Abstract

We introduce a new concept of the nonlinear control of invisibility cloaking. We study the scattering properties of multi-shell plasmonic nanoparticles with a nonlinear response of one of the shells, and demonstrate that the scattering cross-section of such particles can be controlled by a power of the incident electromagnetic radiation. More specifically, we can either increase or decrease the scattering cross-section by changing the intensity of the external field, as well as control the scattering efficiently and even reverse the radiation direction.

© 2012 OSA

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  1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
    [CrossRef] [PubMed]
  2. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
    [CrossRef] [PubMed]
  3. A. Alu and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016623 (2005).
    [CrossRef]
  4. A. Alu and N. Engheta, “Polarizabilities and effective parameters for collections of spherical nanoparticles formed by pairs of concentric double-negative, single-negative, andor double-positive metamaterial layers,” J. Appl. Phys. 97, 094310 (2005).
    [CrossRef]
  5. A. Alu and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic shells,” Phys. Rev. Lett. 100, 113901 (2008).
    [CrossRef] [PubMed]
  6. B. Edwards, A. Alu, M. G. Silveirinha, and N. Engheta, “Experimental verification of plasmonic cloaking at microwave frequencies with metamaterials,” Phys. Rev. Lett. 103, 153901 (2009).
    [CrossRef] [PubMed]
  7. A. A. Zharov and N. A. Zharova, “On the electromagnetic cloaking of (Nano)particles,” Bulletin of the Russian Academy of Sciences: Physics 74, 89–92 (2010).
    [CrossRef]
  8. D. S. Filonov, A. P. Slobozhanyuk, P. A. Belov, and Yu. S. Kivshar, “Double-shell metamaterial coatings for plasmonic cloaking,” Phys. Status Solidi: Rapid Res. Lett. 6, 46–48 (2012).
    [CrossRef]

2012 (1)

D. S. Filonov, A. P. Slobozhanyuk, P. A. Belov, and Yu. S. Kivshar, “Double-shell metamaterial coatings for plasmonic cloaking,” Phys. Status Solidi: Rapid Res. Lett. 6, 46–48 (2012).
[CrossRef]

2010 (1)

A. A. Zharov and N. A. Zharova, “On the electromagnetic cloaking of (Nano)particles,” Bulletin of the Russian Academy of Sciences: Physics 74, 89–92 (2010).
[CrossRef]

2009 (1)

B. Edwards, A. Alu, M. G. Silveirinha, and N. Engheta, “Experimental verification of plasmonic cloaking at microwave frequencies with metamaterials,” Phys. Rev. Lett. 103, 153901 (2009).
[CrossRef] [PubMed]

2008 (1)

A. Alu and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic shells,” Phys. Rev. Lett. 100, 113901 (2008).
[CrossRef] [PubMed]

2006 (2)

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

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

2005 (2)

A. Alu and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016623 (2005).
[CrossRef]

A. Alu and N. Engheta, “Polarizabilities and effective parameters for collections of spherical nanoparticles formed by pairs of concentric double-negative, single-negative, andor double-positive metamaterial layers,” J. Appl. Phys. 97, 094310 (2005).
[CrossRef]

Alu, A.

B. Edwards, A. Alu, M. G. Silveirinha, and N. Engheta, “Experimental verification of plasmonic cloaking at microwave frequencies with metamaterials,” Phys. Rev. Lett. 103, 153901 (2009).
[CrossRef] [PubMed]

A. Alu and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic shells,” Phys. Rev. Lett. 100, 113901 (2008).
[CrossRef] [PubMed]

A. Alu and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016623 (2005).
[CrossRef]

A. Alu and N. Engheta, “Polarizabilities and effective parameters for collections of spherical nanoparticles formed by pairs of concentric double-negative, single-negative, andor double-positive metamaterial layers,” J. Appl. Phys. 97, 094310 (2005).
[CrossRef]

Belov, P. A.

D. S. Filonov, A. P. Slobozhanyuk, P. A. Belov, and Yu. S. Kivshar, “Double-shell metamaterial coatings for plasmonic cloaking,” Phys. Status Solidi: Rapid Res. Lett. 6, 46–48 (2012).
[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, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

Edwards, B.

B. Edwards, A. Alu, M. G. Silveirinha, and N. Engheta, “Experimental verification of plasmonic cloaking at microwave frequencies with metamaterials,” Phys. Rev. Lett. 103, 153901 (2009).
[CrossRef] [PubMed]

Engheta, N.

B. Edwards, A. Alu, M. G. Silveirinha, and N. Engheta, “Experimental verification of plasmonic cloaking at microwave frequencies with metamaterials,” Phys. Rev. Lett. 103, 153901 (2009).
[CrossRef] [PubMed]

A. Alu and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic shells,” Phys. Rev. Lett. 100, 113901 (2008).
[CrossRef] [PubMed]

A. Alu and N. Engheta, “Polarizabilities and effective parameters for collections of spherical nanoparticles formed by pairs of concentric double-negative, single-negative, andor double-positive metamaterial layers,” J. Appl. Phys. 97, 094310 (2005).
[CrossRef]

A. Alu and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016623 (2005).
[CrossRef]

Filonov, D. S.

D. S. Filonov, A. P. Slobozhanyuk, P. A. Belov, and Yu. S. Kivshar, “Double-shell metamaterial coatings for plasmonic cloaking,” Phys. Status Solidi: Rapid Res. Lett. 6, 46–48 (2012).
[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, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

Kivshar, Yu. S.

D. S. Filonov, A. P. Slobozhanyuk, P. A. Belov, and Yu. S. Kivshar, “Double-shell metamaterial coatings for plasmonic cloaking,” Phys. Status Solidi: Rapid Res. Lett. 6, 46–48 (2012).
[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, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

Pendry, J. B.

