Abstract

Variable angle Mueller matrix spectroscopic ellipsometry is used to study the properties of light reflected from the exoskeleton (cuticle) of the scarab beetle Cotinis mutabilis. For unpolarized incident light, the ellipticity and degree of polarization of the reflected light reveal a left-handed helical structure in the beetle cuticle. Analysis of the spectral position of the maxima and minima in the interference oscillations of the Mueller-matrix elements provides evidence for a dispersion relation similar to that of optical modes in chiral nematic liquid crystals calculated within a two-wave approximation. Additionally, a structural model for the cuticle of C. mutabilis is derived from the properties of the optical modes for non-attenuated propagation or selective reflection.

© 2014 Optical Society of America

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    [Crossref] [PubMed]
  2. A. C. Neville, “The need for a constraining layer in the formation of monodomain helicoids in a wide range of biological structures,” Tissue Cell 20(1), 133–143 (1988).
    [Crossref] [PubMed]
  3. G. De Luca and A. D. Rey, “Monodomain and polydomain helicoids in chiral liquid-crystalline phases and their biological analogues,” Eur Phys J E Soft Matter 12(2), 291–302 (2003).
    [Crossref] [PubMed]
  4. D. J. Brink, N. G. van der Berg, L. C. Prinsloo, and I. J. Hodgkinson, “Unusual coloration in scarabaeid beetles,” J. Phys. D Appl. Phys. 40(7), 2189–2196 (2007).
    [Crossref]
  5. S. A. Jewell, P. Vukusic, and N. W. Roberts, “Circularly polarized colour reflection from helicoidal structures in the beetle Plusiotis boucardi,” New J. Phys. 9(4), 99 (2007).
    [Crossref]
  6. S. Lowrey, L. De Silva, I. Hodgkinson, and J. Leader, “Observation and modeling of polarized light from scarab beetles,” J. Opt. Soc. Am. A 24(8), 2418–2425 (2007).
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    [Crossref] [PubMed]
  10. D. W. Berreman and T. J. Scheffer, “Bragg reflection of light from single-domain cholesteric liquid crystal films,” Phys. Rev. Lett. 25(9), 577–581 (1970).
    [Crossref]
  11. H. Takezoe, Y. Ouchi, M. Hara, A. Fukuda, and E. Kuze, “Experimental studies of reflection spectra in monodomain cholesteric liquid crystal cells: total reflection, subsidiary oscillation and its beat or swell structure,” Jpn. J. Appl. Phys. 22(7), 1080–1091 (1983).
    [Crossref]
  12. C. Oldano, E. Miraldi, and P. Taverna Valabrega, “Comparison between measured and calculated reflectance spectra from monodomain cholesteric liquid crystal,” Jpn. J. Appl. Phys. 23(7), 802–809 (1984).
    [Crossref]
  13. W. D. S. John, W. J. Fritz, Z. J. Lu, D. Yang, and D.-K. Yang, “Bragg reflection from cholesteric liquid crystals,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 51(2), 1191–1198 (1995).
  14. A. Sugita, H. Takezoe, Y. Ouchi, A. Fukuda, E. Kuze, and N. Goto, “Numerical calculation of optical eigenmodes in cholesteric liquid crystals by 4×4 matrix method,” Jpn. J. Appl. Phys. 21(11), 1543–1546 (1982).
    [Crossref]
  15. C. Oldano, E. Miraldi, and P. Valabrega, “Dispersion relation for propagation of light in cholesteric liquid crystals,” Phys. Rev. A 27(6), 3291–3299 (1983).
    [Crossref]
  16. E. Miraldi, C. Oldano, P. I. Taverna, and L. Trossi, “Optical properties of cholesteric liquid crystals at oblique incidence,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 103(1–4), 155–176 (1983).
    [Crossref]
  17. C. Oldano, “Many-wave approximations for light propagation in cholesteric liquid crystals,” Phys. Rev. A 31(2), 1014–1021 (1985).
    [Crossref] [PubMed]
  18. 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]
  19. 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(19), 22645–22656 (2013).
    [Crossref] [PubMed]
  20. H. Arwin, L. Fernández del Río, and K. Järrendahl, “Comparison and analysis of Mueller-matrix spectra from exoskeletons of blue, green and red Cetonia aurata,” Thin Solid Films (2014), doi:.
    [Crossref]
  21. E. Muñoz-Pineda, K. Järrendahl, H. Arwin, and A. Mendoza-Galván, “Symmetries and relationships between elements of the Mueller matrix spectra of the cuticle of the beetle Cotinis mutabilis,” Thin Solid Films (2014), doi:.
    [Crossref]
  22. L. Fernández del Río, H. Arwin, and K. Järrendahl, “Polarizing properties and structural characteristics of the cuticle of the scarab Beetle Chrysina gloriosa,” Thin Solid Films (2014), doi:.
    [Crossref]
  23. C. Deloya and B. C. Ratcliffe, “Las especies de Cotinis Burmeister en México (Coleoptera: Melolonthidae: Cetoniinae),” Acta Zoologica Mex. (n.s.)  28, 1–52 (1988).
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    [Crossref]
  25. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North Holland, Amsterdam, 1977).
  26. S. Caveney, “Cuticle reflectivity and optical activity in scarab beetles: the rôle of uric acid,” Proc. R. Soc. Lond. B Biol. Sci. 178(1051), 205–225 (1971).
    [Crossref] [PubMed]
  27. M. Z. Harutyunyan, A. H. Gevorgyan, and S. A. Mkhitaryan, “Influence of dielectric boundaries, angle of incidence, and polarization of light on the optical properties of chiral photonic crystals,” J. Contemp. Phys. 42(6), 271–276 (2007).
    [Crossref]

