Abstract

Enhancement of chirality near plasmonic objects has been investigated in terms of circular dichroism and optical activity. Here, we examine plasmonic effects on chirality, which is the most fundamental quantity in describing chiral medium, using generalized wavenumber eigenvalue simulation. Generalization of wavenumber eigenvalue simulation from isotropic medium to bi-isotropic medium is presented. Enhanced chirality of the composite material of chiral medium and plasmonic sphere is calculated for a variety of geometrical and optical properties of the sphere. This method enables eigenvalue simulation of more general bi-isotropic medium including natural chiral materials.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. F. Lu, Y. Tian, M. Liu, D. Su, H. Zhang, A. O. Govorov, and O. Gang, “Discrete nanocubes as plasmonic reporters of molecular chirality,” Nano Lett. 13, 3145–3151 (2013).
    [Crossref] [PubMed]
  2. Y. Zhao, L. Xu, W. Ma, L. Wang, H. Kuang, C. Xu, and N. A. Kotov, “Shell-engineered chiroplasmonic assemblies of nanoparticles for zeptomolar DNA detection,” Nano Lett. 14, 3908–3913 (2014).
    [Crossref] [PubMed]
  3. C. E. Román-Velázquez, C. Noguez, and I. L. Garzón, “Circular dichroism simulated spectra of chiral gold nanoclusters: a dipole approximation,” J. Phys. Chem. B 107, 12035–12038 (2003).
    [Crossref]
  4. G. Shemer, O. Krichevski, G. Markovich, T. Molotsky, I. Lubitz, and A. B. Kotlyar, “Chirality of silver nanoparticles synthesized on DNA,” J. Am. Chem. Soc. 128, 11006–11007 (2006).
    [Crossref] [PubMed]
  5. B. M. Maoz, Y. Chaikin, A. B. Tesler, O. B. Elli, Z. Fan, A. O. Govorov, and G. Markovich, “Amplification of chiroptical activity of chiral biomolecules by surface plasmons,” Nano Lett. 13, 1203–1209 (2013).
    [Crossref] [PubMed]
  6. A. García-Etxarri and J. A. Dionne, “Surface-enhanced circular dichroism spectroscopy mediated by nonchiral nanoantennas,” Phys. Rev. B 87, 235409 (2013).
    [Crossref]
  7. S. F. Mason, Molecular Optical Activity and the Chiral Discriminations (Cambridge University Press, 1982).
  8. A. Ghosh and P. Fischer, “Chiral molecules split light: Reflection and refraction in a chiral liquid,” Phys. Rev. Lett. 97, 173002 (2006).
    [Crossref] [PubMed]
  9. S. Kazuaki, Optical Properties of Photonic Crystals (Springer, 2004).
  10. G. Shvets and Y. A. Urzhumov, “Engineering the electromagnetic properties of periodic nanostructures using electrostatic resonances,” Phys. Rev. Lett. 93, 243902 (2004).
    [Crossref]
  11. T. Suzuki and P. K. L. Yu, “Tunneling in photonic band structures,” J. Opt. Soc. Am. B 2, 804–820 (1995).
    [Crossref]
  12. E. Istrate, A. A. Green, and E. H. Sargent, “Behavior of light at photonic crystal interfaces,” Phys. Rev. B 71, 195122 (2005).
    [Crossref]
  13. A. J. Ward, J. B. Pendry, and W. J. Stewart, “Photonic dispersion surfaces,” J. Phys.: Condens. Matter 7, 2217–2224 (1995).
  14. Z. Y. Li and L. L. Lin, “Photonic band structures solved by a plane-wave-based transfer-matrix method,” Phys. Rev. E 67, 046607 (2003).
    [Crossref]
  15. M. Davanco, Y. Urzhumov, and G. Shvets, “The complex bloch bands of a 2d plasmonic crystal displaying isotropic negative refraction,” Opt. Express 15, 9681–9691 (2007).
    [Crossref] [PubMed]
  16. C. Fietz, Y. Urzhumov, and G. Shvets, “Complex k band diagrams of 3d metamaterial/photonic crystals,” Opt. Express 19, 19027–19041 (2011).
    [Crossref] [PubMed]
  17. J. Jin, The Finite Element Method in Electromagnetics, 2nd ed. (John Wiley & Sons, Inc., 2002).
  18. I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic waves in chiral and bi-isotropic media (Artech House, 1994).

