Abstract

Following our recently developed idea of employing plasmonic covers to cloak an isolated conducting, plasmonic or insulating sphere through scattering cancellation, here we extend this concept by investigating the possibility of cloaking multiple objects placed in close proximity of each other, or even joined together to form a single object of large electrical size. We show how the coupling among the single particles, even when placed in the very near zone of each other, is drastically lowered by the presence of suitably designed covers, thus providing the possibility of making collections of objects transparent and “cloaked” to the impinging radiation even when the total physical size of the system is sensibly larger than the wavelength. Numerical simulations and animations validate these results and give further insights into the anomalous phenomenon of transparency and cloaking induced by plasmonic materials and metamaterials.

© 2007 Optical Society of America

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  1. A. Alù and N. Engheta, "Achieving transparency with plasmonic and metamaterial coatings," Phys. Rev. E 72, 016623 (2005).
    [CrossRef]
  2. A. Alù and N. Engheta, "Plasmonic materials in transparency and cloaking problems: mechanism, robustness, and physical insights," Opt. Express 15, 3318-3332 (2007).
    [CrossRef] [PubMed]
  3. M. G. Silveirinha, A. Alù, and N. Engheta, "Parallel plate metamaterials for total scattering reduction," Phys. Rev. E 75, 036603 (2007).
    [CrossRef]
  4. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, U.S.A., 1983).
  5. J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
    [CrossRef] [PubMed]
  6. 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]
  7. N. A. Nicorovici, R. C. McPhedran, and G. W. Milton, "Optical and dielectric properties of partially resonant composites," Phys. Rev. B 49, 8479-8482 (1994).
    [CrossRef]
  8. G. W. Milton and N. A. Nicorovici, "On the cloaking effects associated with anomalous localized resonance," Proc. R. Soc. Lond. A: Math. Phys. Sci. 462, 3027-59 (2006).
    [CrossRef]
  9. U. Leonhardt, "Optical conformal mapping," Science 312, 1777-1780 (2006).
    [CrossRef] [PubMed]
  10. CST Studio Suite 2006B, CST of America, Inc., www.cst.com.
  11. R. W. Ziolkowski and N. Engheta, (guest editors), IEEE Trans. Antennas Propag. 51, 2546-2750 (2003).
    [CrossRef]
  12. W. Rotman, "Plasma simulation by artificial dielectrics and parallel-plate media," IRE Trans. Antennas Propag. 10, 82-95 (1962).
    [CrossRef]
  13. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Low frequency plasmons in thin-wire structures," J. Phys. Condens. Matter 10, 4785-4809 (1998).
    [CrossRef]
  14. C. H. Papas, Theory of Electromagnetic Wave Propagation (Dover Publications, New York, U.S.A., 1988).
  15. J. D. Jackson, Classical Electrodynamics (Wiley, New York, U.S.A., 1998).
  16. A. Alù and N. Engheta, "Polarizabilities and effective parameters for collections of spherical nano-particles formed by pairs of concentric double-negative (DNG), single-negative (SNG) and/or double-positive (DPS) metamaterial layers," J. Appl. Phys. 97, 094310 (2005); erratum in: J. Appl. Phys. 99, 069901 (2006).
    [CrossRef]
  17. M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, New York, U.S.A., 1972).
  18. We understand that a material like the one considered here, with combined plasmonic properties and magnetic permeability higher than that of free space, may not be readily available in nature. However, here and in [2] we are mainly concerned in showing the fundamental theoretical possibilities of this cloaking technique. In the present simulations, therefore, we have employed a sample cover that may simultaneously cancel two multipolar orders (i.e., electric dipole and magnetic dipole moments), requiring electric and magnetic parameters different from those of the background. In different cases, or for different purposes, however, as shown in [1], [3], it may be enough to rely just on plasmonic materials with required permittivity (with no magnetic response, i.e., with relative permeability of unity), which may be available in different ranges of frequencies. Moreover, the material suggested here may be fabricated in some frequency range, in order to have required values of permittivity and permeability. Distinctly from other proposed techniques for metamaterial cloaking, the examples reported here rely on isotropic and homogeneous materials or metamaterials.
  19. Heuristically, we may justify this down-shift in the cloaking frequency for the horizontal polarization, when the objects touch or are merged together, with the following considerations: in the horizontal polarization the electrical contact and the resulting current flow between the two objects may generate an electric dipole moment somehow larger than those of two separate objects. Therefore, for the same cover geometry and material, a slightly lower frequency provides a closer-to-zero permittivity for the material cover, or effectively a larger induced "opposite" dipole moment that may cancel the increase in the dipole moment scattered by the merged object. In reality, the dynamics is more complex than this simple picture, due to contributions from higher-order multipoles and interactions between the object and the cover, but the results in Fig. 1-2 appears to be consistent with this explanation. The cloaking frequency may be easily re-tuned to the desired value by slightly increasing the cover thickness or changing the plasma frequency of the cloaking material.

