Abstract

We show spectroscopic Mueller-matrix data measured at multiple incidence angles of the scarab beetle C. aurata. A method of regression decomposition can decompose the Mueller matrix into a set of two matrices representing one polarizer and one dielectric reflector. We also report on a tentative decomposition of the beetle C. argenteola using the same method.

© 2016 Optical Society of America

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References

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  1. E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekker, 1993).
  2. H. Fujiwara, Spectroscopic Ellipsometry: Principles and Applications (Wiley, 2007).
  3. D. H. Goldstein, “Polarization properties of scarabaeidae,” Appl. Opt. 45, 7944–7950 (2006).
    [Crossref]
  4. H. Arwin, R. Magnusson, J. Landin, and K. Järrendahl, “Chirality-induced polarization effects in the cuticle of scarab beetles: 100 years after Michelson,” Philos. Mag. 92(12), 1583–1599 (2012).
    [Crossref]
  5. A. Saito, “Material design and structural color inspired by biomimetic approach,” Sci. Technol. Adv. Mater. 12, 064709 (2011).
    [Crossref]
  6. I. Hodgkinson, S. Lowrey, L. Bourke, A. Parker, and M. W. McCall, “Mueller-matrix characterization of beetle cuticle: polarized and unpolarized reflections from representative architectures,” Appl. Opt. 49, 4558–4567 (2010).
    [Crossref]
  7. H. Arwin, T. Berlind, B. Johs, and K. Järrendahl, “Cuticle structure of the scarab beetle Cetonia aurata analyzed by regression analysis of Mueller-matrix ellipsometric data,” Opt. Express 21, 22645–22656 (2013).
    [Crossref]
  8. S. R. Cloude, “Conditions for the physical realisability of matrix operators in polarimetry,” Proc. SPIE 1166, 177–187 (1990).
    [Crossref]
  9. R. Ossikovski, M. Anastasiadou, S. Ben Hatit, E. Garcia-Caurel, and A. De Martino, “Depolarizing Mueller matrices: how to decompose them?” Phys. Status Solidi A 205, 720–727 (2008).
    [Crossref]
  10. R. Ossikovski, M. Foldyna, C. Fallet, and A. De Martino, “Experimental evidence for naturally occurring nondiagonal depolarizers,” Opt. Lett. 34, 2426–2428 (2009).
    [Crossref]
  11. H. Arwin, R. Magnusson, E. Garcia-Caurel, C. Fallet, K. Järrendahl, M. Foldyna, A. De Martino, and R. Ossikovski, “Sum decomposition of Mueller-matrix images and spectra of beetle cuticles,” Opt. Express 23, 1951–1966 (2015).
    [Crossref]
  12. J. J. Gil, “Polarimetric characterization of light and media,” Eur. Phys. J. 40, 1–47 (2007).
    [Crossref]
  13. G. H. Golub and C. F. V. Loan, Matrix Computations, 3rd ed. (JHU, 1996).
  14. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, 1999).
  15. D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy, 2nd ed. (Academic, 1990).
  16. H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981), reprinted.
  17. L. Li, “Symmetries of cross-polarization diffraction coefficients of gratings,” J. Opt. Soc. Am. A 17, 881–887 (2000).
    [Crossref]
  18. E. Garcia-Caurel, R. Ossikovski, M. Foldyna, A. Pierangelo, B. Drevillon, and A. De Martino, “Advanced Mueller ellipsometry instrumentation and data analysis,” in Ellipsometry at the Nanoscale, M. Losurdo and K. Hingerl, eds. (Springer, 2013).
  19. A. Mendoza-Galván, E. Muñoz-Pineda, K. Järrendahl, and H. Arwin, “Evidence for a dispersion relation of optical modes in the cuticle of the scarab beetle Cotinis mutabilis,” Opt. Mater. Express 4, 2484–2496 (2014).
    [Crossref]

2015 (1)

2014 (1)

2013 (1)

2012 (1)

H. Arwin, R. Magnusson, J. Landin, and K. Järrendahl, “Chirality-induced polarization effects in the cuticle of scarab beetles: 100 years after Michelson,” Philos. Mag. 92(12), 1583–1599 (2012).
[Crossref]

2011 (1)

A. Saito, “Material design and structural color inspired by biomimetic approach,” Sci. Technol. Adv. Mater. 12, 064709 (2011).
[Crossref]