2014 (1)

Y. Zhao, L. Xu, W. Ma, L. Wang, H. Kuang, C. Xu, and N. A. Kotov, “Shell-engineered chiroplasmonic assemblies of nanoparticles for zeptomolar DNA detection,” Nano Lett. 14, 3908–3913 (2014).
[Crossref] [PubMed]

2013 (3)

F. Lu, Y. Tian, M. Liu, D. Su, H. Zhang, A. O. Govorov, and O. Gang, “Discrete nanocubes as plasmonic reporters of molecular chirality,” Nano Lett. 13, 3145–3151 (2013).
[Crossref] [PubMed]

B. M. Maoz, Y. Chaikin, A. B. Tesler, O. B. Elli, Z. Fan, A. O. Govorov, and G. Markovich, “Amplification of chiroptical activity of chiral biomolecules by surface plasmons,” Nano Lett. 13, 1203–1209 (2013).
[Crossref] [PubMed]

A. García-Etxarri and J. A. Dionne, “Surface-enhanced circular dichroism spectroscopy mediated by nonchiral nanoantennas,” Phys. Rev. B 87, 235409 (2013).
[Crossref]

2011 (1)

2007 (1)

2006 (2)

A. Ghosh and P. Fischer, “Chiral molecules split light: Reflection and refraction in a chiral liquid,” Phys. Rev. Lett. 97, 173002 (2006).
[Crossref] [PubMed]

G. Shemer, O. Krichevski, G. Markovich, T. Molotsky, I. Lubitz, and A. B. Kotlyar, “Chirality of silver nanoparticles synthesized on DNA,” J. Am. Chem. Soc. 128, 11006–11007 (2006).
[Crossref] [PubMed]

2005 (1)

E. Istrate, A. A. Green, and E. H. Sargent, “Behavior of light at photonic crystal interfaces,” Phys. Rev. B 71, 195122 (2005).
[Crossref]

2004 (1)

G. Shvets and Y. A. Urzhumov, “Engineering the electromagnetic properties of periodic nanostructures using electrostatic resonances,” Phys. Rev. Lett. 93, 243902 (2004).
[Crossref]

2003 (2)

C. E. Román-Velázquez, C. Noguez, and I. L. Garzón, “Circular dichroism simulated spectra of chiral gold nanoclusters: a dipole approximation,” J. Phys. Chem. B 107, 12035–12038 (2003).
[Crossref]

Z. Y. Li and L. L. Lin, “Photonic band structures solved by a plane-wave-based transfer-matrix method,” Phys. Rev. E 67, 046607 (2003).
[Crossref]

1995 (2)

A. J. Ward, J. B. Pendry, and W. J. Stewart, “Photonic dispersion surfaces,” J. Phys.: Condens. Matter 7, 2217–2224 (1995).

T. Suzuki and P. K. L. Yu, “Tunneling in photonic band structures,” J. Opt. Soc. Am. B 2, 804–820 (1995).
[Crossref]

Chaikin, Y.

B. M. Maoz, Y. Chaikin, A. B. Tesler, O. B. Elli, Z. Fan, A. O. Govorov, and G. Markovich, “Amplification of chiroptical activity of chiral biomolecules by surface plasmons,” Nano Lett. 13, 1203–1209 (2013).
[Crossref] [PubMed]

Davanco, M.

Dionne, J. A.

A. García-Etxarri and J. A. Dionne, “Surface-enhanced circular dichroism spectroscopy mediated by nonchiral nanoantennas,” Phys. Rev. B 87, 235409 (2013).
[Crossref]

Elli, O. B.