2013 (1)

2012 (2)

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]

M. Mitov, “Cholesteric liquid crystals with a broad light reflection band,” Adv. Mater. 24(47), 6260–6276 (2012).
[Crossref] [PubMed]

2010 (1)

2007 (5)

D. J. Brink, N. G. van der Berg, L. C. Prinsloo, and I. J. Hodgkinson, “Unusual coloration in scarabaeid beetles,” J. Phys. D Appl. Phys. 40(7), 2189–2196 (2007).
[Crossref]

S. A. Jewell, P. Vukusic, and N. W. Roberts, “Circularly polarized colour reflection from helicoidal structures in the beetle Plusiotis boucardi,” New J. Phys. 9(4), 99 (2007).
[Crossref]

S. Lowrey, L. De Silva, I. Hodgkinson, and J. Leader, “Observation and modeling of polarized light from scarab beetles,” J. Opt. Soc. Am. A 24(8), 2418–2425 (2007).
[Crossref] [PubMed]

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

M. Z. Harutyunyan, A. H. Gevorgyan, and S. A. Mkhitaryan, “Influence of dielectric boundaries, angle of incidence, and polarization of light on the optical properties of chiral photonic crystals,” J. Contemp. Phys. 42(6), 271–276 (2007).
[Crossref]

2006 (1)

2003 (1)

G. De Luca and A. D. Rey, “Monodomain and polydomain helicoids in chiral liquid-crystalline phases and their biological analogues,” Eur Phys J E Soft Matter 12(2), 291–302 (2003).
[Crossref] [PubMed]

1995 (1)

W. D. S. John, W. J. Fritz, Z. J. Lu, D. Yang, and D.-K. Yang, “Bragg reflection from cholesteric liquid crystals,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 51(2), 1191–1198 (1995).

1988 (2)

A. C. Neville, “The need for a constraining layer in the formation of monodomain helicoids in a wide range of biological structures,” Tissue Cell 20(1), 133–143 (1988).
[Crossref] [PubMed]

C. Deloya and B. C. Ratcliffe, “Las especies de Cotinis Burmeister en México (Coleoptera: Melolonthidae: Cetoniinae),” Acta Zoologica Mex. (n.s.)  28, 1–52 (1988).

1985 (1)

C. Oldano, “Many-wave approximations for light propagation in cholesteric liquid crystals,” Phys. Rev. A 31(2), 1014–1021 (1985).
[Crossref] [PubMed]

1984 (1)

C. Oldano, E. Miraldi, and P. Taverna Valabrega, “Comparison between measured and calculated reflectance spectra from monodomain cholesteric liquid crystal,” Jpn. J. Appl. Phys. 23(7), 802–809 (1984).
[Crossref]

1983 (3)

H. Takezoe, Y. Ouchi, M. Hara, A. Fukuda, and E. Kuze, “Experimental studies of reflection spectra in monodomain cholesteric liquid crystal cells: total reflection, subsidiary oscillation and its beat or swell structure,” Jpn. J. Appl. Phys. 22(7), 1080–1091 (1983).
[Crossref]

C. Oldano, E. Miraldi, and P. Valabrega, “Dispersion relation for propagation of light in cholesteric liquid crystals,” Phys. Rev. A 27(6), 3291–3299 (1983).
[Crossref]