2007

A. Alù and N. Engheta, "Plasmonic materials in transparency and cloaking problems: mechanism, robustness, and physical insights," Opt. Express 15, 3318-3332 (2007).
[CrossRef] [PubMed]

M. G. Silveirinha, A. Alù, and N. Engheta, "Parallel plate metamaterials for total scattering reduction," Phys. Rev. E 75, 036603 (2007).
[CrossRef]

2006

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]

G. W. Milton and N. A. Nicorovici, "On the cloaking effects associated with anomalous localized resonance," Proc. R. Soc. Lond. A: Math. Phys. Sci. 462, 3027-59 (2006).
[CrossRef]

U. Leonhardt, "Optical conformal mapping," Science 312, 1777-1780 (2006).
[CrossRef] [PubMed]

A. Alù and N. Engheta, "Polarizabilities and effective parameters for collections of spherical nano-particles formed by pairs of concentric double-negative (DNG), single-negative (SNG) and/or double-positive (DPS) metamaterial layers," J. Appl. Phys. 97, 094310 (2005); erratum in: J. Appl. Phys. 99, 069901 (2006).
[CrossRef]

2005

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

2003

R. W. Ziolkowski and N. Engheta, (guest editors), IEEE Trans. Antennas Propag. 51, 2546-2750 (2003).
[CrossRef]

1998

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Low frequency plasmons in thin-wire structures," J. Phys. Condens. Matter 10, 4785-4809 (1998).
[CrossRef]

1994

N. A. Nicorovici, R. C. McPhedran, and G. W. Milton, "Optical and dielectric properties of partially resonant composites," Phys. Rev. B 49, 8479-8482 (1994).
[CrossRef]

1962

W. Rotman, "Plasma simulation by artificial dielectrics and parallel-plate media," IRE Trans. Antennas Propag. 10, 82-95 (1962).
[CrossRef]

Alù, A.

A. Alù and N. Engheta, "Plasmonic materials in transparency and cloaking problems: mechanism, robustness, and physical insights," Opt. Express 15, 3318-3332 (2007).
[CrossRef] [PubMed]

M. G. Silveirinha, A. Alù, and N. Engheta, "Parallel plate metamaterials for total scattering reduction," Phys. Rev. E 75, 036603 (2007).
[CrossRef]

A. Alù and N. Engheta, "Polarizabilities and effective parameters for collections of spherical nano-particles formed by pairs of concentric double-negative (DNG), single-negative (SNG) and/or double-positive (DPS) metamaterial layers," J. Appl. Phys. 97, 094310 (2005); erratum in: J. Appl. Phys. 99, 069901 (2006).
[CrossRef]

A. Alù and N. Engheta, "Achieving transparency with plasmonic and metamaterial coatings," Phys. Rev. E 72, 016623 (2005).
[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]

Engheta, N.

A. Alù and N. Engheta, "Plasmonic materials in transparency and cloaking problems: mechanism, robustness, and physical insights," Opt. Express 15, 3318-3332 (2007).
[CrossRef] [PubMed]

M. G. Silveirinha, A. Alù, and N. Engheta, "Parallel plate metamaterials for total scattering reduction," Phys. Rev. E 75, 036603 (2007).
[CrossRef]

A. Alù and N. Engheta, "Polarizabilities and effective parameters for collections of spherical nano-particles formed by pairs of concentric double-negative (DNG), single-negative (SNG) and/or double-positive (DPS) metamaterial layers," J. Appl. Phys. 97, 094310 (2005); erratum in: J. Appl. Phys. 99, 069901 (2006).
[CrossRef]

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

R. W. Ziolkowski and N. Engheta, (guest editors), IEEE Trans. Antennas Propag. 51, 2546-2750 (2003).
[CrossRef]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Low frequency plasmons in thin-wire structures," J. Phys. Condens. Matter 10, 4785-4809 (1998).
[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]

Leonhardt, U.

U. Leonhardt, "Optical conformal mapping," Science 312, 1777-1780 (2006).
[CrossRef] [PubMed]

McPhedran, R. C.

N. A. Nicorovici, R. C. McPhedran, and G. W. Milton, "Optical and dielectric properties of partially resonant composites," Phys. Rev. B 49, 8479-8482 (1994).
[CrossRef]

Milton, G. W.

