Abstract

Strong reduction of the scattering cross section is obtained for subwavelength dielectric and conducting cylinders without any magnetism for both TE and TM polarizations. The suggested approach is based on the use of Fabry-Perot type radial resonances, which can appear in single-layer, high-ε, isotropic, and homogeneous shells with the properly chosen parameters. Frequencies of the minima of the scattering cross section, which are associated with the cloaking, typically depend on whether TE or TM polarization is considered. In some cases, large-positive-ε and large-negative-ε objects can be cloaked. In other cases, non-ideal multifrequency cloaking can be realized.

© 2009 OSA

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References

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  1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 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(5801), 977–980 (2006).
    [CrossRef] [PubMed]
  3. S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering theory derivation of a 3D acoustic cloaking shell,” Phys. Rev. Lett. 100(2), 024301 (2008).
    [CrossRef] [PubMed]
  4. N.-A. P. Nicorovici, G. W. Milton, R. C. McPhedran, and L. C. Botten, “Quasistatic cloaking of two-dimensional polarizable discrete systems by anomalous resonance,” Opt. Express 15(10), 6314–6323 (2007).
    [CrossRef] [PubMed]
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    [CrossRef]
  6. A. Alù and N. Engheta, “Plasmonic materials in transparency and cloaking problems: mechanism, robustness, and physical insights,” Opt. Express 15(6), 3318–3332 (2007).
    [CrossRef] [PubMed]
  7. A. Alù and N. Engheta, “Effects of size and frequency dispersion in plasmonic cloaking,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(4), 045602 (2008).
    [CrossRef] [PubMed]
  8. P. Alitalo, O. Luukkonen, J. Mosig, and S. Tretyakov, “Broadband cloaking with volumetric structures composed of two-dimensional transmission-line networks,” Microw. Opt. Technol. Lett. 51(7), 1627–1631 (2009).
    [CrossRef]
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    [CrossRef]
  10. A. E. Serebryannikov and E. Ozbay, “Multifrequency invisibility and masking of cylindrical dielectric objects using double-positive and double-negative metamaterials,” J. Opt. A, Pure Appl. Opt. (to appear).
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    [CrossRef]
  12. D. P. Gaillot, C. Croënne, and D. Lippens, “An all-dielectric route for terahertz cloaking,” Opt. Express 16(6), 3986–3992 (2008).
    [CrossRef] [PubMed]
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    [CrossRef]
  14. S. Tusseau-Nenez, J.-P. Ganne, M. Maglione, A. Morell, J.-C. Niepce, and M. Pate, “BST ceramics: effect of attrition milling on dielectric properties,” J. Eur. Ceram. Soc. 24(10-11), 3003–3011 (2004).
    [CrossRef]
  15. A. V. Kildishev and E. E. Narimanov, “Impedance-matched hyperlens,” Opt. Lett. 32(23), 3432–3434 (2007).
    [CrossRef] [PubMed]
  16. A. Alù and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic shells,” Phys. Rev. Lett. 100(11), 113901 (2008).
    [CrossRef] [PubMed]

2009 (2)

P. Alitalo, O. Luukkonen, J. Mosig, and S. Tretyakov, “Broadband cloaking with volumetric structures composed of two-dimensional transmission-line networks,” Microw. Opt. Technol. Lett. 51(7), 1627–1631 (2009).
[CrossRef]

P. Alitalo, F. Bongard, J.-F. Zurcher, J. Mosig, and S. Tretyakov, “Expermental verification of broadband cloaking using a volumetric cloak composed of periodically stacked cylindrical transmission-line networks,” Appl. Phys. Lett. 94(1), 014103 (2009).
[CrossRef]

2008 (7)

N. M. Litchinitser and V. M. Shalaev, “Photonic metamaterials,” Laser Phys. Lett. 5(6), 411–420 (2008).
[CrossRef]

N.-A. P. Nicorovici, R. C. McPhedran, S. Enoch, and G. Tayeb, “Finite wavelength cloaking by plasmonic resonance,” N. J. Phys. 10(11), 115020 (2008).
[CrossRef]

F. Bilotti, S. Tricarico, and L. Vegni, “Electromagnetic cloaking devices for TE and TM polarizations,” N. J. Phys. 10(11), 115035 (2008).
[CrossRef]

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering theory derivation of a 3D acoustic cloaking shell,” Phys. Rev. Lett. 100(2), 024301 (2008).
[CrossRef] [PubMed]

