Abstract

An approach for simulation of light scattering from beetles exhibiting structural colors originating from periodic helicoidal structures is presented. Slight irregularities of the periodic structure in the exoskeleton of the beetles are considered as a major cause of light scattering. Two sources of scattering are taken into account: surface roughness and volume non-uniformity. The Kirchhoff approximation is applied to simulate the effect of surface roughness. To describe volume non-uniformity, the whole structure is modeled as a set of domains distributed in space in different orientations. Each domain is modeled as an ideal uniformly twisted uniaxial medium and differs from each other by the pitch. Distributions of the domain parameters are assumed to be Gaussian. The analysis is performed using the Mueller matrix formalism which, in addition to spectral and spatial characteristics, also provides polarization properties of the scattered light.

© 2016 Optical Society of America

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References

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  1. A. A. Michelson, “On metallic colouring in birds and insects,” Philos. Mag. 21(124), 554–567 (1911).
    [Crossref]
  2. C. W. Mason, “Structural colors in Insects. I,” J. Phys. Chem. 30(3), 383–395 (1925).
    [Crossref]
  3. C. W. Mason, “Structural colors in Insects. II,” J. Phys. Chem. 31(3), 321–354 (1926).
    [Crossref]
  4. T. F. Anderson and A. G. Richards, “An electron microscope study of some structural colors of insects,” J. Appl. Phys. 13(12), 748–758 (1942).
    [Crossref]
  5. 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]
  6. V. Sharma, M. Crne, J. O. Park, and M. Srinivasarao, “Structural origin of circularly polarized iridescence in jeweled beetles,” Science 325(5939), 449–451 (2009).
    [Crossref] [PubMed]
  7. 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(99), 1–10 (2007).
  8. A. E. Seago, P. Brady, J.-P. Vigneron, and T. D. Schultz, “Gold bugs and beyond: a review of iridescence and structural colour mechanisms in beetles (Coleoptera),” J. R. Soc. Interface 6(2), S165–S184 (2009).
    [Crossref] [PubMed]
  9. D. Mckenzie, M. Large, and M. C. J. Large, “Multilayer reflectors in animals using green and gold beetles as contrasting examples,” J. Exp. Biol. 201(Pt 9), 1307–1313 (1998).
    [PubMed]
  10. 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]
  11. 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 571, 410–415 (2014).
    [Crossref]
  12. C. Åkerlind, H. Arwin, T. Hallberg, J. Landin, J. Gustafsson, H. Kariis, and K. Järrendahl, “Scattering and polarization properties of the scarab beetle Cyphochilus insulanus cuticle,” Appl. Opt. 54(19), 6037–6045 (2015).
    [Crossref] [PubMed]
  13. D. G. Stavenga, B. D. Wilts, H. L. Leertouwer, and T. Hariyama, “Polarized iridescence of the multilayered elytra of the Japanese jewel beetle, Chrysochroa fulgidissima,” Philos. Trans. R. Soc. Lond. B Biol. Sci. 366(1565), 709–723 (2011).
    [Crossref] [PubMed]
  14. V. Sharma, M. Crne, J. O. Park, and M. Srinivasarao, “Bouligand Structures Underlie Circularly Polarized Iridescence of Scarab Beetles: A Closer View,” Materials Today: Proceedings 1, 161–171 (2014).
    [Crossref]
  15. S. Yoshioka and S. Kinoshita, “Direct determination of the refractive index of natural multilayer systems,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(5), 051917 (2011).
    [Crossref] [PubMed]
  16. O. Deparis, C. Vandenbem, M. Rassart, V. Welch, and J.-P. Vigneron, “Color-selecting reflectors inspired from biological periodic multilayer structures,” Opt. Express 14(8), 3547–3555 (2006).
    [Crossref] [PubMed]
  17. M. Saba, B. D. Wilts, J. Hielschera, and G. E. Schroder-Turk, “Absence of circular polarisation in reflections of butterfly wing scales with chiral Gyroid structure,” Materials Today: Proceedings 1, 193–208 (2014).
    [Crossref]
  18. V. A. Belyakov, Diffraction Optics of Complex-Structured Periodic Media (Springer, 1992).
  19. 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).
    [Crossref] [PubMed]
  20. W. A. Goddard III, D. Brenner, S. E. Lyshevski, and G. J. Iafrate, Handbook of Nanoscience, Engineering, and Technology (3ed.) (CRC Press, 2012).
  21. M. F. Cohen and J. R. Wallace, Radiosity and Realistic Image Synthesis (Academic Press, 1993).
  22. E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekker, 1992).
  23. H. Motulsky, Intuitive Biostatistics: A Nonmathematical Guide to Statistical Thinking (Oxford University, 2013).
  24. T. G. Mackay and A. Lakhtakia, Electromagnetic Anisotropy and Bianisotropy: A Field Guide, First edition (World Scientific, 2010).
  25. J. A. Ogilvy, “Wave scattering from rough surfaces,” Rep. Prog. Phys. 50(12), 1553–1608 (1987).
    [Crossref]
  26. K. Sarabandi and T. Chiu, “Electromagnetic scattering from slightly rough surfaces with inhomogeneous dielectric profile,” IEEE Trans. Antenn. Propag. 45(9), 1419–1430 (1997).
    [Crossref]
  27. M. Schubert, “Polarization-dependent optical parameters of arbitrarily anisotropic homogeneous layered systems,” Phys. Rev. B Condens. Matter 53(8), 4265–4274 (1996).
    [Crossref] [PubMed]
  28. P. Yeh, Optical Waves in Layered Media (Wiley, 2005).
  29. R. Hegedüs, G. Szél, and G. Horváth, “Imaging polarimetry of the circularly polarizing cuticle of scarab beetles (Coleoptera: Rutelidae, Cetoniidae),” Vision Res. 46(17), 2786–2797 (2006).
    [Crossref] [PubMed]
  30. 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(24), 4558–4567 (2010).
    [Crossref] [PubMed]
  31. G. Thullier, M. Herse, D. Labs, T. Foujols, W. Peetermans, D. Gillotay, P. C. Simon, and H. Mandel, “The solar spectral irradiance from 200 to 2400 nm as measured by the solspec spectrometer from the atlas and eureka missions,” Sol. Phys. 214(1), 1–22 (2003).
    [Crossref]
  32. Z. Montiel-González, G. Luna-Bárcenas, and A. Mendoza-Galván, “Thermal behaviour of chitosan and chitin thin films studied by spectroscopic ellipsometry,” phys. Stat. Sol. 5, 1434–1437 (2008).
  33. L. De Silva, I. Hodgkinson, P. Murray, Q. H. Wu, M. Arnold, J. Leader, and A. Mcnaughton, “Natural and Nanoengineered Chiral Reflectors: Structural Color of Manuka Beetles and Titania Coatings,” Electromagnetics 25(5), 391–408 (2005).
    [Crossref]

