Abstract

We present a systematic study to separate the different contributions to the dichroic response of complex plasmonic split-ring/ring magneto-chiral systems. For this, we first construct metastructures with plasmonic, chiral and magneto-optical functionalities by specific arrangements of different building blocks, each of them responsible for one of the functionalities. Then, by the use of Mueller matrices in forward/backward spectroscopic measurements under magnetic field, we separate optical anisotropy from pure chiral contributions to the overall dichroic response of the system. This allows determining the pure chiral response of the structures and the corresponding magnetic field modulation mediated by the magneto-optical effect present in the corresponding building block, which reaches values of 25% at 740 nm. This fabrication and characterization procedure, assigning the different optical functionalities to different building blocks, and decomposing the different contributions to the global optical response, allows an easy and rational identification of the different phenomena exhibited by the magneto-chiral system.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  31. S. Eslami, J. G. Gibbs, Y. Rechkemmer, J. van Slageren, M. Alarcón-Correa, T.-C. Lee, A. G. Mark, G. L. J. A. Rikken, and P. Fisher, “Chiral nanomagnets,” ACS Photonics 1, 1231–1236 (2014).

2017 (3)

M. Hentschel, M. Schäferling, X. Duan, H. Giessen, and N. Liu, “Chiral plasmonics,” Sci. Adv. 3(5), e1602735 (2017).
[PubMed]

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).
[PubMed]

H. Y. Feng, F. Luo, R. Arenal, L. Henrard, F. García, G. Armelles, and A. Cebollada, “Active magnetoplasmonic split-ring/ring nanoantennas,” Nanoscale 9(1), 37–44 (2017).
[PubMed]

2015 (5)

V. Yannopapas and A. Vanakaras, “Strong magnetochiral dichroism in suspensions of magnetoplasmonic nanohelices,” ACS Photonics 2, 1030–1038 (2015).

V. Yannopapas, “Magnetochirality in hierarchical magnetoplasmonic clusters,” Solid State Commun. 217, 47 (2015).

X. Lan, X. Lu, C. Shen, Y. Ke, W. Ni, and Q. Wang, “Au nanorod helical superstructures with designed chirality,” J. Am. Chem. Soc. 137(1), 457–462 (2015).
[PubMed]

O. Arteaga, “Spectroscopic sensing of reflection optical activity in achiral AgGaS2,” Opt. Lett. 40(18), 4277–4280 (2015).
[PubMed]

G. Armelles, A. Cebollada, H. Y. Feng, A. García-Martín, D. Meneses-Rodríguez, J. Zhao, and H. Giessen, “Interaction effects between magnetic and chiral building blocks: a new route for tunable magneto-chiral plasmonic structures,” ACS Photonics 2, 1272–1277 (2015).

2014 (4)

J. Zhao, B. Frank, F. Neubrech, C. Zhang, P. V. Braun, and H. Giessen, “Hole-mask colloidal nanolithography combined with tilted-angle-rotation evaporation: A versatile method for fabrication of low-cost and large-area complex plasmonic nanostructures and metamaterials,” Beilstein J. Nanotechnol. 5, 577–586 (2014).
[PubMed]

R. Ogier, Y. Fang, M. Svedendahl, P. Johansson, and M. Käll, “Macroscopic layers of chiral plasmonic nanoparticle oligomers from colloidal lithography,” ACS Photonics 1, 1074–1081 (2014).

G. Armelles, B. Caballero, P. Prieto, F. García, A. Cebollada, M. U. González, and A. García-Martin, “Magnetic field modulation of chirooptical effects in magnetoplasmonic structures,” Nanoscale 6(7), 3737–3741 (2014).
[PubMed]

S. Eslami, J. G. Gibbs, Y. Rechkemmer, J. van Slageren, M. Alarcón-Correa, T.-C. Lee, A. G. Mark, G. L. J. A. Rikken, and P. Fisher, “Chiral nanomagnets,” ACS Photonics 1, 1231–1236 (2014).

