Abstract

This paper introduces a procedure aimed to quantitatively measure the optical properties of nanoparticles, namely the complex polarizability and the extinction, scattering, and absorption cross sections, simultaneously. The method is based on the processing of intensity and wavefront images of a light beam illuminating the nanoparticle of interest. Intensity and wavefront measurements are carried out using quadriwave lateral shearing interferometry, a quantitative phase imaging technique with high spatial resolution and sensitivity. The method does not require any preknowledge on the particle and involves a single interferogram image acquisition. The full determination of the actual optical properties of nanoparticles is of particular interest in plasmonics and nanophotonics for the active search and characterization of new materials, e.g., aimed to replace noble metals in future applications of nanoplasmonics with less-lossy or refractory materials.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2019 (4)

J. Langer, D. J. de Aberasturi, J. Aizpurua, R. A. Alvarez-Puebla, B. Auguié, J. J. Baumberg, G. C. Bazan, S. E. J. Bell, A. Boisen, A. G. Brolo, J. Choo, D. Cialla-May, V. Deckert, L. Fabris, K. Faulds, F. J. García de Abajo, R. Goodacre, D. Graham, A. J. Haes, C. L. Haynes, C. Huck, T. Itoh, M. Käll, J. Kneipp, N. A. Kotov, H. Kuang, E. C. Le Ru, H. K. Lee, J.-F. Li, X. Y. Ling, S. A. Maier, T. Mayerhöfer, M. Moskovits, K. Murakoshi, J.-M. Nam, S. Nie, Y. Ozaki, I. Pastoriza-Santos, J. Perez-Juste, J. Popp, A. Pucci, S. Reich, B. Ren, G. C. Schatz, T. Shegai, S. Schlücker, L.-L. Tay, K. G. Thomas, Z.-Q. Tian, R. P. Van Duyne, T. Vo-Dinh, Y. Wang, K. A. Willets, C. Xu, H. Xu, Y. Xu, Y. S. Yamamoto, B. Zhao, and L. M. Liz-Marzán, “Present and future of surface-enhanced Raman scattering,” ACS Nano 14, 28–117 (2019).
[Crossref]

J. Grand, B. Auguie, and E. C. Le Ru, “Combined extinction and absorption UV–visible spectroscopy as a method for revealing shape imperfections of metallic nanoparticles,” Anal. Chem. 91, 14639–14648 (2019).
[Crossref]

A. Zilli, W. Langbein, and P. Borri, “Quantitative measurement of the optical cross sections of single nano-objects by correlative transmission and scattering microspectroscopy,” ACS Photon. 6, 2149–2160 (2019).
[Crossref]

S. Khadir, P. C. Chaumet, G. Baffou, and A. Sentenac, “Quantitative model of the image of a radiating dipole through a microscope,” J. Opt. Soc. Am. A 36, 478–484 (2019).
[Crossref]

2018 (2)

A. Agrawal, S. H. Cho, O. Zandi, S. Ghosh, R. W. Johns, and D. J. Milliron, “Localized surface plasmon resonance in semiconductor nanocrystals,” Chem. Rev. 118, 3121–3207 (2018).
[Crossref]

G. Vasquez, Y. Hernández, and Y. Coello, “Portable low-cost instrumentation for monitoring Rayleigh scattering from chemical sensors based on metallic nanoparticles,” Sci. Rep. 8, 14903 (2018).
[Crossref]

2017 (3)

J. Babocky, A. Krizova, L. Strbkova, L. Kejik, F. Ligmajer, M. Hrton, P. Dvorak, M. Tyc, J. Collakova, V. Krapek, R. Kalousek, R. Chmelik, and T. Sikola, “Quantitative 3D phase imaging of plasmonic metasurfaces,” ACS Photon. 4, 1389–1397 (2017).
[Crossref]

D. G. Baranov, D. A. Zuev, S. I. Lepeshov, O. V. Kotov, A. E. Krasnok, A. B. Evlyukhin, and B. N. Chichkov, “All-dielectric nanophotonics: the quest for better materials and fabrication techniques,” Optica 4, 814–825 (2017).
[Crossref]

