Abstract

We have obtained analytical expressions for the radiative decay rate of the spontaneous emission of a chiral molecule located near a dielectric spherical particle with a chiral nonconcentric spherical shell made of a bi-isotropic material. Our numerical and graphical analyses show that material composition, thickness and degree of non-concentricity of the shell can influence significantly the spontaneous radiation of the chiral molecule. In particular, the radiative decay rates can differ in orders of magnitude for a chiral molecule located near the thin and thick parts of a nonconcentric shell as well as near a concentric shell made of chiral metamaterial. We also find that the radiative decay rates of the “right” and “left” chiral molecule enantiomers located near a nanoparticle with a chiral metamaterial shell can differ pronouncedly from each other. Our findings therefore suggest a way to tune the spontaneous emission of chiral molecules by varying the material composition, thickness and degree of non-concentricity of the shell in the nearby composite nanoparticle and also to enhance the chirality selection of chiral molecules in racemic mixtures.

© 2017 Optical Society of America

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References

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2017 (1)

Y. Zhao, A. N. Askarpour, L. Sun, J. Shi, X. Li, and A. Alù, “Chirality detection of enantiomers using twisted optical metamaterials,” Nat. Commun. 8, 14180 (2017).
[Crossref] [PubMed]

2016 (1)

M. L. Nesterov, X. Yin, M. Schäferling, H. Giessen, and T. Weiss, “The role of plasmon-generated near fields for enhanced circular dichroism spectroscopy,” ACS Photonics 3(4), 578–583 (2016).
[Crossref]

2015 (2)

D. V. Guzatov and V. V. Klimov, “Spontaneous emission of a chiral molecule near a cluster of two chiral spherical particles,” Quantum Electron. 45(3), 250–257 (2015).
[Crossref]

G. Pariente and F. Quéré, “Spatio-temporal light springs: extended encoding of orbital angular momentum in ultrashort pulses,” Opt. Lett. 40(9), 2037–2040 (2015).
[Crossref] [PubMed]

2014 (2)

2013 (2)

A. García-Etxarri and J. A. Dionne, “Surface-enhanced circular dichroism spectroscopy mediated by nonchiral nanoantennas,” Phys. Rev. B 87(23), 235409 (2013).
[Crossref]

J. Zhang and A. Zayats, “Multiple Fano resonances in single-layer nonconcentric core-shell nanostructures,” Opt. Express 21(7), 8426–8436 (2013).
[Crossref] [PubMed]

2012 (4)

M. Schäferling, D. Dregely, M. Hentschel, and H. Giessen, “Tailoring enhanced optical chirality: design principles for chiral plasmonic nanostructures,” Phys. Rev. X 2(3), 031010 (2012).
[Crossref]

V. V. Klimov, D. V. Guzatov, and M. Ducloy, “Engineering of radiation of optically active molecules with chiral nano-meta-particles,” Europhys. Lett. 97(4), 47004 (2012).
[Crossref]

D. V. Guzatov and V. V. Klimov, “The influence of chiral spherical particles on the radiation of optically active molecules,” New J. Phys. 14(12), 123009 (2012).
[Crossref]

V. V. Klimov and D. V. Guzatov, “Using chiral nano-meta-particles to control chiral molecule radiation,” Phys. Uspekhi 182(10), 1130–1135 (2012).

2011 (1)

Y. Liu and X. Zhang, “Metamaterials: a new frontier of science and technology,” Chem. Soc. Rev. 40(5), 2494–2507 (2011).
[Crossref] [PubMed]

2010 (2)

A. O. Govorov, Z. Fan, P. Hernandez, J. M. Slocik, and R. R. Naik, “Theory of circular dichroism of nanomaterials comprising chiral molecules and nanocrystals: plasmon enhancement, dipole interactions, and dielectric effects,” Nano Lett. 10(4), 1374–1382 (2010).
[Crossref] [PubMed]

Y. Tang and A. E. Cohen, “Optical chirality and its interaction with matter,” Phys. Rev. Lett. 104(16), 163901 (2010).
[Crossref] [PubMed]

2009 (4)

Y. L. Geng, C. W. Qiu, and N. Yuan, “Scattering by an impedance sphere coated with a uniaxial anisotropic layer,” IEEE Trans. Antenn. Propag. 57(2), 572–576 (2009).
[Crossref]

B. Wang, J. Zhou, T. Koschny, and C. M. Soukoulis, “Nonplanar chiral metamaterials with negative index,” Appl. Phys. Lett. 94(15), 151112 (2009).
[Crossref]

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79(3), 035407 (2009).
[Crossref]

S. Zhang, Y.-S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett. 102(2), 023901 (2009).
[Crossref] [PubMed]

2008 (2)

