Abstract

Morpho butterflies are well-known for their iridescence originating from nanostructures in the scales of their wings. These optical active structures integrate three design principles leading to the wide angle reflection: alternating lamellae layers, “Christmas tree” like shape, and offsets between neighboring ridges. We study their individual effects rigorously by 2D FEM simulations of the nanostructures of the Morpho sulkowskyi butterfly and show how the reflection spectrum can be controlled by the design of the nanostructures. The width of the spectrum is broad (≈ 90 nm) for alternating lamellae layers (or “brunches”) of the structure while the “Christmas tree” pattern together with a height offset between neighboring ridges reduces the directionality of the reflectance. Furthermore, we fabricated the simulated structures by e-beam lithography. The resulting samples mimicked all important optical features of the original Morpho butterfly scales and feature the intense blue iridescence with a wide angular range of reflection.

© 2013 OSA

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2013

2012

M. Aryal, D.-H. Ko, J. R. Tumbleston, A. Gadisa, E. T. Samulski, and R. Lopez, “Large area nanofabrication of butterfly wing’s three dimensional ultrastructures,” J. Vac. Sci. Technol. B30, 061802 (2012).
[CrossRef]

M. A. Steindorfer, V. Schmidt, M. Belegratis, B. Stadlober, and J. R. Krenn, “Detailed simulation of structural color generation inspired by the morpho butterfly,” Opt. Exp.20, 21485–21494 (2012).
[CrossRef]

A. D. Pris, Y. Utturkar, C. Surman, W. G. Morris, A. Vert, S. Zalyubovskiy, T. Deng, H. T. Ghiradella, and R. A. Potyrailo, “Towards high-speed imaging of infrared photons with bio-inspired nanoarchitectures,” Nature Photonics6, 195–200 (2012).
[CrossRef]

S. Lou, X. Guo, T. Fan, and D. Zhang, “Butterflies: inspiration for solar cells and sunlight water-splitting catalysts,” Energy Environ. Sci.5, 91–95 (2012).
[CrossRef]

A. Saito, J. Murase, M. Yonezawa, H. Watanabe, T. Shibuya, M. Sasaki, T. Ninomiya, S. Noguchi, M. Akaikasaya, and Y. Kuwahara, “High-throughput reproduction of the morpho butterfly’s specific high contrast blue,” Proc. SPIE8339, 83390C1–83390C10 (2012).

K. Chung, S. Yu, C.-J. Heo, J. W. Shim, S.-M. Yang, M. G. Han, H.-S. Lee, Y. Jin, S. Y. Lee, N. Park, and J. H. Shin, “Flexible, angle-independent, structural color reflectors inspired by morpho butterfly wings,” Adv. Mat.24, 2375–2379 (2012).
[CrossRef]

2011

L. Biró and J. Vigneron, “Photonic nanoarchitectures in butterflies and beetles: valuable sources for bioinspiration,” Laser & Photonics Reviews5, 27–51 (2011).
[CrossRef]

2010

M. Kolle, P. M. Salgard-Cunha, M. R. J. Scherer, F. Huang, P. Vukusic, S. Mahajan, J. J. Baumberg, and U. Steiner, “Mimicking the colourful wing scale structure of the Papilio blumei butterfly,” Nat. Nanotech.5, 511–515 (2010).
[CrossRef]

2009

R. T. Lee and G. S. Smith, “Detailed electromagnetic simulation for the structural color of butterfly wings,” Appl. Opt.48, 4177–4190 (2009).
[CrossRef] [PubMed]

D. Zhu, S. Kinoshita, D. Cai, and J. Cole, “Investigation of structural colors in morpho butterflies using the nonstandard-finite-difference time-domain method: Effects of alternately stacked shelves and ridge density,” Phys. Rev. E80, 1–12 (2009).
[CrossRef]

W. Zhang, D. Zhang, T. Fan, and J. Gu, “Novel photoanode structure templated from butterfly wing scales,” Chem. Mater.21, 33–40 (2009).
[CrossRef]

2007

A. Saito, Y. Ishikawa, Y. Miyamura, M. Akai-Kasaya, and Y. Kuwahara, “Optimization of reproduced morpho-blue coloration,”Proc. SPIE6767, 676706 (2007).
[CrossRef]

R. A. Potyrailo, H. Ghiradella, A. Vertiatchick, K. Dovidenko, J. R. Cournoyer, and E. Olson, “Morpho butterfly wing scales demonstrate highly selective vapor response,” Nature Photonics1, 123–128 (2007).
[CrossRef]

S. Banerjee and Z. Dong, “Optical characterization of iridescent wings of morpho butterflies using a high accuracy nonstandard finite-difference time-domain algorithm,” Opt. Rev.14, 359–361 (2007).
[CrossRef]

2005

K. Watanabe, T. Hoshino, K. Kanda, Y. Haruyama, and S. Matsui, “Brilliant blue observation from a morpho -butterfly-scale quasi-structure,” Jpn. J. Appl. Phys.44, 48–50 (2005).
[CrossRef]

S. Kinoshita and S. Yoshioka, “Structural colors in nature: the role of regularity and irregularity in the structure,” ChemPhysChem6, 1442–1459 (2005).
[CrossRef] [PubMed]

2003

P. Vukusic and J. R. Samples, “Photonic structures in biology,” Nature424, 852–860 (2003).
[CrossRef] [PubMed]

2002

S. K. Kinoshita, S. Y. Oshioka, Y. F. Ujii, and N. O. Kamoto, “Photophysics of structural color in the morpho butterflies,” Jpn. J. Appl. Phys.17, 103–121 (2002).

2001

M. Asano, T. Kuroda, S. Shimizu, A. Sakihara, K. Kumazawa, and H. Tabata, “Morphotex fiber,” Patent No. US6326094 (2001).