S. A. Mann, B. Sciacca, Y. Zhang, J. Wang, E. Kontoleta, H. Liu, and E. C. Garnett, “Integrating sphere microscopy for direct absorption measurements of single nanostructures,” ACS Nano 11, 1412–1418 (2017).
[Crossref]

2016 (1)

A. Lalisse, G. Tessier, J. Plain, and G. Baffou, “Plasmonic efficiencies of nanoparticles made of metal nitrides (tin, zrn) compared with gold,” Sci. Rep. 6, 38647 (2016).
[Crossref]

2015 (5)

F. Sterl, N. Strohfeldt, R. Walter, R. Griessen, A. Tittl, and H. Giessen, “Magnesium as novel material for active plasmonics in the visible wavelength range,” Nano Lett. 15, 7949–7955 (2015).
[Crossref]

A. Lalisse, G. Tessier, J. Plain, and G. Baffou, “Quantifying the efficiency of plasmonic materials for near-field enhancement and photothermal conversion,” J. Phys. Chem. C 119, 25518–25528 (2015).
[Crossref]

P. Patsalas, N. Kalfagiannis, and S. Kassavetis, “Optical properties and plasmonic performances of titanium nitride,” Materials 8, 3128–3154 (2015).
[Crossref]

U. Guler, V. M. Shalaev, and A. Boltasseva, “Nanoparticle plasmonics: going practical with transition metal nitrides,” Mater. Today 18(4), 227–237 (2015).
[Crossref]

P. Bon, N. Bourg, S. Lécart, S. Monneret, E. Fort, J. Wenger, and S. Léveque-Fort, “Three-dmensional nanometre localization of nanoparticles to enhance super-resolution microscopy,” Nat. Commun. 6, 7764 (2015).
[Crossref]

2014 (3)

S. D. Gennaro, Y. Sonnerfraud, N. Verellen, P. Van Dorpe, V. V. Moshchalkov, S. A. Maier, and R. F. Oulton, “Spectral interferometric microscopy reveals absorption by individual optical nanoantennas from extinction phase,” Nat. Commun. 5, 3748 (2014).
[Crossref]

A. Comin and L. Manna, “New materials for tunable plasmonic colloidal nanocrystals,” Chem. Soc. Rev. 43, 3957–3975 (2014).
[Crossref]

R. He, Y.-C. Wang, X. Wang, Z. Wang, G. Liu, W. Zhou, L. Wen, Q. Li, X. Wang, X. Chen, J. Zeng, and J. G. Hou, “Facile synthesis of pentacle gold–copper alloy nanocrystals and their plasmonic and catalytic properties,” Nat. Commun. 5, 4327 (2014).
[Crossref]

2013 (2)

G. Baffou and R. Quidant, “Thermo-plasmonics: using metallic nanostructures as nano-sources of heat,” Laser Photon. Rev. 7, 171–187 (2013).
[Crossref]

E. Stratakis and E. Kymakis, “Nanoparticle-based plasmonic organic photovoltaic devices,” Mater. Today 16(4), 133–146 (2013).
[Crossref]

2012 (4)

D. Cialla, A. März, R. Böhme, F. Theil, K. Weber, M. Schmitt, and J. Popp, “Surface-enhanced Raman spectroscopy (SERS): progress and trends,” Anal. Bioanal. Chem. 403, 27–54 (2012).
[Crossref]

P. Berto, E. Bermúdez Ureña, P. Bon, R. Quidant, H. Rigneault, and G. Baffou, “Quantitative absorption spectroscopy of nano-objects,” Phys. Rev. B 86, 165417 (2012).
[Crossref]

M. Husnik, S. Linden, R. Diehl, J. Niegemann, K. Busch, and M. Wegener, “Quantitative experimental determination of scattering and absorption cross-section spectra of individual optical metallic nanoantennas,” Phys. Rev. Lett. 109, 233902 (2012).
[Crossref]

P. S. Carney, B. Deutsch, A. A. Govyadinov, and R. Hillenbrand, “Phase in nanooptics,” ACS Nano 6, 8–12 (2012).
[Crossref]

2011 (1)

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84, 205428 (2011).
[Crossref]

2010 (2)

M. G. Blaber, M. D. Arnold, and M. J. Ford, “A review of the optical properties of alloys and intermetallics for plasmonics,” J. Phys. Condens. Matter 22, 143201 (2010).
[Crossref]