T. J. Dufva, J. Sarvas, and J. C.-E. Sten, “Unified derivation of the translational addition theorems for the spherical scalar and vector wave functions,” Progr. Electromag. Res. B 4, 79–99 (2008).
[Crossref]

M. W. Knight and N. J. Halas, “Nanoshells to nanoeggs to nanocups: symmetry breaking beyond the quasistatic limit in complex plasmonic nanoparticles,” New J. Phys. 10(10), 105006 (2008).
[Crossref]

2007 (1)

S. Arslanagic, R. W. Ziolkowski, and O. Breinbjerg, “Analytical and numerical investigation of the radiation from concentric metamaterial spheres excited by an electric Hertzian dipole,” Radio Sci. 42(6), RS6S16 (2007).

2006 (1)

H. Wang, Y. Wu, B. Lassiter, C. L. Nehl, J. H. Hafner, P. Nordlander, and N. J. Halas, “Symmetry breaking in individual plasmonic nanoparticles,” Proc. Natl. Acad. Sci. U.S.A. 103(29), 10856–10860 (2006).
[Crossref] [PubMed]

2005 (1)

V. V. Klimov and V. S. Letokhov, “Electric and magnetic dipole transitions of an atom in the presence of spherical dielectric interface,” Laser Phys. 15(1), 61–73 (2005).

2004 (2)

2002 (3)

E. K. N. Yung and B. J. Hu, “Scattering by conducting sphere coated with chiral media,” Microw. Opt. Technol. Lett. 36(4), 288–293 (2002).
[Crossref]

V. V. Klimov, “Spontaneous emission of an excited atom placed near a “left-handed” sphere,” Opt. Commun. 211(1–6), 183–196 (2002).
[Crossref]

J. Enderlein, “Spectral properties of a fluorescing molecule within a spherical metallic nanocavity,” Phys. Chem. Chem. Phys. 4(12), 2780–2786 (2002).
[Crossref]

2001 (1)

D. W. Mackowski, “An effective medium method for calculation of the T matrix of aggregated spheres,” J. Quant. Spectrosc. Radiat. Transf. 70(4–6), 441–464 (2001).
[Crossref]

1999 (1)

V. V. Klimov and V. S. Letokhov, “Enhancement and inhibition of spontaneous emission rates in nanobubbles,” Chem. Phys. Lett. 301(5–6), 441–448 (1999).
[Crossref]

1998 (1)

F. Borghese, P. Denti, R. Saija, M. A. Iati, and O. I. Sindoni, “Optical resonances of spheres containing an eccentric spherical inclusion,” J. Opt. 29(1), 28–34 (1998).
[Crossref]

1996 (3)

A. K. Hamid, “Modeling the scattering from a dielectric spheroid by a system of dielectric spheres,” J. Electromagn. Waves Appl. 10(5), 723–729 (1996).
[Crossref]

M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transf. 55(5), 535–575 (1996).
[Crossref]

D. W. Mackowski and M. I. Mishchenko, “Calculation of the T matrix and the scattering matrix for ensembles of spheres,” J. Opt. Soc. Am. A 13(11), 2266–2278 (1996).
[Crossref]

1995 (2)

M. I. Mishchenko, D. W. Mackowski, and L. D. Travis, “Scattering of light by bispheres with touching and separated components,” Appl. Opt. 34(21), 4589–4599 (1995).
[Crossref] [PubMed]

A. A. Golubkov and V. A. Makarov, “Boundary conditions for electromagnetic field on the surface of media with weak spatial dispersion,” Phys. Uspekhi 38(3), 325–332 (1995).
[Crossref]

1994 (3)

1993 (1)

1992 (1)

1990 (1)

P. L. E. Uslenghi, “Scattering by impedance sphere coated with a chiral layer,” Electromagn. 10(1–2), 201–211 (1990).
[Crossref]

1988 (2)

1987 (1)

H. Chew, “Transition rates of atoms near spherical surfaces,” J. Chem. Phys. 87(2), 1355–1360 (1987).
[Crossref]

1982 (1)

J. M. Gérardy and M. Ausloos, “Absorption spectrum of clusters of spheres from the general solution of Maxwell’s equations. II. Optical properties of aggregated metal spheres,” Phys. Rev. B 25(6), 4204–4229 (1982).
[Crossref]

1979 (1)

1975 (1)

C. F. Bohren, “Scattering of electromagnetic waves by an optically active spherical shell,” J. Chem. Phys. 62(4), 1566–1571 (1975).
[Crossref]

1974 (1)

C. F. Bohren, “Light scattering by an optically active sphere,” Chem. Phys. Lett. 29(3), 458–462 (1974).
[Crossref]

1971 (3)

B. V. Bokut’, A. N. Serdyukov, and F. I. Fedorov, “Phenomenological theory of optically active crystals,” Sov. Phys. Crystallogr. 15, 871–874 (1971).