B. Gralak, G. Tayeb, and S. Enoch, “Morpho butterflies wings color modeled with lamellar grating theory,” Opt. Exp.9, 567–578 (2001).
[CrossRef]

2000

A. R. Parker, “515 million year of structural colors,” J. Opt. A: Pure Appl. Opt.2, R15–R28 (2000).
[CrossRef]

1999

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, “Quantified interference and diffraction in single morpho butterfly scales,” Proc. Roy. Soc. B266, 1403–1411 (1999).
[CrossRef]

1996

H. Tabata, K. Kumazawa, J. T. M. Funakawa, and M. Akimoto, “Microstructures and optical properties of scales of butterfly wings,” Opt. Rev.3, 139–145 (1996).
[CrossRef]

1994

H. Ghiradella, “Structure of butterfly scales: patterning in an insect cuticle,” Microscopy Research and Technique27, 429–438 (1994).
[CrossRef] [PubMed]

B. D. Heilman and I. N. Miaoulis, “Insect thin films as solar collectors,” Appl. Opt.33, 6642–6647 (1994).
[CrossRef] [PubMed]

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comp. Phys.114, 185–200 (1994).
[CrossRef]

1991

Akaikasaya, M.

A. Saito, J. Murase, M. Yonezawa, H. Watanabe, T. Shibuya, M. Sasaki, T. Ninomiya, S. Noguchi, M. Akaikasaya, and Y. Kuwahara, “High-throughput reproduction of the morpho butterfly’s specific high contrast blue,” Proc. SPIE8339, 83390C1–83390C10 (2012).

Akai-Kasaya, M.

A. Saito, Y. Ishikawa, Y. Miyamura, M. Akai-Kasaya, and Y. Kuwahara, “Optimization of reproduced morpho-blue coloration,”Proc. SPIE6767, 676706 (2007).
[CrossRef]

Akimoto, M.

H. Tabata, K. Kumazawa, J. T. M. Funakawa, and M. Akimoto, “Microstructures and optical properties of scales of butterfly wings,” Opt. Rev.3, 139–145 (1996).
[CrossRef]

Aryal, M.

M. Aryal, D.-H. Ko, J. R. Tumbleston, A. Gadisa, E. T. Samulski, and R. Lopez, “Large area nanofabrication of butterfly wing’s three dimensional ultrastructures,” J. Vac. Sci. Technol. B30, 061802 (2012).
[CrossRef]

Asano, M.

M. Asano, T. Kuroda, S. Shimizu, A. Sakihara, K. Kumazawa, and H. Tabata, “Morphotex fiber,” Patent No. US6326094 (2001).

Banerjee, S.

S. Banerjee and Z. Dong, “Optical characterization of iridescent wings of morpho butterflies using a high accuracy nonstandard finite-difference time-domain algorithm,” Opt. Rev.14, 359–361 (2007).
[CrossRef]

Baumberg, J. J.

M. Kolle, P. M. Salgard-Cunha, M. R. J. Scherer, F. Huang, P. Vukusic, S. Mahajan, J. J. Baumberg, and U. Steiner, “Mimicking the colourful wing scale structure of the Papilio blumei butterfly,” Nat. Nanotech.5, 511–515 (2010).
[CrossRef]

Belegratis, M.

M. A. Steindorfer, V. Schmidt, M. Belegratis, B. Stadlober, and J. R. Krenn, “Detailed simulation of structural color generation inspired by the morpho butterfly,” Opt. Exp.20, 21485–21494 (2012).
[CrossRef]

Berenger, J.-P.

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comp. Phys.114, 185–200 (1994).
[CrossRef]

Biró, L.

L. Biró and J. Vigneron, “Photonic nanoarchitectures in butterflies and beetles: valuable sources for bioinspiration,” Laser & Photonics Reviews5, 27–51 (2011).
[CrossRef]

Cai, D.

D. Zhu, S. Kinoshita, D. Cai, and J. Cole, “Investigation of structural colors in morpho butterflies using the nonstandard-finite-difference time-domain method: Effects of alternately stacked shelves and ridge density,” Phys. Rev. E80, 1–12 (2009).
[CrossRef]

Chung, K.

K. Chung and J. H. Shin, “Range and stability of structural colors generated by morpho-inspired color reflectors,” J. Opt. Soc. Am. A30, 962–968 (2013).
[CrossRef]

K. Chung, S. Yu, C.-J. Heo, J. W. Shim, S.-M. Yang, M. G. Han, H.-S. Lee, Y. Jin, S. Y. Lee, N. Park, and J. H. Shin, “Flexible, angle-independent, structural color reflectors inspired by morpho butterfly wings,” Adv. Mat.24, 2375–2379 (2012).
[CrossRef]

Cole, J.

D. Zhu, S. Kinoshita, D. Cai, and J. Cole, “Investigation of structural colors in morpho butterflies using the nonstandard-finite-difference time-domain method: Effects of alternately stacked shelves and ridge density,” Phys. Rev. E80, 1–12 (2009).
[CrossRef]

Cournoyer, J. R.

R. A. Potyrailo, H. Ghiradella, A. Vertiatchick, K. Dovidenko, J. R. Cournoyer, and E. Olson, “Morpho butterfly wing scales demonstrate highly selective vapor response,” Nature Photonics1, 123–128 (2007).
[CrossRef]

Deng, T.

A. D. Pris, Y. Utturkar, C. Surman, W. G. Morris, A. Vert, S. Zalyubovskiy, T. Deng, H. T. Ghiradella, and R. A. Potyrailo, “Towards high-speed imaging of infrared photons with bio-inspired nanoarchitectures,” Nature Photonics6, 195–200 (2012).
[CrossRef]

Dong, Z.

S. Banerjee and Z. Dong, “Optical characterization of iridescent wings of morpho butterflies using a high accuracy nonstandard finite-difference time-domain algorithm,” Opt. Rev.14, 359–361 (2007).
[CrossRef]

Dovidenko, K.

R. A. Potyrailo, H. Ghiradella, A. Vertiatchick, K. Dovidenko, J. R. Cournoyer, and E. Olson, “Morpho butterfly wing scales demonstrate highly selective vapor response,” Nature Photonics1, 123–128 (2007).
[CrossRef]

Enoch, S.

B. Gralak, G. Tayeb, and S. Enoch, “Morpho butterflies wings color modeled with lamellar grating theory,” Opt. Exp.9, 567–578 (2001).
[CrossRef]

Fan, T.

S. Lou, X. Guo, T. Fan, and D. Zhang, “Butterflies: inspiration for solar cells and sunlight water-splitting catalysts,” Energy Environ. Sci.5, 91–95 (2012).
[CrossRef]

W. Zhang, D. Zhang, T. Fan, and J. Gu, “Novel photoanode structure templated from butterfly wing scales,” Chem. Mater.21, 33–40 (2009).
[CrossRef]

Funakawa, J. T. M.