A. Tcherniak, J. W. Ha, S. Dominguez-Medina, L. S. Slaughter, and S. Link, “Probing a century old prediction one plasmonic particle at a time,” Nano Lett. 10, 1398–1404 (2010).
[Crossref]

2009 (3)

M. Celebrano, M. Savoini, P. Biagioni, M. Zavelani-Rossi, P. M. Adam, L. Duò, G. Cerullo, and M. Finazzi, “Retrieving the complex polarizability of single plasmonic nanoresonators,” Phys. Rev. B 80, 153407 (2009).
[Crossref]

M. G. Blaber, M. D. Arnold, and M. J. Ford, “Optical properties of intermetallic compounds from first principles calculations: a search for the ideal plasmonic material,” J. Phys. Condens. Matter 21, 144211 (2009).
[Crossref]

P. Bon, G. Maucort, B. Wattellier, and S. Monneret, “Quadriwave lateral shearing interferometry for quantitative phase microscopy of living cells,” Opt. Express 17, 13080–13094 (2009).
[Crossref]

2008 (3)

2007 (2)

M. G. Blaber, M. D. Arnold, N. Harris, M. J. Ford, and M. B. Cortie, “Plasmon absorption in nanospheres: a comparison of sodium, potassium, aluminium, silver and gold,” Phys. B (Amsterdam) 394, 184–187 (2007).
[Crossref]

R. H. French, K. I. Winey, M. K. Yang, and W. Qiu, “Optical properties and van der Waals–London dispersion interactions of polystyrene determined by vacuum ultraviolet spectroscopy and spectroscopic ellipsometry,” Aust. J. Chem. 60, 251–263 (2007).
[Crossref]

2006 (2)

P. Stoller, V. Jacobsen, and V. Sandoghdar, “Measurement of the complex dielectric constant of a single gold nanoparticle,” Opt. Lett. 31, 2474–2476 (2006).
[Crossref]

M. A. van Dijk, A. L. Tchebotareva, M. Orrit, M. Lippitz, S. Berciaud, D. Lasne, L. Cognet, and B. Lounis, “Absorption and scattering microscopy of single metal nanoparticles,” Phys. Chem. Chem. Phys. 8, 3486–3495 (2006).
[Crossref]

2004 (1)

A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett. 93, 127401 (2004).
[Crossref]

1999 (1)

S. Link, Z. L. Wang, and M. A. El-Sayed, “Alloy formation of gold-silver nanoparticles and the dependence of the plasmon absorption on their composition,” J. Phys. Chem. B 103, 3529–3533 (1999).
[Crossref]

1997 (1)

G. L. Hornyak, C. J. Patrissi, E. B. Oberhauser, C. R. Martin, J.-C. Valmalette, L. Lemaire, J. Dutta, and H. Hofmann, “Effective medium theory characterization of Au/Ag nanoalloy-porous alumina composites,” Nanostruct. Mater. 9, 571–574 (1997).
[Crossref]

1994 (1)

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370 (1972).
[Crossref]

Adam, P. M.

M. Celebrano, M. Savoini, P. Biagioni, M. Zavelani-Rossi, P. M. Adam, L. Duò, G. Cerullo, and M. Finazzi, “Retrieving the complex polarizability of single plasmonic nanoresonators,” Phys. Rev. B 80, 153407 (2009).
[Crossref]

Agrawal, A.

A. Agrawal, S. H. Cho, O. Zandi, S. Ghosh, R. W. Johns, and D. J. Milliron, “Localized surface plasmon resonance in semiconductor nanocrystals,” Chem. Rev. 118, 3121–3207 (2018).
[Crossref]

Aizpurua, J.

