Phys. Rev. B 85, 054430 (2012).
[CrossRef]

D. Huang, Y. Urzhumov, D. R. Smith, K. H. Teo, and J. Zhang, Phys. Rev. B 111, 064902 (2012).
[CrossRef]

Phys. Rev. Lett. (5)

A. Alu and N. Engheta, Phys. Rev. Lett. 100, 113901(2008).
[CrossRef]

S. Tretyakov, P. Alitalo, O. Luukkonen, and C. Simovski, Phys. Rev. Lett. 103, 103905 (2009).
[CrossRef]

B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, Phys. Rev. Lett. 106, 033901 (2011).
[CrossRef]

N. I. Landy, N. Kundtz, and D. R. Smith, Phys. Rev. Lett. 105, 193902 (2010).
[CrossRef]

Y. A. Urzhumov and D. R. Smith, Phys. Rev. Lett. 105, 163901 (2010).
[CrossRef]

Science (3)

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

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef]

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

Other (1)

A. K. Sarychev and V. M. Shalaev, Electrodynamics of Metamaterials (World Scientific, 2007).

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Figures (2)

Fig. 1.
Fig. 1.

Effect of RI scaling in a TM-polarization cloak with a=1m, b/a=0.5, and B/a=1. (a) Field plot (Hz) at λ0=(2a)/40; no RI scaling (fi=1). Black lines are EM flux streamlines, coincident with ray traces in the eikonal limit. (b) Same as (a), but with RI scaling factor fi=2 (sufficient to make ϵ1,21); λ0=(2a)/40. (c) Same as (b) (fi=2), but at λ0=(2a)/34.2. (d) Near-field scattering cross-section (SCS), σNF, versus frequency in the index-scaled cloak with fi=2; abscissa is Δϕ/(2π)=k0(2a)(fi1)/(2π) (number of phase delay cycles per cloak length 2a).

Fig. 2.
Fig. 2.

Directional TM-polarization cloak without magnetic response (μzz=1). (a) Field plot (Hz) at ν=5.396 GHz and (b) near-field SCS (σNF) as a function of frequency, showing a series of FPR-like transmission resonances.

Equations (2)

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

ϵxxI=1,ϵxyI=ϵyxI=r,ϵyyI=1+r2,μzzI=1,ϵxxII=χ,ϵxyII=ϵyxII=0,ϵyyII=1/χ,μzzII=χ,
I:x=x,y=yrxb,II:x=x,y=χ(yb),

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