P. C. Waterman, “Symmetry, unitarity and geometry in electromagnetic scattering,” Phys. Rev. D Part. Fields 3(4), 825–839 (1971).
[Crossref]

J. H. Bruning and Y. T. Lo, “Multiple scattering of EM waves by spheres part I. Multipole expansion and ray-optical solutions,” IEEE Trans. Antenn. Propag. 19(3), 378–390 (1971).
[Crossref]

1970 (1)

V. I. Rozenberg, ““Diffraction and scattering of electromagnetic waves by an inhomogeneous sphere,” Izv. VUZ,” Radiofiz. 13(3), 337–348 (1970).

Alù, A.

Y. Zhao, A. N. Askarpour, L. Sun, J. Shi, X. Li, and A. Alù, “Chirality detection of enantiomers using twisted optical metamaterials,” Nat. Commun. 8, 14180 (2017).
[Crossref] [PubMed]

Arslanagic, S.

S. Arslanagic, R. W. Ziolkowski, and O. Breinbjerg, “Analytical and numerical investigation of the radiation from concentric metamaterial spheres excited by an electric Hertzian dipole,” Radio Sci. 42(6), RS6S16 (2007).

Askarpour, A. N.

Y. Zhao, A. N. Askarpour, L. Sun, J. Shi, X. Li, and A. Alù, “Chirality detection of enantiomers using twisted optical metamaterials,” Nat. Commun. 8, 14180 (2017).
[Crossref] [PubMed]

Ausloos, M.

J. M. Gérardy and M. Ausloos, “Absorption spectrum of clusters of spheres from the general solution of Maxwell’s equations. II. Optical properties of aggregated metal spheres,” Phys. Rev. B 25(6), 4204–4229 (1982).
[Crossref]

Bohren, C. F.

C. F. Bohren, “Scattering of electromagnetic waves by an optically active spherical shell,” J. Chem. Phys. 62(4), 1566–1571 (1975).
[Crossref]

C. F. Bohren, “Light scattering by an optically active sphere,” Chem. Phys. Lett. 29(3), 458–462 (1974).
[Crossref]

Bokut’, B. V.

B. V. Bokut’, A. N. Serdyukov, and F. I. Fedorov, “Phenomenological theory of optically active crystals,” Sov. Phys. Crystallogr. 15, 871–874 (1971).

Borghese, F.

Breinbjerg, O.

S. Arslanagic, R. W. Ziolkowski, and O. Breinbjerg, “Analytical and numerical investigation of the radiation from concentric metamaterial spheres excited by an electric Hertzian dipole,” Radio Sci. 42(6), RS6S16 (2007).

Brixner, T.

C. Kramer, M. Schäferling, T. Weiss, H. Giessen, and T. Brixner, “Analytic optimization of near-field optical chirality enhancement,” ACS Photonics, in press (2017).

Bruning, J. H.

J. H. Bruning and Y. T. Lo, “Multiple scattering of EM waves by spheres part I. Multipole expansion and ray-optical solutions,” IEEE Trans. Antenn. Propag. 19(3), 378–390 (1971).
[Crossref]

Chew, H.

H. Chew, “Radiation and lifetimes of atoms inside dielectric particles,” Phys. Rev. A Gen. Phys. 38(7), 3410–3416 (1988).
[Crossref] [PubMed]

H. Chew, “Transition rates of atoms near spherical surfaces,” J. Chem. Phys. 87(2), 1355–1360 (1987).
[Crossref]

Cohen, A. E.

Y. Tang and A. E. Cohen, “Optical chirality and its interaction with matter,” Phys. Rev. Lett. 104(16), 163901 (2010).
[Crossref] [PubMed]

Demoz, B.

Denti, P.

Di Girolamo, P.

Dionne, J.

C. S. Ho, A. Garcia-Etxarri, Y. Zhao, and J. Dionne, “Enhancing enantioselective absorption using dielectric nanospheres,” ACS Photonics, in press (2016).

Dionne, J. A.

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M. Schäferling, D. Dregely, M. Hentschel, and H. Giessen, “Tailoring enhanced optical chirality: design principles for chiral plasmonic nanostructures,” Phys. Rev. X 2(3), 031010 (2012).
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V. V. Klimov, D. V. Guzatov, and M. Ducloy, “Engineering of radiation of optically active molecules with chiral nano-meta-particles,” Europhys. Lett. 97(4), 47004 (2012).
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T. J. Dufva, J. Sarvas, and J. C.-E. Sten, “Unified derivation of the translational addition theorems for the spherical scalar and vector wave functions,” Progr. Electromag. Res. B 4, 79–99 (2008).
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E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79(3), 035407 (2009).
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C. S. Ho, A. Garcia-Etxarri, Y. Zhao, and J. Dionne, “Enhancing enantioselective absorption using dielectric nanospheres,” ACS Photonics, in press (2016).

