Evolutionary algorithms converge towards evolved biological photonic structures

Abstract

nature features a plethora of extraordinary photonic architectures that have been optimized through natural evolution in order to more efficiently reflect, absorb or scatter light. While numerical optimization is increasingly and successfully used in photonics, it has yet to replicate any of these complex naturally occurring structures. Using evolutionary algorithms inspired by natural evolution and performing particular optimizations (maximize reflection for a given wavelength, for a broad range of wavelength or maximize the scattering of light), we have retrieved the most stereotypical natural photonic structures. Whether those structures are Bragg mirrors, chirped dielectric mirrors or the gratings on top of Morpho butterfly wings, our results indicate how such regular structures might have spontaneously emerged in nature and to which precise optical or fabrication constraints they respond. Comparing algorithms show that recombination between individuals, inspired by sexual reproduction, confers a clear advantage that can be linked to the fact that photonic structures are fundamentally modular: each part of the structure has a role which can be understood almost independently from the rest. Such an in silico evolution also suggests original and elegant solutions to practical problems, as illustrated by the design of counter-intuitive anti-reflective coatings for solar cells. Nature features a diversity of photonic architectures producing the most vivid optical effects 1-3. Regularly alternating chitin and melanin layers constitutes, for instance, a very efficient way to reflect light, giving the structure a colored metallic appearance. Such structures can be found on the cuticle of many insects, including common flies (e.g. Lucilia sericata) or beetles (e.g. Chrysolina americana or Asphidomorpha tecta). These ubiquitous structures have been optimized through natural evolution during millions of years, which suggests that they provide an evolutionary advantage to all the animals. While such dielectric, multilayered mirrors 4 are relatively simple, more complicated architectures can be found in many animals. Most famous are probably the nanosized christmas-tree-like ridge structure of Morpho butterfly wing scales 5,6. These nano-sized christmas-trees, assembled of transparent chitin, are responsible for the bright iridescent blue color of the Morpho rethenor wings which has made the butterfly so famous. Numerical optimization has been extensively used in photonics for the last decades, especially in the context of optical filters 7,8 for their technological importance-the multiplexers used to increase the bandwidth of optical fibers rely on such multilayered structures. By 'simply' choosing the thicknesses of transparent layers with alternating refractive index (RI), it is possible to design and manufacture virtually any kind of optical filter 9. Efficient algorithms have been developed to solve precisely this kind of inverse problem: finding the right geometrical (thicknesses) and optical (RI) parameters of the...

Analysis and fabrication of antireflective coating for photovoltaics based on a photonic-crystal concept and generated by evolutionary optimization

“…The quantity to be maximized here was the short circuit current in the 375-750-nm range, assuming a quantum yield equal to 1, as described in [13]. Among the different algorithms which were tested, differential evolution (DE) proved to be the most efficient algorithm for this kind of problem, generating solutions faster and more reliably than any other global algorithm [10].…”

“…In order to chose the right algorithm as well as the right variant and parameters for our problem, we have compared different algorithms and their variants on the most modular problem we have identified: the case of the high reflectance filter on a broad spectral range, leading to a chirped design [19]. On this problem, the evolutionary algorithm called differential evolution is the most efficient [10], but several variants of DE exist. After comparing the most common variants (DE/rand/1, DE/best/1, DE/randToBest/1, DE/currToBest/1, DE/rand/2, and DE/best/2, identified according to the usual classification [20]) we have selected the DE/randToBest/1 variant.…”

“…refractive indices vary [10]. We underline that in some of our optimizations we allow the refractive indices of each layer to vary.…”

“…A pioneering work however has suggested more than a decade ago that choosing the right optimization algorithm is important, by showing that evolutionary algorithms, which are versatile and global optimization methods, are able to generate regular photonic structures spontaneously. More recently, it has been shown that such algorithms are indeed perfectly able to retrieve naturally occurring photonic structures in the most simple yet emblematic cases [10].…”

“…The emergence of a partially periodic solution may seem at first surprising. Photonic crystals may present a forbidden band, and thus behave as a frequency selective mirror-that is why in all the other optimization problems they emerge when the reflection, not the transmission, is maximized [10]. The optimization results thus suggest that photonic crystals may be utilized when they are transparent as efficient antireflective coatings.…”