Fish-Inspired Fractals Guide Optical Coating Design
STATE COLLEGE, Pa. — Fish scales could serve as a model for better broadband reflectors and custom multispectral filters.
"We are proposing a model that uses fractal geometry to describe the layering in the biological structure of silvery fish," said Pennsylvania State University postdoctoral researcher Jeremy Bossard. "While we are not trying to reproduce the structure found in nature, the same model could guide the design of devices such as broadband mirrors."
An Asian ribbonfish.
The proposed model also contributed to the understanding of reflective layering in the skin of some organisms. The shiny skins of certain ribbonfish reflect light across a broad range of wavelengths, giving them a brilliant metallic appearance. The reflectivity is the result of stacked layers of crystalline organic compounds embedded in the skin's cytoplasm.
Some organisms with metallic sheens have layers that are stacked in a regular pattern, while others, including the ribbonfish, have random stacking patterns. The Penn State team determined that the stacking is not completely random and developed mathematical algorithms to replicate those patterns in semiconductor materials.
"There is an underlying pattern but there is randomness built in, similar to the way that living trees have an overall fractal pattern but do not grow symmetrically," Bossard said.
A transmission electron microscope image of ribbonfish skin (a) shows random arrangements of crystalline guanine embedded in cytoplasm. The scale bar is 5 μm. A superlattice of cytoplasm and crystal layers matching the red dashed line in (a) is reproduced in (b) and transformed in (c) into a fractal pattern with random changes introduced. Courtesy of the Werner Group/Penn State.
Fractals have been called the "geometry of nature" because they can help describe the irregular but self-similar patterns that occur in natural objects such as branching tree limbs. The researchers used a 1D fractal, known as a Cantor bar fractal, which is a line divided by spaces or gaps. Normally Cantor fractals appear to be very regular, but when random changes are introduced to the geometry, a more complex pattern emerges resembling the layering of reflective layers in ribbonfish skin.
The researchers then used another nature-inspired computational method — a genetic algorithm — that mimics Darwinian evolution to create successive generations of fractal patterns from the parent patterns. Over approximately 100 generations, the patterns converged on the best design to meet all the target requirements.
Using these fractals and the genetic algorithm, the researchers mathematically generated patterns targeting optical functions in the mid- and near-infrared ranges, including broadband reflection.
They proposed that the design approach could be used to develop nanoscale stacks with customized reflective spectra. Other applications stemming from the research could include the improvement optical coatings for glass, laser protection, IR imaging systems, optical communication systems and photovoltaics.
The research was published in the Journal of the Royal Society Interface (doi: 10.1098/rsif.2015.0975).
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