H. Tabata, K. Kumazawa, J. T. M. Funakawa, and M. Akimoto, “Microstructures and optical properties of scales of butterfly wings,” Opt. Rev.3, 139–145 (1996).
[CrossRef]

Gadisa, A.

M. Aryal, D.-H. Ko, J. R. Tumbleston, A. Gadisa, E. T. Samulski, and R. Lopez, “Large area nanofabrication of butterfly wing’s three dimensional ultrastructures,” J. Vac. Sci. Technol. B30, 061802 (2012).
[CrossRef]

Ghiradella, H.

R. A. Potyrailo, H. Ghiradella, A. Vertiatchick, K. Dovidenko, J. R. Cournoyer, and E. Olson, “Morpho butterfly wing scales demonstrate highly selective vapor response,” Nature Photonics1, 123–128 (2007).
[CrossRef]

H. Ghiradella, “Structure of butterfly scales: patterning in an insect cuticle,” Microscopy Research and Technique27, 429–438 (1994).
[CrossRef] [PubMed]

H. Ghiradella, “Light and color on the wing: structural colors in butterflies and moths,” Appl. Opt.30, 3492–3500 (1991).
[CrossRef] [PubMed]

Ghiradella, H. T.

A. D. Pris, Y. Utturkar, C. Surman, W. G. Morris, A. Vert, S. Zalyubovskiy, T. Deng, H. T. Ghiradella, and R. A. Potyrailo, “Towards high-speed imaging of infrared photons with bio-inspired nanoarchitectures,” Nature Photonics6, 195–200 (2012).
[CrossRef]

Gralak, B.

B. Gralak, G. Tayeb, and S. Enoch, “Morpho butterflies wings color modeled with lamellar grating theory,” Opt. Exp.9, 567–578 (2001).
[CrossRef]

Gu, J.

W. Zhang, D. Zhang, T. Fan, and J. Gu, “Novel photoanode structure templated from butterfly wing scales,” Chem. Mater.21, 33–40 (2009).
[CrossRef]

Guo, X.

S. Lou, X. Guo, T. Fan, and D. Zhang, “Butterflies: inspiration for solar cells and sunlight water-splitting catalysts,” Energy Environ. Sci.5, 91–95 (2012).
[CrossRef]

Hagness, S.

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).

Han, M. G.

K. Chung, S. Yu, C.-J. Heo, J. W. Shim, S.-M. Yang, M. G. Han, H.-S. Lee, Y. Jin, S. Y. Lee, N. Park, and J. H. Shin, “Flexible, angle-independent, structural color reflectors inspired by morpho butterfly wings,” Adv. Mat.24, 2375–2379 (2012).
[CrossRef]

Haruyama, Y.

K. Watanabe, T. Hoshino, K. Kanda, Y. Haruyama, and S. Matsui, “Brilliant blue observation from a morpho -butterfly-scale quasi-structure,” Jpn. J. Appl. Phys.44, 48–50 (2005).
[CrossRef]

Heilman, B. D.

Heo, C.-J.

K. Chung, S. Yu, C.-J. Heo, J. W. Shim, S.-M. Yang, M. G. Han, H.-S. Lee, Y. Jin, S. Y. Lee, N. Park, and J. H. Shin, “Flexible, angle-independent, structural color reflectors inspired by morpho butterfly wings,” Adv. Mat.24, 2375–2379 (2012).
[CrossRef]

Hoshino, T.

K. Watanabe, T. Hoshino, K. Kanda, Y. Haruyama, and S. Matsui, “Brilliant blue observation from a morpho -butterfly-scale quasi-structure,” Jpn. J. Appl. Phys.44, 48–50 (2005).
[CrossRef]

Huang, F.

M. Kolle, P. M. Salgard-Cunha, M. R. J. Scherer, F. Huang, P. Vukusic, S. Mahajan, J. J. Baumberg, and U. Steiner, “Mimicking the colourful wing scale structure of the Papilio blumei butterfly,” Nat. Nanotech.5, 511–515 (2010).
[CrossRef]

Ishikawa, Y.

A. Saito, Y. Ishikawa, Y. Miyamura, M. Akai-Kasaya, and Y. Kuwahara, “Optimization of reproduced morpho-blue coloration,”Proc. SPIE6767, 676706 (2007).
[CrossRef]

Jin, Y.

K. Chung, S. Yu, C.-J. Heo, J. W. Shim, S.-M. Yang, M. G. Han, H.-S. Lee, Y. Jin, S. Y. Lee, N. Park, and J. H. Shin, “Flexible, angle-independent, structural color reflectors inspired by morpho butterfly wings,” Adv. Mat.24, 2375–2379 (2012).
[CrossRef]

Kamoto, N. O.

S. K. Kinoshita, S. Y. Oshioka, Y. F. Ujii, and N. O. Kamoto, “Photophysics of structural color in the morpho butterflies,” Jpn. J. Appl. Phys.17, 103–121 (2002).

Kanda, K.

K. Watanabe, T. Hoshino, K. Kanda, Y. Haruyama, and S. Matsui, “Brilliant blue observation from a morpho -butterfly-scale quasi-structure,” Jpn. J. Appl. Phys.44, 48–50 (2005).
[CrossRef]

Kinoshita, S.

D. Zhu, S. Kinoshita, D. Cai, and J. Cole, “Investigation of structural colors in morpho butterflies using the nonstandard-finite-difference time-domain method: Effects of alternately stacked shelves and ridge density,” Phys. Rev. E80, 1–12 (2009).
[CrossRef]

S. Kinoshita and S. Yoshioka, “Structural colors in nature: the role of regularity and irregularity in the structure,” ChemPhysChem6, 1442–1459 (2005).
[CrossRef] [PubMed]

S. Kinoshita, Structural Colors in the Realm of Nature (World Scientific, Singapore, 2008).

Kinoshita, S. K.

S. K. Kinoshita, S. Y. Oshioka, Y. F. Ujii, and N. O. Kamoto, “Photophysics of structural color in the morpho butterflies,” Jpn. J. Appl. Phys.17, 103–121 (2002).

Ko, D.-H.