2015 (1)

2014 (3)

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 571, 410–415 (2014).
[Crossref]

V. Sharma, M. Crne, J. O. Park, and M. Srinivasarao, “Bouligand Structures Underlie Circularly Polarized Iridescence of Scarab Beetles: A Closer View,” Materials Today: Proceedings 1, 161–171 (2014).
[Crossref]

M. Saba, B. D. Wilts, J. Hielschera, and G. E. Schroder-Turk, “Absence of circular polarisation in reflections of butterfly wing scales with chiral Gyroid structure,” Materials Today: Proceedings 1, 193–208 (2014).
[Crossref]

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 (2)

D. G. Stavenga, B. D. Wilts, H. L. Leertouwer, and T. Hariyama, “Polarized iridescence of the multilayered elytra of the Japanese jewel beetle, Chrysochroa fulgidissima,” Philos. Trans. R. Soc. Lond. B Biol. Sci. 366(1565), 709–723 (2011).
[Crossref] [PubMed]

S. Yoshioka and S. Kinoshita, “Direct determination of the refractive index of natural multilayer systems,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(5), 051917 (2011).
[Crossref] [PubMed]

2010 (1)

2009 (2)

V. Sharma, M. Crne, J. O. Park, and M. Srinivasarao, “Structural origin of circularly polarized iridescence in jeweled beetles,” Science 325(5939), 449–451 (2009).
[Crossref] [PubMed]

A. E. Seago, P. Brady, J.-P. Vigneron, and T. D. Schultz, “Gold bugs and beyond: a review of iridescence and structural colour mechanisms in beetles (Coleoptera),” J. R. Soc. Interface 6(2), S165–S184 (2009).
[Crossref] [PubMed]

2008 (1)

Z. Montiel-González, G. Luna-Bárcenas, and A. Mendoza-Galván, “Thermal behaviour of chitosan and chitin thin films studied by spectroscopic ellipsometry,” phys. Stat. Sol. 5, 1434–1437 (2008).

2007 (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(99), 1–10 (2007).

2006 (2)

O. Deparis, C. Vandenbem, M. Rassart, V. Welch, and J.-P. Vigneron, “Color-selecting reflectors inspired from biological periodic multilayer structures,” Opt. Express 14(8), 3547–3555 (2006).
[Crossref] [PubMed]

R. Hegedüs, G. Szél, and G. Horváth, “Imaging polarimetry of the circularly polarizing cuticle of scarab beetles (Coleoptera: Rutelidae, Cetoniidae),” Vision Res. 46(17), 2786–2797 (2006).
[Crossref] [PubMed]

2005 (1)

L. De Silva, I. Hodgkinson, P. Murray, Q. H. Wu, M. Arnold, J. Leader, and A. Mcnaughton, “Natural and Nanoengineered Chiral Reflectors: Structural Color of Manuka Beetles and Titania Coatings,” Electromagnetics 25(5), 391–408 (2005).
[Crossref]

2003 (1)