E. Miraldi, C. Oldano, P. I. Taverna, and L. Trossi, “Optical properties of cholesteric liquid crystals at oblique incidence,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 103(1–4), 155–176 (1983).
[Crossref]

1982 (1)

A. Sugita, H. Takezoe, Y. Ouchi, A. Fukuda, E. Kuze, and N. Goto, “Numerical calculation of optical eigenmodes in cholesteric liquid crystals by 4×4 matrix method,” Jpn. J. Appl. Phys. 21(11), 1543–1546 (1982).
[Crossref]

1971 (1)

S. Caveney, “Cuticle reflectivity and optical activity in scarab beetles: the rôle of uric acid,” Proc. R. Soc. Lond. B Biol. Sci. 178(1051), 205–225 (1971).
[Crossref] [PubMed]

1970 (1)

D. W. Berreman and T. J. Scheffer, “Bragg reflection of light from single-domain cholesteric liquid crystal films,” Phys. Rev. Lett. 25(9), 577–581 (1970).
[Crossref]

1969 (1)

A. C. Neville and S. Caveney, “Scarabaeid beetle exocuticle as an optical analogue of cholesteric liquid crystals,” Biol. Rev. Camb. Philos. Soc. 44(4), 531–562 (1969).
[Crossref] [PubMed]

Arwin, H.

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(19), 22645–22656 (2013).
[Crossref] [PubMed]

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]

H. Arwin, L. Fernández del Río, and K. Järrendahl, “Comparison and analysis of Mueller-matrix spectra from exoskeletons of blue, green and red Cetonia aurata,” Thin Solid Films (2014), doi:.
[Crossref]

E. Muñoz-Pineda, K. Järrendahl, H. Arwin, and A. Mendoza-Galván, “Symmetries and relationships between elements of the Mueller matrix spectra of the cuticle of the beetle Cotinis mutabilis,” Thin Solid Films (2014), doi:.
[Crossref]

L. Fernández del Río, H. Arwin, and K. Järrendahl, “Polarizing properties and structural characteristics of the cuticle of the scarab Beetle Chrysina gloriosa,” Thin Solid Films (2014), doi:.
[Crossref]

Berlind, T.

Berreman, D. W.

D. W. Berreman and T. J. Scheffer, “Bragg reflection of light from single-domain cholesteric liquid crystal films,” Phys. Rev. Lett. 25(9), 577–581 (1970).
[Crossref]

Bourke, L.

Brink, D. J.

D. J. Brink, N. G. van der Berg, L. C. Prinsloo, and I. J. Hodgkinson, “Unusual coloration in scarabaeid beetles,” J. Phys. D Appl. Phys. 40(7), 2189–2196 (2007).
[Crossref]

Caveney, S.

S. Caveney, “Cuticle reflectivity and optical activity in scarab beetles: the rôle of uric acid,” Proc. R. Soc. Lond. B Biol. Sci. 178(1051), 205–225 (1971).
[Crossref] [PubMed]

A. C. Neville and S. Caveney, “Scarabaeid beetle exocuticle as an optical analogue of cholesteric liquid crystals,” Biol. Rev. Camb. Philos. Soc. 44(4), 531–562 (1969).
[Crossref] [PubMed]

De Luca, G.

G. De Luca and A. D. Rey, “Monodomain and polydomain helicoids in chiral liquid-crystalline phases and their biological analogues,” Eur Phys J E Soft Matter 12(2), 291–302 (2003).
[Crossref] [PubMed]

De Silva, L.

Deloya, C.

C. Deloya and B. C. Ratcliffe, “Las especies de Cotinis Burmeister en México (Coleoptera: Melolonthidae: Cetoniinae),” Acta Zoologica Mex. (n.s.)  28, 1–52 (1988).

Fernández del Río, L.

H. Arwin, L. Fernández del Río, and K. Järrendahl, “Comparison and analysis of Mueller-matrix spectra from exoskeletons of blue, green and red Cetonia aurata,” Thin Solid Films (2014), doi:.
[Crossref]

L. Fernández del Río, H. Arwin, and K. Järrendahl, “Polarizing properties and structural characteristics of the cuticle of the scarab Beetle Chrysina gloriosa,” Thin Solid Films (2014), doi:.
[Crossref]

Fritz, W. J.

W. D. S. John, W. J. Fritz, Z. J. Lu, D. Yang, and D.-K. Yang, “Bragg reflection from cholesteric liquid crystals,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 51(2), 1191–1198 (1995).

