Elliptical-rod geometries enhance photonic band gaps in disordered stealthy hyperuniform photonic crystals

TL;DR

The paper investigates 2D photonic crystals composed of elliptical dielectric rods arranged on stealthy hyperuniform patterns, defined by $S(m{k})=0$ for $0<|\bm{k}|q K$ and quantified by stealthiness $\chi$. Using plane-wave expansion of Maxwell's equations, the TM-mode band structures are computed, revealing that increasing the rod aspect ratio $\alpha$ and optimizing the rotation angle $\theta$ can enlarge the photonic band gap (PBG) relative to cylindrical rods, with the effect persisting across higher $\chi$ values. The study shows that elliptical rods can outperform cylindrical ones in certain orientation ranges, and that per-rod optimization over $\{\alpha_i,\theta_i\}$ further boosts the relative PBG (e.g., from $36.7\%$ to $39.5\%$), demonstrating a robust design strategy for isotropic PBGs in disordered hyperuniform photonic crystals. Overall, the work highlights a pathway to large, isotropic PBGs in structurally disordered photonic materials, with potential applications in photonic waveguides and integrated circuits, and suggests avenues for exploring alternate dielectrics and geometries beyond silicon.

Abstract

We study two-dimensional photonic crystals composed of elliptical dielectric rods arranged according to stealthy hyperuniform point patterns. These patterns are characterized by the structure factor, which vanishes for 0 < |k| <= K, where k is the wave number and K denotes the cutoff wave number specifying the stealthiness of the pattern. The optical properties of the photonic crystals are analyzed by applying the plane-wave expansion method to Maxwell's equations. We demonstrate that photonic crystals composed of elliptical dielectric rods can exhibit larger photonic band gaps than those with cylindrical rods when both the rod orientation and aspect ratio are properly optimized. This behavior contrasts with that of periodic lattices such as triangular or square arrays. These findings shed light on the crucial role of structural anisotropy and aperiodic structure in enhancing photonic band-gap formation.

Figures (5)

• Figure 1: (a) Stealthy hyperuniform point pattern with $\chi=0.41$ in the system with $N=16$ and $(L_x, L_y)=(4, 2\sqrt{3})$ and (b) its structure factor, plotted on a logarithmic scale. Dashed line indicates the boundary of the window function.
• Figure 2: (a) Dielectric profile for the photonic crystal composed of the elliptrical rods on the triangular lattice with $\alpha=1.1$ and $\theta=60^{\circ}$. (b) Cylindrical and elliptical rods. (c) Dispersion relation for the photonic crystal with $\alpha=1.1$ and $\theta=60^{\circ}$. (d) Relative PBG as a function of $\theta$ in the system with $\alpha = 1.0$ (red dashed line), $1.05$ (blue circles), $1.1$ (green squares), and $1.15$ (red triangles).
• Figure 3: (a) Dielectric profile for the photonic crystal composed of the elliptrical rods with $R=0.2$,$\alpha=1.1$ and $\theta=0^{\circ}$ on the stealthy hyperuniform structure with $\chi = 0.41$. (b) Upper and lower band edges as a function of $\alpha$ for the elliptical rods with $\theta=0^{\circ}$. Red squares (black circles) represent the results for the stealthy hyperuniform point pattern (triangular lattice). (c) Relative PBG as a function of $\theta$ when $\alpha = 1.0$ (red dashed line), $1.05$ (blue circles), $1.1$ (green squares), and $1.15$ (red triangles).
• Figure 4: Dielectric profile (left) and the corresponding relative PBGs (right) for different configurations (a), (b), (c), and (d) with the same stealthiness parameter $\chi=0.63$. The relative PBGs are shown as a function of the rotation angle $\theta$ of the elliptical rods. The red dashed line denotes the relative PBG for cylindrical rods ($\alpha=1$), and blue circles, green squares, red triangles represent elliptical rods with $\alpha=1.05,1.10,1.15$, respectively.
• Figure 5: Dielectric profiles for the (a) cylindrical rod structure and (b) elliptical rod structure optimized with respect to $\{\alpha_i, \theta_i\}$. (c) DOS for the photonic crystals with cylindrical (left) and elliptical rods (right).