2013 (5)

B. Yeom, H. Zhang, H. Zhang, J. I. Park, K. Kim, A. O. Govorov, and N. A. Kotov, “Chiral plasmonic nanostructures on achiral nanopillars,” Nano Lett. 13(11), 5277–5283 (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]

P. Yu, S. Chen, J. Li, H. Cheng, Z. Li, and J. Tian, “Co-enhancing and -confining the electric and magnetic fields of the broken-nanoring and the composite nanoring by azimuthally polarized excitation,” Opt. Express 21(18), 20611–20619 (2013).
[PubMed]

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]

A. Ben-Moshe, B. M. Maoz, A. O. Govorov, and G. Markovich, “Chirality and chiroptical effects in inorganic nanocrystal systems with plasmon and exciton resonances,” Chem. Soc. Rev. 42(16), 7028–7041 (2013).
[PubMed]

2012 (1)

S. Cataldo, J. Zhao, F. Neubrech, B. Frank, C. Zhang, P. V. Braun, and H. Giessen, “Hole-mask colloidal nanolithography for large-area low-cost metamaterials and antenna-assisted surface-enhanced infrared absorption substrates,” ACS Nano 6(1), 979–985 (2012).
[PubMed]

2011 (3)

A. Guerrero-Martínez, J. L. Alonso-Gómez, B. Auguié, M. M. Cid, and L. M. Liz-Marzán, “From individual to collective chirality in metal nanoparticles,” Nano Today 6, 381–400 (2011).

A. Guerrero-Martínez, B. Auguié, J. L. Alonso-Gómez, Z. Dzolic, S. Gómez-Graña, M. M. Mladen Zinic, M.M. Cid, and L. M. Liz-Marzán, “Intense optical activity from three-dimensional chiral ordering of plasmonic nanoantennas,” Angew. Chem. Int. Ed. 50, 5499–5503 (2011).

D. Meneses-Rodríguez, E. Ferreiro-Vila, P. Prieto, J. Anguita, M. U. González, J. M. García-Martín, A. Cebollada, A. García-Martín, and G. Armelles, “Probing the electromagnetic field distribution within a metallic nanodisk,” Small 7(23), 3317–3323 (2011).
[PubMed]

2010 (2)

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

2007 (2)

N. Berova, L. Di Bari, and G. Pescitelli, “Application of electronic circular dichroism in configurational and conformational analysis of organic compounds,” Chem. Soc. Rev. 36(6), 914–931 (2007).
[PubMed]

H. Fredriksson, Y. Alaverdyan, A. Dmitriev, C. Langhammer, D. S. Sutherland, M. Zäch, and B. Kasemo, “Hole-mask colloidal lithography,” Adv. Mater. 19, 4297–4302 (2007).

2006 (1)

L. A. Nguyen, H. He, and C. Pham-Huy, “Chiral drugs: an overview,” Int. J. Biomed. Sci. 2(2), 85–100 (2006).
[PubMed]

1997 (1)

G. L. J. A. Rikken and E. Raupach, “Observation of magneto-chiral dichroism,” Nature 390, 493–494 (1997).

1993 (1)

M. H. Wiedmann, M. H. Engel, R. A. Van Leeuwen, K. Mibu, T. Shinjo, and C. M. Falco, “Anomalous perpendicular anisotropy in thin Co films,” Proc. MRS 313, 531–536 (1993).

1988 (1)

D. Kuiper, W. Hoving, A. P. van de Mosselaer, W. Howing, F.J. den Broeder, and A.P. van de Mosselaer, “Perpendicular magnetic anisotropy of Co-Au multilayers induced by interface sharpening,” Phys. Rev. Lett. 60(26), 2769–2772 (1988).
[PubMed]

1948 (1)

B. D. H. Tellegen, “The gyrator, a new electric network element,” Philips Res. Rep. 3, 81–101 (1948).

Alarcón-Correa, M.

