Abstract

Transformational optics allows for unprecedented control of light with cylindrical cloaks, concentrators, rotators and superscatterers. These are made of different heterogeneous anisotropic media. Can one cloak an s-polarized field and concentrate (or rotate) a p-polarized field with the same metamaterial (or vice versa)? We show the answer is positive provided the geometric transforms underpinning these functionalities take the same values on the outer boundary of what we call a bicephalous metamaterial. In this way, one can also make a metallic cylinder appear invisible for one light polarization, and larger for the other.

© 2014 Optical Society of America

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References

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  1. J. B. Pendry, D. Shurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
    [Crossref] [PubMed]
  2. U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
    [Crossref] [PubMed]
  3. A. Alu and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 95, 016623 (2005).
    [Crossref]
  4. G. Milton and N. A. P. Nicorovici, “On the cloaking effects associated with anomalous localised resonance,” Proc. R. Soc. London A 462, 3027–3059 (2006).
    [Crossref]
  5. J. B. Pendry and S. Anantha Ramakrishna, “Focussing light with negative refractive index,” J. Phys.: Condens. Matter 15, 6345 (2003).
  6. M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct. Fundam. Appl. 6, 87–95 (2008).
    [Crossref]
  7. H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90, 241105 (2007).
    [Crossref]
  8. T. Yang, H. Chen, X. Luo, and H. Ma, “Superscatterer: enhancement of scattering with complementary media,” Opt. Express 16, 18545–18550 (2008).
    [Crossref] [PubMed]
  9. A. Nicolet, F. Zolla, and S. Guenneau, “A finite element modelling for twisted electromagnetic waveguides,” Eur. Phys. J. Appl. Phys. 28, 153–157 (2004).
    [Crossref]
  10. F. Zolla and S. Guenneau, “A duality relation for the Maxwell system,” Phys. Rev. E 67, 026610 (2003).
    [Crossref]
  11. A. J. Danner, T. Tyc, and U. Leonhardt, “Controlling birefringence in dielectrics,” Nat. Photon. 5, 357–359 (2011).
    [Crossref]
  12. V. N. Smolyaninova, H. K. Ermer, A. Piazza, D. Schaefer, and I. I. Smolyaninov, “Experimental demonstration of birefrigent transformation optics devices,” Phys. Rev. B 87, 075406 (2013).
    [Crossref]

2013 (1)

V. N. Smolyaninova, H. K. Ermer, A. Piazza, D. Schaefer, and I. I. Smolyaninov, “Experimental demonstration of birefrigent transformation optics devices,” Phys. Rev. B 87, 075406 (2013).
[Crossref]

2011 (1)

A. J. Danner, T. Tyc, and U. Leonhardt, “Controlling birefringence in dielectrics,” Nat. Photon. 5, 357–359 (2011).
[Crossref]

2008 (2)

T. Yang, H. Chen, X. Luo, and H. Ma, “Superscatterer: enhancement of scattering with complementary media,” Opt. Express 16, 18545–18550 (2008).
[Crossref] [PubMed]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct. Fundam. Appl. 6, 87–95 (2008).
[Crossref]

2007 (1)

H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90, 241105 (2007).
[Crossref]

2006 (3)

J. B. Pendry, D. Shurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[Crossref] [PubMed]

G. Milton and N. A. P. Nicorovici, “On the cloaking effects associated with anomalous localised resonance,” Proc. R. Soc. London A 462, 3027–3059 (2006).
[Crossref]

2005 (1)

A. Alu and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 95, 016623 (2005).
[Crossref]

2004 (1)

A. Nicolet, F. Zolla, and S. Guenneau, “A finite element modelling for twisted electromagnetic waveguides,” Eur. Phys. J. Appl. Phys. 28, 153–157 (2004).
[Crossref]

2003 (2)

F. Zolla and S. Guenneau, “A duality relation for the Maxwell system,” Phys. Rev. E 67, 026610 (2003).
[Crossref]

J. B. Pendry and S. Anantha Ramakrishna, “Focussing light with negative refractive index,” J. Phys.: Condens. Matter 15, 6345 (2003).

Alu, A.

A. Alu and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 95, 016623 (2005).
[Crossref]

Anantha Ramakrishna, S.