B. M. Maoz, Y. Chaikin, A. B. Tesler, O. B. Elli, Z. Fan, A. O. Govorov, and G. Markovich, “Amplification of chiroptical activity of chiral biomolecules by surface plasmons,” Nano Lett. 13, 1203–1209 (2013).
[Crossref] [PubMed]

Fan, Z.

B. M. Maoz, Y. Chaikin, A. B. Tesler, O. B. Elli, Z. Fan, A. O. Govorov, and G. Markovich, “Amplification of chiroptical activity of chiral biomolecules by surface plasmons,” Nano Lett. 13, 1203–1209 (2013).
[Crossref] [PubMed]

Fietz, C.

Fischer, P.

A. Ghosh and P. Fischer, “Chiral molecules split light: Reflection and refraction in a chiral liquid,” Phys. Rev. Lett. 97, 173002 (2006).
[Crossref] [PubMed]

Gang, O.

F. Lu, Y. Tian, M. Liu, D. Su, H. Zhang, A. O. Govorov, and O. Gang, “Discrete nanocubes as plasmonic reporters of molecular chirality,” Nano Lett. 13, 3145–3151 (2013).
[Crossref] [PubMed]

García-Etxarri, A.

A. García-Etxarri and J. A. Dionne, “Surface-enhanced circular dichroism spectroscopy mediated by nonchiral nanoantennas,” Phys. Rev. B 87, 235409 (2013).
[Crossref]

Garzón, I. L.

C. E. Román-Velázquez, C. Noguez, and I. L. Garzón, “Circular dichroism simulated spectra of chiral gold nanoclusters: a dipole approximation,” J. Phys. Chem. B 107, 12035–12038 (2003).
[Crossref]

Ghosh, A.

A. Ghosh and P. Fischer, “Chiral molecules split light: Reflection and refraction in a chiral liquid,” Phys. Rev. Lett. 97, 173002 (2006).
[Crossref] [PubMed]

Govorov, A. O.

B. M. Maoz, Y. Chaikin, A. B. Tesler, O. B. Elli, Z. Fan, A. O. Govorov, and G. Markovich, “Amplification of chiroptical activity of chiral biomolecules by surface plasmons,” Nano Lett. 13, 1203–1209 (2013).
[Crossref] [PubMed]

F. Lu, Y. Tian, M. Liu, D. Su, H. Zhang, A. O. Govorov, and O. Gang, “Discrete nanocubes as plasmonic reporters of molecular chirality,” Nano Lett. 13, 3145–3151 (2013).
[Crossref] [PubMed]

Green, A. A.

E. Istrate, A. A. Green, and E. H. Sargent, “Behavior of light at photonic crystal interfaces,” Phys. Rev. B 71, 195122 (2005).
[Crossref]

Istrate, E.

E. Istrate, A. A. Green, and E. H. Sargent, “Behavior of light at photonic crystal interfaces,” Phys. Rev. B 71, 195122 (2005).
[Crossref]

Jin, J.

J. Jin, The Finite Element Method in Electromagnetics, 2nd ed. (John Wiley & Sons, Inc., 2002).

Kazuaki, S.

S. Kazuaki, Optical Properties of Photonic Crystals (Springer, 2004).

Kotlyar, A. B.

G. Shemer, O. Krichevski, G. Markovich, T. Molotsky, I. Lubitz, and A. B. Kotlyar, “Chirality of silver nanoparticles synthesized on DNA,” J. Am. Chem. Soc. 128, 11006–11007 (2006).
[Crossref] [PubMed]

Kotov, N. A.

Y. Zhao, L. Xu, W. Ma, L. Wang, H. Kuang, C. Xu, and N. A. Kotov, “Shell-engineered chiroplasmonic assemblies of nanoparticles for zeptomolar DNA detection,” Nano Lett. 14, 3908–3913 (2014).
[Crossref] [PubMed]

Krichevski, O.

G. Shemer, O. Krichevski, G. Markovich, T. Molotsky, I. Lubitz, and A. B. Kotlyar, “Chirality of silver nanoparticles synthesized on DNA,” J. Am. Chem. Soc. 128, 11006–11007 (2006).
[Crossref] [PubMed]

Kuang, H.

