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We study a dynamic three-dimensional (3D) field localized states in a medium with percolation disorder, where the percolation cluster is filled by the active nanoemitters. In such a system, the incipient percolating cluster generates a fractal radiating structure in which the field is radiated and scattered by the anisotropic inhomogeneity. Our numerical 3D simulations show that such a nonlinear system with noninteger fractal dimension has well-defined localized solutions for fields (3D speckles). The statistics of speckles is studied too.

Disordered mediums can diffuse or localize the light waves due to random multiple scattering that leads to formation of the electromagnetic modes depending on the structural correlations, scattering strength, and dimensionality of the system [

Various random optical processes may generate the laser speckle patterns when the granular points appear in the scattered light. In this paper we consider the properties of field in materials with random percolating clusters. We studied the field dynamics in a cubical sample

Here

In this section we study the temporal dynamics of the field structures described by the system of (

The specific energy

From Figure

The properties of the speckle patterns generated in 3D cube with

Equations (

The conventional optical speckles normally have stationary statistics; therefore, firstly we compare the latter with statistical properties of emitters for

The initial formation of field patterns for time

The same as in Figure

Figure

The formation of such patterns for longer time

Figure

Figure

Except seeing of the field structure in central 2D slices of 3D system (shown in Figures

The isosurface of the

We investigated a dynamic three-dimensional (3D) field localized states (speckles) in a medium with percolation disorder, where the percolation cluster is filled by the active nanoemitters. In such a system, the incipient percolating cluster represents a fractal radiating structure where the field is radiated and scattered by the anisotropic nonhomogeneity of a cluster. Analysis of the statistics for field patterns shows that the speckle distribution in such a dynamic system for short times is close to the Pareto distribution. Our numerical 3D simulations show that such a nonlinear model with a noninteger fractal dimension has smooth well-defined localized solutions for fields. That allows recognizing such dynamic field domains as 3D field speckles that are formed in the nonlinear active fractal medium with a large disorder.

No data were used to support this study.

The author declares that they have no conflicts of interest.