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Disordered hyperuniform materials are an emerging class of exotic amorphousstates of matter that endow them with singular physical properties. Here, wegeneralize the Fourier-space based numerical construction procedure fordesigning {\it isotropic} disordered hyperuniform two-phase heterogeneousmaterials (i.e., composites) developed by Chen and Torquato [Acta Mater. {\bf142}, 152 (2018)] to {\it anisotropic} microstructures by explicitlyincorporating the {\it vector-dependent} spectral density function ${\tilde\chi}_{_V}({\bf k})$ of {\it arbitrary form} that is realizable. We demonstratethe utility of the procedure by generating a wide spectrum of {\it anisotropic}stealthy hyperuniform (SHU) microstructures with ${\tilde \chi}_{_V}({\bf k}) =0$ for ${\bf k} \in \Omega$. We show how different exclusion-region shapes withvarious discrete symmetries and varying size affect the resulting statisticallyanisotropic microstructures as a function of the and phase volume fraction. Wefind that, among other properties, the directional hyperuniform behaviorsimposed by the shape asymmetry (or anisotropy) of certain exclusion regionsgive rise to distinct anisotropic structures and degree of uniformity in thedistribution of the phases on intermediate and large length scales alongdifferent directions. Moreover, while the anisotropic exclusion regions imposestrong constraints on the {\it global} symmetry of the resulting media, theycan still possess almost isotropic {\it local} structures. Our constructionalgorithm enables one to control the statistical anisotropy of compositemicrostructures which is crucial to engineering directional optical, transportand mechanical properties of two-phase composite media.

Computational Design of Anisotropic Stealthy Hyperuniform Composites with Engineered Directional Scattering Properties