G. Thullier, M. Herse, D. Labs, T. Foujols, W. Peetermans, D. Gillotay, P. C. Simon, and H. Mandel, “The solar spectral irradiance from 200 to 2400 nm as measured by the solspec spectrometer from the atlas and eureka missions,” Sol. Phys. 214(1), 1–22 (2003).
[Crossref]

1998 (1)

D. Mckenzie, M. Large, and M. C. J. Large, “Multilayer reflectors in animals using green and gold beetles as contrasting examples,” J. Exp. Biol. 201(Pt 9), 1307–1313 (1998).
[PubMed]

1997 (1)

K. Sarabandi and T. Chiu, “Electromagnetic scattering from slightly rough surfaces with inhomogeneous dielectric profile,” IEEE Trans. Antenn. Propag. 45(9), 1419–1430 (1997).
[Crossref]

1996 (1)

M. Schubert, “Polarization-dependent optical parameters of arbitrarily anisotropic homogeneous layered systems,” Phys. Rev. B Condens. Matter 53(8), 4265–4274 (1996).
[Crossref] [PubMed]

1995 (1)

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).
[Crossref] [PubMed]

1987 (1)

J. A. Ogilvy, “Wave scattering from rough surfaces,” Rep. Prog. Phys. 50(12), 1553–1608 (1987).
[Crossref]

1942 (1)

T. F. Anderson and A. G. Richards, “An electron microscope study of some structural colors of insects,” J. Appl. Phys. 13(12), 748–758 (1942).
[Crossref]

1926 (1)

C. W. Mason, “Structural colors in Insects. II,” J. Phys. Chem. 31(3), 321–354 (1926).
[Crossref]

1925 (1)

C. W. Mason, “Structural colors in Insects. I,” J. Phys. Chem. 30(3), 383–395 (1925).
[Crossref]

1911 (1)

A. A. Michelson, “On metallic colouring in birds and insects,” Philos. Mag. 21(124), 554–567 (1911).
[Crossref]

Åkerlind, C.

Anderson, T. F.

T. F. Anderson and A. G. Richards, “An electron microscope study of some structural colors of insects,” J. Appl. Phys. 13(12), 748–758 (1942).
[Crossref]

Arnold, M.

L. De Silva, I. Hodgkinson, P. Murray, Q. H. Wu, M. Arnold, J. Leader, and A. Mcnaughton, “Natural and Nanoengineered Chiral Reflectors: Structural Color of Manuka Beetles and Titania Coatings,” Electromagnetics 25(5), 391–408 (2005).
[Crossref]

Arwin, H.

C. Åkerlind, H. Arwin, T. Hallberg, J. Landin, J. Gustafsson, H. Kariis, and K. Järrendahl, “Scattering and polarization properties of the scarab beetle Cyphochilus insulanus cuticle,” Appl. Opt. 54(19), 6037–6045 (2015).
[Crossref] [PubMed]

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 571, 410–415 (2014).
[Crossref]

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]

Berlind, T.

Bourke, L.

Brady, P.

A. E. Seago, P. Brady, J.-P. Vigneron, and T. D. Schultz, “Gold bugs and beyond: a review of iridescence and structural colour mechanisms in beetles (Coleoptera),” J. R. Soc. Interface 6(2), S165–S184 (2009).
[Crossref] [PubMed]

Chiu, T.

K. Sarabandi and T. Chiu, “Electromagnetic scattering from slightly rough surfaces with inhomogeneous dielectric profile,” IEEE Trans. Antenn. Propag. 45(9), 1419–1430 (1997).
[Crossref]

Crne, M.

V. Sharma, M. Crne, J. O. Park, and M. Srinivasarao, “Bouligand Structures Underlie Circularly Polarized Iridescence of Scarab Beetles: A Closer View,” Materials Today: Proceedings 1, 161–171 (2014).
[Crossref]

V. Sharma, M. Crne, J. O. Park, and M. Srinivasarao, “Structural origin of circularly polarized iridescence in jeweled beetles,” Science 325(5939), 449–451 (2009).
[Crossref] [PubMed]

De Silva, L.

L. De Silva, I. Hodgkinson, P. Murray, Q. H. Wu, M. Arnold, J. Leader, and A. Mcnaughton, “Natural and Nanoengineered Chiral Reflectors: Structural Color of Manuka Beetles and Titania Coatings,” Electromagnetics 25(5), 391–408 (2005).
[Crossref]

Deparis, O.

Fernández del Río, L.

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 571, 410–415 (2014).
[Crossref]

Foujols, T.

G. Thullier, M. Herse, D. Labs, T. Foujols, W. Peetermans, D. Gillotay, P. C. Simon, and H. Mandel, “The solar spectral irradiance from 200 to 2400 nm as measured by the solspec spectrometer from the atlas and eureka missions,” Sol. Phys. 214(1), 1–22 (2003).
[Crossref]

Fritz, W. J.

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).
[Crossref] [PubMed]

Gillotay, D.