J. B. Pendry and S. Anantha Ramakrishna, “Focussing light with negative refractive index,” J. Phys.: Condens. Matter 15, 6345 (2003).

Chan, C. T.

H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90, 241105 (2007).
[Crossref]

Chen, H.

T. Yang, H. Chen, X. Luo, and H. Ma, “Superscatterer: enhancement of scattering with complementary media,” Opt. Express 16, 18545–18550 (2008).
[Crossref] [PubMed]

H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90, 241105 (2007).
[Crossref]

Cummer, S. A.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct. Fundam. Appl. 6, 87–95 (2008).
[Crossref]

Danner, A. J.

A. J. Danner, T. Tyc, and U. Leonhardt, “Controlling birefringence in dielectrics,” Nat. Photon. 5, 357–359 (2011).
[Crossref]

Engheta, N.

A. Alu and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 95, 016623 (2005).
[Crossref]

Ermer, H. K.

V. N. Smolyaninova, H. K. Ermer, A. Piazza, D. Schaefer, and I. I. Smolyaninov, “Experimental demonstration of birefrigent transformation optics devices,” Phys. Rev. B 87, 075406 (2013).
[Crossref]

Guenneau, S.

A. Nicolet, F. Zolla, and S. Guenneau, “A finite element modelling for twisted electromagnetic waveguides,” Eur. Phys. J. Appl. Phys. 28, 153–157 (2004).
[Crossref]

F. Zolla and S. Guenneau, “A duality relation for the Maxwell system,” Phys. Rev. E 67, 026610 (2003).
[Crossref]

Leonhardt, U.

A. J. Danner, T. Tyc, and U. Leonhardt, “Controlling birefringence in dielectrics,” Nat. Photon. 5, 357–359 (2011).
[Crossref]

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[Crossref] [PubMed]

Luo, X.

Ma, H.

Milton, G.

G. Milton and N. A. P. Nicorovici, “On the cloaking effects associated with anomalous localised resonance,” Proc. R. Soc. London A 462, 3027–3059 (2006).
[Crossref]

Nicolet, A.

A. Nicolet, F. Zolla, and S. Guenneau, “A finite element modelling for twisted electromagnetic waveguides,” Eur. Phys. J. Appl. Phys. 28, 153–157 (2004).
[Crossref]

Nicorovici, N. A. P.

G. Milton and N. A. P. Nicorovici, “On the cloaking effects associated with anomalous localised resonance,” Proc. R. Soc. London A 462, 3027–3059 (2006).
[Crossref]

Pendry, J. B.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct. Fundam. Appl. 6, 87–95 (2008).
[Crossref]

J. B. Pendry, D. Shurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

J. B. Pendry and S. Anantha Ramakrishna, “Focussing light with negative refractive index,” J. Phys.: Condens. Matter 15, 6345 (2003).

Piazza, A.

V. N. Smolyaninova, H. K. Ermer, A. Piazza, D. Schaefer, and I. I. Smolyaninov, “Experimental demonstration of birefrigent transformation optics devices,” Phys. Rev. B 87, 075406 (2013).
[Crossref]

Rahm, M.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct. Fundam. Appl. 6, 87–95 (2008).
[Crossref]

Roberts, D. A.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct. Fundam. Appl. 6, 87–95 (2008).
[Crossref]

Schaefer, D.

V. N. Smolyaninova, H. K. Ermer, A. Piazza, D. Schaefer, and I. I. Smolyaninov, “Experimental demonstration of birefrigent transformation optics devices,” Phys. Rev. B 87, 075406 (2013).
[Crossref]

Schurig, D.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct. Fundam. Appl. 6, 87–95 (2008).
[Crossref]

Shurig, D.

J. B. Pendry, D. Shurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

Smith, D. R.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct. Fundam. Appl. 6, 87–95 (2008).
[Crossref]

J. B. Pendry, D. Shurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

Smolyaninov, I. I.

V. N. Smolyaninova, H. K. Ermer, A. Piazza, D. Schaefer, and I. I. Smolyaninov, “Experimental demonstration of birefrigent transformation optics devices,” Phys. Rev. B 87, 075406 (2013).
[Crossref]

Smolyaninova, V. N.

