Abstract

We report a strong correlation between the calculated broadband circular differential optical absorption (CDOA) and the geometric chirality of plasmonic meta-atoms with two-dimensional chirality. We investigate this correlation using three common gold meta-atom geometries: L-shapes, triangles, and nanorod dimers, over a broad range of geometric parameters. We show that this correlation holds for both contiguous plasmonic meta-atoms and non-contiguous structures which support plasmonic coupling effects. A potential application for this correlation is the rapid optimization of plasmonic nanostructure for maximum broadband CDOA.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (2)

P. Gutsche and M. Nieto-Vesperinas, “Optical chirality of time-harmonic wavefields for classification of scatterers,” Sci. Rep. 8(1), 9416 (2018).
[PubMed]

K. Imaeda, S. Hasegawa, and K. Imura, “Imaging of plasmonic eigen modes in gold triangular mesoplates by near-field optical microscopy,” J. Phys. Chem. C 122(13), 7399–7409 (2018).

2017 (2)

D. F. Tang, C. Wang, W. K. Pan, M. H. Li, and J. F. Dong, “Broad dual-band asymmetric transmission of circular polarized waves in near-infrared communication band,” Opt. Express 25(10), 11329–11339 (2017).
[PubMed]

J. T. Collins, C. Kuppe, D. C. Hooper, C. Sibilia, M. Centini, and V. K. Valev, “Chirality and chiroptical effects in metal nanostructures: Fundamentals and current trends,” Adv. Opt. Mater. 5(16), 1700182 (2017).

2016 (4)

I. Fernandez-Corbaton, M. Fruhnert, and C. Rockstuhl, “Objects of maximum electromagnetic chirality,” Phys. Rev. X 6(3), 031013 (2016).

L. V. Poulikakos, P. Gutsche, K. M. McPeak, S. Burger, J. Niegemann, C. Hafner, and D. J. Norris, “Optical chirality flux as a useful far-field probe of chiral near fields,” ACS Photonics 3(9), 1619–1625 (2016).

O. Arteaga, J. Sancho-Parramon, S. Nichols, B. M. Maoz, A. Canillas, S. Bosch, G. Markovich, and B. Kahr, “Relation between 2D/3D chirality and the appearance of chiroptical effects in real nanostructures,” Opt. Express 24(3), 2242–2252 (2016).
[PubMed]

S. Chandel, J. Soni, S. K. Ray, A. Das, A. Ghosh, S. Raj, and N. Ghosh, “Complete polarization characterization of single plasmonic nanoparticle enabled by a novel Dark-field Mueller matrix spectroscopy system,” Sci. Rep. 6(1), 26466 (2016).
[PubMed]

2015 (5)

H. Okamoto, T. Narushima, Y. Nishiyama, and K. Imura, “Local optical responses of plasmon resonances visualised by near-field optical imaging,” Phys. Chem. Chem. Phys. 17(9), 6192–6206 (2015).
[PubMed]

S. Burger, P. Gutsche, M. Hammerschmidt, S. Herrmann, J. Pomplun, F. Schmidt, B. Wohlfeil, and L. Zschiedrich, “Hp-finite-elements for simulating electromagnetic fields in optical devices with rough textures,” Proc. SPIE 9630, 7 (2015).

W. Li, Z. J. Coppens, L. V. Besteiro, W. Wang, A. O. Govorov, and J. Valentine, “Circularly polarized light detection with hot electrons in chiral plasmonic metamaterials,” Nat. Commun. 6(1), 8379 (2015).
[PubMed]

K. M. McPeak, C. D. van Engers, S. Bianchi, A. Rossinelli, L. V. Poulikakos, L. Bernard, S. Herrmann, D. K. Kim, S. Burger, M. Blome, S. V. Jayanti, and D. J. Norris, “Ultraviolet plasmonic chirality from colloidal aluminum nanoparticles exhibiting charge-selective protein detection,” Adv. Mater. 27(40), 6244–6250 (2015).
[PubMed]

V. E. Ferry, M. Hentschel, and A. P. Alivisatos, “Circular dichroism in off-resonantly coupled plasmonic nanosystems,” Nano Lett. 15(12), 8336–8341 (2015).
[PubMed]

2014 (3)

K. M. McPeak, C. D. van Engers, M. Blome, J. H. Park, S. Burger, M. A. Gosálvez, A. Faridi, Y. R. Ries, A. Sahu, and D. J. Norris, “Complex chiral colloids and surfaces via high-index off-cut silicon,” Nano Lett. 14(5), 2934–2940 (2014).
[PubMed]