Y. Zhao, L. Xu, W. Ma, L. Wang, H. Kuang, C. Xu, and N. A. Kotov, “Shell-engineered chiroplasmonic assemblies of nanoparticles for zeptomolar DNA detection,” Nano Lett. 14, 3908–3913 (2014).
[Crossref] [PubMed]

Li, Z. Y.

Z. Y. Li and L. L. Lin, “Photonic band structures solved by a plane-wave-based transfer-matrix method,” Phys. Rev. E 67, 046607 (2003).
[Crossref]

Lin, L. L.

Z. Y. Li and L. L. Lin, “Photonic band structures solved by a plane-wave-based transfer-matrix method,” Phys. Rev. E 67, 046607 (2003).
[Crossref]

Lindell, I. V.

I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic waves in chiral and bi-isotropic media (Artech House, 1994).

Liu, M.

F. Lu, Y. Tian, M. Liu, D. Su, H. Zhang, A. O. Govorov, and O. Gang, “Discrete nanocubes as plasmonic reporters of molecular chirality,” Nano Lett. 13, 3145–3151 (2013).
[Crossref] [PubMed]

Lu, F.

F. Lu, Y. Tian, M. Liu, D. Su, H. Zhang, A. O. Govorov, and O. Gang, “Discrete nanocubes as plasmonic reporters of molecular chirality,” Nano Lett. 13, 3145–3151 (2013).
[Crossref] [PubMed]

Lubitz, I.

G. Shemer, O. Krichevski, G. Markovich, T. Molotsky, I. Lubitz, and A. B. Kotlyar, “Chirality of silver nanoparticles synthesized on DNA,” J. Am. Chem. Soc. 128, 11006–11007 (2006).
[Crossref] [PubMed]

Ma, W.

Y. Zhao, L. Xu, W. Ma, L. Wang, H. Kuang, C. Xu, and N. A. Kotov, “Shell-engineered chiroplasmonic assemblies of nanoparticles for zeptomolar DNA detection,” Nano Lett. 14, 3908–3913 (2014).
[Crossref] [PubMed]

Maoz, B. M.

B. M. Maoz, Y. Chaikin, A. B. Tesler, O. B. Elli, Z. Fan, A. O. Govorov, and G. Markovich, “Amplification of chiroptical activity of chiral biomolecules by surface plasmons,” Nano Lett. 13, 1203–1209 (2013).
[Crossref] [PubMed]

Markovich, G.

B. M. Maoz, Y. Chaikin, A. B. Tesler, O. B. Elli, Z. Fan, A. O. Govorov, and G. Markovich, “Amplification of chiroptical activity of chiral biomolecules by surface plasmons,” Nano Lett. 13, 1203–1209 (2013).
[Crossref] [PubMed]

G. Shemer, O. Krichevski, G. Markovich, T. Molotsky, I. Lubitz, and A. B. Kotlyar, “Chirality of silver nanoparticles synthesized on DNA,” J. Am. Chem. Soc. 128, 11006–11007 (2006).
[Crossref] [PubMed]

Mason, S. F.

S. F. Mason, Molecular Optical Activity and the Chiral Discriminations (Cambridge University Press, 1982).

Molotsky, T.

G. Shemer, O. Krichevski, G. Markovich, T. Molotsky, I. Lubitz, and A. B. Kotlyar, “Chirality of silver nanoparticles synthesized on DNA,” J. Am. Chem. Soc. 128, 11006–11007 (2006).
[Crossref] [PubMed]

Noguez, C.

C. E. Román-Velázquez, C. Noguez, and I. L. Garzón, “Circular dichroism simulated spectra of chiral gold nanoclusters: a dipole approximation,” J. Phys. Chem. B 107, 12035–12038 (2003).
[Crossref]

Pendry, J. B.

A. J. Ward, J. B. Pendry, and W. J. Stewart, “Photonic dispersion surfaces,” J. Phys.: Condens. Matter 7, 2217–2224 (1995).

