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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. A schematic of a periodic on average disordered metamaterial consisting of disordered bilayers of two materials with wave speeds c 1c 2respectively.

The thickness of material 1, denoted by d 1varies randomly whereas the thickness of material 2 is kept constant at a value of d 2 which is much smaller than the average value of d 1. This is reminiscent of the random Kronig-Penny model whereby we place scatterers with thickness d 2 and wave speed c 2 randomly along the length of a homogenous background medium with wave speed c 1.

Thus, the parameters of material 2 can be tuned to design materials with a specific frequency response. A butterfly Koi fish, exhibiting a broadband reflectance spectrum. A magnified scanning electron microscopy SEM image of an iridophore cell extracted from the skin of Koi fish [ 11 ], well approximated as an alternating arrangement of guanine crystals Cr and cytoplasm Cy.

## The Design And Analysis Of Algorithms

Image reproduced from Ref. The blue curves correspond to parameters nitib the Koi fish with the thicknesses of cytoplasm layers Gaussian distributed between nm and standard deviation 94 nm and the thickness of the guanine layer nearly constant at 19 nm for a total of 64 layers. The reflection spectrum corresponds to normal incidence.

The average power transmitted as a function of frequency through a disordered metamaterial consisting of a periodic on average alignment of bilayers where the thickness of one of the layers scatterer is held constant at a value of d 2whereas the thickness of the disordered layer is drawn from a uniform distribution between 0.

For illustration, we have chosen two values: The symbols yellow square correspond to numerical data obtained after ensemble averaging realizations of the logarithm of the power transmitted obtained by calculating the product of transfer matrices comprising the disordered metamaterial, the solid curve blue corresponds to the analytical expression derived in Eq.

We compare the spectrum of reflected power obtained analytically solid curves as given in Eq.

### The Design And Analysis Of Algorithms by Nitin Upadhyay

Here, the horizontal black line corresponds to the wavelength- and disorder-independent reflection spectrum obtained using Eq. D1 with the localization length derived in Eq.

Materials 2— Published 5 July Abstract 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. Weyl fermions are observed in a solid.

Figure 1 A schematic of a periodic on average disordered metamaterial consisting of disordered bilayers of two materials with wave speeds c 1c 2respectively. Figure 4 The average power transmitted as a function of frequency through a disordered metamaterial consisting of a periodic on average alignment of bilayers where the thickness of one of the layers scatterer is held constant at a value of d 2whereas the thickness of the disordered layer is drawn ypadhyay a uniform distribution between 0.

Figure 6 We compare the spectrum of reflected power obtained daa solid curves as given in Eq. Sign up to receive regular email alerts from Physical Review Materials. Series I Physics Physique Fizika.