O. Arteaga, B. M. Maoz, S. Nichols, G. Markovich, and B. Kahr, “Complete polarimetry on the asymmetric transmission through subwavelength hole arrays,” Opt. Express 22(11), 13719–13732 (2014).
[PubMed]

M. Wakabayashi, S. Yokojima, T. Fukaminato, K. Shiino, M. Irie, and S. Nakamura, “Anisotropic dissymmetry factor, g: theoretical investigation on single molecule chiroptical spectroscopy,” J. Phys. Chem. A 118(27), 5046–5057 (2014).
[PubMed]

2013 (2)

V. K. Valev, J. J. Baumberg, C. Sibilia, and T. Verbiest, “Chirality and chiroptical effects in plasmonic nanostructures: fundamentals, recent progress, and outlook,” Adv. Mater. 25(18), 2517–2534 (2013).
[PubMed]

O. Arteaga, “Number of independent parameters in the Mueller matrix representation of homogeneous depolarizing media,” Opt. Lett. 38(7), 1131–1133 (2013).
[PubMed]

2012 (2)

M. Hentschel, M. Schäferling, T. Weiss, N. Liu, and H. Giessen, “Three-dimensional chiral plasmonic oligomers,” Nano Lett. 12(5), 2542–2547 (2012).
[PubMed]

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).

2011 (1)

N. J. Halas, S. Lal, W.-S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev. 111(6), 3913–3961 (2011).
[PubMed]

2010 (4)

Z. Fan and A. O. Govorov, “Plasmonic circular dichroism of chiral metal nanoparticle assemblies,” Nano Lett. 10(7), 2580–2587 (2010).
[PubMed]

O. Arteaga and A. Canillas, “Analytic inversion of the Mueller-Jones polarization matrices for homogeneous media,” Opt. Lett. 35(4), 559–561 (2010).
[PubMed]

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5(11), 783–787 (2010).
[PubMed]

C. Menzel, C. Rockstuhl, and F. Lederer, “Advanced jones calculus for the classification of periodic metamaterials,” Phys. Rev. A 82(5), 053811 (2010).

2009 (1)

J. Yang, J.-S. Zhang, X.-F. Wu, and Q.-H. Gong, “Resonant modes of l-shaped gold nanoparticles,” Chin. Phys. Lett. 26(6), 067802 (2009).

2008 (1)

M. Rang, A. C. Jones, F. Zhou, Z.-Y. Li, B. J. Wiley, Y. Xia, and M. B. Raschke, “Optical near-field mapping of plasmonic nanoprisms,” Nano Lett. 8(10), 3357–3363 (2008).
[PubMed]

2006 (2)

L. J. Sherry, R. Jin, C. A. Mirkin, G. C. Schatz, and R. P. Van Duyne, “Localized surface plasmon resonance spectroscopy of single silver triangular nanoprisms,” Nano Lett. 6(9), 2060–2065 (2006).
[PubMed]

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006).
[PubMed]

2005 (1)

2004 (2)

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4(5), 899–903 (2004).

A. Potts, D. M. Bagnall, and N. I. Zheludev, “A new model of geometric chirality for two-dimensional continuous media and planar meta-materials,” J. Opt. A 6(2), 193–203 (2004).

2003 (2)

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
[PubMed]

A. Rassat and P. W. Fowler, “Any scalene triangle is the most chiral triangle,” Helv. Chim. Acta 86(5), 1728–1740 (2003).

1992 (2)

A. B. Buda and K. Mislow, “A hausdorff chirality measure,” J. Am. Chem. Soc. 114(15), 6006–6012 (1992).

A. B. Buda, T. A. der Heyde, and K. Mislow, “On quantifying chirality,” Angew. Chem. Int. Ed. Engl. 31(8), 989–1007 (1992).

1991 (1)

A. B. Buda, T. P. E. Auf der Heyde, and K. Mislow, “Geometric chirality products,” J. Math. Chem. 6(1), 243–253 (1991).

1989 (1)

G. Gilat, “Chiral coefficient-a measure of the amount of structural chirality,” J. Phys. Math. Gen. 22(13), L545–L550 (1989).

1987 (1)

A. Schönhofer and H.-G. Kuball, “Symmetry properties of the mueller matrix,” Chem. Phys. 115(2), 159–167 (1987).

1986 (1)

J. J. Gil and E. Bernabeu, “Depolarization and polarization indices of an optical system,” Opt. Acta (Lond.) 33(2), 185–189 (1986).

