Subwavelength optical spatial solitons and three-dimensional localization in disordered ferroelectrics: Toward metamaterials of nonlinear origin

We predict the existence of a class of multidimensional light localizations in out-of-equilibrium ferroelectric crystals. In two dimensions, the nondiffracting beams form at an arbitrary low-power level and propagate even when their width is well below the optical wavelength. In three dimensions, a subwavelength light bullet is found. The effects emerge when compositionally disordered crystals are brought to their metastable glassy state, and leading to the suppression of evanescent waves, they can have a profound impact on super-resolved imaging and ultradense optical storage, resembling metamaterials in many ways.

Figure 1

Scale-free solutions for various values of $\sigma =(L^2/8{\lambda }^2)$. We show the profile in (a) of the Gaussian solution ($\sigma =0.125$) and in (b, c) of the generalized solution Eq. (5).

Figure 2

(a) Beam waist versus propagation for $\epsilon =0.05$ for various orders of approximation of the nonparaxial equations (black line corresponds to standard paraxial models). As $\sigma =0$ the nonparaxial terms lead to a more pronounced spreading; for $\sigma =0.125$ an invariant propagation is attained at any nonparaxial order. (b) 2D + 1 comparison between the case $\sigma =0$ and $\sigma =0.125$ for $N=3$.

Figure 3

Intensity-independent super-resolution: (a,b) Propagation in the linear regime ($L=\sigma =0$) of a double spot (panel a) in the nonparaxial model Eq. (14) at the third order ($N=3$) with $\epsilon =0.01$; (c, d) as in (a, b) with $\sigma =0.2$; (e) calculated contrast and visibility versus $\sigma$. The initial image in panels (a, c) is the same and is included for the sake of comparison. Propagation distance $z=1$.