García-Etxarri, A.

A. García-Etxarri and J. A. Dionne, “Surface-enhanced circular dichroism spectroscopy mediated by nonchiral nanoantennas,” Phys. Rev. B 87(23), 235409 (2013).
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C. Kramer, M. Schäferling, T. Weiss, H. Giessen, and T. Brixner, “Analytic optimization of near-field optical chirality enhancement,” ACS Photonics, in press (2017).

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A. O. Govorov, Z. Fan, P. Hernandez, J. M. Slocik, and R. R. Naik, “Theory of circular dichroism of nanomaterials comprising chiral molecules and nanocrystals: plasmon enhancement, dipole interactions, and dielectric effects,” Nano Lett. 10(4), 1374–1382 (2010).
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Guzatov, D. V.

D. V. Guzatov and V. V. Klimov, “Spontaneous emission of a chiral molecule near a cluster of two chiral spherical particles,” Quantum Electron. 45(3), 250–257 (2015).
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V. V. Klimov, I. V. Zabkov, A. A. Pavlov, and D. V. Guzatov, “Eigen oscillations of a chiral sphere and their influence on radiation of chiral molecules,” Opt. Express 22(15), 18564–18578 (2014).
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H. Wang, Y. Wu, B. Lassiter, C. L. Nehl, J. H. Hafner, P. Nordlander, and N. J. Halas, “Symmetry breaking in individual plasmonic nanoparticles,” Proc. Natl. Acad. Sci. U.S.A. 103(29), 10856–10860 (2006).
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C. S. Ho, A. Garcia-Etxarri, Y. Zhao, and J. Dionne, “Enhancing enantioselective absorption using dielectric nanospheres,” ACS Photonics, in press (2016).

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E. K. N. Yung and B. J. Hu, “Scattering by conducting sphere coated with chiral media,” Microw. Opt. Technol. Lett. 36(4), 288–293 (2002).
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D. V. Guzatov and V. V. Klimov, “Spontaneous emission of a chiral molecule near a cluster of two chiral spherical particles,” Quantum Electron. 45(3), 250–257 (2015).
[Crossref]

V. V. Klimov, I. V. Zabkov, A. A. Pavlov, and D. V. Guzatov, “Eigen oscillations of a chiral sphere and their influence on radiation of chiral molecules,” Opt. Express 22(15), 18564–18578 (2014).
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D. V. Guzatov and V. V. Klimov, “The influence of chiral spherical particles on the radiation of optically active molecules,” New J. Phys. 14(12), 123009 (2012).
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V. V. Klimov, D. V. Guzatov, and M. Ducloy, “Engineering of radiation of optically active molecules with chiral nano-meta-particles,” Europhys. Lett. 97(4), 47004 (2012).
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V. V. Klimov and D. V. Guzatov, “Using chiral nano-meta-particles to control chiral molecule radiation,” Phys. Uspekhi 182(10), 1130–1135 (2012).

V. V. Klimov and V. S. Letokhov, “Electric and magnetic dipole transitions of an atom in the presence of spherical dielectric interface,” Laser Phys. 15(1), 61–73 (2005).

V. V. Klimov and M. Ducloy, “Spontaneous emission rate of an excited atom placed near a nanofiber,” Phys. Rev. A 69(1), 013812 (2004).
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M. W. Knight and N. J. Halas, “Nanoshells to nanoeggs to nanocups: symmetry breaking beyond the quasistatic limit in complex plasmonic nanoparticles,” New J. Phys. 10(10), 105006 (2008).
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E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79(3), 035407 (2009).
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B. Wang, J. Zhou, T. Koschny, and C. M. Soukoulis, “Nonplanar chiral metamaterials with negative index,” Appl. Phys. Lett. 94(15), 151112 (2009).
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C. Kramer, M. Schäferling, T. Weiss, H. Giessen, and T. Brixner, “Analytic optimization of near-field optical chirality enhancement,” ACS Photonics, in press (2017).

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Lassiter, B.

H. Wang, Y. Wu, B. Lassiter, C. L. Nehl, J. H. Hafner, P. Nordlander, and N. J. Halas, “Symmetry breaking in individual plasmonic nanoparticles,” Proc. Natl. Acad. Sci. U.S.A. 103(29), 10856–10860 (2006).
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V. V. Klimov and V. S. Letokhov, “Electric and magnetic dipole transitions of an atom in the presence of spherical dielectric interface,” Laser Phys. 15(1), 61–73 (2005).