1985 (1)

J. J. Gil and E. Bernabeu, “A depolarization criterion in mueller matrices,” Opt. Acta (Lond.) 32(3), 259–261 (1985).

1942 (1)

F. Perrin, “Polarization of light scattered by isotropic opalescent media,” J. Chem. Phys. 10(7), 415–427 (1942).

1929 (1)

P. Soleillet, “Sur les paramètres caractérisant la polarisation partielle de la lumière dans les phénomènes de fluorescence,” Ann. Phys. (Paris) 10(12), 23–97 (1929).

1895 (1)

K. Pearson, “Note on regression and inheritance in the case of two parents,” Proc. R. Soc. Lond. 58(347-352), 240–242 (1895).

Alivisatos, A. P.

V. E. Ferry, M. Hentschel, and A. P. Alivisatos, “Circular dichroism in off-resonantly coupled plasmonic nanosystems,” Nano Lett. 15(12), 8336–8341 (2015).
[PubMed]

Arteaga, O.

Auf der Heyde, T. P. E.

A. B. Buda, T. P. E. Auf der Heyde, and K. Mislow, “Geometric chirality products,” J. Math. Chem. 6(1), 243–253 (1991).

Bagnall, D. M.

A. Potts, D. M. Bagnall, and N. I. Zheludev, “A new model of geometric chirality for two-dimensional continuous media and planar meta-materials,” J. Opt. A 6(2), 193–203 (2004).

Barron, L. D.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5(11), 783–787 (2010).
[PubMed]

Baumberg, J. J.

V. K. Valev, J. J. Baumberg, C. Sibilia, and T. Verbiest, “Chirality and chiroptical effects in plasmonic nanostructures: fundamentals, recent progress, and outlook,” Adv. Mater. 25(18), 2517–2534 (2013).
[PubMed]

Bernabeu, E.

J. J. Gil and E. Bernabeu, “Depolarization and polarization indices of an optical system,” Opt. Acta (Lond.) 33(2), 185–189 (1986).

J. J. Gil and E. Bernabeu, “A depolarization criterion in mueller matrices,” Opt. Acta (Lond.) 32(3), 259–261 (1985).

Bernard, L.

K. M. McPeak, C. D. van Engers, S. Bianchi, A. Rossinelli, L. V. Poulikakos, L. Bernard, S. Herrmann, D. K. Kim, S. Burger, M. Blome, S. V. Jayanti, and D. J. Norris, “Ultraviolet plasmonic chirality from colloidal aluminum nanoparticles exhibiting charge-selective protein detection,” Adv. Mater. 27(40), 6244–6250 (2015).
[PubMed]

Besteiro, L. V.

W. Li, Z. J. Coppens, L. V. Besteiro, W. Wang, A. O. Govorov, and J. Valentine, “Circularly polarized light detection with hot electrons in chiral plasmonic metamaterials,” Nat. Commun. 6(1), 8379 (2015).
[PubMed]

Bianchi, S.

K. M. McPeak, C. D. van Engers, S. Bianchi, A. Rossinelli, L. V. Poulikakos, L. Bernard, S. Herrmann, D. K. Kim, S. Burger, M. Blome, S. V. Jayanti, and D. J. Norris, “Ultraviolet plasmonic chirality from colloidal aluminum nanoparticles exhibiting charge-selective protein detection,” Adv. Mater. 27(40), 6244–6250 (2015).
[PubMed]

Blome, M.

K. M. McPeak, C. D. van Engers, S. Bianchi, A. Rossinelli, L. V. Poulikakos, L. Bernard, S. Herrmann, D. K. Kim, S. Burger, M. Blome, S. V. Jayanti, and D. J. Norris, “Ultraviolet plasmonic chirality from colloidal aluminum nanoparticles exhibiting charge-selective protein detection,” Adv. Mater. 27(40), 6244–6250 (2015).
[PubMed]

K. M. McPeak, C. D. van Engers, M. Blome, J. H. Park, S. Burger, M. A. Gosálvez, A. Faridi, Y. R. Ries, A. Sahu, and D. J. Norris, “Complex chiral colloids and surfaces via high-index off-cut silicon,” Nano Lett. 14(5), 2934–2940 (2014).
[PubMed]

Bosch, S.

Buda, A. B.

