We introduce a new class of functional correlated disordered materials, termed gyromorphs, which uniquely combine liquidlike translational disorder with quasi-long-range rotational order, induced by a ring of $G$ delta peaks in their structure factor. We generate gyromorphs in 2D and 3D by spectral optimization methods, verifying that they display strong discrete rotational order but no long-range translational order, while maintaining rotational isotropy at short range for sufficiently large $G$. Using a coupled dipoles approximation, we numerically show that these structures outperform quasicrystals, stealthy hyperuniformity, and Vogel spirals in the formation of low-index-contrast isotropic band gaps in 2D, for both scalar and vector waves, and open complete isotropic band gaps in 3D. This claim is further supported by analytical effective-medium theory and by numerical estimates of scattering mean-free paths. Finally, we introduce “polygyromorphs” with several rotational symmetries at different length scales (i.e., multiple rings of delta peaks), enabling the formation of multiple band gaps in a single structure, thereby paving the way for fine control over optical properties.

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• Functional materials
• Inverse problems
• Optimization problems
• Photonics
• Classical electromagnetism
• Green's function methods
• Materials modeling
• Numerical approximation & analysis