2010 (1)

2009 (1)

2008 (1)

R. Ossikovski, M. Anastasiadou, S. Ben Hatit, E. Garcia-Caurel, and A. De Martino, “Depolarizing Mueller matrices: how to decompose them?” Phys. Status Solidi A 205, 720–727 (2008).
[Crossref]

2007 (1)

J. J. Gil, “Polarimetric characterization of light and media,” Eur. Phys. J. 40, 1–47 (2007).
[Crossref]

2006 (1)

2000 (1)

1990 (1)

S. R. Cloude, “Conditions for the physical realisability of matrix operators in polarimetry,” Proc. SPIE 1166, 177–187 (1990).
[Crossref]

Anastasiadou, M.

R. Ossikovski, M. Anastasiadou, S. Ben Hatit, E. Garcia-Caurel, and A. De Martino, “Depolarizing Mueller matrices: how to decompose them?” Phys. Status Solidi A 205, 720–727 (2008).
[Crossref]

Arwin, H.

Azzam, R. M. A.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, 1999).

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, 1999).

Ben Hatit, S.

R. Ossikovski, M. Anastasiadou, S. Ben Hatit, E. Garcia-Caurel, and A. De Martino, “Depolarizing Mueller matrices: how to decompose them?” Phys. Status Solidi A 205, 720–727 (2008).
[Crossref]

Berlind, T.

Bourke, L.

Cloude, S. R.

S. R. Cloude, “Conditions for the physical realisability of matrix operators in polarimetry,” Proc. SPIE 1166, 177–187 (1990).
[Crossref]

Collett, E.

E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekker, 1993).

De Martino, A.

H. Arwin, R. Magnusson, E. Garcia-Caurel, C. Fallet, K. Järrendahl, M. Foldyna, A. De Martino, and R. Ossikovski, “Sum decomposition of Mueller-matrix images and spectra of beetle cuticles,” Opt. Express 23, 1951–1966 (2015).
[Crossref]

R. Ossikovski, M. Foldyna, C. Fallet, and A. De Martino, “Experimental evidence for naturally occurring nondiagonal depolarizers,” Opt. Lett. 34, 2426–2428 (2009).
[Crossref]

R. Ossikovski, M. Anastasiadou, S. Ben Hatit, E. Garcia-Caurel, and A. De Martino, “Depolarizing Mueller matrices: how to decompose them?” Phys. Status Solidi A 205, 720–727 (2008).
[Crossref]

E. Garcia-Caurel, R. Ossikovski, M. Foldyna, A. Pierangelo, B. Drevillon, and A. De Martino, “Advanced Mueller ellipsometry instrumentation and data analysis,” in Ellipsometry at the Nanoscale, M. Losurdo and K. Hingerl, eds. (Springer, 2013).

Drevillon, B.

E. Garcia-Caurel, R. Ossikovski, M. Foldyna, A. Pierangelo, B. Drevillon, and A. De Martino, “Advanced Mueller ellipsometry instrumentation and data analysis,” in Ellipsometry at the Nanoscale, M. Losurdo and K. Hingerl, eds. (Springer, 2013).

Fallet, C.

Foldyna, M.

Fujiwara, H.

H. Fujiwara, Spectroscopic Ellipsometry: Principles and Applications (Wiley, 2007).

Garcia-Caurel, E.

H. Arwin, R. Magnusson, E. Garcia-Caurel, C. Fallet, K. Järrendahl, M. Foldyna, A. De Martino, and R. Ossikovski, “Sum decomposition of Mueller-matrix images and spectra of beetle cuticles,” Opt. Express 23, 1951–1966 (2015).
[Crossref]

R. Ossikovski, M. Anastasiadou, S. Ben Hatit, E. Garcia-Caurel, and A. De Martino, “Depolarizing Mueller matrices: how to decompose them?” Phys. Status Solidi A 205, 720–727 (2008).
[Crossref]

E. Garcia-Caurel, R. Ossikovski, M. Foldyna, A. Pierangelo, B. Drevillon, and A. De Martino, “Advanced Mueller ellipsometry instrumentation and data analysis,” in Ellipsometry at the Nanoscale, M. Losurdo and K. Hingerl, eds. (Springer, 2013).

Gil, J. J.