A. B. Buda and K. Mislow, “A hausdorff chirality measure,” J. Am. Chem. Soc. 114(15), 6006–6012 (1992).

A. B. Buda, T. A. der Heyde, and K. Mislow, “On quantifying chirality,” Angew. Chem. Int. Ed. Engl. 31(8), 989–1007 (1992).

A. B. Buda, T. P. E. Auf der Heyde, and K. Mislow, “Geometric chirality products,” J. Math. Chem. 6(1), 243–253 (1991).

Burger, S.

L. V. Poulikakos, P. Gutsche, K. M. McPeak, S. Burger, J. Niegemann, C. Hafner, and D. J. Norris, “Optical chirality flux as a useful far-field probe of chiral near fields,” ACS Photonics 3(9), 1619–1625 (2016).

K. M. McPeak, C. D. van Engers, S. Bianchi, A. Rossinelli, L. V. Poulikakos, L. Bernard, S. Herrmann, D. K. Kim, S. Burger, M. Blome, S. V. Jayanti, and D. J. Norris, “Ultraviolet plasmonic chirality from colloidal aluminum nanoparticles exhibiting charge-selective protein detection,” Adv. Mater. 27(40), 6244–6250 (2015).
[PubMed]

S. Burger, P. Gutsche, M. Hammerschmidt, S. Herrmann, J. Pomplun, F. Schmidt, B. Wohlfeil, and L. Zschiedrich, “Hp-finite-elements for simulating electromagnetic fields in optical devices with rough textures,” Proc. SPIE 9630, 7 (2015).

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Poulikakos, L. V.

L. V. Poulikakos, P. Gutsche, K. M. McPeak, S. Burger, J. Niegemann, C. Hafner, and D. J. Norris, “Optical chirality flux as a useful far-field probe of chiral near fields,” ACS Photonics 3(9), 1619–1625 (2016).

K. M. McPeak, C. D. van Engers, S. Bianchi, A. Rossinelli, L. V. Poulikakos, L. Bernard, S. Herrmann, D. K. Kim, S. Burger, M. Blome, S. V. Jayanti, and D. J. Norris, “Ultraviolet plasmonic chirality from colloidal aluminum nanoparticles exhibiting charge-selective protein detection,” Adv. Mater. 27(40), 6244–6250 (2015).
[PubMed]

Prodan, E.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4(5), 899–903 (2004).

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
[PubMed]

Prosvirnin, S. L.

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006).
[PubMed]

Radloff, C.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
[PubMed]

Raj, S.

S. Chandel, J. Soni, S. K. Ray, A. Das, A. Ghosh, S. Raj, and N. Ghosh, “Complete polarization characterization of single plasmonic nanoparticle enabled by a novel Dark-field Mueller matrix spectroscopy system,” Sci. Rep. 6(1), 26466 (2016).
[PubMed]

Rang, M.

M. Rang, A. C. Jones, F. Zhou, Z.-Y. Li, B. J. Wiley, Y. Xia, and M. B. Raschke, “Optical near-field mapping of plasmonic nanoprisms,” Nano Lett. 8(10), 3357–3363 (2008).
[PubMed]

Raschke, M. B.

M. Rang, A. C. Jones, F. Zhou, Z.-Y. Li, B. J. Wiley, Y. Xia, and M. B. Raschke, “Optical near-field mapping of plasmonic nanoprisms,” Nano Lett. 8(10), 3357–3363 (2008).
[PubMed]

Rassat, A.

A. Rassat and P. W. Fowler, “Any scalene triangle is the most chiral triangle,” Helv. Chim. Acta 86(5), 1728–1740 (2003).

Ray, S. K.

S. Chandel, J. Soni, S. K. Ray, A. Das, A. Ghosh, S. Raj, and N. Ghosh, “Complete polarization characterization of single plasmonic nanoparticle enabled by a novel Dark-field Mueller matrix spectroscopy system,” Sci. Rep. 6(1), 26466 (2016).
[PubMed]

Ries, Y. R.

K. M. McPeak, C. D. van Engers, M. Blome, J. H. Park, S. Burger, M. A. Gosálvez, A. Faridi, Y. R. Ries, A. Sahu, and D. J. Norris, “Complex chiral colloids and surfaces via high-index off-cut silicon,” Nano Lett. 14(5), 2934–2940 (2014).
[PubMed]

Rockstuhl, C.

I. Fernandez-Corbaton, M. Fruhnert, and C. Rockstuhl, “Objects of maximum electromagnetic chirality,” Phys. Rev. X 6(3), 031013 (2016).

