Abstract

The wide angular range of the treelike structure in Morpho butterfly scales was investigated by finite-difference time-domain (FDTD)/particle-swarm-optimization (PSO) analysis. Using the FDTD method, different parameters in the Morpho butterflies’ treelike structure were studied and their contributions to the angular dependence were analyzed. Then a wide angular range was realized by the PSO method from quantitatively designing the lamellae deviation (Δy), which was a crucial parameter with angular range. The field map of the wide-range reflection in a large area was given to confirm the wide angular range. The tristimulus values and corresponding color coordinates for various viewing directions were calculated to confirm the blue color in different observation angles. The wide angular range realized by the FDTD/PSO method will assist us in understanding the scientific principles involved and also in designing artificial optical materials.

© 2013 Optical Society of America

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References

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    [CrossRef]
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  8. R. T. Lee and G. S. Smith, Appl. Opt. 48, 4177 (2009).
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    [CrossRef]
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    [CrossRef]
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2011 (1)

A. Saito, M. Yonezawa, J. Murase, S. Juodkazis, V. Mizeikis, M. Akai-Kasaya, and Y. Kuwahara, J. Nanosci. Nanotechnol. 11, 2785 (2011).
[CrossRef]

2009 (2)

D. Zhu, S. Kinoshita, D. S. Cai, and J. B. Cole, Phys. Rev. E 80, 051924 (2009).
[CrossRef]

R. T. Lee and G. S. Smith, Appl. Opt. 48, 4177 (2009).
[CrossRef]

2007 (2)

M. Shokooh-Saremi and R. Magnusson, Opt. Lett. 32, 894 (2007).
[CrossRef]

S. Banerjee, J. B. Cole, and T. Yatagai, Micron 38, 97 (2007).
[CrossRef]

2006 (3)

S. Berthier, E. Charron, and J. Boulenguez, Insect Sci. 13, 145 (2006).
[CrossRef]

A. Saito, Y. Miyamura, M. Nakajima, Y. Ishikawa, K. Sogo, Y. Kuwahara, and Y. Hirai, J. Vac. Sci. Technol. B 24, 3248 (2006).
[CrossRef]

S. Genovesi, R. Mittra, A. Monorchio, and G. Manara, IEEE Antennas Wirel. Propag. Lett. 5, 277 (2006).
[CrossRef]

2004 (4)

D. W. Boeringer and D. H. Werner, IEEE Trans. Antennas Propag. 52, 771 (2004).
[CrossRef]

J. Robinson and Y. Rahmat-Samii, IEEE Trans. Antennas Propag. 52, 397 (2004).
[CrossRef]

A. Saito, S. Yoshioka, and S. Kinoshita, Proc. SPIE 5526, 188 (2004).
[CrossRef]

L. Plattner, J. R. Soc. Interface 1, 49 (2004).
[CrossRef]

2002 (1)

S. Kinoshita, S. Yoshioka, and K. Kawagoe, Proc. R. Soc. B 269, 1417 (2002).
[CrossRef]

2001 (1)

1999 (1)

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, Proc. R. Soc. B 266, 1403 (1999).
[CrossRef]

1919 (1)

Lord Rayleigh, Phil. Mag. 37, 98 (1919).
[CrossRef]

1911 (1)

A. Michelson, Phil. Mag. 21, 554 (1911).
[CrossRef]

Akai-Kasaya, M.

A. Saito, M. Yonezawa, J. Murase, S. Juodkazis, V. Mizeikis, M. Akai-Kasaya, and Y. Kuwahara, J. Nanosci. Nanotechnol. 11, 2785 (2011).
[CrossRef]

Banerjee, S.

S. Banerjee, J. B. Cole, and T. Yatagai, Micron 38, 97 (2007).
[CrossRef]

Berthier, S.

S. Berthier, E. Charron, and J. Boulenguez, Insect Sci. 13, 145 (2006).
[CrossRef]

Boeringer, D. W.

D. W. Boeringer and D. H. Werner, IEEE Trans. Antennas Propag. 52, 771 (2004).
[CrossRef]

Boulenguez, J.

S. Berthier, E. Charron, and J. Boulenguez, Insect Sci. 13, 145 (2006).
[CrossRef]

Cai, D. S.

D. Zhu, S. Kinoshita, D. S. Cai, and J. B. Cole, Phys. Rev. E 80, 051924 (2009).
[CrossRef]

Charron, E.

S. Berthier, E. Charron, and J. Boulenguez, Insect Sci. 13, 145 (2006).
[CrossRef]

Cole, J. B.

D. Zhu, S. Kinoshita, D. S. Cai, and J. B. Cole, Phys. Rev. E 80, 051924 (2009).
[CrossRef]

S. Banerjee, J. B. Cole, and T. Yatagai, Micron 38, 97 (2007).
[CrossRef]

Enoch, S.

Genovesi, S.

S. Genovesi, R. Mittra, A. Monorchio, and G. Manara, IEEE Antennas Wirel. Propag. Lett. 5, 277 (2006).
[CrossRef]

Gralak, B.

