Disorder engineering: From structural coloration to acoustic filters

We study localization of waves in a one-dimensional disordered metamaterial of bilayers composed 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 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 metamaterials which selectively allow 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 line shape whose width becomes narrower as the number of disordered layers is increased.