Abstract

We derive an exact expression for the time-averaged electromagnetic (EM) energy inside a chiral dispersive sphere irradiated by a plane wave. The dispersion relations correspond to a chiral metamaterial consisting of uncoupled single-resonance helical resonators. Using a field decomposition scheme and a general expression for the EM energy density in bianisotropic media, we calculate the Lorenz–Mie solution for the internal fields in a medium that is simultaneously magnetic and chiral. We also obtain an explicit analytical relation between the internal EM energy and the absorption cross section. This result is applied to demonstrate that strong chirality leads to an off-resonance field enhancement within weakly absorbing spheres.

© 2013 Optical Society of America

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    [CrossRef]

2013 (1)

T. J. Arruda, A. S. Martinez, and F. A. Pinheiro, “Unconventional Fano effect and off-resonance field enhancement in plasmonic coated spheres,” Phys. Rev. A 87, 043841 (2013).
[CrossRef]

2012 (2)

T. J. Arruda, F. A. Pinheiro, and A. S. Martinez, “Electromagnetic energy within coated spheres containing dispersive metamaterials,” J. Opt. 14, 065101 (2012).
[CrossRef]

C. L. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nano photonics using hyperbolic metamaterials,” J. Opt. 14, 063001 (2012).
[CrossRef]

2011 (2)

2010 (5)

2009 (3)

P. G. Luan, “Power loss and electromagnetic energy density in a dispersive metamaterial medium,” Phys. Rev. E 80, 046601 (2009).
[CrossRef]

N. Zheludev and N. Papasimakis, “Metamaterial-induced transparency: sharp Fano resonances and slow light,” Opt. Photon. News 20(10), 22–27 (2009).
[CrossRef]

B. Wang, J. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Chiral metamaterials: simulations and experiments,” J. Opt. A 11, 114003 (2009).
[CrossRef]

2008 (1)

F. A. Pinheiro, “Statistics of quality factors in three-dimensional disordered magneto-optical systems and its applications to random lasers,” Phys. Rev. A 78, 023812 (2008).
[CrossRef]

2007 (1)

2006 (3)

A. D. Boardman and K. Marinov, “Electromagnetic energy in a dispersive metamaterial,” Phys. Rev. B 73, 165110 (2006).
[CrossRef]

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

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

2005 (4)

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef]

V. A. Podolskiy and E. E. Narimanov, “Strongly anisotropic waveguide as a nonmagnetic left-handed system,” Phys. Rev. B 71, 201101 (2005).
[CrossRef]

S. A. Tretyakov, “Electromagnetic field energy density in artificial microwave materials with strong dispersion and loss,” Phys. Lett. A 343, 231–237 (2005).
[CrossRef]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef]

2004 (3)

J. B. Pendry, “A chiral route to negative refraction,” Science 306, 1353–1355 (2004).
[CrossRef]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788–792 (2004).
[CrossRef]

D. R. Smith, P. Kolinko, and D. Schurig, “Negative refraction in indefinite media,” J. Opt. Soc. Am. B 21, 1032–1043 (2004).
[CrossRef]

2002 (1)

R. Ruppin, “Electromagnetic energy density in a dispersive and absorptive material,” Phys. Lett. A 299, 309–312 (2002).
[CrossRef]

2000 (3)

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef]

F. A. Pinheiro, A. S. Martinez, and L. C. Sampaio, “New effects in light scattering in disordered media and coherent backscattering cone: system of magnetic particles,” Phys. Rev. Lett. 84, 1435–1438 (2000).
[CrossRef]

F. A. Pinheiro, A. S. Martinez, and L. C. Sampaio, “Vanishing of energy transport velocity and diffusion constant of electromagnetic waves in disordered magnetic media,” Phys. Rev. Lett. 85, 5563–5566 (2000).
[CrossRef]

1996 (2)

J. Lekner, “Optical properties of isotropic chiral media,” Pure Appl. Opt. 5, 417–443 (1996).
[CrossRef]

B. A. van Tiggelen and A. Lagendijk, “Resonant multiple scattering of light,” Phys. Rep. 270, 143–215 (1996).
[CrossRef]

1988 (1)

1987 (1)

1986 (1)

1974 (1)

C. F. Bohren, “Light scattering by an optically active sphere,” Chem. Phys. Lett. 29, 458–462 (1974).
[CrossRef]

1970 (1)

R. Loudon, “The propagation of electromagnetic energy through an absorbing dielectric,” J. Phys. A 3, 233–245 (1970).
[CrossRef]

1937 (1)

E. U. Condon, “Theories of optical rotatory power,” Rev. Mod. Phys. 9, 432–457 (1937).
[CrossRef]

Arruda, T. J.

