Abstract

The interaction of nanostructures, periodic or random, with polarized light creates very rich physics where scattering, diffraction and absorbance are linked to a variety of dispersive modes and coupling effects. Each of these excitations depends strongly on polarization, angle of incidence, azimuthal orientation of the sample and wavelength. The entire optical response can be obtained, independently from any model, by measuring the Mueller matrices at various k-vectors over a broad frequency range. This results in complex data hiding the underlying physics. Here we present a simple but versatile method to identify the physical properties present in the Mueller matrices. This method is applicable to a wide variety of photonic and plasmonic samples. Based on the simple example of a one-dimensional gold grating where the optical response is characterized not only by diffraction but also by a complex mixing of polarization, we present a very general procedure to analyze the Mueller matrix data using simple analytical tools. The calculated Mueller matrix contour plots obtained from an effective anisotropic layer model are completed by the presence of plasmonic modes, Rayleigh-Woods anomalies and the interband transition absorbance. A comparison of the so-constructed contour plots with the measured ones satisfactorily connects the optical properties of the grating to their physical origin. This straightforward procedure is very general and will be powerful for the analysis of complex optical nanostructures.

© 2017 Optical Society of America

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Corrections

20 March 2017: A correction was made to the author affiliations.


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References

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2016 (3)

X. Chen, Y. Shi, H. Jiang, C. Zhang, and S. Liu, “Nondestructive analysis of lithographic patterns with natural lineedge roughness from Mueller matrix ellipsometric data,” Appl. Surf. Sci. 388, 524–530 (2016).
[Crossref]

L. Fu, A. Berrier, H. Li, P. Schau, K. Frenner, M. Dressel, and W. Osten, “Depolarization of a randomly distributed plasmonic meander metasurface characterized by Mueller matrix spectroscopic ellipsometry,” Opt. Express 24(24), 28056–28064 (2016).
[Crossref] [PubMed]

S. De Zuani, M. Rommel, B. Gompf, A. Berrier, J. Weis, and M. Dressel, “Suppressed percolation in nearly-closed gold films,” ACS Photonics 3(6), 1109–1115 (2016).
[Crossref]

2015 (5)

2014 (4)

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).
[Crossref] [PubMed]

A. Berrier, B. Gompf, L. Fu, T. Weiss, and H. Schweizer, “Optical anisotropies of single-meander plasmonic metasurfaces analyzed by Mueller matrix spectroscopy,” Phys. Rev. B 89(19), 195434 (2014).
[Crossref]

T. W. H. Oates, T. Shaykhutdinov, T. Wagner, A. Furchner, and K. Hinrichs, “Mid-infrared gyrotropy in split-ring resonators measured by Mueller matrix ellipsometry,” Opt. Mater. Express 4(12), 2646–2655 (2014).
[Crossref]

A. I. Väkeväinen, R. J. Moerland, H. T. Rekola, A.-P. Eskelinen, J.-P. Martikainen, D.-H. Kim, and P. Törmä, “Plasmonic surface lattice resonances at the strong coupling regime,” Nano Lett. 14(4), 1721–1727 (2014).
[Crossref] [PubMed]

2013 (1)

D. Schmidt, C. Briley, E. Schubert, and M. Schubert, “Vector magneto-optical generalized ellipsometry for sculptured thin films,” Appl. Phys. Lett. 102(12), 123109 (2013).
[Crossref]

2012 (3)

2011 (2)

H. Arwin, “Application of ellipsometry techniques to biological materials,” Thin Solid Films 519(9), 2589–2592 (2011).
[Crossref]

B. Gompf, J. Braun, T. Weiss, H. Giessen, M. Dressel, and U. Hübner, “Periodic nanostructures: spatial dispersion mimics chirality,” Phys. Rev. Lett. 106(18), 185501 (2011).
[Crossref] [PubMed]

2010 (3)

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[Crossref]

F. Romanato, K. H. Lee, G. Ruffato, and C. C. Wong, “The role of polarization on surface plasmon polariton excitation on metallic gratings in the conical mounting,” Appl. Phys. Lett. 96(11), 111103 (2010).
[Crossref]

C. Yu and H. Jiang, “Forming wrinkled stiff films on polymeric substrates at room temperature for stretchable interconnects applications,” Thin Solid Films 519(2), 818–822 (2010).
[Crossref]

2009 (1)

G. Vecchi, V. Giannini, and J. Gómez Rivas, “Surface modes in plasmonic crystals induced by diffractive coupling of nanoantennas,” Phys. Rev. B 80(20), 201401 (2009).
[Crossref]

2008 (3)