A. Alù and N. Engheta, “Effects of size and frequency dispersion in plasmonic cloaking,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(4), 045602 (2008).
[CrossRef] [PubMed]

A. Alù and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic shells,” Phys. Rev. Lett. 100(11), 113901 (2008).
[CrossRef] [PubMed]

D. P. Gaillot, C. Croënne, and D. Lippens, “An all-dielectric route for terahertz cloaking,” Opt. Express 16(6), 3986–3992 (2008).
[CrossRef] [PubMed]

2007 (3)

2006 (2)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 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(5801), 977–980 (2006).
[CrossRef] [PubMed]

2004 (1)

S. Tusseau-Nenez, J.-P. Ganne, M. Maglione, A. Morell, J.-C. Niepce, and M. Pate, “BST ceramics: effect of attrition milling on dielectric properties,” J. Eur. Ceram. Soc. 24(10-11), 3003–3011 (2004).
[CrossRef]

Alitalo, P.

P. Alitalo, O. Luukkonen, J. Mosig, and S. Tretyakov, “Broadband cloaking with volumetric structures composed of two-dimensional transmission-line networks,” Microw. Opt. Technol. Lett. 51(7), 1627–1631 (2009).
[CrossRef]

P. Alitalo, F. Bongard, J.-F. Zurcher, J. Mosig, and S. Tretyakov, “Expermental verification of broadband cloaking using a volumetric cloak composed of periodically stacked cylindrical transmission-line networks,” Appl. Phys. Lett. 94(1), 014103 (2009).
[CrossRef]

Alù, A.

A. Alù and N. Engheta, “Effects of size and frequency dispersion in plasmonic cloaking,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(4), 045602 (2008).
[CrossRef] [PubMed]

A. Alù and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic shells,” Phys. Rev. Lett. 100(11), 113901 (2008).
[CrossRef] [PubMed]

A. Alù and N. Engheta, “Plasmonic materials in transparency and cloaking problems: mechanism, robustness, and physical insights,” Opt. Express 15(6), 3318–3332 (2007).
[CrossRef] [PubMed]

Bilotti, F.

F. Bilotti, S. Tricarico, and L. Vegni, “Electromagnetic cloaking devices for TE and TM polarizations,” N. J. Phys. 10(11), 115035 (2008).
[CrossRef]

Bongard, F.

P. Alitalo, F. Bongard, J.-F. Zurcher, J. Mosig, and S. Tretyakov, “Expermental verification of broadband cloaking using a volumetric cloak composed of periodically stacked cylindrical transmission-line networks,” Appl. Phys. Lett. 94(1), 014103 (2009).
[CrossRef]

Botten, L. C.

Croënne, C.

Cummer, S. A.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering theory derivation of a 3D acoustic cloaking shell,” Phys. Rev. Lett. 100(2), 024301 (2008).
[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(5801), 977–980 (2006).
[CrossRef] [PubMed]

Engheta, N.

A. Alù and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic shells,” Phys. Rev. Lett. 100(11), 113901 (2008).
[CrossRef] [PubMed]

A. Alù and N. Engheta, “Effects of size and frequency dispersion in plasmonic cloaking,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(4), 045602 (2008).
[CrossRef] [PubMed]

A. Alù and N. Engheta, “Plasmonic materials in transparency and cloaking problems: mechanism, robustness, and physical insights,” Opt. Express 15(6), 3318–3332 (2007).
[CrossRef] [PubMed]

Enoch, S.

N.-A. P. Nicorovici, R. C. McPhedran, S. Enoch, and G. Tayeb, “Finite wavelength cloaking by plasmonic resonance,” N. J. Phys. 10(11), 115020 (2008).
[CrossRef]

Gaillot, D. P.

Ganne, J.-P.

S. Tusseau-Nenez, J.-P. Ganne, M. Maglione, A. Morell, J.-C. Niepce, and M. Pate, “BST ceramics: effect of attrition milling on dielectric properties,” J. Eur. Ceram. Soc. 24(10-11), 3003–3011 (2004).
[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(5801), 977–980 (2006).
[CrossRef] [PubMed]

Kildishev, A. V.

Lippens, D.

Litchinitser, N. M.

N. M. Litchinitser and V. M. Shalaev, “Photonic metamaterials,” Laser Phys. Lett. 5(6), 411–420 (2008).
[CrossRef]

Luukkonen, O.

