**7. Self-organization of color centers in the course of hologram recording**

The investigation of weakly colored samples with holograms recorded under various power densities of laser radiation, exposure, temperature, and grating period revealed structuring the holographic planes with an increase in the colloidal center concentration: the holographic planes became thinner and were pierced by fragmentary spiral‐like bundles that consisted of colloids.

**Figure 13** shows the 3D view of such hologram composed with the confocal LSM. One may conclude that, under hologram recording, (i) the above self‐organization of color centers took place and (ii) the colloidal centers played an important role in this process [18, 19].

**Figure 13.** 3D LSM image of the sample with bundles in the holographic planes seen in the reflected light of 405 nm laser.

The colloidal particles can be considered as the second phase inclusions in the fluorite lattice. It should be noted that, though metallic calcium and fluorite have the same Bravais lattice and mismatch of their lattice parameter, *a*, is very small (*a*Ca = 0.556 nm, *a*CaF<sup>2</sup> = 0.545 nm), the mutual orientation of the matrix and colloids is not expected to be cube‐on‐cube [5]. Thus, the colloidal centers disturb the fluorite lattice. This disturbance displays itself in broadening the absorption bands with the growth of the colloid content.

It was stated above that the color centers including colloids both form and decay in the hologram recording process. So, recording a hologram on the CaF<sup>2</sup> crystals with color centers is accompanied by continuous phase transitions.

The internal self‐consistency (self‐organization) arises in complex systems due to the interaction of various subsystems [20]. Their interaction is the most effective near the phase transition; when a subsystem that experiences the transition becomes soft and weak, an external perturbation can cause the strong modification of the subsystem state and, in particular, its order parameter. In the case under consideration, such perturbations could be the fluctuations of concentrations of simple centers, vacancies, and electrons. These fluctuations could, in turn, trigger the formation of large‐scale stable spatially inhomogeneous states in the subsystem of colloidal centers located in the holographic planes. Such states are bundles. The bundles arise in the recording conditions and turn out to be frozen on cooling the crystal after finishing the recording process.

The bundle formation is probably governed by (i) bi‐directional "compression" of holographic planes by vacancy flows emanating from the neighboring fringe pattern maxima (the bundle thickness is about the thickness of the holographic planes) and (ii) the direction of the Poynting vector of the interference field that determines successive recording of the hologram deeply into the sample (the bundle orientation coincides with this direction).

Within the framework of the synergetic theory [20], a CaF<sup>2</sup> crystal in the process of hologram recording may be considered as an open system that is in the heat exchange with a heat source having temperature of 150–200°C. From this standpoint, the formation of bundles (dissipative structures) is the result of importing the negative entropy into the crystal.

At some colloid content, the bundles become continuous and correlated with each other, thus forming the 2D superlattice of a symmetry very close to *cmm* plane symmetry group [21] with the lattice parameters as follows: *a* is the doubled period of the hologram and *b* is a separation between the neighboring bundles along the holographic plane (**Figure 14**). For the sample shown in **Figure 13**, *a* = 9 μm and *b* ≈ 4.2 μm. Under further increase in the colloid concentration, however, the correlation between bundles breaks and they tear off.

**7. Self-organization of color centers in the course of hologram recording**

422 Holographic Materials and Optical Systems

The investigation of weakly colored samples with holograms recorded under various power densities of laser radiation, exposure, temperature, and grating period revealed structuring the holographic planes with an increase in the colloidal center concentration: the holographic planes became thinner and were pierced by fragmentary spiral‐like bundles that consisted of colloids. **Figure 13** shows the 3D view of such hologram composed with the confocal LSM. One may conclude that, under hologram recording, (i) the above self‐organization of color centers took

The colloidal particles can be considered as the second phase inclusions in the fluorite lattice. It should be noted that, though metallic calcium and fluorite have the same Bravais lattice and

**Figure 13.** 3D LSM image of the sample with bundles in the holographic planes seen in the reflected light of 405 nm laser.

orientation of the matrix and colloids is not expected to be cube‐on‐cube [5]. Thus, the colloidal centers disturb the fluorite lattice. This disturbance displays itself in broadening the

It was stated above that the color centers including colloids both form and decay in the hologram

= 0.545 nm), the mutual

crystals with color centers is accompa-

mismatch of their lattice parameter, *a*, is very small (*a*Ca = 0.556 nm, *a*CaF<sup>2</sup>

absorption bands with the growth of the colloid content.

recording process. So, recording a hologram on the CaF<sup>2</sup>

nied by continuous phase transitions.

place and (ii) the colloidal centers played an important role in this process [18, 19].

**Figure 14.** Absorption image of a hologram with 2D superlattice in one of orthogonal projections resulted from postprocessed series of their optical slices recorded using LSM at 405 nm (a). The schematic drawing of hologram (b); an arrow indicates the projection shown in (a). The green rectangle in (a) shows the superlattice elementary cell.

Earlier, the colloid cubic superlattice with the lattice parameter of *~*20 nm was observed on the surface of electron‐irradiated crystals (see [22] and references therein).