Hirai, Y.

A. Saito, Y. Miyamura, M. Nakajima, Y. Ishikawa, K. Sogo, Y. Kuwahara, and Y. Hirai, J. Vac. Sci. Technol. B 24, 3248 (2006).
[CrossRef]

Ishikawa, Y.

A. Saito, Y. Miyamura, M. Nakajima, Y. Ishikawa, K. Sogo, Y. Kuwahara, and Y. Hirai, J. Vac. Sci. Technol. B 24, 3248 (2006).
[CrossRef]

Juodkazis, S.

A. Saito, M. Yonezawa, J. Murase, S. Juodkazis, V. Mizeikis, M. Akai-Kasaya, and Y. Kuwahara, J. Nanosci. Nanotechnol. 11, 2785 (2011).
[CrossRef]

Kawagoe, K.

S. Kinoshita, S. Yoshioka, and K. Kawagoe, Proc. R. Soc. B 269, 1417 (2002).
[CrossRef]

Kinoshita, S.

D. Zhu, S. Kinoshita, D. S. Cai, and J. B. Cole, Phys. Rev. E 80, 051924 (2009).
[CrossRef]

A. Saito, S. Yoshioka, and S. Kinoshita, Proc. SPIE 5526, 188 (2004).
[CrossRef]

S. Kinoshita, S. Yoshioka, and K. Kawagoe, Proc. R. Soc. B 269, 1417 (2002).
[CrossRef]

Kuwahara, Y.

A. Saito, M. Yonezawa, J. Murase, S. Juodkazis, V. Mizeikis, M. Akai-Kasaya, and Y. Kuwahara, J. Nanosci. Nanotechnol. 11, 2785 (2011).
[CrossRef]

A. Saito, Y. Miyamura, M. Nakajima, Y. Ishikawa, K. Sogo, Y. Kuwahara, and Y. Hirai, J. Vac. Sci. Technol. B 24, 3248 (2006).
[CrossRef]

Lawrence, C. R.

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, Proc. R. Soc. B 266, 1403 (1999).
[CrossRef]

Lee, R. T.

Magnusson, R.

Manara, G.

S. Genovesi, R. Mittra, A. Monorchio, and G. Manara, IEEE Antennas Wirel. Propag. Lett. 5, 277 (2006).
[CrossRef]

Michelson, A.

A. Michelson, Phil. Mag. 21, 554 (1911).
[CrossRef]

Mittra, R.

S. Genovesi, R. Mittra, A. Monorchio, and G. Manara, IEEE Antennas Wirel. Propag. Lett. 5, 277 (2006).
[CrossRef]

Miyamura, Y.

A. Saito, Y. Miyamura, M. Nakajima, Y. Ishikawa, K. Sogo, Y. Kuwahara, and Y. Hirai, J. Vac. Sci. Technol. B 24, 3248 (2006).
[CrossRef]

Mizeikis, V.

A. Saito, M. Yonezawa, J. Murase, S. Juodkazis, V. Mizeikis, M. Akai-Kasaya, and Y. Kuwahara, J. Nanosci. Nanotechnol. 11, 2785 (2011).
[CrossRef]

Monorchio, A.

S. Genovesi, R. Mittra, A. Monorchio, and G. Manara, IEEE Antennas Wirel. Propag. Lett. 5, 277 (2006).
[CrossRef]

Murase, J.

A. Saito, M. Yonezawa, J. Murase, S. Juodkazis, V. Mizeikis, M. Akai-Kasaya, and Y. Kuwahara, J. Nanosci. Nanotechnol. 11, 2785 (2011).
[CrossRef]

Nakajima, M.

A. Saito, Y. Miyamura, M. Nakajima, Y. Ishikawa, K. Sogo, Y. Kuwahara, and Y. Hirai, J. Vac. Sci. Technol. B 24, 3248 (2006).
[CrossRef]

Plattner, L.

L. Plattner, J. R. Soc. Interface 1, 49 (2004).
[CrossRef]

Rahmat-Samii, Y.

J. Robinson and Y. Rahmat-Samii, IEEE Trans. Antennas Propag. 52, 397 (2004).
[CrossRef]

Rayleigh, Lord

Lord Rayleigh, Phil. Mag. 37, 98 (1919).
[CrossRef]

Robinson, J.

J. Robinson and Y. Rahmat-Samii, IEEE Trans. Antennas Propag. 52, 397 (2004).
[CrossRef]

Saito, A.

A. Saito, M. Yonezawa, J. Murase, S. Juodkazis, V. Mizeikis, M. Akai-Kasaya, and Y. Kuwahara, J. Nanosci. Nanotechnol. 11, 2785 (2011).
[CrossRef]

A. Saito, Y. Miyamura, M. Nakajima, Y. Ishikawa, K. Sogo, Y. Kuwahara, and Y. Hirai, J. Vac. Sci. Technol. B 24, 3248 (2006).
[CrossRef]

A. Saito, S. Yoshioka, and S. Kinoshita, Proc. SPIE 5526, 188 (2004).
[CrossRef]

Sambles, J. R.