Román-Velázquez, C. E.

C. E. Román-Velázquez, C. Noguez, and I. L. Garzón, “Circular dichroism simulated spectra of chiral gold nanoclusters: a dipole approximation,” J. Phys. Chem. B 107, 12035–12038 (2003).
[Crossref]

Sargent, E. H.

E. Istrate, A. A. Green, and E. H. Sargent, “Behavior of light at photonic crystal interfaces,” Phys. Rev. B 71, 195122 (2005).
[Crossref]

Shemer, G.

G. Shemer, O. Krichevski, G. Markovich, T. Molotsky, I. Lubitz, and A. B. Kotlyar, “Chirality of silver nanoparticles synthesized on DNA,” J. Am. Chem. Soc. 128, 11006–11007 (2006).
[Crossref] [PubMed]

Shvets, G.

Sihvola, A. H.

I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic waves in chiral and bi-isotropic media (Artech House, 1994).

Stewart, W. J.

A. J. Ward, J. B. Pendry, and W. J. Stewart, “Photonic dispersion surfaces,” J. Phys.: Condens. Matter 7, 2217–2224 (1995).

Su, D.

F. Lu, Y. Tian, M. Liu, D. Su, H. Zhang, A. O. Govorov, and O. Gang, “Discrete nanocubes as plasmonic reporters of molecular chirality,” Nano Lett. 13, 3145–3151 (2013).
[Crossref] [PubMed]

Suzuki, T.

T. Suzuki and P. K. L. Yu, “Tunneling in photonic band structures,” J. Opt. Soc. Am. B 2, 804–820 (1995).
[Crossref]

Tesler, A. B.

B. M. Maoz, Y. Chaikin, A. B. Tesler, O. B. Elli, Z. Fan, A. O. Govorov, and G. Markovich, “Amplification of chiroptical activity of chiral biomolecules by surface plasmons,” Nano Lett. 13, 1203–1209 (2013).
[Crossref] [PubMed]

Tian, Y.

F. Lu, Y. Tian, M. Liu, D. Su, H. Zhang, A. O. Govorov, and O. Gang, “Discrete nanocubes as plasmonic reporters of molecular chirality,” Nano Lett. 13, 3145–3151 (2013).
[Crossref] [PubMed]

Tretyakov, S. A.

I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic waves in chiral and bi-isotropic media (Artech House, 1994).

Urzhumov, Y.

Urzhumov, Y. A.

G. Shvets and Y. A. Urzhumov, “Engineering the electromagnetic properties of periodic nanostructures using electrostatic resonances,” Phys. Rev. Lett. 93, 243902 (2004).
[Crossref]

Viitanen, A. J.

I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic waves in chiral and bi-isotropic media (Artech House, 1994).

Wang, L.

Y. Zhao, L. Xu, W. Ma, L. Wang, H. Kuang, C. Xu, and N. A. Kotov, “Shell-engineered chiroplasmonic assemblies of nanoparticles for zeptomolar DNA detection,” Nano Lett. 14, 3908–3913 (2014).
[Crossref] [PubMed]

Ward, A. J.

A. J. Ward, J. B. Pendry, and W. J. Stewart, “Photonic dispersion surfaces,” J. Phys.: Condens. Matter 7, 2217–2224 (1995).

Xu, C.

Y. Zhao, L. Xu, W. Ma, L. Wang, H. Kuang, C. Xu, and N. A. Kotov, “Shell-engineered chiroplasmonic assemblies of nanoparticles for zeptomolar DNA detection,” Nano Lett. 14, 3908–3913 (2014).
[Crossref] [PubMed]

Xu, L.

Y. Zhao, L. Xu, W. Ma, L. Wang, H. Kuang, C. Xu, and N. A. Kotov, “Shell-engineered chiroplasmonic assemblies of nanoparticles for zeptomolar DNA detection,” Nano Lett. 14, 3908–3913 (2014).
[Crossref] [PubMed]

Yu, P. K. L.

