Disorder-Immune Photonics Based on Mie-Resonant Dielectric Metamaterials

When the feature size of photonic structures becomes comparable or even smaller than the wavelength of light, the fabrication imperfections inevitably introduce disorder that may eliminate many functionalities of subwavelength photonic devices. Here we suggest a novel concept to achieve a robust band gap which can endure disorder beyond 30% as a result of the transition from photonic crystals to Mie-resonant metamaterials. By utilizing Mie-resonant metamaterials with high refractive index, we demonstrate photonic waveguides and cavities with strong robustness to position disorder, thus providing a novel approach to the band-gap-based nanophotonic devices with new properties and functionalities.

Figure 1

Schematic of photonic structures, composed of dielectric nanorods, with an increasing position disorder $\sigma$, respectively.

Figure 2

Transmission spectra of (a) a photonic crystal (with $ϵ=4$) and (d) a metamaterial (with $ϵ=25$) with different values of the disorder parameter $\eta$. Black solid curves are perfect structures ($\eta =0$), red dashed curves are weak disorder ($\eta =10\%$); green dash-dot curves are moderate disorder ($\eta =20\%$); blue dotted curves correspond to a strong disorder ($\eta =40\%$). Origin of spectral dips are labeled. Magnetic field distribution in (c) and (d) photonic crystal (for $\eta =0$ and $\eta =40\%$, respectively) and (e) and (f) metamaterial (with $\eta =0$ and $\eta =40\%$, respectively). In each of the panels (c),(d) and (e),(f) the waves propagate from the bottom to the top.

Figure 3

Degradation of the reflection $\gamma$ at different values of $ϵ$, illustrating the robustness of the structure for (a) square and (b) hexagonal lattices, respectively.

Figure 4

(a), (b) Field distribution $H_z$ in a straight waveguide created in a square lattice of nanorods with disorder $\eta =10\%$ ($\sigma =50\mathrm{nm}$) for (a) $ϵ=4$ and (b) $ϵ=25$. (c) The corresponding relative transmission $T/T_0$ vs $\eta$ for $ϵ=4$ and $ϵ=25$, respectively, for a square lattice of nanorods. (d),(e) Field distribution $H_z$ in a bent waveguide created in a hexagonal lattice with disorder $\eta =8\%$ ($\sigma =40\mathrm{nm}$) for (d) $ϵ=4$ and (e) $ϵ=17$. (f) The corresponding relative transmission $T/T_0$ vs $\eta$ for $ϵ=4$ and $ϵ=17$, respectively, for a hexagonal lattice of nanorods.

Figure 5

(a) An optical cavity formed by a hexagonal lattice of dielectric rods without disorder (left) and with disorder (right). (b) Degradation of the relative quality factor $Q/Q_0$ with disorder $\sigma$ for $ϵ=4$ and $ϵ=15$. (c) An example of a photonic structure with both position and size disorder, for $\eta =25\%$. (d) Robustness parameter $\gamma$ vs disorder $\eta$ and $ϵ$.