T. J. Arruda, A. S. Martinez, and F. A. Pinheiro, “Unconventional Fano effect and off-resonance field enhancement in plasmonic coated spheres,” Phys. Rev. A 87, 043841 (2013).
[CrossRef]

T. J. Arruda, F. A. Pinheiro, and A. S. Martinez, “Electromagnetic energy within coated spheres containing dispersive metamaterials,” J. Opt. 14, 065101 (2012).
[CrossRef]

T. J. Arruda and A. S. Martinez, “Electromagnetic energy within a magnetic sphere,” J. Opt. Soc. Am. A 27, 992–1001 (2010).
[CrossRef]

T. J. Arruda and A. S. Martinez, “Electromagnetic energy within a magnetic infinite cylinder and scattering properties for oblique incidence,” J. Opt. Soc. Am. A 27, 1679–1687 (2010).
[CrossRef]

Boardman, A. D.

A. D. Boardman and K. Marinov, “Electromagnetic energy in a dispersive metamaterial,” Phys. Rev. B 73, 165110 (2006).
[CrossRef]

Bohren, C. F.

C. F. Bohren, “Light scattering by an optically active sphere,” Chem. Phys. Lett. 29, 458–462 (1974).
[CrossRef]

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

Bott, A.

Burger, S.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef]

Cai, W.

Chettiar, U. K.

Chong, C. T.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

Condon, E. U.

E. U. Condon, “Theories of optical rotatory power,” Rev. Mod. Phys. 9, 432–457 (1937).
[CrossRef]

Cortes, C. L.

C. L. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nano photonics using hyperbolic metamaterials,” J. Opt. 14, 063001 (2012).
[CrossRef]

de Silva, V. C.

Drachev, V. P.

Economou, E. N.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef]

Enkrich, C.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef]

Giessen, H.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

Halas, N. J.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

Huffman, D. R.

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

Jacob, Z.

C. L. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nano photonics using hyperbolic metamaterials,” J. Opt. 14, 063001 (2012).
[CrossRef]

Kafesaki, M.

B. Wang, J. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Chiral metamaterials: simulations and experiments,” J. Opt. A 11, 114003 (2009).
[CrossRef]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef]

Kildishev, A. V.

Kolinko, P.

Koschny, T.

R. Zhao, T. Koschny, and C. M. Soukoulis, “Chiral metamaterials: retrieval of the effective parameters with and without substrate,” Opt. Express 18, 14553–14567 (2010).
[CrossRef]

B. Wang, J. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Chiral metamaterials: simulations and experiments,” J. Opt. A 11, 114003 (2009).
[CrossRef]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef]

Lagendijk, A.

B. A. van Tiggelen and A. Lagendijk, “Resonant multiple scattering of light,” Phys. Rep. 270, 143–215 (1996).
[CrossRef]

Lakhtakia, A.

Lekner, J.

J. Lekner, “Optical properties of isotropic chiral media,” Pure Appl. Opt. 5, 417–443 (1996).
[CrossRef]

Leonhardt, U.

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

Linden, S.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef]

Loudon, R.

R. Loudon, “The propagation of electromagnetic energy through an absorbing dielectric,” J. Phys. A 3, 233–245 (1970).
[CrossRef]

Luan, P. G.

P. G. Luan, Y. T. Wang, S. Zhang, and X. Zhang, “Electromagnetic energy density in a single-resonance chiral metamaterial,” Opt. Lett. 36, 675–677 (2011).
[CrossRef]

P. G. Luan, “Power loss and electromagnetic energy density in a dispersive metamaterial medium,” Phys. Rev. E 80, 046601 (2009).
[CrossRef]

Luk’yanchuk, B.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

Maier, S. A.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

Marinov, K.

A. D. Boardman and K. Marinov, “Electromagnetic energy in a dispersive metamaterial,” Phys. Rev. B 73, 165110 (2006).
[CrossRef]

Martinez, A. S.

T. J. Arruda, A. S. Martinez, and F. A. Pinheiro, “Unconventional Fano effect and off-resonance field enhancement in plasmonic coated spheres,” Phys. Rev. A 87, 043841 (2013).
[CrossRef]

T. J. Arruda, F. A. Pinheiro, and A. S. Martinez, “Electromagnetic energy within coated spheres containing dispersive metamaterials,” J. Opt. 14, 065101 (2012).
[CrossRef]

T. J. Arruda and A. S. Martinez, “Electromagnetic energy within a magnetic sphere,” J. Opt. Soc. Am. A 27, 992–1001 (2010).
[CrossRef]

T. J. Arruda and A. S. Martinez, “Electromagnetic energy within a magnetic infinite cylinder and scattering properties for oblique incidence,” J. Opt. Soc. Am. A 27, 1679–1687 (2010).
[CrossRef]

F. A. Pinheiro, A. S. Martinez, and L. C. Sampaio, “New effects in light scattering in disordered media and coherent backscattering cone: system of magnetic particles,” Phys. Rev. Lett. 84, 1435–1438 (2000).
[CrossRef]

F. A. Pinheiro, A. S. Martinez, and L. C. Sampaio, “Vanishing of energy transport velocity and diffusion constant of electromagnetic waves in disordered magnetic media,” Phys. Rev. Lett. 85, 5563–5566 (2000).
[CrossRef]

Miroshnichenko, A. E.