T. Suzuki and P. K. L. Yu, “Tunneling in photonic band structures,” J. Opt. Soc. Am. B 2, 804–820 (1995).
[Crossref]

Zhang, H.

F. Lu, Y. Tian, M. Liu, D. Su, H. Zhang, A. O. Govorov, and O. Gang, “Discrete nanocubes as plasmonic reporters of molecular chirality,” Nano Lett. 13, 3145–3151 (2013).
[Crossref] [PubMed]

Zhao, Y.

Y. Zhao, L. Xu, W. Ma, L. Wang, H. Kuang, C. Xu, and N. A. Kotov, “Shell-engineered chiroplasmonic assemblies of nanoparticles for zeptomolar DNA detection,” Nano Lett. 14, 3908–3913 (2014).
[Crossref] [PubMed]

J. Am. Chem. Soc. (1)

G. Shemer, O. Krichevski, G. Markovich, T. Molotsky, I. Lubitz, and A. B. Kotlyar, “Chirality of silver nanoparticles synthesized on DNA,” J. Am. Chem. Soc. 128, 11006–11007 (2006).
[Crossref] [PubMed]

J. Opt. Soc. Am. B (1)

T. Suzuki and P. K. L. Yu, “Tunneling in photonic band structures,” J. Opt. Soc. Am. B 2, 804–820 (1995).
[Crossref]

J. Phys. Chem. B (1)

C. E. Román-Velázquez, C. Noguez, and I. L. Garzón, “Circular dichroism simulated spectra of chiral gold nanoclusters: a dipole approximation,” J. Phys. Chem. B 107, 12035–12038 (2003).
[Crossref]

J. Phys.: Condens. Matter (1)

A. J. Ward, J. B. Pendry, and W. J. Stewart, “Photonic dispersion surfaces,” J. Phys.: Condens. Matter 7, 2217–2224 (1995).

Nano Lett. (3)

B. M. Maoz, Y. Chaikin, A. B. Tesler, O. B. Elli, Z. Fan, A. O. Govorov, and G. Markovich, “Amplification of chiroptical activity of chiral biomolecules by surface plasmons,” Nano Lett. 13, 1203–1209 (2013).
[Crossref] [PubMed]

F. Lu, Y. Tian, M. Liu, D. Su, H. Zhang, A. O. Govorov, and O. Gang, “Discrete nanocubes as plasmonic reporters of molecular chirality,” Nano Lett. 13, 3145–3151 (2013).
[Crossref] [PubMed]

Y. Zhao, L. Xu, W. Ma, L. Wang, H. Kuang, C. Xu, and N. A. Kotov, “Shell-engineered chiroplasmonic assemblies of nanoparticles for zeptomolar DNA detection,” Nano Lett. 14, 3908–3913 (2014).
[Crossref] [PubMed]

Opt. Express (2)

Phys. Rev. B (2)

A. García-Etxarri and J. A. Dionne, “Surface-enhanced circular dichroism spectroscopy mediated by nonchiral nanoantennas,” Phys. Rev. B 87, 235409 (2013).
[Crossref]

E. Istrate, A. A. Green, and E. H. Sargent, “Behavior of light at photonic crystal interfaces,” Phys. Rev. B 71, 195122 (2005).
[Crossref]

Phys. Rev. E (1)

Z. Y. Li and L. L. Lin, “Photonic band structures solved by a plane-wave-based transfer-matrix method,” Phys. Rev. E 67, 046607 (2003).
[Crossref]

Phys. Rev. Lett. (2)

G. Shvets and Y. A. Urzhumov, “Engineering the electromagnetic properties of periodic nanostructures using electrostatic resonances,” Phys. Rev. Lett. 93, 243902 (2004).
[Crossref]

A. Ghosh and P. Fischer, “Chiral molecules split light: Reflection and refraction in a chiral liquid,” Phys. Rev. Lett. 97, 173002 (2006).
[Crossref] [PubMed]

Other (4)

S. Kazuaki, Optical Properties of Photonic Crystals (Springer, 2004).

S. F. Mason, Molecular Optical Activity and the Chiral Discriminations (Cambridge University Press, 1982).

J. Jin, The Finite Element Method in Electromagnetics, 2nd ed. (John Wiley & Sons, Inc., 2002).

I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic waves in chiral and bi-isotropic media (Artech House, 1994).