C. Menzel, C. Rockstuhl, and F. Lederer, “Advanced jones calculus for the classification of periodic metamaterials,” Phys. Rev. A 82(5), 053811 (2010).

Rogacheva, A. V.

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006).
[PubMed]

Rossinelli, A.

K. M. McPeak, C. D. van Engers, S. Bianchi, A. Rossinelli, L. V. Poulikakos, L. Bernard, S. Herrmann, D. K. Kim, S. Burger, M. Blome, S. V. Jayanti, and D. J. Norris, “Ultraviolet plasmonic chirality from colloidal aluminum nanoparticles exhibiting charge-selective protein detection,” Adv. Mater. 27(40), 6244–6250 (2015).
[PubMed]

Sahu, A.

K. M. McPeak, C. D. van Engers, M. Blome, J. H. Park, S. Burger, M. A. Gosálvez, A. Faridi, Y. R. Ries, A. Sahu, and D. J. Norris, “Complex chiral colloids and surfaces via high-index off-cut silicon,” Nano Lett. 14(5), 2934–2940 (2014).
[PubMed]

Sancho-Parramon, J.

Schäferling, M.

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).

M. Hentschel, M. Schäferling, T. Weiss, N. Liu, and H. Giessen, “Three-dimensional chiral plasmonic oligomers,” Nano Lett. 12(5), 2542–2547 (2012).
[PubMed]

Schatz, G. C.

L. J. Sherry, R. Jin, C. A. Mirkin, G. C. Schatz, and R. P. Van Duyne, “Localized surface plasmon resonance spectroscopy of single silver triangular nanoprisms,” Nano Lett. 6(9), 2060–2065 (2006).
[PubMed]

Schmidt, F.

S. Burger, P. Gutsche, M. Hammerschmidt, S. Herrmann, J. Pomplun, F. Schmidt, B. Wohlfeil, and L. Zschiedrich, “Hp-finite-elements for simulating electromagnetic fields in optical devices with rough textures,” Proc. SPIE 9630, 7 (2015).

Schönhofer, A.

A. Schönhofer and H.-G. Kuball, “Symmetry properties of the mueller matrix,” Chem. Phys. 115(2), 159–167 (1987).

Sherry, L. J.

L. J. Sherry, R. Jin, C. A. Mirkin, G. C. Schatz, and R. P. Van Duyne, “Localized surface plasmon resonance spectroscopy of single silver triangular nanoprisms,” Nano Lett. 6(9), 2060–2065 (2006).
[PubMed]

Shiino, K.

M. Wakabayashi, S. Yokojima, T. Fukaminato, K. Shiino, M. Irie, and S. Nakamura, “Anisotropic dissymmetry factor, g: theoretical investigation on single molecule chiroptical spectroscopy,” J. Phys. Chem. A 118(27), 5046–5057 (2014).
[PubMed]

Sibilia, C.

J. T. Collins, C. Kuppe, D. C. Hooper, C. Sibilia, M. Centini, and V. K. Valev, “Chirality and chiroptical effects in metal nanostructures: Fundamentals and current trends,” Adv. Opt. Mater. 5(16), 1700182 (2017).

V. K. Valev, J. J. Baumberg, C. Sibilia, and T. Verbiest, “Chirality and chiroptical effects in plasmonic nanostructures: fundamentals, recent progress, and outlook,” Adv. Mater. 25(18), 2517–2534 (2013).
[PubMed]

Soleillet, P.

P. Soleillet, “Sur les paramètres caractérisant la polarisation partielle de la lumière dans les phénomènes de fluorescence,” Ann. Phys. (Paris) 10(12), 23–97 (1929).

Soni, J.

S. Chandel, J. Soni, S. K. Ray, A. Das, A. Ghosh, S. Raj, and N. Ghosh, “Complete polarization characterization of single plasmonic nanoparticle enabled by a novel Dark-field Mueller matrix spectroscopy system,” Sci. Rep. 6(1), 26466 (2016).
[PubMed]

Stockman, M. I.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4(5), 899–903 (2004).

Tang, D. F.

Valentine, J.

W. Li, Z. J. Coppens, L. V. Besteiro, W. Wang, A. O. Govorov, and J. Valentine, “Circularly polarized light detection with hot electrons in chiral plasmonic metamaterials,” Nat. Commun. 6(1), 8379 (2015).
[PubMed]

Valev, V. K.