Fukuda, A.

H. Takezoe, Y. Ouchi, M. Hara, A. Fukuda, and E. Kuze, “Experimental studies of reflection spectra in monodomain cholesteric liquid crystal cells: total reflection, subsidiary oscillation and its beat or swell structure,” Jpn. J. Appl. Phys. 22(7), 1080–1091 (1983).
[Crossref]

A. Sugita, H. Takezoe, Y. Ouchi, A. Fukuda, E. Kuze, and N. Goto, “Numerical calculation of optical eigenmodes in cholesteric liquid crystals by 4×4 matrix method,” Jpn. J. Appl. Phys. 21(11), 1543–1546 (1982).
[Crossref]

Gevorgyan, A. H.

M. Z. Harutyunyan, A. H. Gevorgyan, and S. A. Mkhitaryan, “Influence of dielectric boundaries, angle of incidence, and polarization of light on the optical properties of chiral photonic crystals,” J. Contemp. Phys. 42(6), 271–276 (2007).
[Crossref]

Gil, J. J.

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

Goldstein, D. H.

Goto, N.

A. Sugita, H. Takezoe, Y. Ouchi, A. Fukuda, E. Kuze, and N. Goto, “Numerical calculation of optical eigenmodes in cholesteric liquid crystals by 4×4 matrix method,” Jpn. J. Appl. Phys. 21(11), 1543–1546 (1982).
[Crossref]

Hara, M.

H. Takezoe, Y. Ouchi, M. Hara, A. Fukuda, and E. Kuze, “Experimental studies of reflection spectra in monodomain cholesteric liquid crystal cells: total reflection, subsidiary oscillation and its beat or swell structure,” Jpn. J. Appl. Phys. 22(7), 1080–1091 (1983).
[Crossref]

Harutyunyan, M. Z.

M. Z. Harutyunyan, A. H. Gevorgyan, and S. A. Mkhitaryan, “Influence of dielectric boundaries, angle of incidence, and polarization of light on the optical properties of chiral photonic crystals,” J. Contemp. Phys. 42(6), 271–276 (2007).
[Crossref]

Hodgkinson, I.

Hodgkinson, I. J.

D. J. Brink, N. G. van der Berg, L. C. Prinsloo, and I. J. Hodgkinson, “Unusual coloration in scarabaeid beetles,” J. Phys. D Appl. Phys. 40(7), 2189–2196 (2007).
[Crossref]

Järrendahl, K.

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(19), 22645–22656 (2013).
[Crossref] [PubMed]

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]

E. Muñoz-Pineda, K. Järrendahl, H. Arwin, and A. Mendoza-Galván, “Symmetries and relationships between elements of the Mueller matrix spectra of the cuticle of the beetle Cotinis mutabilis,” Thin Solid Films (2014), doi:.
[Crossref]

L. Fernández del Río, H. Arwin, and K. Järrendahl, “Polarizing properties and structural characteristics of the cuticle of the scarab Beetle Chrysina gloriosa,” Thin Solid Films (2014), doi:.
[Crossref]

H. Arwin, L. Fernández del Río, and K. Järrendahl, “Comparison and analysis of Mueller-matrix spectra from exoskeletons of blue, green and red Cetonia aurata,” Thin Solid Films (2014), doi:.
[Crossref]

Jewell, S. A.

S. A. Jewell, P. Vukusic, and N. W. Roberts, “Circularly polarized colour reflection from helicoidal structures in the beetle Plusiotis boucardi,” New J. Phys. 9(4), 99 (2007).
[Crossref]

John, W. D. S.

W. D. S. John, W. J. Fritz, Z. J. Lu, D. Yang, and D.-K. Yang, “Bragg reflection from cholesteric liquid crystals,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 51(2), 1191–1198 (1995).

Johs, B.

Kuze, E.

H. Takezoe, Y. Ouchi, M. Hara, A. Fukuda, and E. Kuze, “Experimental studies of reflection spectra in monodomain cholesteric liquid crystal cells: total reflection, subsidiary oscillation and its beat or swell structure,” Jpn. J. Appl. Phys. 22(7), 1080–1091 (1983).
[Crossref]

A. Sugita, H. Takezoe, Y. Ouchi, A. Fukuda, E. Kuze, and N. Goto, “Numerical calculation of optical eigenmodes in cholesteric liquid crystals by 4×4 matrix method,” Jpn. J. Appl. Phys. 21(11), 1543–1546 (1982).
[Crossref]

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]

Leader, J.

Lowrey, S.