G. Thullier, M. Herse, D. Labs, T. Foujols, W. Peetermans, D. Gillotay, P. C. Simon, and H. Mandel, “The solar spectral irradiance from 200 to 2400 nm as measured by the solspec spectrometer from the atlas and eureka missions,” Sol. Phys. 214(1), 1–22 (2003).
[Crossref]

Gustafsson, J.

Hallberg, T.

Hariyama, T.

D. G. Stavenga, B. D. Wilts, H. L. Leertouwer, and T. Hariyama, “Polarized iridescence of the multilayered elytra of the Japanese jewel beetle, Chrysochroa fulgidissima,” Philos. Trans. R. Soc. Lond. B Biol. Sci. 366(1565), 709–723 (2011).
[Crossref] [PubMed]

Hegedüs, R.

R. Hegedüs, G. Szél, and G. Horváth, “Imaging polarimetry of the circularly polarizing cuticle of scarab beetles (Coleoptera: Rutelidae, Cetoniidae),” Vision Res. 46(17), 2786–2797 (2006).
[Crossref] [PubMed]

Herse, M.

G. Thullier, M. Herse, D. Labs, T. Foujols, W. Peetermans, D. Gillotay, P. C. Simon, and H. Mandel, “The solar spectral irradiance from 200 to 2400 nm as measured by the solspec spectrometer from the atlas and eureka missions,” Sol. Phys. 214(1), 1–22 (2003).
[Crossref]

Hielschera, J.

M. Saba, B. D. Wilts, J. Hielschera, and G. E. Schroder-Turk, “Absence of circular polarisation in reflections of butterfly wing scales with chiral Gyroid structure,” Materials Today: Proceedings 1, 193–208 (2014).
[Crossref]

Hodgkinson, I.

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(24), 4558–4567 (2010).
[Crossref] [PubMed]

L. De Silva, I. Hodgkinson, P. Murray, Q. H. Wu, M. Arnold, J. Leader, and A. Mcnaughton, “Natural and Nanoengineered Chiral Reflectors: Structural Color of Manuka Beetles and Titania Coatings,” Electromagnetics 25(5), 391–408 (2005).
[Crossref]

Horváth, G.

R. Hegedüs, G. Szél, and G. Horváth, “Imaging polarimetry of the circularly polarizing cuticle of scarab beetles (Coleoptera: Rutelidae, Cetoniidae),” Vision Res. 46(17), 2786–2797 (2006).
[Crossref] [PubMed]

Järrendahl, K.

C. Åkerlind, H. Arwin, T. Hallberg, J. Landin, J. Gustafsson, H. Kariis, and K. Järrendahl, “Scattering and polarization properties of the scarab beetle Cyphochilus insulanus cuticle,” Appl. Opt. 54(19), 6037–6045 (2015).
[Crossref] [PubMed]

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 571, 410–415 (2014).
[Crossref]

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]

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(99), 1–10 (2007).

Johs, B.

Kariis, H.

Kinoshita, S.

S. Yoshioka and S. Kinoshita, “Direct determination of the refractive index of natural multilayer systems,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(5), 051917 (2011).
[Crossref] [PubMed]

Labs, D.

G. Thullier, M. Herse, D. Labs, T. Foujols, W. Peetermans, D. Gillotay, P. C. Simon, and H. Mandel, “The solar spectral irradiance from 200 to 2400 nm as measured by the solspec spectrometer from the atlas and eureka missions,” Sol. Phys. 214(1), 1–22 (2003).
[Crossref]

Landin, J.

C. Åkerlind, H. Arwin, T. Hallberg, J. Landin, J. Gustafsson, H. Kariis, and K. Järrendahl, “Scattering and polarization properties of the scarab beetle Cyphochilus insulanus cuticle,” Appl. Opt. 54(19), 6037–6045 (2015).
[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]

Large, M.

D. Mckenzie, M. Large, and M. C. J. Large, “Multilayer reflectors in animals using green and gold beetles as contrasting examples,” J. Exp. Biol. 201(Pt 9), 1307–1313 (1998).
[PubMed]

Large, M. C. J.

D. Mckenzie, M. Large, and M. C. J. Large, “Multilayer reflectors in animals using green and gold beetles as contrasting examples,” J. Exp. Biol. 201(Pt 9), 1307–1313 (1998).
[PubMed]

Leader, J.

L. De Silva, I. Hodgkinson, P. Murray, Q. H. Wu, M. Arnold, J. Leader, and A. Mcnaughton, “Natural and Nanoengineered Chiral Reflectors: Structural Color of Manuka Beetles and Titania Coatings,” Electromagnetics 25(5), 391–408 (2005).
[Crossref]

Leertouwer, H. L.

D. G. Stavenga, B. D. Wilts, H. L. Leertouwer, and T. Hariyama, “Polarized iridescence of the multilayered elytra of the Japanese jewel beetle, Chrysochroa fulgidissima,” Philos. Trans. R. Soc. Lond. B Biol. Sci. 366(1565), 709–723 (2011).
[Crossref] [PubMed]

Lowrey, S.

Lu, Z. J.

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).
[Crossref] [PubMed]

Luna-Bárcenas, G.