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, Proc. R. Soc. B 266, 1403 (1999).
[CrossRef]

Shokooh-Saremi, M.

Smith, G. S.

Sogo, K.

A. Saito, Y. Miyamura, M. Nakajima, Y. Ishikawa, K. Sogo, Y. Kuwahara, and Y. Hirai, J. Vac. Sci. Technol. B 24, 3248 (2006).
[CrossRef]

Tayeb, G.

Vukusic, P.

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, Proc. R. Soc. B 266, 1403 (1999).
[CrossRef]

Werner, D. H.

D. W. Boeringer and D. H. Werner, IEEE Trans. Antennas Propag. 52, 771 (2004).
[CrossRef]

Wootton, R. J.

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, Proc. R. Soc. B 266, 1403 (1999).
[CrossRef]

Yatagai, T.

S. Banerjee, J. B. Cole, and T. Yatagai, Micron 38, 97 (2007).
[CrossRef]

Yonezawa, M.

A. Saito, M. Yonezawa, J. Murase, S. Juodkazis, V. Mizeikis, M. Akai-Kasaya, and Y. Kuwahara, J. Nanosci. Nanotechnol. 11, 2785 (2011).
[CrossRef]

Yoshioka, S.

A. Saito, S. Yoshioka, and S. Kinoshita, Proc. SPIE 5526, 188 (2004).
[CrossRef]

S. Kinoshita, S. Yoshioka, and K. Kawagoe, Proc. R. Soc. B 269, 1417 (2002).
[CrossRef]

Zhu, D.

D. Zhu, S. Kinoshita, D. S. Cai, and J. B. Cole, Phys. Rev. E 80, 051924 (2009).
[CrossRef]

Appl. Opt. (1)

IEEE Antennas Wirel. Propag. Lett. (1)

S. Genovesi, R. Mittra, A. Monorchio, and G. Manara, IEEE Antennas Wirel. Propag. Lett. 5, 277 (2006).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

D. W. Boeringer and D. H. Werner, IEEE Trans. Antennas Propag. 52, 771 (2004).
[CrossRef]

J. Robinson and Y. Rahmat-Samii, IEEE Trans. Antennas Propag. 52, 397 (2004).
[CrossRef]

Insect Sci. (1)

S. Berthier, E. Charron, and J. Boulenguez, Insect Sci. 13, 145 (2006).
[CrossRef]

J. Nanosci. Nanotechnol. (1)

A. Saito, M. Yonezawa, J. Murase, S. Juodkazis, V. Mizeikis, M. Akai-Kasaya, and Y. Kuwahara, J. Nanosci. Nanotechnol. 11, 2785 (2011).
[CrossRef]

J. R. Soc. Interface (1)

L. Plattner, J. R. Soc. Interface 1, 49 (2004).
[CrossRef]

J. Vac. Sci. Technol. B (1)

A. Saito, Y. Miyamura, M. Nakajima, Y. Ishikawa, K. Sogo, Y. Kuwahara, and Y. Hirai, J. Vac. Sci. Technol. B 24, 3248 (2006).
[CrossRef]

Micron (1)

S. Banerjee, J. B. Cole, and T. Yatagai, Micron 38, 97 (2007).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phil. Mag. (2)

A. Michelson, Phil. Mag. 21, 554 (1911).
[CrossRef]

Lord Rayleigh, Phil. Mag. 37, 98 (1919).
[CrossRef]

Phys. Rev. E (1)

D. Zhu, S. Kinoshita, D. S. Cai, and J. B. Cole, Phys. Rev. E 80, 051924 (2009).
[CrossRef]

Proc. R. Soc. B (2)

S. Kinoshita, S. Yoshioka, and K. Kawagoe, Proc. R. Soc. B 269, 1417 (2002).
[CrossRef]

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, Proc. R. Soc. B 266, 1403 (1999).
[CrossRef]

Proc. SPIE (1)

A. Saito, S. Yoshioka, and S. Kinoshita, Proc. SPIE 5526, 188 (2004).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Schematic of simple treelike structure, model (S).

Fig. 2.
Fig. 2.

Angular dependence of the reflection intensities of model (S): (a) three-dimensional β-wavelength-reflectance color map surface plot, (b) two-dimensional β-wavelength filled contour plot, (c) two-dimensional wavelength-reflectance line plot, and (d) two-dimensional β-reflectance line plot (β is observation angle).

Fig. 3.
Fig. 3.

Filled contour plot of angular dependence versus wavelength of model (S) with (a) T=750nm, (b) T=4×750nm; filled contour plot of angular dependence versus wavelength of model (S), with (c) Δy=0nm and (d) Δy=100nm.

Fig. 4.
Fig. 4.

(a) Schematic of model (F). (b)–(d) Field maps of Δy=0nm, Δy=118nm, and Δy=dn (model F), respectively; the insets are two-dimensional β-reflectance line plots. (e) Chromaticity coordinates of model (F) corresponding to colors with different viewing angles.

Equations (2)

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Δβ=λNdcosβ.
γ=sin1(kλ2d).

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