3D Anderson localization of light in disordered systems of dielectric particles

TL;DR

The paper addresses the question of whether Anderson localization (AL) of light can occur in 3D dielectric disordered media. It employs a full-wave vector Maxwell simulation based on discontinuous Galerkin time-domain (DGTD) methods to model light propagation through densely packed irregular dielectric particles under varied turbidity and high index contrast, aiming to reach the Ioffe-Regel regime $kl^* \lesssim 1$. The key findings show a clear transition from diffusive to localized transport, manifested as non-exponential $T(t)$ with a time-dependent diffusion coefficient $D(t) \sim t^{-1}$, suppression of transverse spreading for focused beams, and a Thouless-type spectrum with $g_{Th} < 1$, together with near-field formation of disorder-induced, long-lived localized modes. These results validate AL in 3D dielectric media and suggest experimental paths using high-index powders like TiO$_2$, highlighting the role of packing density and refractive index contrast in enabling localization.

Abstract

We present the results of full-wave numerical simulations of light transmission through layers of irregular dielectric particles, demonstrating three-dimensional Anderson localization of light in disordered, uncorrelated discrete media. Our simulations show that a high degree of disorder in a dense layer suppresses the transverse spreading of a propagating beam. A transition from the purely diffusive regime to a non-exponential temporal dependence is observed in short-pulse time-resolved transmission measurements as the system approaches the Ioffe-Regel condition. Along with this, near-field dynamics leads over time to the formation of spatially localized modes and the transmission spectrum becomes consistent with the Thouless criterion. The effect depends on the turbidity of the layer: increasing the volume fraction of scatterers and the refractive index contrast enhances the non-exponential behavior induced by disorder, which is a clear signature of Anderson localization.

Figures (13)

• Figure 1: Propagation of a continuous, focused beam through a dense and a sparse layers of irregular particles. (a) and (c), samples with volume fractions of 0.48 (dense) and 0.16 (sparse), respectively. (b) and (d), steady-state near-field intensity distributions $|E|^2$ in XY, YZ and back-XZ planes for both layers. The incident beam is $E_x$-polarized. The size of particles is $X_r=1.1$, and the refractive index is $n=3.0$.
• Figure 2: (a) A layer of 19000 irregular particles packed with a volume fraction of 0.44. The size of particles is $X_r=1.1$ and the refractive index is $n=3.0$. (b) vertical cross-section of the layer, showing intentional defects on the side boundary and the characteristic scale of voids $kl \lesssim 1$. (c) Normalized transmission of a short pulse by layers with volume fractions from $\rho=0.17$ to $0.5$ as a function of time $T(t)$. (d) Diffusion coefficient $D(t)$ obtained by local exponential fitting of $T(t)$. Both axes have logarithmic scale. Dashed line shows a $t^{-1}$ dependence.
• Figure 3: Simulation results for layers with different volume fractions and smooth side boundaries. The refractive index of the material is $n=3.0$. (a) Normalized transmission of a short pulse by layers with volume fractions from $\rho=0.1$ to 0.5 as a function of time $T(t)$. (b) Time-dependent diffusion coefficient $D(t)$ obtained by local exponential fitting of $T(t)$. Dense layers demonstrate a $t^{-1}$ (dashed lines) dependence at times $t > 20t_a$. (c) and (d), Snapshots of the internal electric field (XY-cross-sections, $E_x$ component) distributions showing a whispering-gallery wave propagating along the boundary at time $t = 25 t_a$ for a moderately sparse ($\rho=0.27$) and a dense ($\rho=0.44$) layers. (e) Normalized spectra of transmitted light as functions of the dimensionless size parameter $X_r$ (inverse wavelength expressed relative to the particles size) for sparse $\rho=0.17$ and dense $\rho=0.44$ layers. Dashed line corresponds to a Lorentzian fit for $\rho = 0.44$. The inset shows the Thouless conductance distribution $P(\textrm{ln} ~ g_{Th})$ for $\rho=0.44$ that has a mean value $\mu = -1.25$ and a standard deviation $\sigma = 0.75$.
• Figure 4: (a) Normalized transmission of a short pulse through a layer with a volume fraction $\rho= 0.44$ and a smooth boundary as a function of time $T(t)$ at different refractive indices. (b) Diffusion coefficient $D(t)$ as obtained by a local exponential fitting of $T(t)$. Dashed line shows a $t^{-1}$ dependence.
• Figure S1: (a) Normalized transmission of a short pulse through layers with cylindric symmetry and different thickness $X_L$ as a function of time $T(t)$. The diameter and volume fraction are $X_R=26$ and $\rho= 0.44$, correspondingly, and the refractive index is $n=3.0$. The energy decay from a simple double layer of particles is exponential while thicker layers demonstrate increasingly non-exponential transmission. (b) Diffusion coefficient $D(t)$ obtained by local exponential fitting of $T(t)$. $D(t)$ evolves from a constant to a $t^{-1}$ fit (dashed line) with increasing thickness. (c) Vertical cross-sections of the samples with different thickness.