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

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

Schurig, D.

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

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

Silveirinha, M. G.

B. Edwards, A. Alu, M. G. Silveirinha, and N. Engheta, “Experimental verification of plasmonic cloaking at microwave frequencies with metamaterials,” Phys. Rev. Lett. 103, 153901 (2009).
[CrossRef] [PubMed]

Slobozhanyuk, A. P.

D. S. Filonov, A. P. Slobozhanyuk, P. A. Belov, and Yu. S. Kivshar, “Double-shell metamaterial coatings for plasmonic cloaking,” Phys. Status Solidi: Rapid Res. Lett. 6, 46–48 (2012).
[CrossRef]

Smith, D. R.

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

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

Starr, A. F.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

Zharov, A. A.

A. A. Zharov and N. A. Zharova, “On the electromagnetic cloaking of (Nano)particles,” Bulletin of the Russian Academy of Sciences: Physics 74, 89–92 (2010).
[CrossRef]

Zharova, N. A.

A. A. Zharov and N. A. Zharova, “On the electromagnetic cloaking of (Nano)particles,” Bulletin of the Russian Academy of Sciences: Physics 74, 89–92 (2010).
[CrossRef]

Bulletin of the Russian Academy of Sciences: Physics (1)

A. A. Zharov and N. A. Zharova, “On the electromagnetic cloaking of (Nano)particles,” Bulletin of the Russian Academy of Sciences: Physics 74, 89–92 (2010).
[CrossRef]

J. Appl. Phys. (1)

A. Alu and N. Engheta, “Polarizabilities and effective parameters for collections of spherical nanoparticles formed by pairs of concentric double-negative, single-negative, andor double-positive metamaterial layers,” J. Appl. Phys. 97, 094310 (2005).
[CrossRef]

Phys. Rev. E (1)

A. Alu and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016623 (2005).
[CrossRef]

Phys. Rev. Lett. (2)

A. Alu and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic shells,” Phys. Rev. Lett. 100, 113901 (2008).
[CrossRef] [PubMed]

B. Edwards, A. Alu, M. G. Silveirinha, and N. Engheta, “Experimental verification of plasmonic cloaking at microwave frequencies with metamaterials,” Phys. Rev. Lett. 103, 153901 (2009).
[CrossRef] [PubMed]

Phys. Status Solidi: Rapid Res. Lett. (1)

D. S. Filonov, A. P. Slobozhanyuk, P. A. Belov, and Yu. S. Kivshar, “Double-shell metamaterial coatings for plasmonic cloaking,” Phys. Status Solidi: Rapid Res. Lett. 6, 46–48 (2012).
[CrossRef]

Science (2)

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

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

(a) Normalized scattering cross-sections for several lower-order multipoles (solid lines, m=0,1,2), as well as total SCS (dashed) as functions of the dielectric constant ε2 of the second layer. Parameters are k0R1,2,3 = 0.4, 0.5, 0.866, ε1,3 = 15, 2, (ε2) = 0.02. Inset shows geometry of the problem. (b) Dependencies of the normalized multipole and total scattering cross-sections on the dielectric constant ε3 of the external layer. Dimensions of the cylinders and dielectric permittivity of the core are the same as in (a), ε2 = −0.1+0.02i.

Fig. 2
Fig. 2

Distribution of the intensity of the electric field in (a) the whole space (b) everywhere but layer 2. Sizes of the shells are the same as in Fig. 1. ε1,2,3 = 15; 0.02 + 0.02i; 2. The fields are normalized to the amplitude of the incident wave.

Fig. 3
Fig. 3

Normalized scattering cross-sections for several lower-order multipoles (solid lines, m = 0,1), as well as total SCS (dashed) as functions of the intensity. (a) Defocusing non-linearity, ε2 = 0.1 + 0.02i, (b) focusing nonlinearity, ε2 = −0.1 + 0.02i; α = 5 · 10−8 esu.

Fig. 4
Fig. 4

Directivity of the nonlinear cloak. Color map shows scattering amplitude, while radial coordinate corresponds to the intensity of the incident wave (a) Defocusing nonlinearity, ε2 = 0.1 + 0.02i, (b) focusing nonlinearity, ε2 = −0.1 + 0.02i; α = 5 · 10−8 esu.

Fig. 5
Fig. 5

Distribution of the scattering electric field for three different values of the incident wave intensity: (a) 2.5 · 104W/cm2; (b) 2.51 · 106W/cm2, and (c) 2.66 · 106W/cm2, α = −5 · 10−8, ε2 = 0.1 − 0.02i.

Equations (5)

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R 2 = R 3 ( ε 3 1 ε 3 + 1 ) 1 / 2 .
h = z 0 A 0 exp ( i ω t i k 0 r cos ϕ ) = z 0 A 0 exp ( i ω t ) [ J 0 ( ρ ) + 2 m = 1 i m J m ( ρ ) cos ( m ϕ ) ] ,
H ( j ) = m = 0 M [ A m ( j ) J m ( ρ j ) + B m ( j ) Y m ( ρ j ) ] cos ( m ϕ ) ,
E ϕ ( j ) = m = 0 M k j k 0 { A m ( j ) J m ( ρ j ) + B m ( j ) Y m ( ρ j ) } cos ( m ϕ ) / ( i ε j ) , E r ( j ) = m = 0 M { ( A m ( j ) J m ( ρ j ) + B m ( j ) Y m ( ρ j ) } [ m sin ( m ϕ ) ] / ( i k 0 r ε j ) .
Δ H m ( r ) + [ ε ( r ) + δ ε ( 0 ) ( r ) m 2 / r 2 ] H m ( r ) = [ δ ε H _ ] m ,

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