M. Aryal, D.-H. Ko, J. R. Tumbleston, A. Gadisa, E. T. Samulski, and R. Lopez, “Large area nanofabrication of butterfly wing’s three dimensional ultrastructures,” J. Vac. Sci. Technol. B30, 061802 (2012).
[CrossRef]

Kolle, M.

M. Kolle, P. M. Salgard-Cunha, M. R. J. Scherer, F. Huang, P. Vukusic, S. Mahajan, J. J. Baumberg, and U. Steiner, “Mimicking the colourful wing scale structure of the Papilio blumei butterfly,” Nat. Nanotech.5, 511–515 (2010).
[CrossRef]

M. Kolle, Photonic Structures Inspired by Nature (Springer, Heidelberg, 2011).
[CrossRef]

Krenn, J. R.

M. A. Steindorfer, V. Schmidt, M. Belegratis, B. Stadlober, and J. R. Krenn, “Detailed simulation of structural color generation inspired by the morpho butterfly,” Opt. Exp.20, 21485–21494 (2012).
[CrossRef]

Kumazawa, K.

M. Asano, T. Kuroda, S. Shimizu, A. Sakihara, K. Kumazawa, and H. Tabata, “Morphotex fiber,” Patent No. US6326094 (2001).

H. Tabata, K. Kumazawa, J. T. M. Funakawa, and M. Akimoto, “Microstructures and optical properties of scales of butterfly wings,” Opt. Rev.3, 139–145 (1996).
[CrossRef]

Kuroda, T.

M. Asano, T. Kuroda, S. Shimizu, A. Sakihara, K. Kumazawa, and H. Tabata, “Morphotex fiber,” Patent No. US6326094 (2001).

Kuwahara, Y.

A. Saito, J. Murase, M. Yonezawa, H. Watanabe, T. Shibuya, M. Sasaki, T. Ninomiya, S. Noguchi, M. Akaikasaya, and Y. Kuwahara, “High-throughput reproduction of the morpho butterfly’s specific high contrast blue,” Proc. SPIE8339, 83390C1–83390C10 (2012).

A. Saito, Y. Ishikawa, Y. Miyamura, M. Akai-Kasaya, and Y. Kuwahara, “Optimization of reproduced morpho-blue coloration,”Proc. SPIE6767, 676706 (2007).
[CrossRef]

Lawrence, C. R.

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, “Quantified interference and diffraction in single morpho butterfly scales,” Proc. Roy. Soc. B266, 1403–1411 (1999).
[CrossRef]

Lee, H.-S.

K. Chung, S. Yu, C.-J. Heo, J. W. Shim, S.-M. Yang, M. G. Han, H.-S. Lee, Y. Jin, S. Y. Lee, N. Park, and J. H. Shin, “Flexible, angle-independent, structural color reflectors inspired by morpho butterfly wings,” Adv. Mat.24, 2375–2379 (2012).
[CrossRef]

Lee, R. T.

Lee, S. Y.

K. Chung, S. Yu, C.-J. Heo, J. W. Shim, S.-M. Yang, M. G. Han, H.-S. Lee, Y. Jin, S. Y. Lee, N. Park, and J. H. Shin, “Flexible, angle-independent, structural color reflectors inspired by morpho butterfly wings,” Adv. Mat.24, 2375–2379 (2012).
[CrossRef]

Lopez, R.

M. Aryal, D.-H. Ko, J. R. Tumbleston, A. Gadisa, E. T. Samulski, and R. Lopez, “Large area nanofabrication of butterfly wing’s three dimensional ultrastructures,” J. Vac. Sci. Technol. B30, 061802 (2012).
[CrossRef]

Lou, S.

S. Lou, X. Guo, T. Fan, and D. Zhang, “Butterflies: inspiration for solar cells and sunlight water-splitting catalysts,” Energy Environ. Sci.5, 91–95 (2012).
[CrossRef]

Mahajan, S.

M. Kolle, P. M. Salgard-Cunha, M. R. J. Scherer, F. Huang, P. Vukusic, S. Mahajan, J. J. Baumberg, and U. Steiner, “Mimicking the colourful wing scale structure of the Papilio blumei butterfly,” Nat. Nanotech.5, 511–515 (2010).
[CrossRef]

Matsui, S.

K. Watanabe, T. Hoshino, K. Kanda, Y. Haruyama, and S. Matsui, “Brilliant blue observation from a morpho -butterfly-scale quasi-structure,” Jpn. J. Appl. Phys.44, 48–50 (2005).
[CrossRef]

Miaoulis, I. N.

Miyamura, Y.

A. Saito, Y. Ishikawa, Y. Miyamura, M. Akai-Kasaya, and Y. Kuwahara, “Optimization of reproduced morpho-blue coloration,”Proc. SPIE6767, 676706 (2007).
[CrossRef]

Morris, W. G.

A. D. Pris, Y. Utturkar, C. Surman, W. G. Morris, A. Vert, S. Zalyubovskiy, T. Deng, H. T. Ghiradella, and R. A. Potyrailo, “Towards high-speed imaging of infrared photons with bio-inspired nanoarchitectures,” Nature Photonics6, 195–200 (2012).
[CrossRef]

Murase, J.

A. Saito, J. Murase, M. Yonezawa, H. Watanabe, T. Shibuya, M. Sasaki, T. Ninomiya, S. Noguchi, M. Akaikasaya, and Y. Kuwahara, “High-throughput reproduction of the morpho butterfly’s specific high contrast blue,” Proc. SPIE8339, 83390C1–83390C10 (2012).

Ninomiya, T.

A. Saito, J. Murase, M. Yonezawa, H. Watanabe, T. Shibuya, M. Sasaki, T. Ninomiya, S. Noguchi, M. Akaikasaya, and Y. Kuwahara, “High-throughput reproduction of the morpho butterfly’s specific high contrast blue,” Proc. SPIE8339, 83390C1–83390C10 (2012).

Noguchi, S.

A. Saito, J. Murase, M. Yonezawa, H. Watanabe, T. Shibuya, M. Sasaki, T. Ninomiya, S. Noguchi, M. Akaikasaya, and Y. Kuwahara, “High-throughput reproduction of the morpho butterfly’s specific high contrast blue,” Proc. SPIE8339, 83390C1–83390C10 (2012).

Olson, E.