G. W. Milton and N. A. Nicorovici, "On the cloaking effects associated with anomalous localized resonance," Proc. R. Soc. Lond. A: Math. Phys. Sci. 462, 3027-59 (2006).
[CrossRef]

N. A. Nicorovici, R. C. McPhedran, and G. W. Milton, "Optical and dielectric properties of partially resonant composites," Phys. Rev. B 49, 8479-8482 (1994).
[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]

Nicorovici, N. A.

G. W. Milton and N. A. Nicorovici, "On the cloaking effects associated with anomalous localized resonance," Proc. R. Soc. Lond. A: Math. Phys. Sci. 462, 3027-59 (2006).
[CrossRef]

N. A. Nicorovici, R. C. McPhedran, and G. W. Milton, "Optical and dielectric properties of partially resonant composites," Phys. Rev. B 49, 8479-8482 (1994).
[CrossRef]

Pendry, J. B.

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]

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

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Low frequency plasmons in thin-wire structures," J. Phys. Condens. Matter 10, 4785-4809 (1998).
[CrossRef]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Low frequency plasmons in thin-wire structures," J. Phys. Condens. Matter 10, 4785-4809 (1998).
[CrossRef]

Rotman, W.

W. Rotman, "Plasma simulation by artificial dielectrics and parallel-plate media," IRE Trans. Antennas Propag. 10, 82-95 (1962).
[CrossRef]

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.

M. G. Silveirinha, A. Alù, and N. Engheta, "Parallel plate metamaterials for total scattering reduction," Phys. Rev. E 75, 036603 (2007).
[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]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Low frequency plasmons in thin-wire structures," J. Phys. Condens. Matter 10, 4785-4809 (1998).
[CrossRef]

Ziolkowski, R. W.

R. W. Ziolkowski and N. Engheta, (guest editors), IEEE Trans. Antennas Propag. 51, 2546-2750 (2003).
[CrossRef]

IEEE Trans. Antennas Propag.

R. W. Ziolkowski and N. Engheta, (guest editors), IEEE Trans. Antennas Propag. 51, 2546-2750 (2003).
[CrossRef]

IRE Trans. Antennas Propag.

W. Rotman, "Plasma simulation by artificial dielectrics and parallel-plate media," IRE Trans. Antennas Propag. 10, 82-95 (1962).
[CrossRef]

J. Appl. Phys.

A. Alù and N. Engheta, "Polarizabilities and effective parameters for collections of spherical nano-particles formed by pairs of concentric double-negative (DNG), single-negative (SNG) and/or double-positive (DPS) metamaterial layers," J. Appl. Phys. 97, 094310 (2005); erratum in: J. Appl. Phys. 99, 069901 (2006).
[CrossRef]

J. Phys. Condens. Matter

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Low frequency plasmons in thin-wire structures," J. Phys. Condens. Matter 10, 4785-4809 (1998).
[CrossRef]

Opt. Express

Phys. Rev. B

N. A. Nicorovici, R. C. McPhedran, and G. W. Milton, "Optical and dielectric properties of partially resonant composites," Phys. Rev. B 49, 8479-8482 (1994).
[CrossRef]

Phys. Rev. E

M. G. Silveirinha, A. Alù, and N. Engheta, "Parallel plate metamaterials for total scattering reduction," Phys. Rev. E 75, 036603 (2007).
[CrossRef]

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

Proc. R. Soc. Lond. A: Math. Phys. Sci.

G. W. Milton and N. A. Nicorovici, "On the cloaking effects associated with anomalous localized resonance," Proc. R. Soc. Lond. A: Math. Phys. Sci. 462, 3027-59 (2006).
[CrossRef]

Science

U. Leonhardt, "Optical conformal mapping," Science 312, 1777-1780 (2006).
[CrossRef] [PubMed]

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]

Other

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, U.S.A., 1983).

CST Studio Suite 2006B, CST of America, Inc., www.cst.com.

C. H. Papas, Theory of Electromagnetic Wave Propagation (Dover Publications, New York, U.S.A., 1988).

J. D. Jackson, Classical Electrodynamics (Wiley, New York, U.S.A., 1998).

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, New York, U.S.A., 1972).

We understand that a material like the one considered here, with combined plasmonic properties and magnetic permeability higher than that of free space, may not be readily available in nature. However, here and in [2] we are mainly concerned in showing the fundamental theoretical possibilities of this cloaking technique. In the present simulations, therefore, we have employed a sample cover that may simultaneously cancel two multipolar orders (i.e., electric dipole and magnetic dipole moments), requiring electric and magnetic parameters different from those of the background. In different cases, or for different purposes, however, as shown in [1], [3], it may be enough to rely just on plasmonic materials with required permittivity (with no magnetic response, i.e., with relative permeability of unity), which may be available in different ranges of frequencies. Moreover, the material suggested here may be fabricated in some frequency range, in order to have required values of permittivity and permeability. Distinctly from other proposed techniques for metamaterial cloaking, the examples reported here rely on isotropic and homogeneous materials or metamaterials.