S. Eslami, J. G. Gibbs, Y. Rechkemmer, J. van Slageren, M. Alarcón-Correa, T.-C. Lee, A. G. Mark, G. L. J. A. Rikken, and P. Fisher, “Chiral nanomagnets,” ACS Photonics 1, 1231–1236 (2014).

Alaverdyan, Y.

H. Fredriksson, Y. Alaverdyan, A. Dmitriev, C. Langhammer, D. S. Sutherland, M. Zäch, and B. Kasemo, “Hole-mask colloidal lithography,” Adv. Mater. 19, 4297–4302 (2007).

Alonso-Gómez, J. L.

A. Guerrero-Martínez, J. L. Alonso-Gómez, B. Auguié, M. M. Cid, and L. M. Liz-Marzán, “From individual to collective chirality in metal nanoparticles,” Nano Today 6, 381–400 (2011).

A. Guerrero-Martínez, B. Auguié, J. L. Alonso-Gómez, Z. Dzolic, S. Gómez-Graña, M. M. Mladen Zinic, M.M. Cid, and L. M. Liz-Marzán, “Intense optical activity from three-dimensional chiral ordering of plasmonic nanoantennas,” Angew. Chem. Int. Ed. 50, 5499–5503 (2011).

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).
[PubMed]

Anguita, J.

D. Meneses-Rodríguez, E. Ferreiro-Vila, P. Prieto, J. Anguita, M. U. González, J. M. García-Martín, A. Cebollada, A. García-Martín, and G. Armelles, “Probing the electromagnetic field distribution within a metallic nanodisk,” Small 7(23), 3317–3323 (2011).
[PubMed]

Arenal, R.

H. Y. Feng, F. Luo, R. Arenal, L. Henrard, F. García, G. Armelles, and A. Cebollada, “Active magnetoplasmonic split-ring/ring nanoantennas,” Nanoscale 9(1), 37–44 (2017).
[PubMed]

Armelles, G.

H. Y. Feng, F. Luo, R. Arenal, L. Henrard, F. García, G. Armelles, and A. Cebollada, “Active magnetoplasmonic split-ring/ring nanoantennas,” Nanoscale 9(1), 37–44 (2017).
[PubMed]

G. Armelles, A. Cebollada, H. Y. Feng, A. García-Martín, D. Meneses-Rodríguez, J. Zhao, and H. Giessen, “Interaction effects between magnetic and chiral building blocks: a new route for tunable magneto-chiral plasmonic structures,” ACS Photonics 2, 1272–1277 (2015).

G. Armelles, B. Caballero, P. Prieto, F. García, A. Cebollada, M. U. González, and A. García-Martin, “Magnetic field modulation of chirooptical effects in magnetoplasmonic structures,” Nanoscale 6(7), 3737–3741 (2014).
[PubMed]

D. Meneses-Rodríguez, E. Ferreiro-Vila, P. Prieto, J. Anguita, M. U. González, J. M. García-Martín, A. Cebollada, A. García-Martín, and G. Armelles, “Probing the electromagnetic field distribution within a metallic nanodisk,” Small 7(23), 3317–3323 (2011).
[PubMed]

Arteaga, O.

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).
[PubMed]

Auguié, B.

A. Guerrero-Martínez, J. L. Alonso-Gómez, B. Auguié, M. M. Cid, and L. M. Liz-Marzán, “From individual to collective chirality in metal nanoparticles,” Nano Today 6, 381–400 (2011).

A. Guerrero-Martínez, B. Auguié, J. L. Alonso-Gómez, Z. Dzolic, S. Gómez-Graña, M. M. Mladen Zinic, M.M. Cid, and L. M. Liz-Marzán, “Intense optical activity from three-dimensional chiral ordering of plasmonic nanoantennas,” Angew. Chem. Int. Ed. 50, 5499–5503 (2011).

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]

Ben-Moshe, A.

A. Ben-Moshe, B. M. Maoz, A. O. Govorov, and G. Markovich, “Chirality and chiroptical effects in inorganic nanocrystal systems with plasmon and exciton resonances,” Chem. Soc. Rev. 42(16), 7028–7041 (2013).
[PubMed]

Berova, N.