B. Auguié and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101(14), 143902 (2008).
[Crossref] [PubMed]

V. G. Kravets, F. Schedin, and A. N. Grigorenko, “Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles,” Phys. Rev. Lett. 101(8), 087403 (2008).
[Crossref] [PubMed]

Y. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, “Experimental observation of narrow surface plasmon resonances in gold nanoparticle arrays,” Appl. Phys. Lett. 93(18), 181108 (2008).
[Crossref]

2007 (2)

P. Lin and S. Yang, “Spontaneous formation of one-dimensional ripples in transit to highly ordered two-dimensional herringbone structures through sequential and unequal biaxial mechanical stretching,” Appl. Phys. Lett. 90(24), 241903 (2007).
[Crossref]

A. V. Kats, I. S. Spevak, and N. A. Balakhonova, “Energy redistribution and polarization transformation in conical mount diffraction under resonance excitation of surface waves,” Phys. Rev. B 76(7), 075407 (2007).
[Crossref]

2006 (1)

2005 (1)

1999 (1)

J. Homola, S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B Chem. 54(1), 3–15 (1999).
[Crossref]

1997 (1)

F. Le Roy-Brehonnet and B. Le Jeune, “Utilization of Mueller matrix formalism to obtain optical targets depolarization and polarization properties,” Prog. Quantum Electron. 21(2), 109–151 (1997).
[Crossref]

1991 (1)

S. J. Elston, G. P. Bryan-Brown, and J. R. Sambles, “Polarization conversion from diffraction gratings,” Phys. Rev. B Condens. Matter 44(12), 6393–6400 (1991).
[Crossref] [PubMed]

1990 (1)

G. P. Bryan-Brown, J. R. Sambles, and M. C. Hutley, “Polarization conversion through the excitation of surface plasmons on a metallic grating,” J. Mod. Opt. 37(7), 1227–1232 (1990).
[Crossref]

1986 (1)

1907 (1)

L. Rayleigh, “On the dynamical theory of gratings,” Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character 79(532), 399–416 (1907).
[Crossref]

Agarwal, N.

Albooyeh, M.

Arakawa, E.

Arteaga, O.

Arwin, H.

H. Arwin, “Application of ellipsometry techniques to biological materials,” Thin Solid Films 519(9), 2589–2592 (2011).
[Crossref]

Auguié, B.

B. Auguié and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101(14), 143902 (2008).
[Crossref] [PubMed]

Balakhonova, N. A.

A. V. Kats, I. S. Spevak, and N. A. Balakhonova, “Energy redistribution and polarization transformation in conical mount diffraction under resonance excitation of surface waves,” Phys. Rev. B 76(7), 075407 (2007).
[Crossref]

Barnes, W. L.

B. Auguié and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101(14), 143902 (2008).
[Crossref] [PubMed]

Berini, P.

Berrier, A.

L. Fu, A. Berrier, H. Li, P. Schau, K. Frenner, M. Dressel, and W. Osten, “Depolarization of a randomly distributed plasmonic meander metasurface characterized by Mueller matrix spectroscopic ellipsometry,” Opt. Express 24(24), 28056–28064 (2016).
[Crossref] [PubMed]

S. De Zuani, M. Rommel, B. Gompf, A. Berrier, J. Weis, and M. Dressel, “Suppressed percolation in nearly-closed gold films,” ACS Photonics 3(6), 1109–1115 (2016).
[Crossref]

A. Berrier, B. Gompf, L. Fu, T. Weiss, and H. Schweizer, “Optical anisotropies of single-meander plasmonic metasurfaces analyzed by Mueller matrix spectroscopy,” Phys. Rev. B 89(19), 195434 (2014).
[Crossref]

Bischoff, J.

Bozhevolnyi, S. I.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[Crossref]

Brakstad, T.

Braun, J.

B. Gompf, J. Braun, T. Weiss, H. Giessen, M. Dressel, and U. Hübner, “Periodic nanostructures: spatial dispersion mimics chirality,” Phys. Rev. Lett. 106(18), 185501 (2011).
[Crossref] [PubMed]

Briley, C.

D. Schmidt, C. Briley, E. Schubert, and M. Schubert, “Vector magneto-optical generalized ellipsometry for sculptured thin films,” Appl. Phys. Lett. 102(12), 123109 (2013).
[Crossref]

Brolo, A. G.

A. G. Brolo, “Plasmonics for future biosensors,” Nat. Photonics 6(11), 709–713 (2012).
[Crossref]

Bryan-Brown, G. P.

