Abstract

We analyze electromagnetic field propagation through a random medium that consists of hyperbolic metamaterial domains separated by regions of normal “elliptic” space. This situation may occur in a problem as common as 9 μm light propagation through a pile of sand, or as exotic as electromagnetic field behavior in the early universe immediately after the electroweak phase transition. We demonstrate that spatial field distributions in random hyperbolic and random “elliptic” media look strikingly different. Optical field is strongly enhanced at the boundaries of hyperbolic domains. This effect may potentially be used to evaluate the magnitude of magnetic fields which existed in the early universe.

© 2013 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. I. I. Smolyaninov, J. Opt. 13, 125101 (2011).
    [CrossRef]

2012 (2)

I. I. Smolyaninov, Phys. Rev. D 85, 114013 (2012).
[CrossRef]

I. I. Smolyaninov, E. Hwang, and E. E. Narimanov, Phys. Rev. B 85, 235122 (2012).
[CrossRef]

2011 (3)

I. I. Smolyaninov, J. Opt. 13, 125101 (2011).
[CrossRef]

I. I. Smolyaninov, Phys. Rev. Lett. 107, 253903 (2011).
[CrossRef]

M. N. Chernodub, Phys. Rev. Lett. 106, 142003 (2011).
[CrossRef]

2010 (2)

M. N. Chernodub, Phys. Rev. D 82, 085011 (2010).
[CrossRef]

P. J. E. Peebles and A. Nusser, Nature 465, 565 (2010).
[CrossRef]

2007 (2)

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, Science 315, 1699 (2007).
[CrossRef]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

2006 (2)

A. Salandrino and N. Engheta, Phys. Rev. B 74, 075103 (2006).
[CrossRef]

Z. Jakob, L. V. Alekseyev, and E. Narimanov, Opt. Express 14, 8247 (2006).
[CrossRef]

2003 (1)

D. R. Smith and D. Schurig, Phys. Rev. Lett. 90, 077405 (2003).
[CrossRef]

2001 (1)

D. Grasso and H. R. Rubinstein, Phys. Rep. 348, 163 (2001).
[CrossRef]

1983 (1)

P. R. Griffiths, Science 222, 297 (1983).
[CrossRef]

Alekseyev, L. V.

Chernodub, M. N.

M. N. Chernodub, Phys. Rev. Lett. 106, 142003 (2011).
[CrossRef]

M. N. Chernodub, Phys. Rev. D 82, 085011 (2010).
[CrossRef]

Davis, C. C.

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, Science 315, 1699 (2007).
[CrossRef]

Engheta, N.

A. Salandrino and N. Engheta, Phys. Rev. B 74, 075103 (2006).
[CrossRef]

Grasso, D.

D. Grasso and H. R. Rubinstein, Phys. Rep. 348, 163 (2001).
[CrossRef]

Griffiths, P. R.

P. R. Griffiths, Science 222, 297 (1983).
[CrossRef]

Hung, Y. J.

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, Science 315, 1699 (2007).
[CrossRef]

Hwang, E.

I. I. Smolyaninov, E. Hwang, and E. E. Narimanov, Phys. Rev. B 85, 235122 (2012).
[CrossRef]

Jakob, Z.

Lee, H.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

Liu, Z.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

Narimanov, E.

Narimanov, E. E.

I. I. Smolyaninov, E. Hwang, and E. E. Narimanov, Phys. Rev. B 85, 235122 (2012).
[CrossRef]

Nusser, A.

P. J. E. Peebles and A. Nusser, Nature 465, 565 (2010).
[CrossRef]

Peebles, P. J. E.

P. J. E. Peebles and A. Nusser, Nature 465, 565 (2010).
[CrossRef]

Rubinstein, H. R.

D. Grasso and H. R. Rubinstein, Phys. Rep. 348, 163 (2001).
[CrossRef]

Salandrino, A.

A. Salandrino and N. Engheta, Phys. Rev. B 74, 075103 (2006).
[CrossRef]

Schurig, D.