P. Alitalo, O. Luukkonen, J. Mosig, and S. Tretyakov, “Broadband cloaking with volumetric structures composed of two-dimensional transmission-line networks,” Microw. Opt. Technol. Lett. 51(7), 1627–1631 (2009).
[CrossRef]

Maglione, M.

S. Tusseau-Nenez, J.-P. Ganne, M. Maglione, A. Morell, J.-C. Niepce, and M. Pate, “BST ceramics: effect of attrition milling on dielectric properties,” J. Eur. Ceram. Soc. 24(10-11), 3003–3011 (2004).
[CrossRef]

McPhedran, R. C.

Milton, G. W.

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(5801), 977–980 (2006).
[CrossRef] [PubMed]

Morell, A.

S. Tusseau-Nenez, J.-P. Ganne, M. Maglione, A. Morell, J.-C. Niepce, and M. Pate, “BST ceramics: effect of attrition milling on dielectric properties,” J. Eur. Ceram. Soc. 24(10-11), 3003–3011 (2004).
[CrossRef]

Mosig, J.

P. Alitalo, O. Luukkonen, J. Mosig, and S. Tretyakov, “Broadband cloaking with volumetric structures composed of two-dimensional transmission-line networks,” Microw. Opt. Technol. Lett. 51(7), 1627–1631 (2009).
[CrossRef]

P. Alitalo, F. Bongard, J.-F. Zurcher, J. Mosig, and S. Tretyakov, “Expermental verification of broadband cloaking using a volumetric cloak composed of periodically stacked cylindrical transmission-line networks,” Appl. Phys. Lett. 94(1), 014103 (2009).
[CrossRef]

Narimanov, E. E.

Nicorovici, N.-A. P.

Niepce, J.-C.

S. Tusseau-Nenez, J.-P. Ganne, M. Maglione, A. Morell, J.-C. Niepce, and M. Pate, “BST ceramics: effect of attrition milling on dielectric properties,” J. Eur. Ceram. Soc. 24(10-11), 3003–3011 (2004).
[CrossRef]

Ozbay, E.

A. E. Serebryannikov and E. Ozbay, “Multifrequency invisibility and masking of cylindrical dielectric objects using double-positive and double-negative metamaterials,” J. Opt. A, Pure Appl. Opt. (to appear).

Pate, M.

S. Tusseau-Nenez, J.-P. Ganne, M. Maglione, A. Morell, J.-C. Niepce, and M. Pate, “BST ceramics: effect of attrition milling on dielectric properties,” J. Eur. Ceram. Soc. 24(10-11), 3003–3011 (2004).
[CrossRef]

Pendry, J.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering theory derivation of a 3D acoustic cloaking shell,” Phys. Rev. Lett. 100(2), 024301 (2008).
[CrossRef] [PubMed]

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(5801), 977–980 (2006).
[CrossRef] [PubMed]

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

Popa, B.-I.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering theory derivation of a 3D acoustic cloaking shell,” Phys. Rev. Lett. 100(2), 024301 (2008).
[CrossRef] [PubMed]

Rahm, M.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering theory derivation of a 3D acoustic cloaking shell,” Phys. Rev. Lett. 100(2), 024301 (2008).
[CrossRef] [PubMed]

Schurig, D.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering theory derivation of a 3D acoustic cloaking shell,” Phys. Rev. Lett. 100(2), 024301 (2008).
[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(5801), 977–980 (2006).
[CrossRef] [PubMed]

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

Serebryannikov, A. E.

A. E. Serebryannikov and E. Ozbay, “Multifrequency invisibility and masking of cylindrical dielectric objects using double-positive and double-negative metamaterials,” J. Opt. A, Pure Appl. Opt. (to appear).

Shalaev, V. M.

N. M. Litchinitser and V. M. Shalaev, “Photonic metamaterials,” Laser Phys. Lett. 5(6), 411–420 (2008).
[CrossRef]

Smith, D. R.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering theory derivation of a 3D acoustic cloaking shell,” Phys. Rev. Lett. 100(2), 024301 (2008).
[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(5801), 977–980 (2006).
[CrossRef] [PubMed]

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

Starr, A.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering theory derivation of a 3D acoustic cloaking shell,” Phys. Rev. Lett. 100(2), 024301 (2008).
[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(5801), 977–980 (2006).
[CrossRef] [PubMed]

Tayeb, G.