R. A. Potyrailo, H. Ghiradella, A. Vertiatchick, K. Dovidenko, J. R. Cournoyer, and E. Olson, “Morpho butterfly wing scales demonstrate highly selective vapor response,” Nature Photonics1, 123–128 (2007).
[CrossRef]

Oshioka, S. Y.

S. K. Kinoshita, S. Y. Oshioka, Y. F. Ujii, and N. O. Kamoto, “Photophysics of structural color in the morpho butterflies,” Jpn. J. Appl. Phys.17, 103–121 (2002).

Park, N.

K. Chung, S. Yu, C.-J. Heo, J. W. Shim, S.-M. Yang, M. G. Han, H.-S. Lee, Y. Jin, S. Y. Lee, N. Park, and J. H. Shin, “Flexible, angle-independent, structural color reflectors inspired by morpho butterfly wings,” Adv. Mat.24, 2375–2379 (2012).
[CrossRef]

Parker, A. R.

A. R. Parker, “515 million year of structural colors,” J. Opt. A: Pure Appl. Opt.2, R15–R28 (2000).
[CrossRef]

Potyrailo, R. A.

A. D. Pris, Y. Utturkar, C. Surman, W. G. Morris, A. Vert, S. Zalyubovskiy, T. Deng, H. T. Ghiradella, and R. A. Potyrailo, “Towards high-speed imaging of infrared photons with bio-inspired nanoarchitectures,” Nature Photonics6, 195–200 (2012).
[CrossRef]

R. A. Potyrailo, H. Ghiradella, A. Vertiatchick, K. Dovidenko, J. R. Cournoyer, and E. Olson, “Morpho butterfly wing scales demonstrate highly selective vapor response,” Nature Photonics1, 123–128 (2007).
[CrossRef]

Pris, A. D.

A. D. Pris, Y. Utturkar, C. Surman, W. G. Morris, A. Vert, S. Zalyubovskiy, T. Deng, H. T. Ghiradella, and R. A. Potyrailo, “Towards high-speed imaging of infrared photons with bio-inspired nanoarchitectures,” Nature Photonics6, 195–200 (2012).
[CrossRef]

Saito, A.

A. Saito, J. Murase, M. Yonezawa, H. Watanabe, T. Shibuya, M. Sasaki, T. Ninomiya, S. Noguchi, M. Akaikasaya, and Y. Kuwahara, “High-throughput reproduction of the morpho butterfly’s specific high contrast blue,” Proc. SPIE8339, 83390C1–83390C10 (2012).

A. Saito, Y. Ishikawa, Y. Miyamura, M. Akai-Kasaya, and Y. Kuwahara, “Optimization of reproduced morpho-blue coloration,”Proc. SPIE6767, 676706 (2007).
[CrossRef]

Sakihara, A.

M. Asano, T. Kuroda, S. Shimizu, A. Sakihara, K. Kumazawa, and H. Tabata, “Morphotex fiber,” Patent No. US6326094 (2001).

Salgard-Cunha, P. M.

M. Kolle, P. M. Salgard-Cunha, M. R. J. Scherer, F. Huang, P. Vukusic, S. Mahajan, J. J. Baumberg, and U. Steiner, “Mimicking the colourful wing scale structure of the Papilio blumei butterfly,” Nat. Nanotech.5, 511–515 (2010).
[CrossRef]

Sambles, J. R.

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, “Quantified interference and diffraction in single morpho butterfly scales,” Proc. Roy. Soc. B266, 1403–1411 (1999).
[CrossRef]

Samples, J. R.

P. Vukusic and J. R. Samples, “Photonic structures in biology,” Nature424, 852–860 (2003).
[CrossRef] [PubMed]

Samulski, E. T.

M. Aryal, D.-H. Ko, J. R. Tumbleston, A. Gadisa, E. T. Samulski, and R. Lopez, “Large area nanofabrication of butterfly wing’s three dimensional ultrastructures,” J. Vac. Sci. Technol. B30, 061802 (2012).
[CrossRef]

Sasaki, M.

A. Saito, J. Murase, M. Yonezawa, H. Watanabe, T. Shibuya, M. Sasaki, T. Ninomiya, S. Noguchi, M. Akaikasaya, and Y. Kuwahara, “High-throughput reproduction of the morpho butterfly’s specific high contrast blue,” Proc. SPIE8339, 83390C1–83390C10 (2012).

Scherer, M. R. J.

M. Kolle, P. M. Salgard-Cunha, M. R. J. Scherer, F. Huang, P. Vukusic, S. Mahajan, J. J. Baumberg, and U. Steiner, “Mimicking the colourful wing scale structure of the Papilio blumei butterfly,” Nat. Nanotech.5, 511–515 (2010).
[CrossRef]

Schmidt, V.

M. A. Steindorfer, V. Schmidt, M. Belegratis, B. Stadlober, and J. R. Krenn, “Detailed simulation of structural color generation inspired by the morpho butterfly,” Opt. Exp.20, 21485–21494 (2012).
[CrossRef]

Shibuya, T.

A. Saito, J. Murase, M. Yonezawa, H. Watanabe, T. Shibuya, M. Sasaki, T. Ninomiya, S. Noguchi, M. Akaikasaya, and Y. Kuwahara, “High-throughput reproduction of the morpho butterfly’s specific high contrast blue,” Proc. SPIE8339, 83390C1–83390C10 (2012).

Shim, J. W.

K. Chung, S. Yu, C.-J. Heo, J. W. Shim, S.-M. Yang, M. G. Han, H.-S. Lee, Y. Jin, S. Y. Lee, N. Park, and J. H. Shin, “Flexible, angle-independent, structural color reflectors inspired by morpho butterfly wings,” Adv. Mat.24, 2375–2379 (2012).
[CrossRef]

Shimizu, S.

M. Asano, T. Kuroda, S. Shimizu, A. Sakihara, K. Kumazawa, and H. Tabata, “Morphotex fiber,” Patent No. US6326094 (2001).

Shin, J. H.

K. Chung and J. H. Shin, “Range and stability of structural colors generated by morpho-inspired color reflectors,” J. Opt. Soc. Am. A30, 962–968 (2013).
[CrossRef]

K. Chung, S. Yu, C.-J. Heo, J. W. Shim, S.-M. Yang, M. G. Han, H.-S. Lee, Y. Jin, S. Y. Lee, N. Park, and J. H. Shin, “Flexible, angle-independent, structural color reflectors inspired by morpho butterfly wings,” Adv. Mat.24, 2375–2379 (2012).
[CrossRef]

Smith, G. S.