D. R. Smith and D. Schurig, Phys. Rev. Lett. 90, 077405 (2003).
[CrossRef]

Smith, D. R.

D. R. Smith and D. Schurig, Phys. Rev. Lett. 90, 077405 (2003).
[CrossRef]

Smolyaninov, I. I.

I. I. Smolyaninov, E. Hwang, and E. E. Narimanov, Phys. Rev. B 85, 235122 (2012).
[CrossRef]

I. I. Smolyaninov, Phys. Rev. D 85, 114013 (2012).
[CrossRef]

I. I. Smolyaninov, Phys. Rev. Lett. 107, 253903 (2011).
[CrossRef]

I. I. Smolyaninov, J. Opt. 13, 125101 (2011).
[CrossRef]

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, Science 315, 1699 (2007).
[CrossRef]

Sun, C.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

Xiong, Y.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

Zhang, X.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

J. Opt. (1)

I. I. Smolyaninov, J. Opt. 13, 125101 (2011).
[CrossRef]

Nature (1)

P. J. E. Peebles and A. Nusser, Nature 465, 565 (2010).
[CrossRef]

Opt. Express (1)

Phys. Rep. (1)

D. Grasso and H. R. Rubinstein, Phys. Rep. 348, 163 (2001).
[CrossRef]

Phys. Rev. B (2)

A. Salandrino and N. Engheta, Phys. Rev. B 74, 075103 (2006).
[CrossRef]

I. I. Smolyaninov, E. Hwang, and E. E. Narimanov, Phys. Rev. B 85, 235122 (2012).
[CrossRef]

Phys. Rev. D (2)

I. I. Smolyaninov, Phys. Rev. D 85, 114013 (2012).
[CrossRef]

M. N. Chernodub, Phys. Rev. D 82, 085011 (2010).
[CrossRef]

Phys. Rev. Lett. (3)

I. I. Smolyaninov, Phys. Rev. Lett. 107, 253903 (2011).
[CrossRef]

M. N. Chernodub, Phys. Rev. Lett. 106, 142003 (2011).
[CrossRef]

D. R. Smith and D. Schurig, Phys. Rev. Lett. 90, 077405 (2003).
[CrossRef]

Science (3)

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, Science 315, 1699 (2007).
[CrossRef]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

P. R. Griffiths, Science 222, 297 (1983).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Spatial distribution of εx and εy components of the anisotropic dielectric tensor inside a single hyperbolic domain. In the vector representation used in this plot, the tensor components are shown as a (εx, εy) vector. At the domain boundary indicated by a dashed line both εx and εy change continuously to the vacuum ε=1 value.

Fig. 2.
Fig. 2.

Field distributions around a single circular hyperbolic domain when a dipole source is placed in different locations inside and just outside the domain. The plots show absolute value of electric field. The dipole position is marked by a red dot.

Fig. 3.
Fig. 3.

Example of field distribution in a random three-domain configuration. Panels (a)–(c) show εxx, εxy and εyy components of the dielectric tensor. Field distribution in logarithmic scale is plotted in panel (d). A dipole radiation source is positioned at the center of the field of view.

Fig. 4.
Fig. 4.

(a), (b) Magnitude of electric field in a three-domain configuration depending on the source position: in all cases field is concentrated at domain boundaries. The common scale bar is given in panel (b). (c)–(e) Comparison of electric field behavior in two identical multiple-domain configurations of (d) hyperbolic and (e) “elliptic” domains. Domain configuration in the field of view is shown in (c). The common scale bar is given in panel (e).

Equations (7)

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

2E⃗c2t2=ε1∇⃗×∇⃗×E⃗,
2φc2t2=2φε1z2+1ε2(2φx2+2φy2),
ds2=g2z2dt2+dx2+dy2+dz2,
1g2z22φt2+2φx2+2φy2+2φz2+1zφz=m2c22φ.
2ψτ2=(2x22y22z214z2+m2c22)ψ.
ω2c2=k2+kz214z2+m2c22.
ω2c2=k2ε2+kz2ε1.

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