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S. Zhang, Y.-S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett. 102(2), 023901 (2009).
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Y. Zhao, A. N. Askarpour, L. Sun, J. Shi, X. Li, and A. Alù, “Chirality detection of enantiomers using twisted optical metamaterials,” Nat. Commun. 8, 14180 (2017).
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Mishchenko, M. I.

M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transf. 55(5), 535–575 (1996).
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D. W. Mackowski and M. I. Mishchenko, “Calculation of the T matrix and the scattering matrix for ensembles of spheres,” J. Opt. Soc. Am. A 13(11), 2266–2278 (1996).
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M. I. Mishchenko, D. W. Mackowski, and L. D. Travis, “Scattering of light by bispheres with touching and separated components,” Appl. Opt. 34(21), 4589–4599 (1995).
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A. O. Govorov, Z. Fan, P. Hernandez, J. M. Slocik, and R. R. Naik, “Theory of circular dichroism of nanomaterials comprising chiral molecules and nanocrystals: plasmon enhancement, dipole interactions, and dielectric effects,” Nano Lett. 10(4), 1374–1382 (2010).
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Nehl, C. L.

H. Wang, Y. Wu, B. Lassiter, C. L. Nehl, J. H. Hafner, P. Nordlander, and N. J. Halas, “Symmetry breaking in individual plasmonic nanoparticles,” Proc. Natl. Acad. Sci. U.S.A. 103(29), 10856–10860 (2006).
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Nesterov, M. L.

M. L. Nesterov, X. Yin, M. Schäferling, H. Giessen, and T. Weiss, “The role of plasmon-generated near fields for enhanced circular dichroism spectroscopy,” ACS Photonics 3(4), 578–583 (2016).
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H. Wang, Y. Wu, B. Lassiter, C. L. Nehl, J. H. Hafner, P. Nordlander, and N. J. Halas, “Symmetry breaking in individual plasmonic nanoparticles,” Proc. Natl. Acad. Sci. U.S.A. 103(29), 10856–10860 (2006).
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Park, Y.-S.

S. Zhang, Y.-S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett. 102(2), 023901 (2009).
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Plum, E.

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79(3), 035407 (2009).
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Schäferling, M.

M. L. Nesterov, X. Yin, M. Schäferling, H. Giessen, and T. Weiss, “The role of plasmon-generated near fields for enhanced circular dichroism spectroscopy,” ACS Photonics 3(4), 578–583 (2016).
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M. Schäferling, D. Dregely, M. Hentschel, and H. Giessen, “Tailoring enhanced optical chirality: design principles for chiral plasmonic nanostructures,” Phys. Rev. X 2(3), 031010 (2012).
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C. Kramer, M. Schäferling, T. Weiss, H. Giessen, and T. Brixner, “Analytic optimization of near-field optical chirality enhancement,” ACS Photonics, in press (2017).

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B. V. Bokut’, A. N. Serdyukov, and F. I. Fedorov, “Phenomenological theory of optically active crystals,” Sov. Phys. Crystallogr. 15, 871–874 (1971).

Shi, J.

Y. Zhao, A. N. Askarpour, L. Sun, J. Shi, X. Li, and A. Alù, “Chirality detection of enantiomers using twisted optical metamaterials,” Nat. Commun. 8, 14180 (2017).
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Sindoni, O. I.

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A. O. Govorov, Z. Fan, P. Hernandez, J. M. Slocik, and R. R. Naik, “Theory of circular dichroism of nanomaterials comprising chiral molecules and nanocrystals: plasmon enhancement, dipole interactions, and dielectric effects,” Nano Lett. 10(4), 1374–1382 (2010).
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B. Wang, J. Zhou, T. Koschny, and C. M. Soukoulis, “Nonplanar chiral metamaterials with negative index,” Appl. Phys. Lett. 94(15), 151112 (2009).
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E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79(3), 035407 (2009).
[Crossref]

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T. J. Dufva, J. Sarvas, and J. C.-E. Sten, “Unified derivation of the translational addition theorems for the spherical scalar and vector wave functions,” Progr. Electromag. Res. B 4, 79–99 (2008).
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Y. Zhao, A. N. Askarpour, L. Sun, J. Shi, X. Li, and A. Alù, “Chirality detection of enantiomers using twisted optical metamaterials,” Nat. Commun. 8, 14180 (2017).
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[Crossref]

M. I. Mishchenko, D. W. Mackowski, and L. D. Travis, “Scattering of light by bispheres with touching and separated components,” Appl. Opt. 34(21), 4589–4599 (1995).
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Wu, Y.