V. N. Smolyaninova, H. K. Ermer, A. Piazza, D. Schaefer, and I. I. Smolyaninov, “Experimental demonstration of birefrigent transformation optics devices,” Phys. Rev. B 87, 075406 (2013).
[Crossref]

Tyc, T.

A. J. Danner, T. Tyc, and U. Leonhardt, “Controlling birefringence in dielectrics,” Nat. Photon. 5, 357–359 (2011).
[Crossref]

Yang, T.

Zolla, F.

A. Nicolet, F. Zolla, and S. Guenneau, “A finite element modelling for twisted electromagnetic waveguides,” Eur. Phys. J. Appl. Phys. 28, 153–157 (2004).
[Crossref]

F. Zolla and S. Guenneau, “A duality relation for the Maxwell system,” Phys. Rev. E 67, 026610 (2003).
[Crossref]

Appl. Phys. Lett. (1)

H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90, 241105 (2007).
[Crossref]

Eur. Phys. J. Appl. Phys. (1)

A. Nicolet, F. Zolla, and S. Guenneau, “A finite element modelling for twisted electromagnetic waveguides,” Eur. Phys. J. Appl. Phys. 28, 153–157 (2004).
[Crossref]

J. Phys.: Condens. Matter (1)

J. B. Pendry and S. Anantha Ramakrishna, “Focussing light with negative refractive index,” J. Phys.: Condens. Matter 15, 6345 (2003).

Nat. Photon. (1)

A. J. Danner, T. Tyc, and U. Leonhardt, “Controlling birefringence in dielectrics,” Nat. Photon. 5, 357–359 (2011).
[Crossref]

Opt. Express (1)

Photon. Nanostruct. Fundam. Appl. (1)

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct. Fundam. Appl. 6, 87–95 (2008).
[Crossref]

Phys. Rev. B (1)

V. N. Smolyaninova, H. K. Ermer, A. Piazza, D. Schaefer, and I. I. Smolyaninov, “Experimental demonstration of birefrigent transformation optics devices,” Phys. Rev. B 87, 075406 (2013).
[Crossref]

Phys. Rev. E (2)

F. Zolla and S. Guenneau, “A duality relation for the Maxwell system,” Phys. Rev. E 67, 026610 (2003).
[Crossref]

A. Alu and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 95, 016623 (2005).
[Crossref]

Proc. R. Soc. London A (1)

G. Milton and N. A. P. Nicorovici, “On the cloaking effects associated with anomalous localised resonance,” Proc. R. Soc. London A 462, 3027–3059 (2006).
[Crossref]

Science (2)

J. B. Pendry, D. Shurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[Crossref] [PubMed]

Cited By

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Figures (3)

Fig. 1
Fig. 1

Bicephalous metamaterial rotating Ez field and concentrating Hz field: A plane wave of wavelength 1.4μm incident from the top rotates the longitudinal electric field Ez in p-polarization and concentrates the longitudinal magnetic field Hz in s-polarization. The difference in color scale is due to the large field inside the rotator in (a).

Fig. 2
Fig. 2

Superscatterer in Ez and cloak in Hz with inner radius 2.5μm and outer radius 4μm:: A plane wave of wavelength 1.4μm incident from the top enhances the scattering by an infinite conducting obstacle of radius 2.5μm for the longitudinal electric field Ez in p-polarization (b), which scatters like an infinite conducting obstacle of radius 6.4μm (a). This first bicephalous cloak/superscatterer makes an infinite conducting obstacle of radius 2.5μm (c) invisible for the longitudinal magnetic field Hz in s-polarization (d).

Fig. 3
Fig. 3

Superscatterer in Hz and cloak in Ez with inner radius 2.5μm and outer radius 4μm: A plane wave of wavelength 1.4μm incident from the top enhances the scattering by an infinite conducting obstacle of radius 2.5μm for the longitudinal magnetic field Hz in s-polarization (b), which scatters like an infinite conducting obstacle of radius 6.4μm (a). This second bicephalous cloak/superscatterer makes an infinite conducting obstacle of radius 2.5μm (c) invisible for the longitudinal electric field Ez in p-polarization (d).