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Figures (4)

Fig. 1
Fig. 1 (a) Schematic of a cubic unit cell with lattice constant a and (b) equifrequency contour of an chiral medium of εr = 1, µr = 1 and κ = 0.5. Black and blue curves represent real and imaginary part of kx respectively. Radius of each circle denotes refractive index of circular polarization. (c) and (d) Displacement field of two eigenmodes with k = 1.5 k 0 x ^ for (c) and k = 0.5 k 0 x ^ for (d). Field profiles in three different y-z planes are represented as different colors.
Fig. 2
Fig. 2 (a) Schematic of a cubic unit cell of chiral medium embedding a plasmonic sphere. (b) Equifrequency contour (Bold curve) with r = 16 nm, a = λ 40 = 50 nm. Optical parameters are given as εr = 1, µr = 1 and κ = 0.5 for chiral medium/and εr = −10, µr = 1 and κ = 0 for the sphere.
Fig. 3
Fig. 3 Bandstructure of the cubic lattice of plasmonic sphere in (a) chiral medium and (b) achiral medium. (c) Displacement field profile of two eigenmodes at ω = 1.5c/a, left and right denoting blue and green dots in Fig. 3(a), respectively. (d) Two degenerate eigenmodes at ω = 1.5c/a, corresponding to red dot in Fig. 3(b). Arrows represent displacement field in y and z direction and color shows displacement in x direction.
Fig. 4
Fig. 4 (a) Effective refractive index when relative permittivity of the sphere is −10. (b) Effective refractive index when radius of the sphere is 16 nm. Black and blue lines represent real and imaginary part respectively. (c) Real and (d) imaginary part of effective chirality for various radii and permittivity. (e) Real and (f) imaginary part of effective refractive index by taking average of extracted refractive indices of two eigenmodes.

Equations (11)

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

× ( ε 1 × H ) μ ω 2 H = 0
D = ε E , B = μ H
H ( r ) = u ( r ) exp ( i k r )
( i k + ) × ε   1 ( i k + ) × u µ ω 2 u = 0
0 = d 3 x [ [ ( i k + ) × u ˜ ] ε 1 [ ( i k + ) × u ] μ ω 2 u ˜ u ]
D = ε E + ξ H , B = µ H + ζ E
× ( ε 1 × H ) + i ω [ × ε 1 ξ H ζ ε 1 × H ] ω 2 ( µ ζ ε 1 ξ ) H = 0
( i k + ) × ε 1 ( i k + ) × u + i ω ( i k + ) × ε 1 ξ u i ω ζ ε 1 ( i k + ) × u ω 2 ( µ ζ ε 1 ξ ) u = 0
0 = Ω d 3 x [ [ ( i k + ) × u ˜ ) ε 1 [ ( i k + ) × u ] + i ω ε 1 ξ [ ( i k + ) × u ˜ ) u i ω ζ ε 1 u ˜ [ ( i k + ) × u ] ω 2 ( μ ζ ε 1 ξ ) u ˜ u ] = Ω d 3 x u ˜ [ ( i k + ) × ε 1 ( i k + ) × u + i ω ( i k + ) × ε 1 ξ u i ω ζ ε 1 ( i k + ) × u ω 2 ( μ ζ ε 1 ξ ) u ] Ω d 2 x u ˜ [ n ^ × [ ε 1 ( i k + ) × u + i ω ε 1 ξ u ] ]
D = ε r ε 0 E + i ε 0 μ 0 κ H , B = μ r μ 0 H i ε 0 μ 0 κ E
( k x , ± / k 0 ) 2 + ( k y , ± / k 0 ) 2 + ( k z , ± / k 0 ) 2 = n ±   2