Stadlober, B.

M. A. Steindorfer, V. Schmidt, M. Belegratis, B. Stadlober, and J. R. Krenn, “Detailed simulation of structural color generation inspired by the morpho butterfly,” Opt. Exp.20, 21485–21494 (2012).
[CrossRef]

Steindorfer, M. A.

M. A. Steindorfer, V. Schmidt, M. Belegratis, B. Stadlober, and J. R. Krenn, “Detailed simulation of structural color generation inspired by the morpho butterfly,” Opt. Exp.20, 21485–21494 (2012).
[CrossRef]

Steiner, U.

M. Kolle, P. M. Salgard-Cunha, M. R. J. Scherer, F. Huang, P. Vukusic, S. Mahajan, J. J. Baumberg, and U. Steiner, “Mimicking the colourful wing scale structure of the Papilio blumei butterfly,” Nat. Nanotech.5, 511–515 (2010).
[CrossRef]

Surman, C.

A. D. Pris, Y. Utturkar, C. Surman, W. G. Morris, A. Vert, S. Zalyubovskiy, T. Deng, H. T. Ghiradella, and R. A. Potyrailo, “Towards high-speed imaging of infrared photons with bio-inspired nanoarchitectures,” Nature Photonics6, 195–200 (2012).
[CrossRef]

Tabata, H.

M. Asano, T. Kuroda, S. Shimizu, A. Sakihara, K. Kumazawa, and H. Tabata, “Morphotex fiber,” Patent No. US6326094 (2001).

H. Tabata, K. Kumazawa, J. T. M. Funakawa, and M. Akimoto, “Microstructures and optical properties of scales of butterfly wings,” Opt. Rev.3, 139–145 (1996).
[CrossRef]

Taflove, A.

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).

Tayeb, G.

B. Gralak, G. Tayeb, and S. Enoch, “Morpho butterflies wings color modeled with lamellar grating theory,” Opt. Exp.9, 567–578 (2001).
[CrossRef]

Tumbleston, J. R.

M. Aryal, D.-H. Ko, J. R. Tumbleston, A. Gadisa, E. T. Samulski, and R. Lopez, “Large area nanofabrication of butterfly wing’s three dimensional ultrastructures,” J. Vac. Sci. Technol. B30, 061802 (2012).
[CrossRef]

Ujii, Y. F.

S. K. Kinoshita, S. Y. Oshioka, Y. F. Ujii, and N. O. Kamoto, “Photophysics of structural color in the morpho butterflies,” Jpn. J. Appl. Phys.17, 103–121 (2002).

Utturkar, Y.

A. D. Pris, Y. Utturkar, C. Surman, W. G. Morris, A. Vert, S. Zalyubovskiy, T. Deng, H. T. Ghiradella, and R. A. Potyrailo, “Towards high-speed imaging of infrared photons with bio-inspired nanoarchitectures,” Nature Photonics6, 195–200 (2012).
[CrossRef]

Vert, A.

A. D. Pris, Y. Utturkar, C. Surman, W. G. Morris, A. Vert, S. Zalyubovskiy, T. Deng, H. T. Ghiradella, and R. A. Potyrailo, “Towards high-speed imaging of infrared photons with bio-inspired nanoarchitectures,” Nature Photonics6, 195–200 (2012).
[CrossRef]

Vertiatchick, A.

R. A. Potyrailo, H. Ghiradella, A. Vertiatchick, K. Dovidenko, J. R. Cournoyer, and E. Olson, “Morpho butterfly wing scales demonstrate highly selective vapor response,” Nature Photonics1, 123–128 (2007).
[CrossRef]

Vigneron, J.

L. Biró and J. Vigneron, “Photonic nanoarchitectures in butterflies and beetles: valuable sources for bioinspiration,” Laser & Photonics Reviews5, 27–51 (2011).
[CrossRef]

Vukusic, P.

M. Kolle, P. M. Salgard-Cunha, M. R. J. Scherer, F. Huang, P. Vukusic, S. Mahajan, J. J. Baumberg, and U. Steiner, “Mimicking the colourful wing scale structure of the Papilio blumei butterfly,” Nat. Nanotech.5, 511–515 (2010).
[CrossRef]

P. Vukusic and J. R. Samples, “Photonic structures in biology,” Nature424, 852–860 (2003).
[CrossRef] [PubMed]

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, “Quantified interference and diffraction in single morpho butterfly scales,” Proc. Roy. Soc. B266, 1403–1411 (1999).
[CrossRef]

Watanabe, H.

A. Saito, J. Murase, M. Yonezawa, H. Watanabe, T. Shibuya, M. Sasaki, T. Ninomiya, S. Noguchi, M. Akaikasaya, and Y. Kuwahara, “High-throughput reproduction of the morpho butterfly’s specific high contrast blue,” Proc. SPIE8339, 83390C1–83390C10 (2012).

Watanabe, K.

K. Watanabe, T. Hoshino, K. Kanda, Y. Haruyama, and S. Matsui, “Brilliant blue observation from a morpho -butterfly-scale quasi-structure,” Jpn. J. Appl. Phys.44, 48–50 (2005).
[CrossRef]

Weber, M. J.

M. J. Weber, Handbook of Optical Materials (CRC Press, 2003).

Wootton, R. J.

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, “Quantified interference and diffraction in single morpho butterfly scales,” Proc. Roy. Soc. B266, 1403–1411 (1999).
[CrossRef]

Yang, S.-M.

K. Chung, S. Yu, C.-J. Heo, J. W. Shim, S.-M. Yang, M. G. Han, H.-S. Lee, Y. Jin, S. Y. Lee, N. Park, and J. H. Shin, “Flexible, angle-independent, structural color reflectors inspired by morpho butterfly wings,” Adv. Mat.24, 2375–2379 (2012).
[CrossRef]

Yonezawa, M.

A. Saito, J. Murase, M. Yonezawa, H. Watanabe, T. Shibuya, M. Sasaki, T. Ninomiya, S. Noguchi, M. Akaikasaya, and Y. Kuwahara, “High-throughput reproduction of the morpho butterfly’s specific high contrast blue,” Proc. SPIE8339, 83390C1–83390C10 (2012).