N. Berova, L. Di Bari, and G. Pescitelli, “Application of electronic circular dichroism in configurational and conformational analysis of organic compounds,” Chem. Soc. Rev. 36(6), 914–931 (2007).
[PubMed]

Braun, P. V.

J. Zhao, B. Frank, F. Neubrech, C. Zhang, P. V. Braun, and H. Giessen, “Hole-mask colloidal nanolithography combined with tilted-angle-rotation evaporation: A versatile method for fabrication of low-cost and large-area complex plasmonic nanostructures and metamaterials,” Beilstein J. Nanotechnol. 5, 577–586 (2014).
[PubMed]

S. Cataldo, J. Zhao, F. Neubrech, B. Frank, C. Zhang, P. V. Braun, and H. Giessen, “Hole-mask colloidal nanolithography for large-area low-cost metamaterials and antenna-assisted surface-enhanced infrared absorption substrates,” ACS Nano 6(1), 979–985 (2012).
[PubMed]

Caballero, B.

G. Armelles, B. Caballero, P. Prieto, F. García, A. Cebollada, M. U. González, and A. García-Martin, “Magnetic field modulation of chirooptical effects in magnetoplasmonic structures,” Nanoscale 6(7), 3737–3741 (2014).
[PubMed]

Carpy, T.

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]

Cataldo, S.

S. Cataldo, J. Zhao, F. Neubrech, B. Frank, C. Zhang, P. V. Braun, and H. Giessen, “Hole-mask colloidal nanolithography for large-area low-cost metamaterials and antenna-assisted surface-enhanced infrared absorption substrates,” ACS Nano 6(1), 979–985 (2012).
[PubMed]

Cebollada, A.

H. Y. Feng, F. Luo, R. Arenal, L. Henrard, F. García, G. Armelles, and A. Cebollada, “Active magnetoplasmonic split-ring/ring nanoantennas,” Nanoscale 9(1), 37–44 (2017).
[PubMed]

G. Armelles, A. Cebollada, H. Y. Feng, A. García-Martín, D. Meneses-Rodríguez, J. Zhao, and H. Giessen, “Interaction effects between magnetic and chiral building blocks: a new route for tunable magneto-chiral plasmonic structures,” ACS Photonics 2, 1272–1277 (2015).

G. Armelles, B. Caballero, P. Prieto, F. García, A. Cebollada, M. U. González, and A. García-Martin, “Magnetic field modulation of chirooptical effects in magnetoplasmonic structures,” Nanoscale 6(7), 3737–3741 (2014).
[PubMed]

D. Meneses-Rodríguez, E. Ferreiro-Vila, P. Prieto, J. Anguita, M. U. González, J. M. García-Martín, A. Cebollada, A. García-Martín, and G. Armelles, “Probing the electromagnetic field distribution within a metallic nanodisk,” Small 7(23), 3317–3323 (2011).
[PubMed]

Chen, S.

Cheng, H.

Cid, M. M.

A. Guerrero-Martínez, J. L. Alonso-Gómez, B. Auguié, M. M. Cid, and L. M. Liz-Marzán, “From individual to collective chirality in metal nanoparticles,” Nano Today 6, 381–400 (2011).

Cid, M.M.

A. Guerrero-Martínez, B. Auguié, J. L. Alonso-Gómez, Z. Dzolic, S. Gómez-Graña, M. M. Mladen Zinic, M.M. Cid, and L. M. Liz-Marzán, “Intense optical activity from three-dimensional chiral ordering of plasmonic nanoantennas,” Angew. Chem. Int. Ed. 50, 5499–5503 (2011).

Cohen, A. E.

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

den Broeder, F.J.

D. Kuiper, W. Hoving, A. P. van de Mosselaer, W. Howing, F.J. den Broeder, and A.P. van de Mosselaer, “Perpendicular magnetic anisotropy of Co-Au multilayers induced by interface sharpening,” Phys. Rev. Lett. 60(26), 2769–2772 (1988).
[PubMed]

Di Bari, L.