A. E. Miroshnichenko, “Off-resonance field enhancement by spherical nanoshells,” Phys. Rev. A 81, 053818 (2010).
[CrossRef]

Molesky, S.

C. L. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nano photonics using hyperbolic metamaterials,” J. Opt. 14, 063001 (2012).
[CrossRef]

Narimanov, E. E.

V. A. Podolskiy and E. E. Narimanov, “Strongly anisotropic waveguide as a nonmagnetic left-handed system,” Phys. Rev. B 71, 201101 (2005).
[CrossRef]

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef]

Newman, W.

C. L. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nano photonics using hyperbolic metamaterials,” J. Opt. 14, 063001 (2012).
[CrossRef]

Nordlander, P.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef]

Papasimakis, N.

N. Zheludev and N. Papasimakis, “Metamaterial-induced transparency: sharp Fano resonances and slow light,” Opt. Photon. News 20(10), 22–27 (2009).
[CrossRef]

Pendry, J. B.

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

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef]

J. B. Pendry, “A chiral route to negative refraction,” Science 306, 1353–1355 (2004).
[CrossRef]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788–792 (2004).
[CrossRef]

Pinheiro, F. A.

T. J. Arruda, A. S. Martinez, and F. A. Pinheiro, “Unconventional Fano effect and off-resonance field enhancement in plasmonic coated spheres,” Phys. Rev. A 87, 043841 (2013).
[CrossRef]

T. J. Arruda, F. A. Pinheiro, and A. S. Martinez, “Electromagnetic energy within coated spheres containing dispersive metamaterials,” J. Opt. 14, 065101 (2012).
[CrossRef]

F. A. Pinheiro, “Statistics of quality factors in three-dimensional disordered magneto-optical systems and its applications to random lasers,” Phys. Rev. A 78, 023812 (2008).
[CrossRef]

F. A. Pinheiro, A. S. Martinez, and L. C. Sampaio, “New effects in light scattering in disordered media and coherent backscattering cone: system of magnetic particles,” Phys. Rev. Lett. 84, 1435–1438 (2000).
[CrossRef]

F. A. Pinheiro, A. S. Martinez, and L. C. Sampaio, “Vanishing of energy transport velocity and diffusion constant of electromagnetic waves in disordered magnetic media,” Phys. Rev. Lett. 85, 5563–5566 (2000).
[CrossRef]

Podolskiy, V. A.

V. A. Podolskiy and E. E. Narimanov, “Strongly anisotropic waveguide as a nonmagnetic left-handed system,” Phys. Rev. B 71, 201101 (2005).
[CrossRef]

Ruppin, R.

R. Ruppin, “Electric and magnetic energies within dispersive metamaterial spheres,” J. Opt. 13, 095101 (2011).
[CrossRef]

R. Ruppin, “Electromagnetic energy density in a dispersive and absorptive material,” Phys. Lett. A 299, 309–312 (2002).
[CrossRef]

Sampaio, L. C.

F. A. Pinheiro, A. S. Martinez, and L. C. Sampaio, “New effects in light scattering in disordered media and coherent backscattering cone: system of magnetic particles,” Phys. Rev. Lett. 84, 1435–1438 (2000).
[CrossRef]

F. A. Pinheiro, A. S. Martinez, and L. C. Sampaio, “Vanishing of energy transport velocity and diffusion constant of electromagnetic waves in disordered magnetic media,” Phys. Rev. Lett. 85, 5563–5566 (2000).
[CrossRef]

Schmidt, F.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef]

Schultz, S.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef]

Schurig, D.

Semchenko, I.

A. Serdyukov, I. Semchenko, S. Tretyakov, and A. Sihvola, Electromagnetics of Bi-anisotropic Materials: Theory and Applications (Gordon and Breach Science, 2001).

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A. Serdyukov, I. Semchenko, S. Tretyakov, and A. Sihvola, Electromagnetics of Bi-anisotropic Materials: Theory and Applications (Gordon and Breach Science, 2001).

G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge University, 1958).

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