Z. Montiel-González, G. Luna-Bárcenas, and A. Mendoza-Galván, “Thermal behaviour of chitosan and chitin thin films studied by spectroscopic ellipsometry,” phys. Stat. Sol. 5, 1434–1437 (2008).

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]

Mandel, H.

G. Thullier, M. Herse, D. Labs, T. Foujols, W. Peetermans, D. Gillotay, P. C. Simon, and H. Mandel, “The solar spectral irradiance from 200 to 2400 nm as measured by the solspec spectrometer from the atlas and eureka missions,” Sol. Phys. 214(1), 1–22 (2003).
[Crossref]

Mason, C. W.

C. W. Mason, “Structural colors in Insects. II,” J. Phys. Chem. 31(3), 321–354 (1926).
[Crossref]

C. W. Mason, “Structural colors in Insects. I,” J. Phys. Chem. 30(3), 383–395 (1925).
[Crossref]

McCall, M. W.

Mckenzie, D.

D. Mckenzie, M. Large, and M. C. J. Large, “Multilayer reflectors in animals using green and gold beetles as contrasting examples,” J. Exp. Biol. 201(Pt 9), 1307–1313 (1998).
[PubMed]

Mcnaughton, A.

L. De Silva, I. Hodgkinson, P. Murray, Q. H. Wu, M. Arnold, J. Leader, and A. Mcnaughton, “Natural and Nanoengineered Chiral Reflectors: Structural Color of Manuka Beetles and Titania Coatings,” Electromagnetics 25(5), 391–408 (2005).
[Crossref]

Mendoza-Galván, A.

Z. Montiel-González, G. Luna-Bárcenas, and A. Mendoza-Galván, “Thermal behaviour of chitosan and chitin thin films studied by spectroscopic ellipsometry,” phys. Stat. Sol. 5, 1434–1437 (2008).

Michelson, A. A.

A. A. Michelson, “On metallic colouring in birds and insects,” Philos. Mag. 21(124), 554–567 (1911).
[Crossref]

Montiel-González, Z.

Z. Montiel-González, G. Luna-Bárcenas, and A. Mendoza-Galván, “Thermal behaviour of chitosan and chitin thin films studied by spectroscopic ellipsometry,” phys. Stat. Sol. 5, 1434–1437 (2008).

Murray, P.

L. De Silva, I. Hodgkinson, P. Murray, Q. H. Wu, M. Arnold, J. Leader, and A. Mcnaughton, “Natural and Nanoengineered Chiral Reflectors: Structural Color of Manuka Beetles and Titania Coatings,” Electromagnetics 25(5), 391–408 (2005).
[Crossref]

Ogilvy, J. A.

J. A. Ogilvy, “Wave scattering from rough surfaces,” Rep. Prog. Phys. 50(12), 1553–1608 (1987).
[Crossref]

Park, J. O.

V. Sharma, M. Crne, J. O. Park, and M. Srinivasarao, “Bouligand Structures Underlie Circularly Polarized Iridescence of Scarab Beetles: A Closer View,” Materials Today: Proceedings 1, 161–171 (2014).
[Crossref]

V. Sharma, M. Crne, J. O. Park, and M. Srinivasarao, “Structural origin of circularly polarized iridescence in jeweled beetles,” Science 325(5939), 449–451 (2009).
[Crossref] [PubMed]

Parker, A.

Peetermans, W.

G. Thullier, M. Herse, D. Labs, T. Foujols, W. Peetermans, D. Gillotay, P. C. Simon, and H. Mandel, “The solar spectral irradiance from 200 to 2400 nm as measured by the solspec spectrometer from the atlas and eureka missions,” Sol. Phys. 214(1), 1–22 (2003).
[Crossref]

Rassart, M.

Richards, A. G.

T. F. Anderson and A. G. Richards, “An electron microscope study of some structural colors of insects,” J. Appl. Phys. 13(12), 748–758 (1942).
[Crossref]

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(99), 1–10 (2007).

Saba, M.

M. Saba, B. D. Wilts, J. Hielschera, and G. E. Schroder-Turk, “Absence of circular polarisation in reflections of butterfly wing scales with chiral Gyroid structure,” Materials Today: Proceedings 1, 193–208 (2014).
[Crossref]

Sarabandi, K.

K. Sarabandi and T. Chiu, “Electromagnetic scattering from slightly rough surfaces with inhomogeneous dielectric profile,” IEEE Trans. Antenn. Propag. 45(9), 1419–1430 (1997).
[Crossref]

Schroder-Turk, G. E.

M. Saba, B. D. Wilts, J. Hielschera, and G. E. Schroder-Turk, “Absence of circular polarisation in reflections of butterfly wing scales with chiral Gyroid structure,” Materials Today: Proceedings 1, 193–208 (2014).
[Crossref]

Schubert, M.

M. Schubert, “Polarization-dependent optical parameters of arbitrarily anisotropic homogeneous layered systems,” Phys. Rev. B Condens. Matter 53(8), 4265–4274 (1996).
[Crossref] [PubMed]

Schultz, T. D.

