Gyromorphs: a new class of functional disordered materials

Abstract

We introduce a new class of functional correlated disordered materials, termed Gyromorphs, which uniquely combine liquid-like 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 bandgaps in $2d$, for both scalar and vector waves, and open complete isotropic bandgaps 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 bandgaps in a single structure, thereby paving the way for fine control over optical properties.

Figures (10)

• Figure 1: Introducing: Gyromorphs.$(a)$ Section of the point pattern of a $60$-fold gyromorph. We show the shortest distance displaying 60-fold order. $(b)$ Corresponding structure factor. $(c)$ Corresponding pair correlation function $g(\bm{r})$ near the origin. $(d)$ Radial structure factor $S(k)$ (top) and radial distribution function $g(r)$ (bottom) for the 60-fold gyromorph.
• Figure 2: Order in gyromorphs.$(a)$$S(k)$ of a $60$-fold gyromorph (blue) with $N\sim 10^5$ ($K L / 2\pi = 300$), compared to a Percus-Yevick $S(k)$ for $\phi = 0.57$ (dashed red line) in log scales. $(b)$ Corresponding radially averaged profile of peaks across $K$ values, rescaled by peak height (colored lines). A solid black line indicates the radial profile of $\text{sinc}^2(k_x L/2)\text{sinc}^2(k_y L/2)$. Inset: Rescaled peak height $G S(\bm{k}_p)$ against $N$, in log scales, across $G$ (colored symbols). A dashed black line shows $GS(\bm{k}_p) = 3.5 N$.
• Figure 3: Optical properties of gyromorphs We use an example 60-fold gyromorph and focus on TE polarization. $(a)$ Intensity transmission for frequencies $40 \leq k_0L/2\pi \leq 60$ (radial direction) and $360$ incident angles (orthoradial direction) of a source Gaussian beam. $(b)$ Relative LDOS change with respect to vacuum, averaged over $1000$ random points, highlighting a dip close to $k_0 = K / 2$ (here $K L / 2\pi = 100$). $(c)$ Spatial map of the intensity at angle $0$ and $k_0 L / 2\pi = 47.6$, which corresponds to the minimum of both transmission and LDOS. $(d)$ Corresponding LDOS map.
• Figure 4: Comparison with other systems Top row: TE intensity transmissions as a function of $k_0$ (radial) and beam orientation (orthoradial) for (from left to right) $10$- and $60$-fold de Bruijn quasicrystals, an SHU structure, and a Vogel spiral. Bottom row: Corresponding $\delta\varrho$ (red lines), with the $60$-fold gyromorph shown as a light gray line. All results are obtained for $n=3$, $\phi = 0.05$.
• Figure 5: Opening the gap. Intensity maps of DOS against frequency and filling fraction at $n=3$, averaged over $30$ systems, for $(a)$ gyromorphs and $(b)$ SHU systems. Dotted red line: $\phi = 0.05$. $(c)-(d)$ Same plots for scalar waves.