J. J. Gil, “Polarimetric characterization of light and media,” Eur. Phys. J. 40, 1–47 (2007).
[Crossref]

Goldstein, D. H.

Golub, G. H.

G. H. Golub and C. F. V. Loan, Matrix Computations, 3rd ed. (JHU, 1996).

Hodgkinson, I.

Järrendahl, K.

Johs, B.

Kliger, D. S.

D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy, 2nd ed. (Academic, 1990).

Landin, J.

H. Arwin, R. Magnusson, J. Landin, and K. Järrendahl, “Chirality-induced polarization effects in the cuticle of scarab beetles: 100 years after Michelson,” Philos. Mag. 92(12), 1583–1599 (2012).
[Crossref]

Lewis, J. W.

D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy, 2nd ed. (Academic, 1990).

Li, L.

Loan, C. F. V.

G. H. Golub and C. F. V. Loan, Matrix Computations, 3rd ed. (JHU, 1996).

Lowrey, S.

Magnusson, R.

H. Arwin, R. Magnusson, E. Garcia-Caurel, C. Fallet, K. Järrendahl, M. Foldyna, A. De Martino, and R. Ossikovski, “Sum decomposition of Mueller-matrix images and spectra of beetle cuticles,” Opt. Express 23, 1951–1966 (2015).
[Crossref]

H. Arwin, R. Magnusson, J. Landin, and K. Järrendahl, “Chirality-induced polarization effects in the cuticle of scarab beetles: 100 years after Michelson,” Philos. Mag. 92(12), 1583–1599 (2012).
[Crossref]

McCall, M. W.

Mendoza-Galván, A.

Muñoz-Pineda, E.

Ossikovski, R.

H. Arwin, R. Magnusson, E. Garcia-Caurel, C. Fallet, K. Järrendahl, M. Foldyna, A. De Martino, and R. Ossikovski, “Sum decomposition of Mueller-matrix images and spectra of beetle cuticles,” Opt. Express 23, 1951–1966 (2015).
[Crossref]

R. Ossikovski, M. Foldyna, C. Fallet, and A. De Martino, “Experimental evidence for naturally occurring nondiagonal depolarizers,” Opt. Lett. 34, 2426–2428 (2009).
[Crossref]

R. Ossikovski, M. Anastasiadou, S. Ben Hatit, E. Garcia-Caurel, and A. De Martino, “Depolarizing Mueller matrices: how to decompose them?” Phys. Status Solidi A 205, 720–727 (2008).
[Crossref]

E. Garcia-Caurel, R. Ossikovski, M. Foldyna, A. Pierangelo, B. Drevillon, and A. De Martino, “Advanced Mueller ellipsometry instrumentation and data analysis,” in Ellipsometry at the Nanoscale, M. Losurdo and K. Hingerl, eds. (Springer, 2013).

Parker, A.

Pierangelo, A.

E. Garcia-Caurel, R. Ossikovski, M. Foldyna, A. Pierangelo, B. Drevillon, and A. De Martino, “Advanced Mueller ellipsometry instrumentation and data analysis,” in Ellipsometry at the Nanoscale, M. Losurdo and K. Hingerl, eds. (Springer, 2013).

Randall, C. E.

D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy, 2nd ed. (Academic, 1990).

Saito, A.

A. Saito, “Material design and structural color inspired by biomimetic approach,” Sci. Technol. Adv. Mater. 12, 064709 (2011).
[Crossref]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981), reprinted.

Appl. Opt. (2)

Eur. Phys. J. (1)

J. J. Gil, “Polarimetric characterization of light and media,” Eur. Phys. J. 40, 1–47 (2007).
[Crossref]

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

Opt. Express (2)

Opt. Lett. (1)

Opt. Mater. Express (1)

Philos. Mag. (1)

H. Arwin, R. Magnusson, J. Landin, and K. Järrendahl, “Chirality-induced polarization effects in the cuticle of scarab beetles: 100 years after Michelson,” Philos. Mag. 92(12), 1583–1599 (2012).
[Crossref]

Phys. Status Solidi A (1)

R. Ossikovski, M. Anastasiadou, S. Ben Hatit, E. Garcia-Caurel, and A. De Martino, “Depolarizing Mueller matrices: how to decompose them?” Phys. Status Solidi A 205, 720–727 (2008).
[Crossref]

Proc. SPIE (1)

S. R. Cloude, “Conditions for the physical realisability of matrix operators in polarimetry,” Proc. SPIE 1166, 177–187 (1990).
[Crossref]

Sci. Technol. Adv. Mater. (1)

A. Saito, “Material design and structural color inspired by biomimetic approach,” Sci. Technol. Adv. Mater. 12, 064709 (2011).
[Crossref]

Other (7)

E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekker, 1993).