A. E. Seago, P. Brady, J.-P. Vigneron, and T. D. Schultz, “Gold bugs and beyond: a review of iridescence and structural colour mechanisms in beetles (Coleoptera),” J. R. Soc. Interface 6(2), S165–S184 (2009).
[Crossref] [PubMed]

Seago, A. E.

A. E. Seago, P. Brady, J.-P. Vigneron, and T. D. Schultz, “Gold bugs and beyond: a review of iridescence and structural colour mechanisms in beetles (Coleoptera),” J. R. Soc. Interface 6(2), S165–S184 (2009).
[Crossref] [PubMed]

Sharma, V.

V. Sharma, M. Crne, J. O. Park, and M. Srinivasarao, “Bouligand Structures Underlie Circularly Polarized Iridescence of Scarab Beetles: A Closer View,” Materials Today: Proceedings 1, 161–171 (2014).
[Crossref]

V. Sharma, M. Crne, J. O. Park, and M. Srinivasarao, “Structural origin of circularly polarized iridescence in jeweled beetles,” Science 325(5939), 449–451 (2009).
[Crossref] [PubMed]

Simon, P. C.

G. Thullier, M. Herse, D. Labs, T. Foujols, W. Peetermans, D. Gillotay, P. C. Simon, and H. Mandel, “The solar spectral irradiance from 200 to 2400 nm as measured by the solspec spectrometer from the atlas and eureka missions,” Sol. Phys. 214(1), 1–22 (2003).
[Crossref]

Srinivasarao, M.

V. Sharma, M. Crne, J. O. Park, and M. Srinivasarao, “Bouligand Structures Underlie Circularly Polarized Iridescence of Scarab Beetles: A Closer View,” Materials Today: Proceedings 1, 161–171 (2014).
[Crossref]

V. Sharma, M. Crne, J. O. Park, and M. Srinivasarao, “Structural origin of circularly polarized iridescence in jeweled beetles,” Science 325(5939), 449–451 (2009).
[Crossref] [PubMed]

Stavenga, D. G.

D. G. Stavenga, B. D. Wilts, H. L. Leertouwer, and T. Hariyama, “Polarized iridescence of the multilayered elytra of the Japanese jewel beetle, Chrysochroa fulgidissima,” Philos. Trans. R. Soc. Lond. B Biol. Sci. 366(1565), 709–723 (2011).
[Crossref] [PubMed]

Szél, G.

R. Hegedüs, G. Szél, and G. Horváth, “Imaging polarimetry of the circularly polarizing cuticle of scarab beetles (Coleoptera: Rutelidae, Cetoniidae),” Vision Res. 46(17), 2786–2797 (2006).
[Crossref] [PubMed]

Thullier, G.

G. Thullier, M. Herse, D. Labs, T. Foujols, W. Peetermans, D. Gillotay, P. C. Simon, and H. Mandel, “The solar spectral irradiance from 200 to 2400 nm as measured by the solspec spectrometer from the atlas and eureka missions,” Sol. Phys. 214(1), 1–22 (2003).
[Crossref]

Vandenbem, C.

Vigneron, J.-P.

A. E. Seago, P. Brady, J.-P. Vigneron, and T. D. Schultz, “Gold bugs and beyond: a review of iridescence and structural colour mechanisms in beetles (Coleoptera),” J. R. Soc. Interface 6(2), S165–S184 (2009).
[Crossref] [PubMed]

O. Deparis, C. Vandenbem, M. Rassart, V. Welch, and J.-P. Vigneron, “Color-selecting reflectors inspired from biological periodic multilayer structures,” Opt. Express 14(8), 3547–3555 (2006).
[Crossref] [PubMed]

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(99), 1–10 (2007).

Welch, V.

Wilts, B. D.

M. Saba, B. D. Wilts, J. Hielschera, and G. E. Schroder-Turk, “Absence of circular polarisation in reflections of butterfly wing scales with chiral Gyroid structure,” Materials Today: Proceedings 1, 193–208 (2014).
[Crossref]

D. G. Stavenga, B. D. Wilts, H. L. Leertouwer, and T. Hariyama, “Polarized iridescence of the multilayered elytra of the Japanese jewel beetle, Chrysochroa fulgidissima,” Philos. Trans. R. Soc. Lond. B Biol. Sci. 366(1565), 709–723 (2011).
[Crossref] [PubMed]

Wu, Q. H.

L. De Silva, I. Hodgkinson, P. Murray, Q. H. Wu, M. Arnold, J. Leader, and A. Mcnaughton, “Natural and Nanoengineered Chiral Reflectors: Structural Color of Manuka Beetles and Titania Coatings,” Electromagnetics 25(5), 391–408 (2005).
[Crossref]

Yang, D.

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).
[Crossref] [PubMed]

Yang, D.-K.

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).
[Crossref] [PubMed]

Yoshioka, S.