Lu, Z. J.

W. D. S. John, W. J. Fritz, Z. J. Lu, D. Yang, and D.-K. Yang, “Bragg reflection from cholesteric liquid crystals,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 51(2), 1191–1198 (1995).

Magnusson, R.

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.

E. Muñoz-Pineda, K. Järrendahl, H. Arwin, and A. Mendoza-Galván, “Symmetries and relationships between elements of the Mueller matrix spectra of the cuticle of the beetle Cotinis mutabilis,” Thin Solid Films (2014), doi:.
[Crossref]

Miraldi, E.

C. Oldano, E. Miraldi, and P. Taverna Valabrega, “Comparison between measured and calculated reflectance spectra from monodomain cholesteric liquid crystal,” Jpn. J. Appl. Phys. 23(7), 802–809 (1984).
[Crossref]

C. Oldano, E. Miraldi, and P. Valabrega, “Dispersion relation for propagation of light in cholesteric liquid crystals,” Phys. Rev. A 27(6), 3291–3299 (1983).
[Crossref]

E. Miraldi, C. Oldano, P. I. Taverna, and L. Trossi, “Optical properties of cholesteric liquid crystals at oblique incidence,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 103(1–4), 155–176 (1983).
[Crossref]

Mitov, M.

M. Mitov, “Cholesteric liquid crystals with a broad light reflection band,” Adv. Mater. 24(47), 6260–6276 (2012).
[Crossref] [PubMed]

Mkhitaryan, S. A.

M. Z. Harutyunyan, A. H. Gevorgyan, and S. A. Mkhitaryan, “Influence of dielectric boundaries, angle of incidence, and polarization of light on the optical properties of chiral photonic crystals,” J. Contemp. Phys. 42(6), 271–276 (2007).
[Crossref]

Muñoz-Pineda, E.

E. Muñoz-Pineda, K. Järrendahl, H. Arwin, and A. Mendoza-Galván, “Symmetries and relationships between elements of the Mueller matrix spectra of the cuticle of the beetle Cotinis mutabilis,” Thin Solid Films (2014), doi:.
[Crossref]

Neville, A. C.

A. C. Neville, “The need for a constraining layer in the formation of monodomain helicoids in a wide range of biological structures,” Tissue Cell 20(1), 133–143 (1988).
[Crossref] [PubMed]

A. C. Neville and S. Caveney, “Scarabaeid beetle exocuticle as an optical analogue of cholesteric liquid crystals,” Biol. Rev. Camb. Philos. Soc. 44(4), 531–562 (1969).
[Crossref] [PubMed]

Oldano, C.

C. Oldano, “Many-wave approximations for light propagation in cholesteric liquid crystals,” Phys. Rev. A 31(2), 1014–1021 (1985).
[Crossref] [PubMed]

C. Oldano, E. Miraldi, and P. Taverna Valabrega, “Comparison between measured and calculated reflectance spectra from monodomain cholesteric liquid crystal,” Jpn. J. Appl. Phys. 23(7), 802–809 (1984).
[Crossref]

E. Miraldi, C. Oldano, P. I. Taverna, and L. Trossi, “Optical properties of cholesteric liquid crystals at oblique incidence,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 103(1–4), 155–176 (1983).
[Crossref]

C. Oldano, E. Miraldi, and P. Valabrega, “Dispersion relation for propagation of light in cholesteric liquid crystals,” Phys. Rev. A 27(6), 3291–3299 (1983).
[Crossref]

Ouchi, Y.

H. Takezoe, Y. Ouchi, M. Hara, A. Fukuda, and E. Kuze, “Experimental studies of reflection spectra in monodomain cholesteric liquid crystal cells: total reflection, subsidiary oscillation and its beat or swell structure,” Jpn. J. Appl. Phys. 22(7), 1080–1091 (1983).
[Crossref]

A. Sugita, H. Takezoe, Y. Ouchi, A. Fukuda, E. Kuze, and N. Goto, “Numerical calculation of optical eigenmodes in cholesteric liquid crystals by 4×4 matrix method,” Jpn. J. Appl. Phys. 21(11), 1543–1546 (1982).
[Crossref]

Parker, A.

Prinsloo, L. C.

D. J. Brink, N. G. van der Berg, L. C. Prinsloo, and I. J. Hodgkinson, “Unusual coloration in scarabaeid beetles,” J. Phys. D Appl. Phys. 40(7), 2189–2196 (2007).
[Crossref]

Ratcliffe, B. C.

