Disorder engineering: From structural coloration to acoustic filters

TL;DR

This paper explores Anderson localization in one-dimensional disordered meta-materials, revealing a new strong disorder regime where localization depends on frequency and scatterer properties, with applications in structural coloration and acoustic filtering.

Contribution

It identifies a novel strong disorder regime where localization length is independent of disorder amount, and demonstrates how tuning scatterer thickness can engineer disordered meta-materials with selective transmission.

Findings

Localization length depends on frequency and scatterer properties.

Natural example: Koi fish coloration explained by Anderson localization.

Disordered layers produce Gaussian transmission lineshapes that narrow with more layers.

Abstract

We study Anderson localization of waves in a one dimensional disordered meta-material of bilayers comprising of thin fixed length scatterers placed randomly along a homogenous medium. As an interplay between order and disorder, we identify a new regime of strong disorder where the localization length becomes independent of the amount of disorder but depends on the frequency of the wave excitation and on the properties of the fixed length scatterer. As an example of a naturally occurring nearly one dimensional disordered bilayer, we calculate the wavelength dependent reflection spectrum for Koi fish using the experimentally measured parameters, and find that the main mechanisms for the emergence of their silver structural coloration can be explained through the phenomenon of Anderson localization of light in the regime of strong disorder discussed above. Finally, we show that by tuning the thickness of the fixed length scatterer, the above design principles could be used to engineer disordered meta-materials which selectively allows harmonics of a fundamental frequency to be transmitted in an effect which is similar to the insertion of a half wave cavity in a quarter wavelength stack. However, in contrast to the Lorentzian resonant peak of a half-wave cavity, we find that our disordered layer has a Gaussian lineshape whose width becomes narrower as the number of disordered layers is increased.