S. Yoshioka and S. Kinoshita, “Direct determination of the refractive index of natural multilayer systems,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(5), 051917 (2011).
[Crossref] [PubMed]

Appl. Opt. (2)

Electromagnetics (1)

L. De Silva, I. Hodgkinson, P. Murray, Q. H. Wu, M. Arnold, J. Leader, and A. Mcnaughton, “Natural and Nanoengineered Chiral Reflectors: Structural Color of Manuka Beetles and Titania Coatings,” Electromagnetics 25(5), 391–408 (2005).
[Crossref]

IEEE Trans. Antenn. Propag. (1)

K. Sarabandi and T. Chiu, “Electromagnetic scattering from slightly rough surfaces with inhomogeneous dielectric profile,” IEEE Trans. Antenn. Propag. 45(9), 1419–1430 (1997).
[Crossref]

J. Appl. Phys. (1)

T. F. Anderson and A. G. Richards, “An electron microscope study of some structural colors of insects,” J. Appl. Phys. 13(12), 748–758 (1942).
[Crossref]

J. Exp. Biol. (1)

D. Mckenzie, M. Large, and M. C. J. Large, “Multilayer reflectors in animals using green and gold beetles as contrasting examples,” J. Exp. Biol. 201(Pt 9), 1307–1313 (1998).
[PubMed]

J. Phys. Chem. (2)

C. W. Mason, “Structural colors in Insects. I,” J. Phys. Chem. 30(3), 383–395 (1925).
[Crossref]

C. W. Mason, “Structural colors in Insects. II,” J. Phys. Chem. 31(3), 321–354 (1926).
[Crossref]

J. R. Soc. Interface (1)

A. E. Seago, P. Brady, J.-P. Vigneron, and T. D. Schultz, “Gold bugs and beyond: a review of iridescence and structural colour mechanisms in beetles (Coleoptera),” J. R. Soc. Interface 6(2), S165–S184 (2009).
[Crossref] [PubMed]

Materials Today: Proceedings (2)

M. Saba, B. D. Wilts, J. Hielschera, and G. E. Schroder-Turk, “Absence of circular polarisation in reflections of butterfly wing scales with chiral Gyroid structure,” Materials Today: Proceedings 1, 193–208 (2014).
[Crossref]

V. Sharma, M. Crne, J. O. Park, and M. Srinivasarao, “Bouligand Structures Underlie Circularly Polarized Iridescence of Scarab Beetles: A Closer View,” Materials Today: Proceedings 1, 161–171 (2014).
[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(99), 1–10 (2007).

Opt. Express (2)

Philos. Mag. (2)

A. A. Michelson, “On metallic colouring in birds and insects,” Philos. Mag. 21(124), 554–567 (1911).
[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]

Philos. Trans. R. Soc. Lond. B Biol. Sci. (1)

D. G. Stavenga, B. D. Wilts, H. L. Leertouwer, and T. Hariyama, “Polarized iridescence of the multilayered elytra of the Japanese jewel beetle, Chrysochroa fulgidissima,” Philos. Trans. R. Soc. Lond. B Biol. Sci. 366(1565), 709–723 (2011).
[Crossref] [PubMed]

Phys. Rev. B Condens. Matter (1)

M. Schubert, “Polarization-dependent optical parameters of arbitrarily anisotropic homogeneous layered systems,” Phys. Rev. B Condens. Matter 53(8), 4265–4274 (1996).
[Crossref] [PubMed]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

S. Yoshioka and S. Kinoshita, “Direct determination of the refractive index of natural multilayer systems,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(5), 051917 (2011).
[Crossref] [PubMed]

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

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).
[Crossref] [PubMed]

phys. Stat. Sol. (1)

Z. Montiel-González, G. Luna-Bárcenas, and A. Mendoza-Galván, “Thermal behaviour of chitosan and chitin thin films studied by spectroscopic ellipsometry,” phys. Stat. Sol. 5, 1434–1437 (2008).

Rep. Prog. Phys. (1)

J. A. Ogilvy, “Wave scattering from rough surfaces,” Rep. Prog. Phys. 50(12), 1553–1608 (1987).
[Crossref]

Science (1)

V. Sharma, M. Crne, J. O. Park, and M. Srinivasarao, “Structural origin of circularly polarized iridescence in jeweled beetles,” Science 325(5939), 449–451 (2009).
[Crossref] [PubMed]

Sol. Phys. (1)

G. Thullier, M. Herse, D. Labs, T. Foujols, W. Peetermans, D. Gillotay, P. C. Simon, and H. Mandel, “The solar spectral irradiance from 200 to 2400 nm as measured by the solspec spectrometer from the atlas and eureka missions,” Sol. Phys. 214(1), 1–22 (2003).
[Crossref]

Thin Solid Films (1)

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 571, 410–415 (2014).
[Crossref]

Vision Res. (1)

R. Hegedüs, G. Szél, and G. Horváth, “Imaging polarimetry of the circularly polarizing cuticle of scarab beetles (Coleoptera: Rutelidae, Cetoniidae),” Vision Res. 46(17), 2786–2797 (2006).
[Crossref] [PubMed]

Other (7)

P. Yeh, Optical Waves in Layered Media (Wiley, 2005).

W. A. Goddard III, D. Brenner, S. E. Lyshevski, and G. J. Iafrate, Handbook of Nanoscience, Engineering, and Technology (3ed.) (CRC Press, 2012).