C. Deloya and B. C. Ratcliffe, “Las especies de Cotinis Burmeister en México (Coleoptera: Melolonthidae: Cetoniinae),” Acta Zoologica Mex. (n.s.)  28, 1–52 (1988).

Rey, A. D.

G. De Luca and A. D. Rey, “Monodomain and polydomain helicoids in chiral liquid-crystalline phases and their biological analogues,” Eur Phys J E Soft Matter 12(2), 291–302 (2003).
[Crossref] [PubMed]

Roberts, N. W.

S. A. Jewell, P. Vukusic, and N. W. Roberts, “Circularly polarized colour reflection from helicoidal structures in the beetle Plusiotis boucardi,” New J. Phys. 9(4), 99 (2007).
[Crossref]

Scheffer, T. J.

D. W. Berreman and T. J. Scheffer, “Bragg reflection of light from single-domain cholesteric liquid crystal films,” Phys. Rev. Lett. 25(9), 577–581 (1970).
[Crossref]

Sugita, A.

A. Sugita, H. Takezoe, Y. Ouchi, A. Fukuda, E. Kuze, and N. Goto, “Numerical calculation of optical eigenmodes in cholesteric liquid crystals by 4×4 matrix method,” Jpn. J. Appl. Phys. 21(11), 1543–1546 (1982).
[Crossref]

Takezoe, H.

H. Takezoe, Y. Ouchi, M. Hara, A. Fukuda, and E. Kuze, “Experimental studies of reflection spectra in monodomain cholesteric liquid crystal cells: total reflection, subsidiary oscillation and its beat or swell structure,” Jpn. J. Appl. Phys. 22(7), 1080–1091 (1983).
[Crossref]

A. Sugita, H. Takezoe, Y. Ouchi, A. Fukuda, E. Kuze, and N. Goto, “Numerical calculation of optical eigenmodes in cholesteric liquid crystals by 4×4 matrix method,” Jpn. J. Appl. Phys. 21(11), 1543–1546 (1982).
[Crossref]

Taverna, P. I.

E. Miraldi, C. Oldano, P. I. Taverna, and L. Trossi, “Optical properties of cholesteric liquid crystals at oblique incidence,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 103(1–4), 155–176 (1983).
[Crossref]

Taverna Valabrega, P.

C. Oldano, E. Miraldi, and P. Taverna Valabrega, “Comparison between measured and calculated reflectance spectra from monodomain cholesteric liquid crystal,” Jpn. J. Appl. Phys. 23(7), 802–809 (1984).
[Crossref]

Trossi, L.

E. Miraldi, C. Oldano, P. I. Taverna, and L. Trossi, “Optical properties of cholesteric liquid crystals at oblique incidence,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 103(1–4), 155–176 (1983).
[Crossref]

Valabrega, P.

C. Oldano, E. Miraldi, and P. Valabrega, “Dispersion relation for propagation of light in cholesteric liquid crystals,” Phys. Rev. A 27(6), 3291–3299 (1983).
[Crossref]

van der Berg, N. G.

D. J. Brink, N. G. van der Berg, L. C. Prinsloo, and I. J. Hodgkinson, “Unusual coloration in scarabaeid beetles,” J. Phys. D Appl. Phys. 40(7), 2189–2196 (2007).
[Crossref]

Vukusic, P.

S. A. Jewell, P. Vukusic, and N. W. Roberts, “Circularly polarized colour reflection from helicoidal structures in the beetle Plusiotis boucardi,” New J. Phys. 9(4), 99 (2007).
[Crossref]

Yang, D.

W. D. S. John, W. J. Fritz, Z. J. Lu, D. Yang, and D.-K. Yang, “Bragg reflection from cholesteric liquid crystals,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 51(2), 1191–1198 (1995).

Yang, D.-K.

W. D. S. John, W. J. Fritz, Z. J. Lu, D. Yang, and D.-K. Yang, “Bragg reflection from cholesteric liquid crystals,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 51(2), 1191–1198 (1995).

Acta Zoologica Mex. (1)

C. Deloya and B. C. Ratcliffe, “Las especies de Cotinis Burmeister en México (Coleoptera: Melolonthidae: Cetoniinae),” Acta Zoologica Mex. (n.s.)  28, 1–52 (1988).