J. Langer, D. J. de Aberasturi, J. Aizpurua, R. A. Alvarez-Puebla, B. Auguié, J. J. Baumberg, G. C. Bazan, S. E. J. Bell, A. Boisen, A. G. Brolo, J. Choo, D. Cialla-May, V. Deckert, L. Fabris, K. Faulds, F. J. García de Abajo, R. Goodacre, D. Graham, A. J. Haes, C. L. Haynes, C. Huck, T. Itoh, M. Käll, J. Kneipp, N. A. Kotov, H. Kuang, E. C. Le Ru, H. K. Lee, J.-F. Li, X. Y. Ling, S. A. Maier, T. Mayerhöfer, M. Moskovits, K. Murakoshi, J.-M. Nam, S. Nie, Y. Ozaki, I. Pastoriza-Santos, J. Perez-Juste, J. Popp, A. Pucci, S. Reich, B. Ren, G. C. Schatz, T. Shegai, S. Schlücker, L.-L. Tay, K. G. Thomas, Z.-Q. Tian, R. P. Van Duyne, T. Vo-Dinh, Y. Wang, K. A. Willets, C. Xu, H. Xu, Y. Xu, Y. S. Yamamoto, B. Zhao, and L. M. Liz-Marzán, “Present and future of surface-enhanced Raman scattering,” ACS Nano 14, 28–117 (2019).
[Crossref]

Alù, A.

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84, 205428 (2011).
[Crossref]

Alvarez-Puebla, R. A.

J. Langer, D. J. de Aberasturi, J. Aizpurua, R. A. Alvarez-Puebla, B. Auguié, J. J. Baumberg, G. C. Bazan, S. E. J. Bell, A. Boisen, A. G. Brolo, J. Choo, D. Cialla-May, V. Deckert, L. Fabris, K. Faulds, F. J. García de Abajo, R. Goodacre, D. Graham, A. J. Haes, C. L. Haynes, C. Huck, T. Itoh, M. Käll, J. Kneipp, N. A. Kotov, H. Kuang, E. C. Le Ru, H. K. Lee, J.-F. Li, X. Y. Ling, S. A. Maier, T. Mayerhöfer, M. Moskovits, K. Murakoshi, J.-M. Nam, S. Nie, Y. Ozaki, I. Pastoriza-Santos, J. Perez-Juste, J. Popp, A. Pucci, S. Reich, B. Ren, G. C. Schatz, T. Shegai, S. Schlücker, L.-L. Tay, K. G. Thomas, Z.-Q. Tian, R. P. Van Duyne, T. Vo-Dinh, Y. Wang, K. A. Willets, C. Xu, H. Xu, Y. Xu, Y. S. Yamamoto, B. Zhao, and L. M. Liz-Marzán, “Present and future of surface-enhanced Raman scattering,” ACS Nano 14, 28–117 (2019).
[Crossref]

Arbouet, A.

A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett. 93, 127401 (2004).
[Crossref]

Arnaud, L.

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ACS Nano (3)

J. Langer, D. J. de Aberasturi, J. Aizpurua, R. A. Alvarez-Puebla, B. Auguié, J. J. Baumberg, G. C. Bazan, S. E. J. Bell, A. Boisen, A. G. Brolo, J. Choo, D. Cialla-May, V. Deckert, L. Fabris, K. Faulds, F. J. García de Abajo, R. Goodacre, D. Graham, A. J. Haes, C. L. Haynes, C. Huck, T. Itoh, M. Käll, J. Kneipp, N. A. Kotov, H. Kuang, E. C. Le Ru, H. K. Lee, J.-F. Li, X. Y. Ling, S. A. Maier, T. Mayerhöfer, M. Moskovits, K. Murakoshi, J.-M. Nam, S. Nie, Y. Ozaki, I. Pastoriza-Santos, J. Perez-Juste, J. Popp, A. Pucci, S. Reich, B. Ren, G. C. Schatz, T. Shegai, S. Schlücker, L.-L. Tay, K. G. Thomas, Z.-Q. Tian, R. P. Van Duyne, T. Vo-Dinh, Y. Wang, K. A. Willets, C. Xu, H. Xu, Y. Xu, Y. S. Yamamoto, B. Zhao, and L. M. Liz-Marzán, “Present and future of surface-enhanced Raman scattering,” ACS Nano 14, 28–117 (2019).
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ACS Photon. (2)

A. Zilli, W. Langbein, and P. Borri, “Quantitative measurement of the optical cross sections of single nano-objects by correlative transmission and scattering microspectroscopy,” ACS Photon. 6, 2149–2160 (2019).
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Anal. Bioanal. Chem. (1)