M. F. Cohen and J. R. Wallace, Radiosity and Realistic Image Synthesis (Academic Press, 1993).

E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekker, 1992).

H. Motulsky, Intuitive Biostatistics: A Nonmathematical Guide to Statistical Thinking (Oxford University, 2013).

T. G. Mackay and A. Lakhtakia, Electromagnetic Anisotropy and Bianisotropy: A Field Guide, First edition (World Scientific, 2010).

V. A. Belyakov, Diffraction Optics of Complex-Structured Periodic Media (Springer, 1992).

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Figures (7)

Fig. 1
Fig. 1 Helicoidal periodic structure having slight irregularities mimicking that of beetle exoskeletons.
Fig. 2
Fig. 2 Scattering in reflection and refraction of light incident at a rough air-cuticle interface.
Fig. 3
Fig. 3 Directions of the scattered light components in the considered model.
Fig. 4
Fig. 4 Orientations of the vectors.
Fig. 5
Fig. 5 Specimen of the tribe Anomalini of the subfamily Rutelinae.
Fig. 6
Fig. 6 Spectral and spatial distribution in the yz-plane of the scattered light (a) intensity and (b) degree of polarization.
Fig. 7
Fig. 7 Degree of circular polarization Pc of light scattered in the yz-plane versus angle of the observation.

Equations (29)

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ε ^ (z)=( ε II + ε 2 0 0 0 ε II + ε 2 0 0 0 ε )+ ε II ε 2 ( cos(qz) sin(qz) 0 sin(qz) cos(qz) 0 0 0 0 ),
k i k r = q ,
S=[ I Q U V ]
S S r (α)= S spec r (α)+ S dif r (α),
S AC,S t (β)= S refr t (β)+ S dif t (β),
M spec r (α, α o )=(1ξ) M spec ro ( α o +γ(α, α o )) f γ (γ(α, α o ))Δγ,
M=H(JJ*) H 1 ,
M dif r (α, α o )=ξ( 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 )exp( A 2 (α, α o ) 2 σ 2 C 2 (α, α o ) ).
S S r (α)=( M spec r (α, α o )+ M dif r (α, α o ) ) S i ( α o )= M S r (α, α o ) S i ( α o )
M refr t (β, α o )=(1ξ) M refr to ( α o +γ(β) ) f γ (γ(β))Δγ,
sin( α o +γ)= n ¯ sin(β+γ).
M dif t (β, α o )=ξ cosα(β) n ¯ cosβ ( 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 )( 1exp( A 2 (α(β), α o ) 2 σ 2 C 2 (α(β), α o ) ) ),
sinα= n ¯ sinβ.
S AC,S t (β)=( M spec t (β, α o )+ M dif t (β, α o ) ) S i ( α o )= M AC,S t (β, α o ) S i ( α o ).
M D (λ,β',β)=( p min p max M d (β,θ,λ,p) f p (p)dp ) f θ (θ)Δθ,
β'=β+2θ.
S D,V (λ,β')= M D,V (λ,β',β) S AC,S t (λ,β).
S r (λ,α)= S S r (λ,α)+ S V r (λ,α),
M AC,refr t (α,β')=(1ξ) M AC,refr to ( β'γ(α) ) f γ (γ(α))Δγ,
M AC,dif t (α,β')=ξ n ¯ cosβ cosα ( 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 )( 1exp( A 2 (β(α),β') 2 σ 2 C 2 (β(α),β') ) ).
M cuticle ( α, α o )= M S r ( α, α o )+ M CA,S t ( β'(β(α)),α ) M D,V ( λ,β'(β(α)),β(α) ) M AC,S t ( β(α), α o ).
M cuticle ( α, α o )= M S r ( α, α o )+ θ min θ max γ min γ min γ min γ mxa M CA,S t ( β'(β(α,γ),θ),α ) M D,V ( λ,β'(β(α,γ),θ),β(α,γ) ) M AC,S t ( β(α,γ), α o ) f θ (θ) f γ 2 (γ)dγdγ dθ ,
s γ = r i α o r s α | r i α o r s α | .
cos α o =( r i α o , z ), cosα=( r s α , z ), and cosγ=( s γ , z )
r t β = r tII β s γ 1 ( r tII β ) 2 and r t β' = r tII β' s γ 1 ( r tII β' ) 2 ,
h d = r t β r r β' | r t β r r β' | .
cosθ=( h d , z ), cosβ=( r t β , z ) and cosβ'=( r t β' , z )
P= Q 2 + U 2 + V 2 I = m 21 2 + m 31 2 + m 41 2 m 11 .
P C = m 41 m 11 .

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