Adv. Mater. (1)

M. Mitov, “Cholesteric liquid crystals with a broad light reflection band,” Adv. Mater. 24(47), 6260–6276 (2012).
[Crossref] [PubMed]

Appl. Opt. (2)

Biol. Rev. Camb. Philos. Soc. (1)

A. C. Neville and S. Caveney, “Scarabaeid beetle exocuticle as an optical analogue of cholesteric liquid crystals,” Biol. Rev. Camb. Philos. Soc. 44(4), 531–562 (1969).
[Crossref] [PubMed]

Eur Phys J E Soft Matter (1)

G. De Luca and A. D. Rey, “Monodomain and polydomain helicoids in chiral liquid-crystalline phases and their biological analogues,” Eur Phys J E Soft Matter 12(2), 291–302 (2003).
[Crossref] [PubMed]

Eur. Phys. J. Appl. Phys. (1)

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

J. Contemp. Phys. (1)

M. Z. Harutyunyan, A. H. Gevorgyan, and S. A. Mkhitaryan, “Influence of dielectric boundaries, angle of incidence, and polarization of light on the optical properties of chiral photonic crystals,” J. Contemp. Phys. 42(6), 271–276 (2007).
[Crossref]

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

J. Phys. D Appl. Phys. (1)

D. J. Brink, N. G. van der Berg, L. C. Prinsloo, and I. J. Hodgkinson, “Unusual coloration in scarabaeid beetles,” J. Phys. D Appl. Phys. 40(7), 2189–2196 (2007).
[Crossref]

Jpn. J. Appl. Phys. (3)

H. Takezoe, Y. Ouchi, M. Hara, A. Fukuda, and E. Kuze, “Experimental studies of reflection spectra in monodomain cholesteric liquid crystal cells: total reflection, subsidiary oscillation and its beat or swell structure,” Jpn. J. Appl. Phys. 22(7), 1080–1091 (1983).
[Crossref]

C. Oldano, E. Miraldi, and P. Taverna Valabrega, “Comparison between measured and calculated reflectance spectra from monodomain cholesteric liquid crystal,” Jpn. J. Appl. Phys. 23(7), 802–809 (1984).
[Crossref]

A. Sugita, H. Takezoe, Y. Ouchi, A. Fukuda, E. Kuze, and N. Goto, “Numerical calculation of optical eigenmodes in cholesteric liquid crystals by 4×4 matrix method,” Jpn. J. Appl. Phys. 21(11), 1543–1546 (1982).
[Crossref]

Mol. Cryst. Liq. Cryst. (Phila. Pa.) (1)

E. Miraldi, C. Oldano, P. I. Taverna, and L. Trossi, “Optical properties of cholesteric liquid crystals at oblique incidence,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 103(1–4), 155–176 (1983).
[Crossref]

New J. Phys. (1)

S. A. Jewell, P. Vukusic, and N. W. Roberts, “Circularly polarized colour reflection from helicoidal structures in the beetle Plusiotis boucardi,” New J. Phys. 9(4), 99 (2007).
[Crossref]

Opt. 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. Rev. A (2)

C. Oldano, “Many-wave approximations for light propagation in cholesteric liquid crystals,” Phys. Rev. A 31(2), 1014–1021 (1985).
[Crossref] [PubMed]

C. Oldano, E. Miraldi, and P. Valabrega, “Dispersion relation for propagation of light in cholesteric liquid crystals,” Phys. Rev. A 27(6), 3291–3299 (1983).
[Crossref]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (1)

W. D. S. John, W. J. Fritz, Z. J. Lu, D. Yang, and D.-K. Yang, “Bragg reflection from cholesteric liquid crystals,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 51(2), 1191–1198 (1995).

Phys. Rev. Lett. (1)

D. W. Berreman and T. J. Scheffer, “Bragg reflection of light from single-domain cholesteric liquid crystal films,” Phys. Rev. Lett. 25(9), 577–581 (1970).
[Crossref]

Proc. R. Soc. Lond. B Biol. Sci. (1)

S. Caveney, “Cuticle reflectivity and optical activity in scarab beetles: the rôle of uric acid,” Proc. R. Soc. Lond. B Biol. Sci. 178(1051), 205–225 (1971).
[Crossref] [PubMed]

Tissue Cell (1)

A. C. Neville, “The need for a constraining layer in the formation of monodomain helicoids in a wide range of biological structures,” Tissue Cell 20(1), 133–143 (1988).
[Crossref] [PubMed]

Other (4)

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North Holland, Amsterdam, 1977).