S. J. Elston, G. P. Bryan-Brown, and J. R. Sambles, “Polarization conversion from diffraction gratings,” Phys. Rev. B Condens. Matter 44(12), 6393–6400 (1991).
[Crossref] [PubMed]

G. P. Bryan-Brown, J. R. Sambles, and M. C. Hutley, “Polarization conversion through the excitation of surface plasmons on a metallic grating,” J. Mod. Opt. 37(7), 1227–1232 (1990).
[Crossref]

Bykov, A.

Charbonneau, R.

Chen, X.

X. Chen, Y. Shi, H. Jiang, C. Zhang, and S. Liu, “Nondestructive analysis of lithographic patterns with natural lineedge roughness from Mueller matrix ellipsometric data,” Appl. Surf. Sci. 388, 524–530 (2016).
[Crossref]

S. Liu, X. Chen, and C. Zhang, “Development of a broadband Mueller matrix ellipsometer as a powerful tool for nanostructure metrology,” Thin Solid Films 584, 176–185 (2015).
[Crossref]

Chu, Y.

Y. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, “Experimental observation of narrow surface plasmon resonances in gold nanoparticle arrays,” Appl. Phys. Lett. 93(18), 181108 (2008).
[Crossref]

Crozier, K. B.

Y. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, “Experimental observation of narrow surface plasmon resonances in gold nanoparticle arrays,” Appl. Phys. Lett. 93(18), 181108 (2008).
[Crossref]

De Toni, A.

De Zuani, S.

S. De Zuani, M. Rommel, B. Gompf, A. Berrier, J. Weis, and M. Dressel, “Suppressed percolation in nearly-closed gold films,” ACS Photonics 3(6), 1109–1115 (2016).
[Crossref]

Dirnstorfer, I.

Dressel, M.

L. Fu, A. Berrier, H. Li, P. Schau, K. Frenner, M. Dressel, and W. Osten, “Depolarization of a randomly distributed plasmonic meander metasurface characterized by Mueller matrix spectroscopic ellipsometry,” Opt. Express 24(24), 28056–28064 (2016).
[Crossref] [PubMed]

S. De Zuani, M. Rommel, B. Gompf, A. Berrier, J. Weis, and M. Dressel, “Suppressed percolation in nearly-closed gold films,” ACS Photonics 3(6), 1109–1115 (2016).
[Crossref]

B. Gompf, J. Braun, T. Weiss, H. Giessen, M. Dressel, and U. Hübner, “Periodic nanostructures: spatial dispersion mimics chirality,” Phys. Rev. Lett. 106(18), 185501 (2011).
[Crossref] [PubMed]

Elston, S. J.

S. J. Elston, G. P. Bryan-Brown, and J. R. Sambles, “Polarization conversion from diffraction gratings,” Phys. Rev. B Condens. Matter 44(12), 6393–6400 (1991).
[Crossref] [PubMed]

Eskelinen, A.-P.

A. I. Väkeväinen, R. J. Moerland, H. T. Rekola, A.-P. Eskelinen, J.-P. Martikainen, D.-H. Kim, and P. Törmä, “Plasmonic surface lattice resonances at the strong coupling regime,” Nano Lett. 14(4), 1721–1727 (2014).
[Crossref] [PubMed]

Frenner, K.

Fu, L.

L. Fu, A. Berrier, H. Li, P. Schau, K. Frenner, M. Dressel, and W. Osten, “Depolarization of a randomly distributed plasmonic meander metasurface characterized by Mueller matrix spectroscopic ellipsometry,” Opt. Express 24(24), 28056–28064 (2016).
[Crossref] [PubMed]

A. Berrier, B. Gompf, L. Fu, T. Weiss, and H. Schweizer, “Optical anisotropies of single-meander plasmonic metasurfaces analyzed by Mueller matrix spectroscopy,” Phys. Rev. B 89(19), 195434 (2014).
[Crossref]

Furchner, A.

Garcia-Caurel, E.

Gauglitz, G.

J. Homola, S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B Chem. 54(1), 3–15 (1999).
[Crossref]

Ghadyani, Z.

Giannini, V.

G. Vecchi, V. Giannini, and J. Gómez Rivas, “Surface modes in plasmonic crystals induced by diffractive coupling of nanoantennas,” Phys. Rev. B 80(20), 201401 (2009).
[Crossref]

Giessen, H.

B. Gompf, J. Braun, T. Weiss, H. Giessen, M. Dressel, and U. Hübner, “Periodic nanostructures: spatial dispersion mimics chirality,” Phys. Rev. Lett. 106(18), 185501 (2011).
[Crossref] [PubMed]

Gómez Rivas, J.

G. Vecchi, V. Giannini, and J. Gómez Rivas, “Surface modes in plasmonic crystals induced by diffractive coupling of nanoantennas,” Phys. Rev. B 80(20), 201401 (2009).
[Crossref]

Gompf, B.