N.-A. P. Nicorovici, R. C. McPhedran, S. Enoch, and G. Tayeb, “Finite wavelength cloaking by plasmonic resonance,” N. J. Phys. 10(11), 115020 (2008).
[CrossRef]

Tretyakov, S.

P. Alitalo, F. Bongard, J.-F. Zurcher, J. Mosig, and S. Tretyakov, “Expermental verification of broadband cloaking using a volumetric cloak composed of periodically stacked cylindrical transmission-line networks,” Appl. Phys. Lett. 94(1), 014103 (2009).
[CrossRef]

P. Alitalo, O. Luukkonen, J. Mosig, and S. Tretyakov, “Broadband cloaking with volumetric structures composed of two-dimensional transmission-line networks,” Microw. Opt. Technol. Lett. 51(7), 1627–1631 (2009).
[CrossRef]

Tricarico, S.

F. Bilotti, S. Tricarico, and L. Vegni, “Electromagnetic cloaking devices for TE and TM polarizations,” N. J. Phys. 10(11), 115035 (2008).
[CrossRef]

Tusseau-Nenez, S.

S. Tusseau-Nenez, J.-P. Ganne, M. Maglione, A. Morell, J.-C. Niepce, and M. Pate, “BST ceramics: effect of attrition milling on dielectric properties,” J. Eur. Ceram. Soc. 24(10-11), 3003–3011 (2004).
[CrossRef]

Vegni, L.

F. Bilotti, S. Tricarico, and L. Vegni, “Electromagnetic cloaking devices for TE and TM polarizations,” N. J. Phys. 10(11), 115035 (2008).
[CrossRef]

Zurcher, J.-F.

P. Alitalo, F. Bongard, J.-F. Zurcher, J. Mosig, and S. Tretyakov, “Expermental verification of broadband cloaking using a volumetric cloak composed of periodically stacked cylindrical transmission-line networks,” Appl. Phys. Lett. 94(1), 014103 (2009).
[CrossRef]

Appl. Phys. Lett. (1)

P. Alitalo, F. Bongard, J.-F. Zurcher, J. Mosig, and S. Tretyakov, “Expermental verification of broadband cloaking using a volumetric cloak composed of periodically stacked cylindrical transmission-line networks,” Appl. Phys. Lett. 94(1), 014103 (2009).
[CrossRef]

J. Eur. Ceram. Soc. (1)

S. Tusseau-Nenez, J.-P. Ganne, M. Maglione, A. Morell, J.-C. Niepce, and M. Pate, “BST ceramics: effect of attrition milling on dielectric properties,” J. Eur. Ceram. Soc. 24(10-11), 3003–3011 (2004).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

A. E. Serebryannikov and E. Ozbay, “Multifrequency invisibility and masking of cylindrical dielectric objects using double-positive and double-negative metamaterials,” J. Opt. A, Pure Appl. Opt. (to appear).

Laser Phys. Lett. (1)

N. M. Litchinitser and V. M. Shalaev, “Photonic metamaterials,” Laser Phys. Lett. 5(6), 411–420 (2008).
[CrossRef]

Microw. Opt. Technol. Lett. (1)

P. Alitalo, O. Luukkonen, J. Mosig, and S. Tretyakov, “Broadband cloaking with volumetric structures composed of two-dimensional transmission-line networks,” Microw. Opt. Technol. Lett. 51(7), 1627–1631 (2009).
[CrossRef]

N. J. Phys. (2)

N.-A. P. Nicorovici, R. C. McPhedran, S. Enoch, and G. Tayeb, “Finite wavelength cloaking by plasmonic resonance,” N. J. Phys. 10(11), 115020 (2008).
[CrossRef]

F. Bilotti, S. Tricarico, and L. Vegni, “Electromagnetic cloaking devices for TE and TM polarizations,” N. J. Phys. 10(11), 115035 (2008).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

A. Alù and N. Engheta, “Effects of size and frequency dispersion in plasmonic cloaking,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(4), 045602 (2008).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering theory derivation of a 3D acoustic cloaking shell,” Phys. Rev. Lett. 100(2), 024301 (2008).
[CrossRef] [PubMed]

A. Alù and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic shells,” Phys. Rev. Lett. 100(11), 113901 (2008).
[CrossRef] [PubMed]

Science (2)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 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(5801), 977–980 (2006).
[CrossRef] [PubMed]

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Figures (9)

Fig. 1
Fig. 1

Upper left plot: general geometry of the problem; Middle plots: scattering cross section at εs = 200 and R/r = 1.4 (upper), and εs = 400 and R/r = 1.6 (lower), εc = μs = μc = 1, TM polarization; Lower left plot: fragment of the upper middle plot (blue line) and lower middle plot (green line); Right plots: modulus of the axial (upper) and azimuthal (lower) field components at kR = 1.566 and same remaining parameters as in the upper middle plot.

