Disorder fingerprint: Intensity distributions in the near field of random media

The structural morphology of complex dielectric media determines their functionalities by driving the statistical properties of the electromagnetic fields. Our controlled experiments and full electromagnetic calculations that go beyond common dipolar approximations demonstrate that the specific characteristics of disorder lead to non-Rayleigh statistics of detected intensity, which can be directly accessed in the near field of random media and can be unambiguously related to the short-range correlations of disorder.

Figure 1

Top view of the randomly packed 3D structures of (a) hard spheres, (b) adhesive spheres, and (c) clustering distribution of spheres. The volume fraction of spheres is 11% in all cases. (d)–(f) Corresponding configurational entropy spectra.

Figure 2

(a)–(c) Typical near-field intensity distributions and intensity probability density functions evaluated over $8\times 8\mu {\mathrm{m}}^2$ areas at 50 nm above cylindrical slabs with a 7-$\mu \mathrm{m}$ radius and a 3.5-$\mu \mathrm{m}$ thickness containing 11% volume fractions of 250-nm diameter $\mathrm{Ti}{\mathrm{O}}_2$ particles in air. The slabs have different types of structural disorder, as shown in Fig. 1. The intensity probability density functions are evaluated from 10 different realizations of disorder. The dashed line denotes the Γ probability distribution corresponding to the superposition of three uncorrelated speckle patterns.

Figure 3

Scanning electron micrographs of locally uniform (a) and locally nonuniform (b) distributions of nanometer-size $\mathrm{Ti}{\mathrm{O}}_2$ particles embedded in a polymer matrix. (c) and (d) Corresponding NSOM scans collected over $10\times 10\mu {\mathrm{m}}^2$ areas in intermittent contact mode. (e) Intensity probability density functions evaluated from scans over 10 regions of the sample in (a) (blue triangles) and the sample in (b) (red squares). Each intensity ensemble contains more than ${10}^6$ values. The dashed line denotes the Γ probability distribution corresponding to the superposition of three uncorrelated speckle patterns. The inset shows the values of the first four moments of measured intensity distributions. The error bars in the inset indicate the uncertainty in evaluating the moments with 0.9 confidence.