S. De Zuani, M. Rommel, B. Gompf, A. Berrier, J. Weis, and M. Dressel, “Suppressed percolation in nearly-closed gold films,” ACS Photonics 3(6), 1109–1115 (2016).
[Crossref]

A. Berrier, B. Gompf, L. Fu, T. Weiss, and H. Schweizer, “Optical anisotropies of single-meander plasmonic metasurfaces analyzed by Mueller matrix spectroscopy,” Phys. Rev. B 89(19), 195434 (2014).
[Crossref]

B. Gompf, J. Braun, T. Weiss, H. Giessen, M. Dressel, and U. Hübner, “Periodic nanostructures: spatial dispersion mimics chirality,” Phys. Rev. Lett. 106(18), 185501 (2011).
[Crossref] [PubMed]

Goudonnet, J.

Gramotnev, D. K.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[Crossref]

Grigorenko, A. N.

V. G. Kravets, F. Schedin, and A. N. Grigorenko, “Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles,” Phys. Rev. Lett. 101(8), 087403 (2008).
[Crossref] [PubMed]

Heinrich, A.

Hinrichs, K.

Homola, J.

J. Homola, S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B Chem. 54(1), 3–15 (1999).
[Crossref]

Hübner, U.

B. Gompf, J. Braun, T. Weiss, H. Giessen, M. Dressel, and U. Hübner, “Periodic nanostructures: spatial dispersion mimics chirality,” Phys. Rev. Lett. 106(18), 185501 (2011).
[Crossref] [PubMed]

Hutley, M. C.

G. P. Bryan-Brown, J. R. Sambles, and M. C. Hutley, “Polarization conversion through the excitation of surface plasmons on a metallic grating,” J. Mod. Opt. 37(7), 1227–1232 (1990).
[Crossref]

Inagaki, T.

Jiang, H.

X. Chen, Y. Shi, H. Jiang, C. Zhang, and S. Liu, “Nondestructive analysis of lithographic patterns with natural lineedge roughness from Mueller matrix ellipsometric data,” Appl. Surf. Sci. 388, 524–530 (2016).
[Crossref]

C. Yu and H. Jiang, “Forming wrinkled stiff films on polymeric substrates at room temperature for stretchable interconnects applications,” Thin Solid Films 519(2), 818–822 (2010).
[Crossref]

Kahr, B.

Kats, A. V.

A. V. Kats, I. S. Spevak, and N. A. Balakhonova, “Energy redistribution and polarization transformation in conical mount diffraction under resonance excitation of surface waves,” Phys. Rev. B 76(7), 075407 (2007).
[Crossref]

Kildemo, M.

Kim, D.-H.

A. I. Väkeväinen, R. J. Moerland, H. T. Rekola, A.-P. Eskelinen, J.-P. Martikainen, D.-H. Kim, and P. Törmä, “Plasmonic surface lattice resonances at the strong coupling regime,” Nano Lett. 14(4), 1721–1727 (2014).
[Crossref] [PubMed]

Kravets, V. G.

V. G. Kravets, F. Schedin, and A. N. Grigorenko, “Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles,” Phys. Rev. Lett. 101(8), 087403 (2008).
[Crossref] [PubMed]

Lahoud, N.

Le Jeune, B.

F. Le Roy-Brehonnet and B. Le Jeune, “Utilization of Mueller matrix formalism to obtain optical targets depolarization and polarization properties,” Prog. Quantum Electron. 21(2), 109–151 (1997).
[Crossref]

Le Roy-Brehonnet, F.

F. Le Roy-Brehonnet and B. Le Jeune, “Utilization of Mueller matrix formalism to obtain optical targets depolarization and polarization properties,” Prog. Quantum Electron. 21(2), 109–151 (1997).
[Crossref]

Lee, K. H.

F. Romanato, K. H. Lee, G. Ruffato, and C. C. Wong, “The role of polarization on surface plasmon polariton excitation on metallic gratings in the conical mounting,” Appl. Phys. Lett. 96(11), 111103 (2010).
[Crossref]

Li, H.

Lin, P.

P. Lin and S. Yang, “Spontaneous formation of one-dimensional ripples in transit to highly ordered two-dimensional herringbone structures through sequential and unequal biaxial mechanical stretching,” Appl. Phys. Lett. 90(24), 241903 (2007).
[Crossref]

Liu, S.

X. Chen, Y. Shi, H. Jiang, C. Zhang, and S. Liu, “Nondestructive analysis of lithographic patterns with natural lineedge roughness from Mueller matrix ellipsometric data,” Appl. Surf. Sci. 388, 524–530 (2016).
[Crossref]

S. Liu, X. Chen, and C. Zhang, “Development of a broadband Mueller matrix ellipsometer as a powerful tool for nanostructure metrology,” Thin Solid Films 584, 176–185 (2015).
[Crossref]

Maier, S. A.