N. Berova, L. Di Bari, and G. Pescitelli, “Application of electronic circular dichroism in configurational and conformational analysis of organic compounds,” Chem. Soc. Rev. 36(6), 914–931 (2007).
[PubMed]

Dmitriev, A.

H. Fredriksson, Y. Alaverdyan, A. Dmitriev, C. Langhammer, D. S. Sutherland, M. Zäch, and B. Kasemo, “Hole-mask colloidal lithography,” Adv. Mater. 19, 4297–4302 (2007).

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M. Hentschel, M. Schäferling, X. Duan, H. Giessen, and N. Liu, “Chiral plasmonics,” Sci. Adv. 3(5), e1602735 (2017).
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M. H. Wiedmann, M. H. Engel, R. A. Van Leeuwen, K. Mibu, T. Shinjo, and C. M. Falco, “Anomalous perpendicular anisotropy in thin Co films,” Proc. MRS 313, 531–536 (1993).

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S. Eslami, J. G. Gibbs, Y. Rechkemmer, J. van Slageren, M. Alarcón-Correa, T.-C. Lee, A. G. Mark, G. L. J. A. Rikken, and P. Fisher, “Chiral nanomagnets,” ACS Photonics 1, 1231–1236 (2014).

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M. H. Wiedmann, M. H. Engel, R. A. Van Leeuwen, K. Mibu, T. Shinjo, and C. M. Falco, “Anomalous perpendicular anisotropy in thin Co films,” Proc. MRS 313, 531–536 (1993).

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R. Ogier, Y. Fang, M. Svedendahl, P. Johansson, and M. Käll, “Macroscopic layers of chiral plasmonic nanoparticle oligomers from colloidal lithography,” ACS Photonics 1, 1074–1081 (2014).

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H. Y. Feng, F. Luo, R. Arenal, L. Henrard, F. García, G. Armelles, and A. Cebollada, “Active magnetoplasmonic split-ring/ring nanoantennas,” Nanoscale 9(1), 37–44 (2017).
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D. Meneses-Rodríguez, E. Ferreiro-Vila, P. Prieto, J. Anguita, M. U. González, J. M. García-Martín, A. Cebollada, A. García-Martín, and G. Armelles, “Probing the electromagnetic field distribution within a metallic nanodisk,” Small 7(23), 3317–3323 (2011).
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J. Zhao, B. Frank, F. Neubrech, C. Zhang, P. V. Braun, and H. Giessen, “Hole-mask colloidal nanolithography combined with tilted-angle-rotation evaporation: A versatile method for fabrication of low-cost and large-area complex plasmonic nanostructures and metamaterials,” Beilstein J. Nanotechnol. 5, 577–586 (2014).
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D. Meneses-Rodríguez, E. Ferreiro-Vila, P. Prieto, J. Anguita, M. U. González, J. M. García-Martín, A. Cebollada, A. García-Martín, and G. Armelles, “Probing the electromagnetic field distribution within a metallic nanodisk,” Small 7(23), 3317–3323 (2011).
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M. Hentschel, M. Schäferling, X. Duan, H. Giessen, and N. Liu, “Chiral plasmonics,” Sci. Adv. 3(5), e1602735 (2017).
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J. Zhao, B. Frank, F. Neubrech, C. Zhang, P. V. Braun, and H. Giessen, “Hole-mask colloidal nanolithography combined with tilted-angle-rotation evaporation: A versatile method for fabrication of low-cost and large-area complex plasmonic nanostructures and metamaterials,” Beilstein J. Nanotechnol. 5, 577–586 (2014).
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G. Armelles, B. Caballero, P. Prieto, F. García, A. Cebollada, M. U. González, and A. García-Martin, “Magnetic field modulation of chirooptical effects in magnetoplasmonic structures,” Nanoscale 6(7), 3737–3741 (2014).
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A. Ben-Moshe, B. M. Maoz, A. O. Govorov, and G. Markovich, “Chirality and chiroptical effects in inorganic nanocrystal systems with plasmon and exciton resonances,” Chem. Soc. Rev. 42(16), 7028–7041 (2013).
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A. Ben-Moshe, B. M. Maoz, A. O. Govorov, and G. Markovich, “Chirality and chiroptical effects in inorganic nanocrystal systems with plasmon and exciton resonances,” Chem. Soc. Rev. 42(16), 7028–7041 (2013).
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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).
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B. Yeom, H. Zhang, H. Zhang, J. I. Park, K. Kim, A. O. Govorov, and N. A. Kotov, “Chiral plasmonic nanostructures on achiral nanopillars,” Nano Lett. 13(11), 5277–5283 (2013).
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ACS Photonics (4)