J. T. Collins, C. Kuppe, D. C. Hooper, C. Sibilia, M. Centini, and V. K. Valev, “Chirality and chiroptical effects in metal nanostructures: Fundamentals and current trends,” Adv. Opt. Mater. 5(16), 1700182 (2017).

V. K. Valev, J. J. Baumberg, C. Sibilia, and T. Verbiest, “Chirality and chiroptical effects in plasmonic nanostructures: fundamentals, recent progress, and outlook,” Adv. Mater. 25(18), 2517–2534 (2013).
[PubMed]

Van Duyne, R. P.

L. J. Sherry, R. Jin, C. A. Mirkin, G. C. Schatz, and R. P. Van Duyne, “Localized surface plasmon resonance spectroscopy of single silver triangular nanoprisms,” Nano Lett. 6(9), 2060–2065 (2006).
[PubMed]

van Engers, C. D.

K. M. McPeak, C. D. van Engers, S. Bianchi, A. Rossinelli, L. V. Poulikakos, L. Bernard, S. Herrmann, D. K. Kim, S. Burger, M. Blome, S. V. Jayanti, and D. J. Norris, “Ultraviolet plasmonic chirality from colloidal aluminum nanoparticles exhibiting charge-selective protein detection,” Adv. Mater. 27(40), 6244–6250 (2015).
[PubMed]

K. M. McPeak, C. D. van Engers, M. Blome, J. H. Park, S. Burger, M. A. Gosálvez, A. Faridi, Y. R. Ries, A. Sahu, and D. J. Norris, “Complex chiral colloids and surfaces via high-index off-cut silicon,” Nano Lett. 14(5), 2934–2940 (2014).
[PubMed]

Verbiest, T.

V. K. Valev, J. J. Baumberg, C. Sibilia, and T. Verbiest, “Chirality and chiroptical effects in plasmonic nanostructures: fundamentals, recent progress, and outlook,” Adv. Mater. 25(18), 2517–2534 (2013).
[PubMed]

Wakabayashi, M.

M. Wakabayashi, S. Yokojima, T. Fukaminato, K. Shiino, M. Irie, and S. Nakamura, “Anisotropic dissymmetry factor, g: theoretical investigation on single molecule chiroptical spectroscopy,” J. Phys. Chem. A 118(27), 5046–5057 (2014).
[PubMed]

Wang, C.

Wang, W.

W. Li, Z. J. Coppens, L. V. Besteiro, W. Wang, A. O. Govorov, and J. Valentine, “Circularly polarized light detection with hot electrons in chiral plasmonic metamaterials,” Nat. Commun. 6(1), 8379 (2015).
[PubMed]

Weiss, T.

M. Hentschel, M. Schäferling, T. Weiss, N. Liu, and H. Giessen, “Three-dimensional chiral plasmonic oligomers,” Nano Lett. 12(5), 2542–2547 (2012).
[PubMed]

Wiley, B. J.

M. Rang, A. C. Jones, F. Zhou, Z.-Y. Li, B. J. Wiley, Y. Xia, and M. B. Raschke, “Optical near-field mapping of plasmonic nanoprisms,” Nano Lett. 8(10), 3357–3363 (2008).
[PubMed]

Wohlfeil, B.

S. Burger, P. Gutsche, M. Hammerschmidt, S. Herrmann, J. Pomplun, F. Schmidt, B. Wohlfeil, and L. Zschiedrich, “Hp-finite-elements for simulating electromagnetic fields in optical devices with rough textures,” Proc. SPIE 9630, 7 (2015).

Wu, X.-F.

J. Yang, J.-S. Zhang, X.-F. Wu, and Q.-H. Gong, “Resonant modes of l-shaped gold nanoparticles,” Chin. Phys. Lett. 26(6), 067802 (2009).

Xia, Y.

M. Rang, A. C. Jones, F. Zhou, Z.-Y. Li, B. J. Wiley, Y. Xia, and M. B. Raschke, “Optical near-field mapping of plasmonic nanoprisms,” Nano Lett. 8(10), 3357–3363 (2008).
[PubMed]

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J. Yang, J.-S. Zhang, X.-F. Wu, and Q.-H. Gong, “Resonant modes of l-shaped gold nanoparticles,” Chin. Phys. Lett. 26(6), 067802 (2009).