Maoz, B. M.

Markovich, G.

Martikainen, J.-P.

A. I. Väkeväinen, R. J. Moerland, H. T. Rekola, A.-P. Eskelinen, J.-P. Martikainen, D.-H. Kim, and P. Törmä, “Plasmonic surface lattice resonances at the strong coupling regime,” Nano Lett. 14(4), 1721–1727 (2014).
[Crossref] [PubMed]

Mattiussi, G.

Meglinski, I.

Meiner, K.

Mikolajick, T.

Moerland, R. J.

A. I. Väkeväinen, R. J. Moerland, H. T. Rekola, A.-P. Eskelinen, J.-P. Martikainen, D.-H. Kim, and P. Törmä, “Plasmonic surface lattice resonances at the strong coupling regime,” Nano Lett. 14(4), 1721–1727 (2014).
[Crossref] [PubMed]

Nichols, S.

Novikova, T.

Oates, T. W. H.

Ossikovski, R.

Osten, W.

Paccagnella, A.

Pasqualotto, E.

Perino, M.

Pierangelo, A.

Popov, A.

Rayleigh, L.

L. Rayleigh, “On the dynamical theory of gratings,” Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character 79(532), 399–416 (1907).
[Crossref]

Rekola, H. T.

A. I. Väkeväinen, R. J. Moerland, H. T. Rekola, A.-P. Eskelinen, J.-P. Martikainen, D.-H. Kim, and P. Törmä, “Plasmonic surface lattice resonances at the strong coupling regime,” Nano Lett. 14(4), 1721–1727 (2014).
[Crossref] [PubMed]

Richter, U.

Romanato, F.

G. Ruffato and F. Romanato, “Grating-coupled surface plasmon resonance in conical mounting with polarization modulation,” Opt. Lett. 37(13), 2718–2720 (2012).
[Crossref] [PubMed]

F. Romanato, K. H. Lee, G. Ruffato, and C. C. Wong, “The role of polarization on surface plasmon polariton excitation on metallic gratings in the conical mounting,” Appl. Phys. Lett. 96(11), 111103 (2010).
[Crossref]

Rommel, M.

S. De Zuani, M. Rommel, B. Gompf, A. Berrier, J. Weis, and M. Dressel, “Suppressed percolation in nearly-closed gold films,” ACS Photonics 3(6), 1109–1115 (2016).
[Crossref]

Ruffato, G.

G. Ruffato and F. Romanato, “Grating-coupled surface plasmon resonance in conical mounting with polarization modulation,” Opt. Lett. 37(13), 2718–2720 (2012).
[Crossref] [PubMed]

F. Romanato, K. H. Lee, G. Ruffato, and C. C. Wong, “The role of polarization on surface plasmon polariton excitation on metallic gratings in the conical mounting,” Appl. Phys. Lett. 96(11), 111103 (2010).
[Crossref]

Sambles, J. R.

S. J. Elston, G. P. Bryan-Brown, and J. R. Sambles, “Polarization conversion from diffraction gratings,” Phys. Rev. B Condens. Matter 44(12), 6393–6400 (1991).
[Crossref] [PubMed]

G. P. Bryan-Brown, J. R. Sambles, and M. C. Hutley, “Polarization conversion through the excitation of surface plasmons on a metallic grating,” J. Mod. Opt. 37(7), 1227–1232 (1990).
[Crossref]

Scaramuzza, M.

Schau, P.

Schedin, F.

V. G. Kravets, F. Schedin, and A. N. Grigorenko, “Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles,” Phys. Rev. Lett. 101(8), 087403 (2008).
[Crossref] [PubMed]

Schmidt, D.

D. Schmidt, C. Briley, E. Schubert, and M. Schubert, “Vector magneto-optical generalized ellipsometry for sculptured thin films,” Appl. Phys. Lett. 102(12), 123109 (2013).
[Crossref]

Schonbrun, E.

Y. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, “Experimental observation of narrow surface plasmon resonances in gold nanoparticle arrays,” Appl. Phys. Lett. 93(18), 181108 (2008).
[Crossref]

Schubert, E.

D. Schmidt, C. Briley, E. Schubert, and M. Schubert, “Vector magneto-optical generalized ellipsometry for sculptured thin films,” Appl. Phys. Lett. 102(12), 123109 (2013).
[Crossref]

Schubert, M.

D. Schmidt, C. Briley, E. Schubert, and M. Schubert, “Vector magneto-optical generalized ellipsometry for sculptured thin films,” Appl. Phys. Lett. 102(12), 123109 (2013).
[Crossref]

Schweizer, H.