Fig. 2
Fig. 2

Left plot: scattering cross section at εs = 200 and εc = μs = μc = 1 for several values of R/r, TM polarization; solid yellow, red, blue, green, and cyan lines correspond to R/r = 1.39, 1.395, 1.4, 1.405, and 1.41; dashed and dotted blue lines correspond to the outer-to-inner-radii ratio R 1 /r 1 = 1.4 where R 1 = ηR and r 1 = ηr with η = 1.01 and η = 0.99, respectively; Middle plot: phase map of the axial component in free space (εs = εc = μs = μc = 1) at kR = 1.566; Right plot: phase map corresponding to |Ez | in the upper right plot in Fig. 1.

Fig. 3
Fig. 3

Left plot: scattering cross section at εs = 200, εc = −10.2, and R/r = 1.4 (blue line), εs = 400, εc = −10.2, and R/r = 1.6 (green line), and εs = 1 and εc = −10.2 (red line); Middle plot: fragment of the left plot; Right plot: modulus of the axial field at kR = 0.856 (kr = 0.535, m = 2) and same remaining parameters as in case shown by green line; μs = μc = 1, TM polarization.

Fig. 4
Fig. 4

Left plot: scattering cross section at εs = 400, εc = 10.2, and μs = μc = 1 for several values of R/r, TM polarization; solid yellow, red, blue, green, and cyan lines correspond to R/r = 1.58, 1.59, 1.6, 1.61, and 1.62; dashed and dotted blue lines correspond to the outer-to-inner-radii ratio R 1 /r 1 = 1.6 where R 1 = ηR and r 1 = ηr with η = 1.01 and η = 0.99, respectively; Middle plot: phase map in free space (εs = εc = μs = μc = 1) at kR = 0.856; Right plot: phase map for the field shown in the right plot in Fig. 3.

Fig. 5
Fig. 5

Left plot: scattering cross section at εs = 200 (blue line), εs = 900 (green line), and εs = 1 (red line), εc = 10.2 and R/r = 1.4; Middle plot: same as left plot but for εc = 5.8; Right plot: modulus of the axial field at kR = 0.719 (kr = 0.5136, m = 2) and the same remaining parameters as in the case shown in left plot by green line; μs = μc = 1, TM polarization.

Fig. 6
Fig. 6

Left plot: scattering cross section at εs = 900, εc = 10.2, and μs = μc = 1 for several values of R/r, TM polarization; solid yellow, red, blue, green, and cyan lines correspond to R/r = 1.39, 1.395, 1.4, 1.405, and 1.41; dashed and dotted blue lines correspond to the outer-to-inner-radii ratio R 1 /r 1 = 1.4 where R 1 = ηR and r 1 = ηr with η = 1.01 and η = 0.99, respectively; Middle plot: phase map in free space (εs = εc = μs = μc = 1) at kR = 0.719; Right plot: phase map for the field shown in the right plot in Fig. 5.

Fig. 7
Fig. 7

Left plot: scattering cross section at εs = 900 (blue line) and εs = 1 (red line), εc = 5.8 and R/r = 2; Middle plot: fragment of the left plot; Right plot: modulus of the axial field at kR = 2.093 (kr = 1.0465, m = 10) and the same remaining parameters as in the case shown by a blue line; μs = μc = 1, TE polarization.

Fig. 8
Fig. 8

Left plot: scattering cross section at εs = 200 (green line) and εs = 1 (blue line), εc = 5.8, and R/r = 2.4; Right plot: modulus of the axial field at kR = 3.433 (kr = 1.4304, m = 9) and the same remaining parameters as in case shown in left plot by green line; μs = μc = 1, TE polarization.

Fig. 9
Fig. 9

Left plot: scattering cross section at εs = 30 (blue line) and εs = 1 (red line), εc = 2.8, R/r = 2, TM polarization; Right plot: scattering cross section at εs = 30 (blue line) and εs = 1 (violet line), εc = 2.8, R/r = 1.4, TE polarization; μs = μc = 1.

Equations (1)

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σ=(kR)1n=cn2,

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