Elucidating the stop bands of structurally colored systems through recursion. Amir, A. & Vukusic, P. American Journal of Physics, 81(4):253--257, April, 2013. ![Elucidating the stop bands of structurally colored systems through recursion [link]](https://bibbase.org/img/filetypes/link.svg "link")
Paper doi abstract bibtex Interference is the source of some of the spectacular colors of animals and plants in nature. In some of these systems, the physical structure consists of an ordered array of layers with alternating high and low refractive indices. This periodicity leads to an optical band structure that is analogous to the electronic band structure encountered in semiconductor physics: specific bands of wavelengths (the stop bands) are perfectly reflected. Here, we present a minimal model for optical band structure in a periodic multilayer structure and solve it using recursion relations. The stop bands emerge in the limit of an infinite number of layers by finding the fixed point of the recursion. We compare to experimental data for various beetles, whose optical structure resembles the proposed model. Thus, using only the phenomenon of interference and the idea of recursion, we are able to elucidate the concept of band structure in the context of the experimentally observed high reflectance and iridescent appearance of structurally colored beetles.
@article{amir_elucidating_2013,
title = {Elucidating the stop bands of structurally colored systems through recursion},
volume = {81},
issn = {0002-9505, 1943-2909},
url = {http://scitation.aip.org/content/aapt/journal/ajp/81/4/10.1119/1.4789883},
doi = {10.1119/1.4789883},
abstract = {Interference is the source of some of the spectacular colors of animals and plants in nature. In some of these systems, the physical structure consists of an ordered array of layers with alternating high and low refractive indices. This periodicity leads to an optical band structure that is analogous to the electronic band structure encountered in semiconductor physics: specific bands of wavelengths (the stop bands) are perfectly reflected. Here, we present a minimal model for optical band structure in a periodic multilayer structure and solve it using recursion relations. The stop bands emerge in the limit of an infinite number of layers by finding the fixed point of the recursion. We compare to experimental data for various beetles, whose optical structure resembles the proposed model. Thus, using only the phenomenon of interference and the idea of recursion, we are able to elucidate the concept of band structure in the context of the experimentally observed high reflectance and iridescent appearance of structurally colored beetles.},
number = {4},
urldate = {2014-10-03},
journal = {American Journal of Physics},
author = {Amir, Ariel and Vukusic, Peter},
month = apr,
year = {2013},
keywords = {Band structure, Fabry-Perot interferometers, Mechanical waves, Reflection coefficient, Refractive index},
pages = {253--257},
file = {Amir and Vukusic - 2012 - Elucidating the stop bands of structurally colored.pdf:/Users/baptiste/Library/Application Support/Zotero/Profiles/d9rq1atq.default/zotero/storage/FQDH8SSC/Amir and Vukusic - 2012 - Elucidating the stop bands of structurally colored.pdf:application/pdf}
}
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