A. Berrier, B. Gompf, L. Fu, T. Weiss, and H. Schweizer, “Optical anisotropies of single-meander plasmonic metasurfaces analyzed by Mueller matrix spectroscopy,” Phys. Rev. B 89(19), 195434 (2014).
[Crossref]

Shaykhutdinov, T.

Shi, Y.

X. Chen, Y. Shi, H. Jiang, C. Zhang, and S. Liu, “Nondestructive analysis of lithographic patterns with natural lineedge roughness from Mueller matrix ellipsometric data,” Appl. Surf. Sci. 388, 524–530 (2016).
[Crossref]

Simonsen, I.

Simovski, C. R.

Spevak, I. S.

A. V. Kats, I. S. Spevak, and N. A. Balakhonova, “Energy redistribution and polarization transformation in conical mount diffraction under resonance excitation of surface waves,” Phys. Rev. B 76(7), 075407 (2007).
[Crossref]

Törmä, P.

A. I. Väkeväinen, R. J. Moerland, H. T. Rekola, A.-P. Eskelinen, J.-P. Martikainen, D.-H. Kim, and P. Törmä, “Plasmonic surface lattice resonances at the strong coupling regime,” Nano Lett. 14(4), 1721–1727 (2014).
[Crossref] [PubMed]

Väkeväinen, A. I.

A. I. Väkeväinen, R. J. Moerland, H. T. Rekola, A.-P. Eskelinen, J.-P. Martikainen, D.-H. Kim, and P. Törmä, “Plasmonic surface lattice resonances at the strong coupling regime,” Nano Lett. 14(4), 1721–1727 (2014).
[Crossref] [PubMed]

Vanel, J. C.

Vecchi, G.

G. Vecchi, V. Giannini, and J. Gómez Rivas, “Surface modes in plasmonic crystals induced by diffractive coupling of nanoantennas,” Phys. Rev. B 80(20), 201401 (2009).
[Crossref]

Wagner, T.

Weis, J.

S. De Zuani, M. Rommel, B. Gompf, A. Berrier, J. Weis, and M. Dressel, “Suppressed percolation in nearly-closed gold films,” ACS Photonics 3(6), 1109–1115 (2016).
[Crossref]

Weiss, T.

A. Berrier, B. Gompf, L. Fu, T. Weiss, and H. Schweizer, “Optical anisotropies of single-meander plasmonic metasurfaces analyzed by Mueller matrix spectroscopy,” Phys. Rev. B 89(19), 195434 (2014).
[Crossref]

B. Gompf, J. Braun, T. Weiss, H. Giessen, M. Dressel, and U. Hübner, “Periodic nanostructures: spatial dispersion mimics chirality,” Phys. Rev. Lett. 106(18), 185501 (2011).
[Crossref] [PubMed]

Wong, C. C.

F. Romanato, K. H. Lee, G. Ruffato, and C. C. Wong, “The role of polarization on surface plasmon polariton excitation on metallic gratings in the conical mounting,” Appl. Phys. Lett. 96(11), 111103 (2010).
[Crossref]

Yang, S.

P. Lin and S. Yang, “Spontaneous formation of one-dimensional ripples in transit to highly ordered two-dimensional herringbone structures through sequential and unequal biaxial mechanical stretching,” Appl. Phys. Lett. 90(24), 241903 (2007).
[Crossref]

Yang, T.

Y. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, “Experimental observation of narrow surface plasmon resonances in gold nanoparticle arrays,” Appl. Phys. Lett. 93(18), 181108 (2008).
[Crossref]

Yee, S.

J. Homola, S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B Chem. 54(1), 3–15 (1999).
[Crossref]

Yoon, J.

Yu, C.

C. Yu and H. Jiang, “Forming wrinkled stiff films on polymeric substrates at room temperature for stretchable interconnects applications,” Thin Solid Films 519(2), 818–822 (2010).
[Crossref]

Zhang, C.

