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  • January 2014

Optics InfoBase > Spotlight on Optics > Design of structurally colored surfaces based on scalar diffraction theory


Design of structurally colored surfaces based on scalar diffraction theory

Published in JOSA B, Vol. 31 Issue 2, pp.207-217 (2014)
by Villads Egede Johansen, Jacob Andkjær, and Ole Sigmund

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Spotlight summary: Some of the most striking colors observed in nature are produced by structural coloration. The colors of peacock feathers, morpho butterfly wings, marble berries and jewel beetle shells are all produced, at least in part, by nano-scale features which rely on spatial structure to selectively reflect certain optical wavelengths. Man-made objects also exhibit structural coloration, with a familiar example being the characteristic ‘rainbow’ patterns reflected from a compact disk. More deliberately designed structural coloration has also been successfully demonstrated; however, even using direct biomimicry, the complexity of natural structural coloration has not been artificially rivaled. A major challenge in engineering structurally-colored surfaces is determining what spatial patterns will produce a desired reflectivity response. The work presented here, by Johansen and coworkers, provides a new tool for designing spatial profiles for structural coloration.

There are mature methods for determining the reflectivity of a surface (as a function of incidence angle, reflected angles and wavelength) given the spatial structure of a surface and the bulk optical properties of the constituent material. However, solving the inverse problem - that is, designing an optical surface to have a desired angular and spectral response - has proven more difficult. It is this inverse problem that the authors address here. The approach taken is one of numerical optimization: a spatially discretized representation of the surface provides a finite dimensional search space; and a metric rewarding brightness and fidelity to the target reflectivity is used as an objective function. The stability of the optimization (and the practicality of the resultant design) is also improved by penalizing sharp spatial gradients in a regularization term.

While the principle of the numerical optimization is relatively simple, the computational practicalities of realizing the search are difficult. Many candidate surface profiles need to be considered and doing so involves solving a very general diffraction problem. The authors attack this problem on two fronts: first, reasonable simplifications are made to the physical-optics model (i.e., scalar diffraction theory is employed); and second, the problem is cast in a computationally efficient manner. This second activity includes an elegant recursive method and the casting of the problem in a manner compatible with gradient-based search algorithms. The resulting framework is well suited for numerical optimization and the authors present a number of illustrative examples. While the modeling assumptions and the sheer dimensionality of the problem lead to some limits to the applicability of the method (e.g., only a single incidence angle is considered, the spatial structures shown vary in only one dimension, the surface sizes are relatively modest, and the scalar diffraction model does not represent complex effects such as multi-path reflection), the authors are forthright in their discussion of the framework’s capabilities. I expect that future work (and ever-improving computational hardware) will expand these capabilities and help spur extended application of this framework for the quantitative design of structurally colored surfaces.

--Brynmor Davis



Technical Division: Optical Design and Instrumentation
ToC Category: Diffraction and Gratings
OCIS Codes: (050.2770) Diffraction and gratings : Gratings
(230.1950) Optical devices : Diffraction gratings
(240.6700) Optics at surfaces : Surfaces
(330.1690) Vision, color, and visual optics : Color
(050.6624) Diffraction and gratings : Subwavelength structures
(330.7326) Vision, color, and visual optics : Visual optics, modeling


Posted on January 08, 2014

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