Structural color of Morpho butterflies

American Journal of Physics

Volumn 77, Issue 11, 2009, Pages 1010-1019

  Smith, Glenn S ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 70350007914     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.3192768     Document Type: Article

References (41)

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17. 2 =-1.
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19. Pigmentary color is caused by the absorption of certain wavelengths in the visible spectrum. Absorption occurs because a photon of the incident light has the right energy to excite an electron from a lower state to a higher state in a region of a molecule known as a "chromophore." A bleaching agent, such as hydrogen peroxide (a strong oxidizer), alters the chromophore and either destroys the mechanism for absorption or moves it to wavelengths outside the visible spectrum. K. Nassau, The Physics and Chemistry of Color: The Fifteen Causes of Color, 2nd ed. (Wiley-Interscience, New York, 2001); Also see 〈 en.wikipedia.org/wiki/Chromophore 〉 and 〈 en.wikipedia.org/wiki/Bleach 〉.
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21. Some of the authors provided results for incident light with two orthogonal states of linear polarization (TE and TM). In such cases, these states have been combined to obtain results for unpolarized light.
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26. Notice, in the model (shown in dark gray), a small section of the lowest lamella has been included that is outside the unit cell to make all of the sections of lamellae in the model the same size, which greatly simplifies the calculations.
27. The notation TE (TM) indicates that the electric (magnetic) field of the incident plane wave is transverse to the plane of symmetry of the ridge (x-y plane), which is also the plane of incidence: the plane containing the vector wave number for the incident wave and the normal to the surface of the lamellae. Sometimes, the TE case is indicated by E, ⊥, s, or σ (electric field perpendicular to the plane of incidence) and the TM case by H, p, or π (electric field parallel to the plane of incidence).
28. ωt].
29. This relation for the equivalent current may be more familiar in the time domain: J b = P /t.
30. G. S. Smith, An Introduction to Classical Electromagnetic Radiation (Cambridge U. P., Cambridge, 1997), pp. 352-355.
31. The superscript sr is used to indicate that this is the "scattered radiated" field: The part of the scattered field that behaves as 1/r, where r is the radial distance from the ridge.
32. This topic is covered in many introductory textbooks on electromagnetism and optics, for example, P. C. Clemmow, An Introduction to Electromagnetic Theory (Cambridge U. P., Cambridge, 1973), pp. 201-203; E. Hecht, Optics, 4th ed. (Addison-Wesley, San Francisco, CA, 2002), pp. 111-122. Here the convention used is one in which the TE (TM) reflection and transmission coefficients apply to the w component of the electric field (magnetic field), and the angles are measured with respect to the normal to the interface.
33. Because of the many approximations made in estimating the electric field within the lamellae, the analysis is accurate only for obtaining the relative amount of scattering for different wavelengths. Therefore, all plots are presented in the normalized form.
34. A factor of 1/N has been added before the sum; this factor does not affect the proportionality.
35. For visible wavelengths (400 nmλ700 nm), we have 0.09h/λ0.16, and the value of the first sinc function is within the range of 0.73-0.90.
36. n cos φ/cos γ.
37. Reference, pp. 493-506.
38. 0, Eq. becomes comparable to the results for the two-dimensional structure described in Ref..
39. The small gaps in the curves for A 2 at angles near φ=0° occur because there are no real solutions to the equations in this region.
40. K. Watanabe, T. Hoshino, K. Kanda, Y. Haruyama, and S. Matsui, " Brilliant blue observation from a Morpho-buttterfly-scale quasi-structure., " Jpn. J. Appl. Phys., Part 2 0021-4922 44, L48-L50 (2005). 10.1143/JJAP.44.L48 (Pubitemid 40540763)
41. A. Saito, Y. Ishikawa, Y. Miyamura, M. Akai-Kasaya, and Y. Kuwahara, " Optimization of reproduced Morpho-blue coloration.," Proc. SPIE 0277-786X 6767, 676706-1-8 (2007). 10.1117/12.733954 (Pubitemid 351563203)