X. Chen, Y. Shi, H. Jiang, C. Zhang, and S. Liu, “Nondestructive analysis of lithographic patterns with natural lineedge roughness from Mueller matrix ellipsometric data,” Appl. Surf. Sci. 388, 524–530 (2016).
[Crossref]

S. Liu, X. Chen, and C. Zhang, “Development of a broadband Mueller matrix ellipsometer as a powerful tool for nanostructure metrology,” Thin Solid Films 584, 176–185 (2015).
[Crossref]

ACS Photonics (1)

S. De Zuani, M. Rommel, B. Gompf, A. Berrier, J. Weis, and M. Dressel, “Suppressed percolation in nearly-closed gold films,” ACS Photonics 3(6), 1109–1115 (2016).
[Crossref]

Appl. Phys. Lett. (4)

F. Romanato, K. H. Lee, G. Ruffato, and C. C. Wong, “The role of polarization on surface plasmon polariton excitation on metallic gratings in the conical mounting,” Appl. Phys. Lett. 96(11), 111103 (2010).
[Crossref]

Y. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, “Experimental observation of narrow surface plasmon resonances in gold nanoparticle arrays,” Appl. Phys. Lett. 93(18), 181108 (2008).
[Crossref]

D. Schmidt, C. Briley, E. Schubert, and M. Schubert, “Vector magneto-optical generalized ellipsometry for sculptured thin films,” Appl. Phys. Lett. 102(12), 123109 (2013).
[Crossref]

P. Lin and S. Yang, “Spontaneous formation of one-dimensional ripples in transit to highly ordered two-dimensional herringbone structures through sequential and unequal biaxial mechanical stretching,” Appl. Phys. Lett. 90(24), 241903 (2007).
[Crossref]

Appl. Surf. Sci. (1)

X. Chen, Y. Shi, H. Jiang, C. Zhang, and S. Liu, “Nondestructive analysis of lithographic patterns with natural lineedge roughness from Mueller matrix ellipsometric data,” Appl. Surf. Sci. 388, 524–530 (2016).
[Crossref]

J. Mod. Opt. (1)

G. P. Bryan-Brown, J. R. Sambles, and M. C. Hutley, “Polarization conversion through the excitation of surface plasmons on a metallic grating,” J. Mod. Opt. 37(7), 1227–1232 (1990).
[Crossref]

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

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

Nano Lett. (1)

A. I. Väkeväinen, R. J. Moerland, H. T. Rekola, A.-P. Eskelinen, J.-P. Martikainen, D.-H. Kim, and P. Törmä, “Plasmonic surface lattice resonances at the strong coupling regime,” Nano Lett. 14(4), 1721–1727 (2014).
[Crossref] [PubMed]

Nat. Photonics (2)

A. G. Brolo, “Plasmonics for future biosensors,” Nat. Photonics 6(11), 709–713 (2012).
[Crossref]

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[Crossref]

Opt. Express (6)

Opt. Lett. (3)

Opt. Mater. Express (1)

Phys. Rev. B (3)

A. Berrier, B. Gompf, L. Fu, T. Weiss, and H. Schweizer, “Optical anisotropies of single-meander plasmonic metasurfaces analyzed by Mueller matrix spectroscopy,” Phys. Rev. B 89(19), 195434 (2014).
[Crossref]

G. Vecchi, V. Giannini, and J. Gómez Rivas, “Surface modes in plasmonic crystals induced by diffractive coupling of nanoantennas,” Phys. Rev. B 80(20), 201401 (2009).
[Crossref]

A. V. Kats, I. S. Spevak, and N. A. Balakhonova, “Energy redistribution and polarization transformation in conical mount diffraction under resonance excitation of surface waves,” Phys. Rev. B 76(7), 075407 (2007).
[Crossref]

Phys. Rev. B Condens. Matter (1)

S. J. Elston, G. P. Bryan-Brown, and J. R. Sambles, “Polarization conversion from diffraction gratings,” Phys. Rev. B Condens. Matter 44(12), 6393–6400 (1991).
[Crossref] [PubMed]

Phys. Rev. Lett. (3)

B. Auguié and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101(14), 143902 (2008).
[Crossref] [PubMed]

V. G. Kravets, F. Schedin, and A. N. Grigorenko, “Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles,” Phys. Rev. Lett. 101(8), 087403 (2008).
[Crossref] [PubMed]

B. Gompf, J. Braun, T. Weiss, H. Giessen, M. Dressel, and U. Hübner, “Periodic nanostructures: spatial dispersion mimics chirality,” Phys. Rev. Lett. 106(18), 185501 (2011).
[Crossref] [PubMed]

Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character (1)

L. Rayleigh, “On the dynamical theory of gratings,” Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character 79(532), 399–416 (1907).
[Crossref]

Prog. Quantum Electron. (1)

F. Le Roy-Brehonnet and B. Le Jeune, “Utilization of Mueller matrix formalism to obtain optical targets depolarization and polarization properties,” Prog. Quantum Electron. 21(2), 109–151 (1997).
[Crossref]

Sens. Actuators B Chem. (1)

J. Homola, S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B Chem. 54(1), 3–15 (1999).
[Crossref]

Thin Solid Films (3)

H. Arwin, “Application of ellipsometry techniques to biological materials,” Thin Solid Films 519(9), 2589–2592 (2011).
[Crossref]