Equations (20)

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ε ̳ = ε 0 ε r T 1 and μ ̳ = μ 0 μ r T 1 ,
× ( μ ̳ 1 × E l ) ω 2 ε ̳ E l = 0 ,
( ε ̳ 1 × H l ) ω 2 μ ̳ H l = 0 ,
M ( x , y ) = ( m 11 ( x , y ) m ( x , y ) 0 m ( x , y ) m 22 ( x , y ) 0 0 0 m 33 ( x , y ) ) = ( M T ( x , y ) 0 0 m 33 ( x , y ) ) .
× ( M × ( u ( x , y ) e z ) ) = ( R ( π / 2 ) M T R ( π / 2 ) u ( x , y ) ) e z .
( μ r 1 R ( π / 2 ) T T R ( π / 2 ) ) E z ) + μ 0 ε 0 ε r ( T 33 ) 1 ω 2 E z = 0 ,
( ε r 1 R ( π / 2 ) T T R ( π / 2 ) ) H z ) + μ 0 ε 0 μ r ( T 33 ) 1 ω 2 H z = 0 .
ε ̳ 1 = ε 0 1 ε r 1 T 1 = ( T 11 T 12 0 T 21 T 22 0 0 0 T 33 ) , μ ̳ 1 = μ 0 1 μ r 1 T 2 = ( T 11 T 12 0 T 21 T 22 0 0 0 T 33 ) ,
{ R 1 ( θ ) = 0.4 R ( 1 + 0.2 sin ( 3 θ ) ) ; R 2 ( θ ) = 0.6 R ( 1 + 0.2 sin ( 3 θ ) ) R = 0.4 ; R 3 ( θ ) = R ( 1 + 0.2 sin ( 3 θ ) + cos ( 4 θ ) ) )
r = α r + β , 0 r < + , θ = θ , 0 < θ 2 π , z = z , < z <
{ α = R 1 ( θ ) R 2 ( θ ) β = 0 ( 0 r R 1 ( θ ) ) α = R 3 ( θ ) R 1 ( θ ) R 3 ( θ ) R 2 ( θ ) β = R 3 ( θ ) R 1 ( θ ) R 2 ( θ ) R 3 ( θ ) R 2 ( θ ) ( R 1 ( θ ) r R 3 ( θ ) )
T 1 = ( ( T 1 ) 11 ( T 1 ) 12 0 ( T 1 ) 21 ( T 1 ) 22 0 0 0 ( T 1 ) 33 ) = R ( θ ) ( ( r β ) 2 + c 22 2 α 2 ( r β ) r c 22 α r β 0 c 22 α r β r r β 0 0 0 r β α 2 r ) R ( θ ) T
r = r , 0 r < + , θ = α r + β , 0 < θ 2 π , z = z , < z <
α = θ o R 1 ( θ ) R 2 ( θ ) , β = θ + R 2 ( θ ) θ o R 2 ( θ ) R 1 ( θ ) , R 1 ( θ ) r R 2 ( θ ) ,
T 1 = ( ( T 1 ) 11 ( T 1 ) 12 0 ( T 1 ) 21 ( T 1 ) 22 0 0 0 1 ) = R ( θ ) ( c 22 α r 0 α r 1 + α 2 r 2 c 22 0 0 0 c 22 ) R ( θ ) T
1 r ε z z r ( r μ θ θ E z r ) + 1 r 2 ε z z θ ( r μ r r E z θ ) + μ 0 ε 0 ω 2 E z = 0 ,
1 r μ z z r ( r ε θ θ H z r ) + 1 r 2 μ z z θ ( r ε r r H z θ ) + μ 0 ε 0 ω 2 H z = 0 ,
r = f ( r ) = ( r R 1 ) / α , 0 < r < + , θ = θ , 0 < θ 2 π , z = z , < z <
r = g ( r ) = r R 1 2 / R 2 2 , 0 < r < R 2 2 / R 1 , θ = θ , 0 < θ 2 π , z = z , < z < r = g ( r ) = R 2 2 / r , R 1 r R 2 , θ = θ , 0 < θ 2 π , z = z , < z <
ε ̳ = ε r Diag ( f / ( f r ) , r f / f , g / ( r g ) ) = ε r Diag ( R 1 + α r α r , α r R 1 + α r , ± 1 ) , μ ̳ = μ r Diag ( g / ( g r ) , r g / g , f / ( r f ) ) = μ r Diag ( ± 1 , ± 1 , R 1 + α r α r ) ,

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