H. Arwin, L. Fernández del Río, and K. Järrendahl, “Comparison and analysis of Mueller-matrix spectra from exoskeletons of blue, green and red Cetonia aurata,” Thin Solid Films (2014), doi:.
[Crossref]

E. Muñoz-Pineda, K. Järrendahl, H. Arwin, and A. Mendoza-Galván, “Symmetries and relationships between elements of the Mueller matrix spectra of the cuticle of the beetle Cotinis mutabilis,” Thin Solid Films (2014), doi:.
[Crossref]

L. Fernández del Río, H. Arwin, and K. Järrendahl, “Polarizing properties and structural characteristics of the cuticle of the scarab Beetle Chrysina gloriosa,” Thin Solid Films (2014), doi:.
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 Green specimen of C. mutabilis and SEM image of a cross section of its cuticle on the abdominal side. The epicuticle (Ep) as well as the outer (o-Ex) and inner (i-Ex) parts of the exocuticle are shown.
Fig. 2
Fig. 2 Properties of polarized light reflected from a green C. mutabilis for unpolarized incident light: (a) degree of polarization, (b) ellipticity, and (c) azimuth. The depolarizance of the Mueller matrix is shown in (d).
Fig. 3
Fig. 3 Spectral dependence of the last three elements (the polarizance vector) in the first column in the Mueller matrix of a green specimen of C. mutabilis at three angles of incidence. Notice that scales differ among the graphs.
Fig. 4
Fig. 4 (a) Spectral position of maxima and minima in m21 of a green specimen for θ between 25° and 75° in steps of 10° from left to right. Dispersion relations in Eq. (7) for θ = 25° and 75° after off-set correction for (b) the green specimen studied in this work and (c) the red specimen previously studied [21].
Fig. 5
Fig. 5 (a) Anisotropic layers with local principal components ε1, ε2, and ε3 comprising the ChNCL structure; the counter-clockwise rotation of ε1 (and ε2) around the axis of the helix (z) generates a left-handed chiral structure. (b) Wave vectors geometry for oblique incidence on a ChNLC structure; the full rotation of 360° of the principal axes defines the pitch Λ.
Fig. 6
Fig. 6 (a) Calculated dispersion relation of optical modes for a ChNLC structure of pitch Λ = 390 nm at two angles of incidence and refractive indices n1 = 1.58, n2 = n3 = 1.5; (b) magnification near the spectral range of Bragg-like reflection for three angles of incidence; (c) attenuation lengths for the mode k2 producing selective reflection. The two modes of the normalized complex wave vector k = k´ + ik´´ are represented with the continuous and dashed lines.
Fig. 7
Fig. 7 (a) Schematics of wave propagation in a ChNLC-like structure with two chiral stacks of pitches Λ1 and Λ2 and of thicknesses d1 and d2. (b) and (c) Real part of the wave vector of the optical mode producing Bragg-like reflection at angles of incidence 25° and 75°, respectively; (d) and (e) show the corresponding attenuation lengths. The dispersion relations were calculated for semi-infinite uniaxial structures with pitches Λ = 390 and 360 nm and refractive indices n1 = 1.58 and n2 = n3 = 1.5.

Equations (13)

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M=[ m 11 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 ],
S=[ I p + I s I p I s I +45º I 45º I R I L ],
P= m 21 2 + m 31 2 + m 41 2 .
e=tan( 1 2 arcsin m 41 m 21 2 + m 31 2 + m 41 2 ),
φ= 1 2 arctan( m 31 m 21 ).
D=1| [ 1 3 ( tr( M T M ) m 11 2 1 ) ] 1/2 |.
β = 2 K | | d = 4 π d λ n a v 2 n i 2 sin 2 θ = m π ,
k a = Λ 2 λ ε m ε 3 ε 3 n i 2 sin 2 θ k b = Λ 2 λ ε m n i 2 sin 2 θ
( x 2 X a 2 )( x 2 X b 2 )( x 2 x a 2 )( x 2 x b 2 ) c 2 a ' 2 ( x 2 X c 2 )( x 2 x c 2 )=0,
x=k1/2 , x a,b,c = k a,b,c 1/2 , X a,b,c = k a,b,c +1/2 ,
a´= 1 2 2 ε 3 n i 2 sin 2 θ ε 3 ε 3 n i 2 sin 2 θ , c= ( ε 1 ε 2 ) Λ 2 8 λ 2 ε 3 ε 3 n i 2 sin 2 θ , k c = ( k a 2 + k b 2 ) ε 3 k b 2 n i 2 sin 2 θ 2 ε 3 n i 2 sin 2 θ .
β I =2 K 1,|| d 1 +2 K 2,|| d 2 .
β III =2 K 1,|| d 1 +2 K 2,|| η 2 .

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