S. Liu, X. Chen, and C. Zhang, “Development of a broadband Mueller matrix ellipsometer as a powerful tool for nanostructure metrology,” Thin Solid Films 584, 176–185 (2015).
[Crossref]

C. Yu and H. Jiang, “Forming wrinkled stiff films on polymeric substrates at room temperature for stretchable interconnects applications,” Thin Solid Films 519(2), 818–822 (2010).
[Crossref]

Other (5)

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

H. Tompkins and E. Irene, Handbook of Ellipsometry (William Andrew Publishing, 2005).

D. H. Goldstein, Polarized Light (Taylor & Fransis Group, 2011).

D. Sarid and W. A. Challener, Modern Introduction to Surface Plasmons (Cambridge University, 2010).

A. P. Hibbins, Grating Coupling of Surface Plasmon Polaritons at Visible and Microwave Frequencies (University of Exeter, PhD thesis, 1999).

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Figures (8)

Fig. 1
Fig. 1

(a) Schematic illustration of Au grating fabrication procedure. (b) Measurement configuration θ is the angle of incidence, α is the azimuthal angle with α = 0° for classical mounting and α≠0° for conical mounting.

Fig. 2
Fig. 2

(a) Schematic drawing and (b) 3D AFM image of the sinusoidal Au grating with period p = 570nm, amplitude H = 100nm and Au thickness h = 35nm. (c) Five photographs taken from different reflection angles with sunlight coming from the incident side with fixed incident angle. The numbers of the photographs are related to the angles in the schematics in the right inset.

Fig. 3
Fig. 3

(a) Contour plot of the reflectance with p-polarized light between AOI 25° and 65° in steps of 5° at α = 0° in the spectral range between 210 and 1200nm. (b) Contour plot of the reflectance with s-polarized light between AOI 25° and 65° in steps of 5° at α = 90° in the spectral range between 210 and 1000nm. The dashed lines in the contour plots correspond to SPPs and RWAs. The line cuts in the left side of (a) and (b) are reflectance measured at AOI 45°, along the dotted lines, with p-polarized light at α = 0° and with s-polarized light at α = 90°, respectively.

Fig. 4
Fig. 4

Contour plots of experimental reflectance with p-polarized (a) and s-polarized light (b) together with the SPPs, different order RWAs and the interband transition lines. The excitations are only plotted in the upper half-space to avoid masking of the raw data in the other half space. (c), (d) experimental polarization conversion Rps and Rsp with SPP lines. All the contour plots are at AOI 45° over a complete azimuthal rotation in step of 5° in the spectral range between 210nm and 1200nm. The polar axis represents the wavelength λ and the polar angle represents the azimuthal angle α.

Fig. 5
Fig. 5

MMEs measured in reflection at AOI 45° over the complete azimuthal rotation in the spectral range between 210nm and 1200nm. All MMEs are normalized to M11.

Fig. 6
Fig. 6

Rpp (a) and Rss (b) measured at AOI 45° over a complete azimuthal rotation in the spectral range between 210nm and 1200nm. Rpp(c) and Rss(d) generated from the p- and s-biaxial models, respectively. All the plots are shown together with the calculated SPP lines in the top half space.

Fig. 7
Fig. 7

Simulated Mueller matrix at AOI 45ᵒ in the spectral range between 210nm and 1200nm with full azimuthal rotation generated from P biaxial model (a) and S biaxial model (b). Multiplication factors are used to scale the data to [-1;1].

Fig. 8
Fig. 8

Measured and simulated Mueller matrix elements M12, M13, M24 and M34 together with the SPP, RWA and interband transitions draws in the upper half space at AOI 45°. Simulated p- and s-model means, that the Mueller matrices are calculated only from the anisotropic effective medium approach obtained from the s- and p-reflectance measurements. The multiplication factors give the enhancement factor in respect to the scale bar.

Equations (7)

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K s p = K 0 ε 1 ε 2 ε 1 + ε 2 .
K s p = K i + m   G = K 0   [ ( sin  θ sin α   ) x + ( sin  θ  cos  α ) y ] + 2 π m P y .  
K 0 ε 1 ε 2 ε 1 + ε 2 =   K 0   [ ( sin  θ    sin α ) x +   ( sin  θ  cos  α ) y ] +   2 π m P y .
  ( sin θ ) 2 +   2 m λ P sin   θ cos   α +   ( m λ P ) 2 = ε 1 ε 2 ε 1 + ε 2 .
tan φ = cos θ tan α .
K / / + m G = n K 0 .  
  λ m =   P m   ( sin  θ   | cos  α | ±   n 2 2 ( sin θ ) 2 ( sin α ) 2   ) .

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