Heuristically, we may justify this down-shift in the cloaking frequency for the horizontal polarization, when the objects touch or are merged together, with the following considerations: in the horizontal polarization the electrical contact and the resulting current flow between the two objects may generate an electric dipole moment somehow larger than those of two separate objects. Therefore, for the same cover geometry and material, a slightly lower frequency provides a closer-to-zero permittivity for the material cover, or effectively a larger induced "opposite" dipole moment that may cancel the increase in the dipole moment scattered by the merged object. In reality, the dynamics is more complex than this simple picture, due to contributions from higher-order multipoles and interactions between the object and the cover, but the results in Fig. 1-2 appears to be consistent with this explanation. The cloaking frequency may be easily re-tuned to the desired value by slightly increasing the cover thickness or changing the plasma frequency of the cloaking material.

Supplementary Material (6)

» Media 1: GIF (1590 KB)     
» Media 2: GIF (1221 KB)     
» Media 3: GIF (2181 KB)     
» Media 4: GIF (1685 KB)     
» Media 5: GIF (1784 KB)     
» Media 6: GIF (1233 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

Maximum peak in the scattering cross section pattern for a system of two spheres, each of them composed of an impenetrable core with diameter 2a = 0.4λ 0 and (only for the solid lines) a cover shell with εc = ε 0 (1-ωp 2/[ω(ω-)]), μc = 5.1μ 0, ac = 1.09a, ωp = 0.95ω 0, γ = 0.016 ω 0. The black lines correspond to vertical polarization of the impinging electric field, the red lines to horizontal polarization. (By ‘vertical’ and ‘horizontal’, we mean the electric field vector of the incident wave is ‘perpendicular’ and ‘parallel’ with the axis of the chain of spheres, respectively.) The dashed lines correspond to the uncovered cases. The four figures correspond to: (a) closely spaced spheres with a gap between the covers of λ 0/25; (b) touching covers; (c) touching cores and merged covers; (d) merged cores and covers. In all these figures, for sake of comparison, the lines relative to a single isolated sphere have also been plotted.

Fig. 2.
Fig. 2.

Maximum peak in the scattering cross section pattern for a system of four spheres, analogous to Fig. 1. Different colors correspond to various angles of incidence of the impinging wave (with the electric field in the plane of incidence). The four figures correspond to different spacing between the spheres, analogously to Fig. 1.

Fig. 3.
Fig. 3.

Phase of the total magnetic field distribution in the E plane for the case of four aligned spheres as in Fig. 2(a) with: (a) angle of incidence θ = 0°, covered case (movie, 1.55 MB) [Media 1]; (b) angle of incidence θ = 0°, uncovered case (movie, 1.19 MB) [Media 2]; (c) oblique incidence θ = 45° , covered (movie, 2.12 MB) [Media 3]; (d) oblique incidence θ = 45° , uncovered (movie, 1.64 MB) [Media 4]; (e) angle of incidence θ = 90°, covered (movie, 1.74 MB) [Media 5]; (f) angle of incidence θ = 90°, uncovered (movie, 1.20 MB) [Media 6]. The movies show the time-domain animations relative to the same field distribution to which each one of the panels refers.

Fig. 4.
Fig. 4.

Amplitude of the total magnetic field distribution in the E plane for the case of four aligned spheres: (a) with a gap of λ 0/25 between neighboring covers, covered case; (b) with touching core spheres and intersecting covers; (c) with merged core spheres; (d)-(f) are the same as (a)-(c) but removing the cover materials. A TM plane wave impinges at θ = 45° to excite the system.

Fig. 5.
Fig. 5.

Real part of the time-averaged Poynting vector (power flow) distribution in the E plane for the same cases as in Fig. 4.

Equations (2)

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

E = n = 1 m = n n a n m × × ( r ψ n m ) + i ω μ 0 n = 1 m = n n b n m × ( r ψ n m ) H = n = 1 m = n n b n m × × ( r ψ n m ) i ω ε 0 n = 1 m = n n a n m × ( r ψ n m ) ,
j n ( k a ) j n ( k c a ) y n ( k c a ) 0 [ k a j n ( k a ) ]′ ε [ k c a j n ( k c a ) ]′ ε c [ k c a y n ( k c a ) ]′ ε c 0 0 j n ( k c a c ) y n ( k c a c ) j n ( k 0 a c ) 0 [ k c a c j n ( k c a c ) ]′ ε c [ k c a c y n ( k c a c ) ]′ ε c [ k 0 a c j n ( k 0 a c ) ]′ ε 0 = 0 ,

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