High-$Q$ optical cavities in hyperuniform disordered materials

We introduce designs for high-$Q$ photonic cavities in slab architectures in hyperuniform disordered solids displaying isotropic band gaps. Despite their disordered character, hyperuniform disordered structures have the ability to tightly confine the transverse electric-polarized radiation in slab configurations that are readily fabricable. The architectures are based on carefully designed local modifications of otherwise unperturbed hyperuniform dielectric structures. We identify a wide range of confined cavity modes, which can be classified according to their approximate symmetry (monopole, dipole, quadrupole, etc.) of the confined electromagnetic wave pattern. We demonstrate that quality factors $Q>{10}^9$ can be achieved for purely two-dimensional structures, and that for three-dimensional finite-height photonic slabs, quality factors $Q>20000$ can be maintained.

Figure 1

Magnetic field distributions of two Anderson-like localized modes, below the lower (left) and above the upper (right) PBG edge, respectively.

Figure 2

Magnetic field distribution for the four defect modes in the unmodified H1 cavity in a structure of wall thickness $w=0.2a$. The modes are labeled $D_1,D_2,Q_1,Q_2$ (shown from left to right in the figure).

Figure 3

Frequencies of the cavity modes in the band gap obtained for different radii of a hole placed at the center of the cavity.

Figure 4

Magnetic field distribution for the five cavity modes in the enlarged H1 cavity with center hole $r=0.2a$ in a structure of wall thickness $w=0.4a$. The modes are labeled $D_1,D_2$, $Q$, $H$, $O$, left to right.

Figure 5

Frequencies of the cavity modes in the band gap obtained for different radii of a hole placed at the center of the cavity. Modes are labeled according to their number of pole lobes and their approximate symmetry. Different colors are used for modes with the same number of lobes and same approximate symmetry, but have distinct field patterns. Crossover intermediate modes are colored black.

Figure 6

Intensity distribution (yellow) of a confined cavity mode in a hyperuniform disordered honeycomb photonic slab (blue).

Figure 7

Spectrum of the Fourier components of the electric field distribution for the $D_1$ mode before (top left) and after modification (top right) and $D_2$ mode before (bottom left) and after modification (bottom right). Logarithmic color scale.

Figure 8

Spectrum of the Fourier components of the electric field distribution for a modified cavity with neighbor cell size of 52% (left) and 44% (right), both shifted by 8%. Logarithmic color scale.