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S. Kinoshita and S. Yoshioka, “Structural colors in nature: the role of regularity and irregularity in the structure,” ChemPhysChem6, 1442–1459 (2005).
[CrossRef] [PubMed]

Yu, S.

K. Chung, S. Yu, C.-J. Heo, J. W. Shim, S.-M. Yang, M. G. Han, H.-S. Lee, Y. Jin, S. Y. Lee, N. Park, and J. H. Shin, “Flexible, angle-independent, structural color reflectors inspired by morpho butterfly wings,” Adv. Mat.24, 2375–2379 (2012).
[CrossRef]

Zalyubovskiy, S.

A. D. Pris, Y. Utturkar, C. Surman, W. G. Morris, A. Vert, S. Zalyubovskiy, T. Deng, H. T. Ghiradella, and R. A. Potyrailo, “Towards high-speed imaging of infrared photons with bio-inspired nanoarchitectures,” Nature Photonics6, 195–200 (2012).
[CrossRef]

Zhang, D.

S. Lou, X. Guo, T. Fan, and D. Zhang, “Butterflies: inspiration for solar cells and sunlight water-splitting catalysts,” Energy Environ. Sci.5, 91–95 (2012).
[CrossRef]

W. Zhang, D. Zhang, T. Fan, and J. Gu, “Novel photoanode structure templated from butterfly wing scales,” Chem. Mater.21, 33–40 (2009).
[CrossRef]

Zhang, W.

W. Zhang, D. Zhang, T. Fan, and J. Gu, “Novel photoanode structure templated from butterfly wing scales,” Chem. Mater.21, 33–40 (2009).
[CrossRef]

Zhu, D.

D. Zhu, S. Kinoshita, D. Cai, and J. Cole, “Investigation of structural colors in morpho butterflies using the nonstandard-finite-difference time-domain method: Effects of alternately stacked shelves and ridge density,” Phys. Rev. E80, 1–12 (2009).
[CrossRef]

Adv. Mat.

K. Chung, S. Yu, C.-J. Heo, J. W. Shim, S.-M. Yang, M. G. Han, H.-S. Lee, Y. Jin, S. Y. Lee, N. Park, and J. H. Shin, “Flexible, angle-independent, structural color reflectors inspired by morpho butterfly wings,” Adv. Mat.24, 2375–2379 (2012).
[CrossRef]

Appl. Opt.

Chem. Mater.

W. Zhang, D. Zhang, T. Fan, and J. Gu, “Novel photoanode structure templated from butterfly wing scales,” Chem. Mater.21, 33–40 (2009).
[CrossRef]

ChemPhysChem

S. Kinoshita and S. Yoshioka, “Structural colors in nature: the role of regularity and irregularity in the structure,” ChemPhysChem6, 1442–1459 (2005).
[CrossRef] [PubMed]

Energy Environ. Sci.

S. Lou, X. Guo, T. Fan, and D. Zhang, “Butterflies: inspiration for solar cells and sunlight water-splitting catalysts,” Energy Environ. Sci.5, 91–95 (2012).
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J. Comp. Phys.

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comp. Phys.114, 185–200 (1994).
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J. Opt. A: Pure Appl. Opt.

A. R. Parker, “515 million year of structural colors,” J. Opt. A: Pure Appl. Opt.2, R15–R28 (2000).
[CrossRef]

J. Opt. Soc. Am. A

J. Vac. Sci. Technol. B

M. Aryal, D.-H. Ko, J. R. Tumbleston, A. Gadisa, E. T. Samulski, and R. Lopez, “Large area nanofabrication of butterfly wing’s three dimensional ultrastructures,” J. Vac. Sci. Technol. B30, 061802 (2012).
[CrossRef]

Jpn. J. Appl. Phys.

K. Watanabe, T. Hoshino, K. Kanda, Y. Haruyama, and S. Matsui, “Brilliant blue observation from a morpho -butterfly-scale quasi-structure,” Jpn. J. Appl. Phys.44, 48–50 (2005).
[CrossRef]

S. K. Kinoshita, S. Y. Oshioka, Y. F. Ujii, and N. O. Kamoto, “Photophysics of structural color in the morpho butterflies,” Jpn. J. Appl. Phys.17, 103–121 (2002).

Laser & Photonics Reviews

L. Biró and J. Vigneron, “Photonic nanoarchitectures in butterflies and beetles: valuable sources for bioinspiration,” Laser & Photonics Reviews5, 27–51 (2011).
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Microscopy Research and Technique

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M. Kolle, P. M. Salgard-Cunha, M. R. J. Scherer, F. Huang, P. Vukusic, S. Mahajan, J. J. Baumberg, and U. Steiner, “Mimicking the colourful wing scale structure of the Papilio blumei butterfly,” Nat. Nanotech.5, 511–515 (2010).
[CrossRef]

Nature

P. Vukusic and J. R. Samples, “Photonic structures in biology,” Nature424, 852–860 (2003).
[CrossRef] [PubMed]

Nature Photonics

R. A. Potyrailo, H. Ghiradella, A. Vertiatchick, K. Dovidenko, J. R. Cournoyer, and E. Olson, “Morpho butterfly wing scales demonstrate highly selective vapor response,” Nature Photonics1, 123–128 (2007).
[CrossRef]

A. D. Pris, Y. Utturkar, C. Surman, W. G. Morris, A. Vert, S. Zalyubovskiy, T. Deng, H. T. Ghiradella, and R. A. Potyrailo, “Towards high-speed imaging of infrared photons with bio-inspired nanoarchitectures,” Nature Photonics6, 195–200 (2012).
[CrossRef]

Opt. Exp.