H. Wang, Y. Wu, B. Lassiter, C. L. Nehl, J. H. Hafner, P. Nordlander, and N. J. Halas, “Symmetry breaking in individual plasmonic nanoparticles,” Proc. Natl. Acad. Sci. U.S.A. 103(29), 10856–10860 (2006).
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M. L. Nesterov, X. Yin, M. Schäferling, H. Giessen, and T. Weiss, “The role of plasmon-generated near fields for enhanced circular dichroism spectroscopy,” ACS Photonics 3(4), 578–583 (2016).
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Y. Zhao, A. N. Askarpour, L. Sun, J. Shi, X. Li, and A. Alù, “Chirality detection of enantiomers using twisted optical metamaterials,” Nat. Commun. 8, 14180 (2017).
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E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79(3), 035407 (2009).
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ACS Photonics (1)

M. L. Nesterov, X. Yin, M. Schäferling, H. Giessen, and T. Weiss, “The role of plasmon-generated near fields for enhanced circular dichroism spectroscopy,” ACS Photonics 3(4), 578–583 (2016).
[Crossref]

Appl. Opt. (4)

Appl. Phys. Lett. (1)

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Figures (8)

Fig. 1
Fig. 1 Geometry of a chiral molecule with electric and magnetic dipole moments d0 and –im0, located near an asymmetric chiral particle consisting of a spherical core (blue circle) with a spherical nonconcentric shell (green region).
Fig. 2
Fig. 2 Radiative decay rate of the spontaneous emission of a chiral molecule located close to the surface ( r 1 a ) of a spherical particle with a dielectric core ( ε 2 =2 , μ 2 =1 and b/a=0.75 ) and a concentric spherical shell as the function of k 0 a . (a) The shell is made of a chiral dielectric ( ε 1 =3 , μ 1 =1 and χ 1 =0.1 ). (b) The shell is made of a chiral DNG-metamaterial ( ε 1 =3 , μ 1 =1 and χ 1 =0.1 ). The solid lines correspond to the “right” molecule ( m 0 =0.1 d 0 ), and the dashed lines correspond to the “left” molecule ( m 0 =0.1 d 0 ). The cases of the pure dielectric ( b=a ) and pure chiral ( b=0 ) spheres are also presented.
Fig. 3
Fig. 3 Radiative decay rate of the spontaneous emission of a chiral molecule located close to the surface ( r 1 a ) of a spherical particle with a dielectric core ( ε 2 =2 and μ 2 =1 ) and a concentric spherical shell as the function of b/a for the selected values of k 0 a . (a) The shell is made of a chiral dielectric ( ε 1 =3 , μ 1 =1 and χ 1 =0.1 ). (b) The shell is made of a chiral DNG-metamaterial ( ε 1 =3 , μ 1 =1 and χ 1 =0.1 ). The solid lines correspond to the “right” molecule ( m 0 =0.1 d 0 ), and the dashed lines correspond to the “left” molecule ( m 0 =0.1 d 0 ).
Fig. 4
Fig. 4 Radiative decay rate of the spontaneous emission of a chiral molecule located close to the surface ( r 1 a ) of a spherical particle with a dielectric core ( ε 2 =2 , μ 2 =1 and k 0 b=0.5 ) and a nonconcentric spherical shell ( h/b=0.1 ) as the function of b/a . (a) The shell is made of a chiral dielectric ( ε 1 =3 , μ 1 =1 and χ 1 =0.1 ). (b) The shell is made of a chiral DNG-metamaterial ( ε 1 =3 , μ 1 =1 and χ 1 =0.1 ). The solid lines correspond to the “right” molecule ( m 0 =0.1 d 0 ), and the dashed lines correspond to the “left” molecule ( m 0 =0.1 d 0 ). The sketches represent the cases of the molecule position near the thin and thick parts of a shell. The case of a concentric shell ( h=0 ) is also presented.
Fig. 5
Fig. 5 Radiative decay rate of the spontaneous emission of a chiral molecule located close to the surface ( r 1 a ) of a spherical particle with a dielectric core ( ε 2 =2 , μ 2 =1 and b/a=0.5 ) and a nonconcentric spherical shell as the function of h/a for the selected values of k 0 a . (a) The shell is made of a chiral dielectric ( ε 1 =3 , μ 1 =1 and χ 1 =0.1 ). (b) The shell is made of a chiral DNG-metamaterial ( ε 1 =3 , μ 1 =1 and χ 1 =0.1 ). The solid lines correspond to the “right” molecule ( m 0 =0.1 d 0 ), and the dashed lines correspond to the “left” molecule ( m 0 =0.1 d 0 ). The sketches represent the cases of the molecule position near the thin and thick parts of a shell.
Fig. 6
Fig. 6 Radiative decay rate of the spontaneous emission of a chiral molecule located close to the surface ( r 1 a ) of a spherical nanoparticle ( k 0 a=0.1 ) with a dielectric core ( ε 2 =2 , μ 2 =1 and b/a=0.5 ) and a chiral ( χ 1 =0.2 ) nonconcentric spherical shell ( h/b=0.1 ) as the function of the real part of the permittivity ε 1 = ε 1 +i0.1 for the selected permeability: (a) μ 1 =2.3+i0.1 and (b) μ 1 =3+i0.1 . The solid lines correspond to the “right” molecule ( m 0 =0.1 d 0 ), and the dashed lines correspond to the “left” molecule ( m 0 =0.1 d 0 ). The colors represent the cases of the molecule position near the thin (blue), thick (red) parts of a shell, and the case of concentric shell (green). The insets show near-field patterns Re(Ez) at (a) ε 1 =1.33 and (b) ε 1 =0.833 on the z = 0 plane. The scale colorbars are in units of V/m.
Fig. 7
Fig. 7 Spatial distribution of Re(Ez) for parameters corresponding to Fig. 6a. Upper three panels are for the “right” molecule ( m 0 =0.1 d 0 ), and lower ones correspond to the “left” molecule ( m 0 =0.1 d 0 ). The scale colorbars are in units of V/m.
Fig. 8
Fig. 8 Spatial distribution of Re(Ez) for parameters corresponding to Fig. 6b. Upper three pictures are for the “right” molecule ( m 0 =0.1 d 0 ), and lower ones correspond to the “left” molecule ( m 0 =0.1 d 0 ). The scale colorbars are in units of V/m.