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M. Wakabayashi, S. Yokojima, T. Fukaminato, K. Shiino, M. Irie, and S. Nakamura, “Anisotropic dissymmetry factor, g: theoretical investigation on single molecule chiroptical spectroscopy,” J. Phys. Chem. A 118(27), 5046–5057 (2014).
[PubMed]

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J. Yang, J.-S. Zhang, X.-F. Wu, and Q.-H. Gong, “Resonant modes of l-shaped gold nanoparticles,” Chin. Phys. Lett. 26(6), 067802 (2009).

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V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006).
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M. Rang, A. C. Jones, F. Zhou, Z.-Y. Li, B. J. Wiley, Y. Xia, and M. B. Raschke, “Optical near-field mapping of plasmonic nanoprisms,” Nano Lett. 8(10), 3357–3363 (2008).
[PubMed]

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S. Burger, P. Gutsche, M. Hammerschmidt, S. Herrmann, J. Pomplun, F. Schmidt, B. Wohlfeil, and L. Zschiedrich, “Hp-finite-elements for simulating electromagnetic fields in optical devices with rough textures,” Proc. SPIE 9630, 7 (2015).

ACS Photonics (1)

L. V. Poulikakos, P. Gutsche, K. M. McPeak, S. Burger, J. Niegemann, C. Hafner, and D. J. Norris, “Optical chirality flux as a useful far-field probe of chiral near fields,” ACS Photonics 3(9), 1619–1625 (2016).

Adv. Mater. (2)

V. K. Valev, J. J. Baumberg, C. Sibilia, and T. Verbiest, “Chirality and chiroptical effects in plasmonic nanostructures: fundamentals, recent progress, and outlook,” Adv. Mater. 25(18), 2517–2534 (2013).
[PubMed]

K. M. McPeak, C. D. van Engers, S. Bianchi, A. Rossinelli, L. V. Poulikakos, L. Bernard, S. Herrmann, D. K. Kim, S. Burger, M. Blome, S. V. Jayanti, and D. J. Norris, “Ultraviolet plasmonic chirality from colloidal aluminum nanoparticles exhibiting charge-selective protein detection,” Adv. Mater. 27(40), 6244–6250 (2015).
[PubMed]

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A. Rassat and P. W. Fowler, “Any scalene triangle is the most chiral triangle,” Helv. Chim. Acta 86(5), 1728–1740 (2003).

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M. Wakabayashi, S. Yokojima, T. Fukaminato, K. Shiino, M. Irie, and S. Nakamura, “Anisotropic dissymmetry factor, g: theoretical investigation on single molecule chiroptical spectroscopy,” J. Phys. Chem. A 118(27), 5046–5057 (2014).
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K. M. McPeak, C. D. van Engers, M. Blome, J. H. Park, S. Burger, M. A. Gosálvez, A. Faridi, Y. R. Ries, A. Sahu, and D. J. Norris, “Complex chiral colloids and surfaces via high-index off-cut silicon,” Nano Lett. 14(5), 2934–2940 (2014).
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Figures (15)

