Scale-dependent anisotropic polarizability in mesoscopic structures

Optical properties of inhomogeneous materials are, in general, scale dependent. We show that, when observed at mesoscopic scales, the local anisotropic polarizabilities depend on the volume of interaction, which may be limited by either the excitation field or material dimensions. We demonstrate the existence of a specific interaction length scale corresponding to the maximum degree of local anisotropy and discuss its relation to the detailed morphology of a disordered medium. Probing these mesoscopic scales provides information about the local structure and allows characterizing material systems that otherwise may appear similar.

Figure 1

(Color online) (a) An inhomogeneous material system probed at mesoscopic scales through a local excitation provided by a near-field optical probe. (b) The observed far field response of the material system may be interpreted as being determined by a discrete array of anisotropic Rayleigh scatterers with different local magnitudes and orientations. (c) An inhomogeneous material system where the physical dimensions of the object limit the extents of the field material interaction and the effective anisotropic Rayleigh scatterer (d) producing an equivalent scattered field.

Figure 2

(Color online) Probability density functions of ordered (see text) diagonal elements of the reconstructed polarizability tensor. The volume of interaction corresponds to a sphere of 50 nm in diameter having a host refractive index of 1.33 and (a) inclusions with a refractive index of 2 and a volume fraction of 0.27 and (b) inclusions with a refractive index of 2.4 and a volume fraction of 0.18. The dots are the results of the numerical simulations while the solid lines are guessed “best fit” of numerical data.

Figure 3

(Color online) Effective anisotropy factor $\Delta$ as a function of excitation volume $R$ normalized by inclusion diameter $d$ for spherical inclusions with a refractive index of 1.5 randomly distributed in vacuum. The continuous lines correspond to inclusions with diameter $\lambda /32$ while the dashed lines correspond to inclusions of diameter $\lambda /64$. Curves 1 to 4 correspond to a volume fractions of inclusions of 0.3, 0.2, 0.1, and 0.025, respectively.

Figure 4

(Color online) Maximum anisotropy length $\left(\Lambda \right)$ normalized by the diameter of inclusions $d$ versus the volume fraction of inclusions $f$. Open circles and crosses represent MAL values corresponding to inhomogeneous media with inclusions of diameters of $\lambda /64$, $\lambda /32$, respectively. The solid line corresponds to the volume containing on average 3 inclusions.

Figure 5

(Color online) Maximum of anisotropy factor ${\Delta }_{\text{max}}$ as a function of volume fraction $f$ of inclusions with 50 nm in diameter and having different refractive index contrasts.