Disorder-Induced Phase Transitions in the Transmission of Dielectric Metasurfaces

Light interaction with disordered materials is both complex and fascinating at the same time. Here, we reveal disorder-induced phase transitions in a dielectric Huygens’ metasurface made from silicon nanocylinders that simultaneously support an electric and magnetic dipole resonance. Depending on the degree of positional disorder and the spectral detuning of the two resonances, the phase angle of the transmission coefficient exhibits a clear phase transition from normal to anomalous dispersion. Combined with the considerations of whether the resonances of spectrally detuned particles appear as separated or overlapping, we distinguish four different phase states. We study this phenomenon analytically by employing dipole particles and disclose the entire phase diagram, support our insights with full-wave simulations of actual structures, and corroborate the findings with experimental results. Unveiling this phenomenon is a milestone simultaneously in the growing fields of metamaterial-inspired silicon nanophotonics, photonics in disordered media, and the fundamental physics of phase transitions.

Figure 1

The effect of positional disorder on dual and detuned metasurfaces with a perturbed square array arrangement. Transmission coefficient $t(\lambda )$ of (a),(b) dual and (c),(d) detuned metasurfaces. (b),(d) Spectra of the phase angle ${\varphi }_t(\lambda )$ of $t(\lambda )$ and (a),(c) parametric plots of the respective $t(\lambda )$ in dependence on the wavelength. Each metasurface consists of nonabsorbing point-dipole particles that have a Lorentzian line shape with a full width at half maximum of 50 nm, and a spectral detuning of $\mathrm{\Delta }{\lambda }_{\text{res}}$ among their electric and magnetic polarizability resonances. The reference metasurface ($\mathcal{P}\mathcal{D}=0\%$) is a square array with lattice constant $a=800\mathrm{nm}$. The wavelengths are encoded by rainbow colors and correspond to those used on the abscissa of (b),(d). The line markers encode the degree of positional disorder. (e) Phase diagram as a function of positional disorder $\mathcal{P}\mathcal{D}$ and spectral detuning $\mathrm{\Delta }{\lambda }_{\text{res}}$.

Figure 2

Scanning electron micrographs of silicon nanocylinders before embedding in fused silica, arranged in a (a) square array, (b) perturbed square array, (c) Matérn type-III soft-core, and (d) hard-core distribution. All scale bars, $1\mu \mathrm{m}$.

Figure 3

Experimental measurement of (a) transmission coefficient $t(\lambda )$ and (b) its phase angle ${\varphi }_t(\lambda )$ through four metasurfaces with different arrangements of equal density: Square array, perturbed square array, Matérn type-III soft-core and hard-core point processes, as shown in Fig. 2. Simulation results are shown with dashed lines of the same color.