Fig. 1
Fig. 1 (ABCD) is a planar chiral object and (AˈBˈCˈDˈ) is its mirror reflection. A tot is the area of (ABCD) andAis the non-overlapping area (light-grey) between (ABCD) and (AˈBˈCˈDˈ). By varying (AˈBˈCˈDˈ) through any proper translations and/or rotations a minimum non-overlapping area, A min can be found. χ= A min /2 A tot is the chiral coefficient of (ABCD). Objects with larger values ofχare more geometrically chiral.
Fig. 2
Fig. 2 Calculated circular differential optical absorption and geometric chirality for L-shaped and triangle meta-atoms. (a) Sketch of the parameterized L-shaped meta-atom. The structure sits in the x−y plane and is excited with a plane wave in the –z-direction. (b) Circular differential anisotropy factor, g abs for large Au L-shapes with select l values, d = 195 nm and h values calculated using Eq. (5). (c) The integrated circular differential anisotropy factor, g ¯ (blue) and the chiral coefficient, χ (black) for large Au L-shaped meta-atoms calculated for all l values. (d) Sketch of triangular meta-atom with a base width, b of 400 nm. Two vertices defining the base of the triangle are fixed (origin and black dot). The third point is defined by z = x + yi with y fixed at 200 nm. (e) Circular differential anisotropy factor, g abs for triangles with select x values. (f) The integrated circular differential anisotropy factor, g ¯ (blue) and the chiral coefficient, χ (black) for triangular meta-atoms for all calculated x values.
Fig. 3
Fig. 3 Calculated circular differential optical absorption and geometric chirality for the dimer meta-atoms. (a) Sketch of parameterized dimer meta-atom with b as the dimer height, a the width, d the vertical offset distance, and r the horizontal offset distance. (b) Absorption plots, Ir and Il, for the dimer at r = 240 nm, d = 200 nm excited with RCPL and LCPL orthogonal to the plane of the paper, respectively. (c) Circular differential anisotropy factor, g abs for dimers with select d values. (d) The integrated circular differential anistropy factor, g ¯ (blue) and the chiral coefficient, χ (black) for dimers for all calculated d values. (e) Circular differential anisotropy factor, g abs for dimers with select r values. (f) The integrated circular differential anistropy factor, g ¯ (blue) and the chiral coefficient, χ (black) for dimers for all calculated r values.
Fig. 4
Fig. 4 (a) Calculated Mueller matrix for the Au dimer meta-atom which demonstrated both maximum broadband differential absorption, g ¯ , and geometric chirality, χ. The geometric parameters for the meta-atom are, a = 100 nm, b = 300 nm, r = 240 nm and, d = 200 nm. (b) Eq. (4) relating the Mueller Matrix to the six fundamental optical polarization effects. (c - h) The six elementary optical polarization properties for a dimer meta-atom in (a) calculated using the analytical inversion method [4]. This meta-atom does not show optical activity but rather a combination of linear optical polarization effects.
Fig. 5
Fig. 5 Calculated g abs spectra for (a) small (A = 22500 nm2, d = 87 nm), (b) medium, (A = 50700 nm2, d = 130 nm), and (c) large (A = 114100 nm2, d = 195 nm), Au L-shaped meta-atoms for all studied l values.
Fig. 6
Fig. 6 Integrated circular differential anisotropy factor, g ¯ blue, and chiral coefficient χ (black) vs. l for (a) small and, (b) medium sized Au L-shaped meta-atoms.
Fig. 7
Fig. 7 g abs spectra for (a) medium and (b) large L-shaped Au meta-atoms with varying d values and l fixed at (a) 100 nm and (b) 150 nm.
Fig. 8
Fig. 8 Integrated circular differential anisotropy factor, g ¯ (blue), and chiral coefficient χ (black) vs. d for (a) medium and (b) large L-shaped Au meta-atoms with l fixed at a) 100 nm and b) 150 nm.
Fig. 9
Fig. 9 The six elementary polarization properties for a large L-shaped meta-atom with l = 248 nm, h = 337 nm and d = 195 nm. The meta-atom does not show optical activity but rather linear optical effects.
Fig. 10
Fig. 10 The six elementary polarization properties for the medium-scale Au L-shaped meta-atoms with l = 100 nm, h = 217 nm and d = 160 nm. The lack of LD45 and LB45 is consistent with zero CDOA shown in Fig. 8(a) for d-values > 145 nm.
Fig. 11
Fig. 11 g abs spectra for the triangle meta-atoms for all x values with a base length b = 400 nm and y = 200 nm for the upper vertex position defined by z=x+yi
Fig. 12
Fig. 12 The six elementary polarization properties for an obtuse triangle meta-atom with x = −103 nm and y = 200 nm which demonstrated both maximum broadband differential absorption, g ¯ and geometric chirality, χ. The meta-atom does not show optical activity but rather linear polarization effects.
Fig. 13
Fig. 13 g abs spectra for the dimer Au meta-atoms with d varied, r fixed at 150 nm, a fixed at 100 nm, and b fixed at 300 nm.
Fig. 14
Fig. 14 g abs spectra for the dimer Au meta-atoms with r varied, d fixed at 200 nm, a fixed at 100 nm, and b fixed at 300 nm.
Fig. 15
Fig. 15 Examples of meshes used for electromagnetic simulation in JCMwave. (a) Triangular meta-atom with x = −103 nm, y = 200 nm, b = 400 nm. (b) Dimer meta-atom with d = 200 nm, r = 240 nm, a = 100 nm, b = 300 nm. (c) L-shaped meta-atom with l = 100 nm, h = 323 nm, d = 120 nm.

Equations (6)

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g abs = I L I R 1 2 ( I L + I R )
χ= A min 2 A tot
g ¯ = | g abs |dλ dλ
M=exp( L )=exp( A LD LD' CD LD A CB LB' LD' CB A LB CD LB' LB A )
h=A/dl
CDOA= G 0 {CD+ 1 2 ( L D LBLDL B )+(L D sin( 2θ )LDcos( 2θ )sin( α )}