Equations (18)

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k 0 D shell = ε 1 ( k 0 E shell + χ 1 rot E shell ), k 0 B shell = μ 1 ( k 0 H shell + χ 1 rot H shell ),
E 1 0 ={ ( d 0 )+ d 0 k 0 2 i k 0 [ ( i m 0 )× ] } e i k 0 | r 1 r 1 0 | | r 1 r 1 0 | , H 1 0 = 1 i k 0 [ × E 1 0 ],
E 1 0 ={ n=1 m=n n ( A 1 mn ( 0 ) N 1 ψ mn ( 0 ) + B 1 mn ( 0 ) M 1 ψ mn ( 0 ) ) , | r 1 |<| r 1 0 |, n=1 m=n n ( C 1 mn ( 0 ) N 1 ζ mn ( 0 ) + D 1 mn ( 0 ) M 1 ζ mn ( 0 ) ) , | r 1 |>| r 1 0 |,
E 1 out = n=1 m=n n ( C 1 mn N 1 ζ mn ( 0 ) + D 1 mn M 1 ζ mn ( 0 ) ) , H 1 out = 1 i k 0 [ × E 1 out ],
E 2 core = n=1 m=n n ( A 2 mn N 2 ψ mn ( 2 ) + B 2 mn M 2 ψ mn ( 2 ) ) , H 2 core = 1 i k 2 Z 2 [ × E 2 core ],
E shell = E 1 + E 2 , H shell = H 1 + H 2 ,
E s = Q s L i Z 1 Q s R , H s = i Z 1 Q s L + Q s R ,
Q 1 L = n=1 m=n n A 1 mn ( N 1 ψ mn ( L ) + M 1 ψ mn ( L ) ) , Q 1 R = n=1 m=n n B 1 mn ( N 1 ψ mn ( R ) M 1 ψ mn ( R ) ) , Q 2 L = n=1 m=n n C 2 mn ( N 2 ζ mn ( L ) + M 2 ζ mn ( L ) ) , Q 2 R = n=1 m=n n D 2 mn ( N 2 ζ mn ( R ) M 2 ζ mn ( R ) ) ,
A L n ( 2 ) ( b ) q=| m | ( V mnq ( L ) + W mnq ( L ) ) A 1 mq i Z 1 A R n ( 2 ) ( b ) q=| m | ( V mnq ( R ) W mnq ( R ) ) B 1 mq + C L n ( 2 ) ( b ) C 2 mn i Z 1 C R n ( 2 ) ( b ) D 2 mn =0, B L n ( 2 ) ( b ) q=| m | ( V mnq ( L ) + W mnq ( L ) ) A 1 mq +i Z 1 B R n ( 2 ) ( b ) q=| m | ( V mnq ( R ) W mnq ( R ) ) B 1 mq + D L n ( 2 ) ( b ) C 2 mn +i Z 1 D R n ( 2 ) ( b ) D 2 mn =0,
V L n ( 0 ) ( a ) A 1 mn i Z 1 V R n ( 0 ) ( a ) B 1 mn + X L n ( 0 ) ( a ) q=| m | ( 1 ) n+q ( V ˜ mnq ( L ) W ˜ mnq ( L ) ) C 2 mq i Z 1 X R n ( 0 ) ( a ) q=| m | ( 1 ) n+q ( V ˜ mnq ( R ) + W ˜ mnq ( R ) ) D 2 mq = i Z 1 ( k 0 a ) 2 A 1 mn ( 0 ) , W L n ( 0 ) ( a ) A 1 mn +i Z 1 W R n ( 0 ) ( a ) B 1 mn + Y L n ( 0 ) ( a ) q=| m | ( 1 ) n+q ( V ˜ mnq ( L ) W ˜ mnq ( L ) ) C 2 mq +i Z 1 Y R n ( 0 ) ( a ) q=| m | ( 1 ) n+q ( V ˜ mnq ( R ) + W ˜ mnq ( R ) ) D 2 mq = i Z 1 ( k 0 a ) 2 B 1 mn ( 0 ) ,