B. Gralak, G. Tayeb, and S. Enoch, “Morpho butterflies wings color modeled with lamellar grating theory,” Opt. Exp.9, 567–578 (2001).
[CrossRef]

M. A. Steindorfer, V. Schmidt, M. Belegratis, B. Stadlober, and J. R. Krenn, “Detailed simulation of structural color generation inspired by the morpho butterfly,” Opt. Exp.20, 21485–21494 (2012).
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[CrossRef]

Phys. Rev. E

D. Zhu, S. Kinoshita, D. Cai, and J. Cole, “Investigation of structural colors in morpho butterflies using the nonstandard-finite-difference time-domain method: Effects of alternately stacked shelves and ridge density,” Phys. Rev. E80, 1–12 (2009).
[CrossRef]

Proc. Roy. Soc. B

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, “Quantified interference and diffraction in single morpho butterfly scales,” Proc. Roy. Soc. B266, 1403–1411 (1999).
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Proc. SPIE

A. Saito, J. Murase, M. Yonezawa, H. Watanabe, T. Shibuya, M. Sasaki, T. Ninomiya, S. Noguchi, M. Akaikasaya, and Y. Kuwahara, “High-throughput reproduction of the morpho butterfly’s specific high contrast blue,” Proc. SPIE8339, 83390C1–83390C10 (2012).

A. Saito, Y. Ishikawa, Y. Miyamura, M. Akai-Kasaya, and Y. Kuwahara, “Optimization of reproduced morpho-blue coloration,”Proc. SPIE6767, 676706 (2007).
[CrossRef]

Other

M. Asano, T. Kuroda, S. Shimizu, A. Sakihara, K. Kumazawa, and H. Tabata, “Morphotex fiber,” Patent No. US6326094 (2001).

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Figures (6)

Fig. 1
Fig. 1

(a) The wings of blue Morpho butterflies like Morpho menelaus show strong blue iridescence. (b) A TEM image of the cross-section of the Morpho sulkowskyi ground scale reveal the “Christmas tree” like structure responsible for the famous blue iridescence. Reproduced from Pris et al.[10]. (c) Schematics of the structures and dimensions (all units in nm) used in this study for simulation and fabrication. All values are extracted from the TEM and SEM images of Morpho sulkowskyi[9]. The ‘simple’ grating like structure resembles a simple stack of thin films. The structure shown next consists of ‘alternating’ lamellae layers without “Christmas tree” type shape. The ‘inspired’ structure is shaped like a “Christmas tree” without alternating layers. Finally, the ‘original’ Morpho-type structure features both properties: alternating layers together with “Christmas tree” like shape.

Fig. 2
Fig. 2

Optical FEM simulations of Morpho butterfly nanostructures. (a) 3D Schematic of the periodic cell assumed in the simulations. The dotted cross-sectional plane in the schematic corresponds to the 2D simulation plane. Periodic boundary conditions are used on the left and right side of the cell to repeat the structures in horizontal direction. To confine the cell in top and bottom direction, perfectly matched layers are applied. Two ridges are considered to implement the offset between the structures. (b) A comparison of the scattered electric field norm at 490 nm in the xy plane for the ‘simple’ (left) and the ‘original’ (right) type structures with four ridges already reveal differences in the scattering behavior. (c) The reflectance is numerically calculated for different types of structures by measuring the scattered field power normalized by the incident power. The simulated structural patterns are displayed as insets. A broadening of the reflection spectrum is noticed for alternating layers of lamellae. The intensity peak, however, is highest for the simple grating like structure. (d) Simulations of the reflectance for variable incidence angles at 490 nm for the ‘simple’, ‘inspired’ and ‘original’ structures with and without an inclusion of 50 nm offset between successive ridges.

Fig. 3
Fig. 3

Fabrication by e-beam lithography and corresponding SEM images of the Morpho inspired nanostructures. (a) The process flow diagram of the fabrication procedure. SEM images of (b) the ‘simple’ grating like structure with dimensions corresponding to the original butterfly; (c) the ‘inspired’ “Christmas tree” like structure without the alternating lamellae pattern; (d) the ‘original’ Morpho like structure with the dimension of the Morpho sulkowskyi butterfly, and, (e) the ‘original’ Morpho structure considering also the 50 nm offset between two neighboring ridges. The inset at the lower right shows a single “Christmas tree” structure from an inclined view angle.

Fig. 4
Fig. 4

(a) Photos of the blue reflection from the artificial Morpho structure with the inclusion of an offset between neighboring ridges. The illumination area of this sample is 500 μm × 200 nm at an incidence angle of 0°. A bright reflection is still visible in the blue color regime for a tilting angle of 25°. Since the “Christmas trees” lay flat on the sample the size of the visible area increases with the tilting angle. (b) Schematic of the optical setup to measure the angle resolved reflectance quantitatively. A halogen lamp with an aperture to reduce the beam spot is used as the light source. It is followed by back to back lenses to focus the light on the sample. An optical needle with a diameter of 50 μm is used to collect the reflected light which is fed into an optical spectrometer for the subsequent analysis.

Fig. 5
Fig. 5

(a) The reflectance spectra of the four fabricated samples for a normal light incidence. The ‘simple’ grating like structure (Fig. 3(b)) shows the highest and sharp intense blue reflection (solid line). The ‘inspired’ structure (Fig. 3(c)) reveals a narrow band spectrum as expected from the simulation (circles). The ‘original’ structure (Fig. 3(d)) has a broader spectrum with a bandwidth of 50 nm (quadrangles). The inclusion of an offset of 50 nm between neighboring ridges (see Fig. 3(e)) does not change the spectrum for normal illumination (crosses) and the corresponding curve partly covers the data of the ‘original’ structure without offset. (b) The reflection spectra change for a reflection angle of 15°. The reflection of the ‘simple’ grating reduces by 25% and moves out of the blue regime. The ‘original’ structure has a reduction of only 5% in intensity. The intensity reduction is even lower for the structure ‘with offset’. Consequently, the alternating lamellae pattern and the alternating offsets between the ridges are responsible for the wide angular reflection of the Morpho butterfly in the blue regime.

Fig. 6
Fig. 6

Reflection spectra of fabricated original Morpho-type structures with and without offset between the ridges are compared in (a) and (b), respectively. With an offset of 50 nm between neighboring ridges, no reduction of intensity is observed for an angle of 15° and only 5% reduction of intensity with a shift of 45 nm towards UV region for an angle of 25°. The reduction of intensity is much higher for original structure without offset for an angle of 15° degree. This effect becomes even more evident at an angle of 25°.

Equations (3)

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× μ r 1 ( × E ) k 0 2 ( ε r j σ ω ε 0 ) E = 0 ,
σ = 2 n r n i ω ,
ε r = n r 2 n i 2 ,

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