H. Fujiwara, Spectroscopic Ellipsometry: Principles and Applications (Wiley, 2007).

E. Garcia-Caurel, R. Ossikovski, M. Foldyna, A. Pierangelo, B. Drevillon, and A. De Martino, “Advanced Mueller ellipsometry instrumentation and data analysis,” in Ellipsometry at the Nanoscale, M. Losurdo and K. Hingerl, eds. (Springer, 2013).

G. H. Golub and C. F. V. Loan, Matrix Computations, 3rd ed. (JHU, 1996).

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, 1999).

D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy, 2nd ed. (Academic, 1990).

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981), reprinted.

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Figures (8)

Fig. 1.
Fig. 1. Contour plot of experimentally determined 4 × 4 Mueller matrices of C. aurata.
Fig. 2.
Fig. 2. Result of regression analysis of data from C. aurata using the ansatz in Eq. (16).
Fig. 3.
Fig. 3. First term of Eq. (16), a ( λ , θ ) M P , R elliptic ( α , ε ) .
Fig. 4.
Fig. 4. Second term of Eq. (16), b ( λ , θ ) M R Iso ( ψ , δ ) .
Fig. 5.
Fig. 5. Difference between the experimental Mueller matrix and M reg as calculated by Eq. (16) for C. aurata.
Fig. 6.
Fig. 6. Contour plot of the experimentally determined Mueller matrix of C. argenteola.
Fig. 7.
Fig. 7. Result of regression analysis of data from C. argenteola using the ansatz in Eq. (16).
Fig. 8.
Fig. 8. Eigenvalues from a Cloude decomposition of (a) C. argenteola and (b) C. aurata, both at 45° incidence angle.

Equations (16)

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S o = MS i ,
[ I o Q o U o V o ] = [ 1 m 12 m 13 m 14 m 21 m 22 m 23 m 24 m 31 m 32 m 33 m 34 m 41 m 42 m 43 m 44 ] [ 1 Q i U i V i ] ,
M reg = a M 1 reg + b M 2 reg + c M 3 reg + d M 4 reg .
F = M M reg F ,
M = R ( α ) MR ( α ) ,
R ( α ) = [ 1 0 0 0 0 cos 2 α sin 2 α 0 0 sin 2 α cos 2 α 0 0 0 0 1 ] .
M P linear = 1 2 [ 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 ] .
M P linear ( α ) = 1 2 [ 1 cos 2 α sin 2 α 0 cos 2 α cos 2 2 α sin 2 α cos 2 α 0 sin 2 α sin 2 α cos 2 α sin 2 2 α 0 0 0 0 0 ] .
M P circular = 1 2 [ 1 0 0 ± 1 0 0 0 0 0 0 0 0 ± 1 0 0 1 ] ,
M P elliptic ( ε ) = 1 2 [ 1 cos 2 ε 0 sin 2 ε cos 2 ε cos 2 2 ε 0 cos 2 ε sin 2 ε 0 0 0 0 sin 2 ε cos 2 ε sin 2 ε 0 sin 2 2 ε ] ,
M P elliptic ( ε , α ) = 1 2 [ 1 a b a c d a b a 2 b 2 a 2 b c a b d a c a 2 b c a 2 c 2 a c d d a b d a c d d 2 ] ,
M P , R elliptic ( ε , α ) = 1 2 [ 1 a b a c d a b a 2 b 2 a 2 b c a b d a c a 2 b c a 2 c 2 a c d d a b d a c d d 2 ] .
M R Iso = [ 1 cos 2 ψ 0 0 cos 2 ψ 1 0 0 0 0 sin 2 ψ cos δ sin 2 ψ sin δ 0 0 sin 2 ψ sin δ sin 2 ψ cos δ ] .
M M = [ 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ] ,
M LP = [ 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 ] ,
M reg = a ( λ , θ ) M P , R elliptic ( α , ε ) + b ( λ , θ ) M R Iso ( ψ , δ ) ,

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