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Adv. Mater. (2)

H. Fredriksson, Y. Alaverdyan, A. Dmitriev, C. Langhammer, D. S. Sutherland, M. Zäch, and B. Kasemo, “Hole-mask colloidal lithography,” Adv. Mater. 19, 4297–4302 (2007).

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).
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Figures (6)

Fig. 1
Fig. 1 (a) The different building blocks that will form part of the final structures. (b) Resulted chiral plasmonic and magnetoplasmonic metastructures fabricated and studied in this work. The specific location of the Au or Au/Co multilayer disk at either side of the split ring edge induces an in plane optical anisotropy and determines the handedness of the system. (c) SEM image of a representative structure obtained in this way. Scale bar: 100nm. (d) Comparative MO hysteresis loops for an Au/Co/Au ring structure with in plane magnetic anisotropy and a split ring/ring structure with an Au/Co multilayer, with perpendicular magnetic anisotropy. As it can be seen, magnetic saturation along surface normal requires a much smaller magnetic field for the multilayer case.
Fig. 2
Fig. 2 Sketch of the measurement configurations and the Mueller matrix elements dependence on the specific light polarization relative to the structure main axes.
Fig. 3
Fig. 3 Representative Mueller matrix elements (normalized to m11) of the two pure Au chiral samples of Fig. 2 for forward (red) and backward (blue) illuminations. The dots are experimental data and the lines theoretical simulations.
Fig. 4
Fig. 4 Effective dielectric and chiral tensors of the pure Au chiral nanoparticle layers of sample A and B (Fig. 3) as a function of the wavelength. The curves with full dots correspond to the real part of the different elements of the dielectric and chiral tensors. The full line curves correspond to the imaginary part of the different elements of the dielectric and chiral tensors.
Fig. 5
Fig. 5 g spectra of pure Au chiral samples A and B.
Fig. 6
Fig. 6 Spectral dependence of g for the Au/Co multilayer disk-Au chiral structures. The optical anisotropy contribution has been removed with the methodology introduced previously. Black and red curves represent the spectral responses for the two structures with opposite chirality. Solid curves are for + B magnetization and dotted curves for –B magnetization. Scale bar: 300nm.

Equations (5)

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

m 12 F =( 1 2 )( t xx t xx * t yy t yy * 4Re( t a t sy * )) m 13 F =Re(( t xx + t yy ) t sy * )+Re(( t xx t yy ) t a * ) m 14 F =Im(( t xx t yy ) t sy * )+Im((( t xx + t yy ) t a * ) m 12 B =( 1 2 )( t xx t xx * t yy t yy * +4Re( t a t sy * )) m 13 B =Re(( t xx + t yy ) t sy * )+Re(( t xx t yy ) t a * ) m 14 B =Im(( t xx t yy ) t sy * )+Im((( t xx + t yy ) t a * )
F:( t xx t sy + t a t sy t a t yy );B:( t xx t sy + t a t sy t a t yy )
[ D B ]=[ ε 0 ε eff i κ eff /c i κ eff /c μ 0 μ eff ][ E H ]
g=2 A + A A + + A ; A +, =log( T +, )
g= log( 1+ m 14 1 m 14 ) log(T(1 m 14 2 ) ;T= T + + T 2

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