P rad = c 8π S dSRe( [ ( E 1 out + E 1 0 )×( H 1 out* + H 1 0 * ) ]n ) ,
P rad,0 = c 8π S dSRe( [ E 1 0 × H 1 0 * ]n ) = c k 0 4 3 ( | d 0 | 2 + | m 0 | 2 ).
γ rad γ 0 = P rad P rad,0 = 3 k 0 6 ( | d 0 | 2 + | m 0 | 2 ) n=1 m=n n n( n+1 ) 4n+2 ( n+m )! ( nm )! ( | C 1 mn ( 0 ) + C 1 mn | 2 + | D 1 mn ( 0 ) + D 1 mn | 2 ),
{ N 1 ψ mq ( J ) M 1 ψ mq ( J ) }= n=| m | [ V mnq ( J ) { N 2 ψ mn ( J ) M 2 ψ mn ( J ) }+ W mnq ( J ) { M 2 ψ mn ( J ) N 2 ψ mn ( J ) } ] , { N 2 ζ mq ( J ) M 2 ζ mq ( J ) }= n=| m | ( 1 ) n+q [ V ˜ mnq ( J ) { N 1 ζ mn ( J ) M 1 ζ mn ( J ) } W ˜ mnq ( J ) { M 1 ζ mn ( J ) N 1 ζ mn ( J ) } ] ,| r 1 |>h,
{ V mnq ( J ) V ˜ mnq }={ U mnq ( J ) U ˜ mnq ( J ) } k J h( nm n( 2n1 ) { U m,n1,q ( J ) U ˜ m,n1,q ( J ) }+ n+m+1 ( n+1 )( 2n+3 ) { U m,n+1,q ( J ) U ˜ m,n+1,q ( J ) } ), { W mnq ( J ) W ˜ mnq ( J ) }= im k J h n( n+1 ) { U mnq ( J ) U ˜ mnq ( J ) },{ U mnq ( J ) U ˜ mnq ( J ) }= [ ( nm )!( q+m )! ( n+m )!( qm )! ] 1/2 × × σ=| nq | n+q i nqσ ψ σ ( k J h ) k J h { ( 1 ) m ( 2n+1 ) C qmn,m σ0 C q0n0 σ0 ( 2σ+1 ) C qmσ0 nm C q0σ0 n0 } ,
{ A J n ( p ) ( ξ ) B J n ( p ) ( ξ ) }={ Z p Z 1 } ψ n ( k J ξ ) k J ξ ψ n ( k p ξ ) k p ξ { Z 1 Z p } ψ n ( k J ξ ) k J ξ ψ n ( k p ξ ) k p ξ , { C J n ( p ) ( ξ ) D J n ( p ) ( ξ ) }={ Z p Z 1 } ζ n ( k J ξ ) k J ξ ψ n ( k p ξ ) k p ξ { Z 1 Z p } ζ n ( k J ξ ) k J ξ ψ n ( k p ξ ) k p ξ ,
{ V J n ( p ) ( ξ ) W J n ( p ) ( ξ ) }={ Z p Z 1 } ψ n ( k J ξ ) k J ξ ζ n ( k p ξ ) k p ξ { Z 1 Z p } ψ n ( k J ξ ) k J ξ ζ n ( k p ξ ) k p ξ , { X J n ( p ) ( ξ ) Y J n ( p ) ( ξ ) }={ Z p Z 1 } ζ n ( k J ξ ) k J ξ ζ n ( k p ξ ) k p ξ { Z 1 Z p } ζ n ( k J ξ ) k J ξ ζ n ( k p ξ ) k p ξ ,
k L = k 0 ε 1 μ 1 1 χ 1 ε 1 μ 1 , k R = k 0 ε 1 μ 1 1+ χ 1 ε 1 μ 1

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