D. Cialla, A. März, R. Böhme, F. Theil, K. Weber, M. Schmitt, and J. Popp, “Surface-enhanced Raman spectroscopy (SERS): progress and trends,” Anal. Bioanal. Chem. 403, 27–54 (2012).
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Chem. Rev. (1)

A. Agrawal, S. H. Cho, O. Zandi, S. Ghosh, R. W. Johns, and D. J. Milliron, “Localized surface plasmon resonance in semiconductor nanocrystals,” Chem. Rev. 118, 3121–3207 (2018).
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Supplementary Material (1)

NameDescription
» Supplement 1       more details on experiments and numerical simulations

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Figures (4)

Fig. 1.
Fig. 1. (a) Intensity (left) and OPD (right) images of a 100 nm gold NP. (b) Radially averaged intensity and OPD profiles (200× magnification; 1.3 NA, $ {\lambda _0} = 530 \;{\rm nm} $; scale bar, $ 1\,\,\unicode{x00B5}{\rm m} $).
Fig. 2.
Fig. 2. (a) Intensity and OPD images of 100 nm gold and 200 nm polystyrene beads acquired by QLSI at $ {\lambda _0} = 530 \;{\rm nm} $. Gold and polystyrene are indicated with orange and blue arrows, respectively ($ 100 \times $ magnification; 1.3 NA; scale bar, $ 2\,\,\unicode{x00B5}{\rm m} $). (b) Extracted polarizabilities using PIWI for gold and polystyrene NPs. Squares represent DDA numerical simulations for gold nanoparticles $ 100 \pm 8 \;{\rm nm} $ in diameter, and PS nanoparticles $ 200 \pm 16 \;{\rm nm} $ in diameter. (c) Extracted extinction, scattering, and absorption cross sections compared to theoretical values given DDA. Experimental (d) real and (e) imaginary parts of the polarizability of a 100 nm Au nanosphere determined by PIWI (circles), and compared with DDA simulations (solid lines). (f) Cross sections determined from the measured polarizabilities reported in (d) and (e) (circles), and compared with DDA (solid lines).
Fig. 3.
Fig. 3. (a) Measured longitudinal (orange dots) and transverse (blue dots) polarizabilities of a set of gold nanorods compared with theoretical longitudinal (circle symbol) and transverse (square symbol) polarizabilities of nanorods with dimensions of $ 120 \times 50 \times 50 \;{{\rm nm}^3} $ in a medium of $ n = 1.5 $. (b) and (c) Examples of the intensity and OPD images of the nanorods at two different polarization states ($ 100 \times $ magnification, 1.3 NA).
Fig. 4.
Fig. 4. (a) Intensity and OPD images of a 100 nm gold NP at different $ z $ positions, along with their profiles. (b) Extracted real and imaginary parts of the polarizability for different $ z $ positions showing no effect of the focus of the microscope on the measurements (scale bar, $ 1\,\,\unicode{x00B5}{\rm m} $). (c) Intensity and OPD images of a 100 nm gold nanoparticle recorded with different numerical apertures (NA) of the microscope objective. (d) Corresponding real and imaginary parts of the polarizability as a function of NA.

Equations (12)

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σ e x t = k 0 n I m ( α ) ,
σ s c a = k 0 4 6 π | α | 2 ,
σ a b s = σ e x t σ s c a ,
t t 0 ( x , y ) = t ¯ ( x , y ) = T ( x , y ) e i 2 π λ 0 δ ( x , y ) ,
p = ε 0 α E i n c ( r 0 ) ,
α xx = 1 ε 0 | E i n c ( r 0 ) | 2 E i n c ( r 0 ) p .
α ¯ ¯ = 1 ε 0 | E i n c | 2 V E i n c ( r ) P ( r ) d r ,
σ e x t = k n ε 0 | E i n c | 2 V ( E i n c ( r ) P ( r ) ) d r .
α = i λ 0 n π ( 1 t ¯ ( x , y ) ) d x d y .
α r = λ 0 n π T ( x , y ) sin ( k 0 δ ( x , y ) ) d x d y ,
α i = λ 0 n π [ 1 T ( x , y ) cos ( k 0 δ ( x , y ) ) ] d x d y .
σ e x t = 2 [ 1 T ( x , y ) cos ( k 0 δ ( x , y ) ) ] d x d y .