**4. Mechanism and kinetics of hologram recording**

When recording a hologram, the crystal and optical scheme of interferometer beginning with the beam splitter are placed into the temperature‐controlled windowed housing equipped with a heater and a thermocouple. The feedback circuit of the heater power supply maintains a temperature in the housing of 150–200°C with an error of 0.1°C.

The specific diffusion‐drift mechanism of hologram recording in ionic crystals with color centers [8–10] results not only in the transformation of the types of centers but also in their spatial redistribution over the crystal bulk. This mechanism is similar to Dember effect in semiconductors. If there are two carrier types with different mobilities in a semiconductor, its illumination with inhomogeneous light field results in the concentration gradient of more mobile carriers. The perturbation in local neutrality of the crystal forms local electric fields. Dember effect is responsible for the appearance of bulk charge when the mobilities of electrons and holes differ from one another.

A similar phenomenon occurs in ionic crystals with color centers. Two components that arise under the impact of light field in a crystal with color centers at elevated temperatures, i.e., electrons and anion vacancies, differ greatly in mobilities. Photoionization of the centers in the maxima of the fringe pattern gives birth to the free electrons that diffuse towards the minima, where they are captured by traps (the same color centers). This process creates electric fields between the minima and maxima. Under the impact of these fields, vacancies that are split off the photoionized centers at the recording temperature, drift towards minima and recombine with electrons released from traps with the formation of new color centers. Thus, the holographic planes coincide with the minima of the fringe pattern. A resultant increase in the vacancy and electron concentrations in minima compared to their mean concentrations in the sample favors the formation of colloidal centers.

Generally, the hologram recording process is linked to the simple → colloidal center conversion. This conversion in the holographic planes and the depletion of centers between them create the modulation of optical constants of the crystal, i.e., forms the holographic grating. One should note that, actually, the conversion process passes through several stages in accord with an increase in the number of center components: simple centers → long‐wavelength quasi‐colloids → shortwavelength quasi‐colloids → colloids; of course, this scheme is simplified with allowance for the occurrence of several kinds of simple centers and a lot of kinds of quasi‐colloidal centers.

According to the preceding section, the use of reverse colloidal → simple center process for hologram recording requires substantially high temperature of the crystal.

The most suitable laser wavelength for hologram recording is less than 500 nm; however, the radiation with *λ* = 532 nm is also effective though it is absorbed by both simple and colloidal centers (as mentioned above, the temperature range of 150–200°C is favorable for colloidal center formation).

One should note that the hologram recording in CaF<sup>2</sup> crystals with color centers is a dynamic process. At the recording temperature, the thermal dissociation of color centers in the minima of fringe pattern occurs, thus resulting in the formation of the "counter‐flows" of electrons and vacancies towards the maxima of the fringe pattern. The study of ESR and dielectric constants of CaF<sup>2</sup> crystals irradiated with electrons shows that the most stable colloidal color centers break up and form at temperature above 150°C [11].

**4. Mechanism and kinetics of hologram recording**

a temperature in the housing of 150–200°C with an error of 0.1°C.

holes differ from one another.

lines, respectively).

410 Holographic Materials and Optical Systems

When recording a hologram, the crystal and optical scheme of interferometer beginning with the beam splitter are placed into the temperature‐controlled windowed housing equipped with a heater and a thermocouple. The feedback circuit of the heater power supply maintains

**Figure 4.** Absorption spectra of samples additively colored (*p* = 3 × 10-4 Torr and *T* = 830°C) and irradiated for 30 hours with the high‐pressure mercury lamp (*λ* = 365 nm) at *T* = 70, 85, 125, and 160°C (solid, dotted, dashed‐dotted, and dashed

The specific diffusion‐drift mechanism of hologram recording in ionic crystals with color centers [8–10] results not only in the transformation of the types of centers but also in their spatial redistribution over the crystal bulk. This mechanism is similar to Dember effect in semiconductors. If there are two carrier types with different mobilities in a semiconductor, its illumination with inhomogeneous light field results in the concentration gradient of more mobile carriers. The perturbation in local neutrality of the crystal forms local electric fields. Dember effect is responsible for the appearance of bulk charge when the mobilities of electrons and

A similar phenomenon occurs in ionic crystals with color centers. Two components that arise under the impact of light field in a crystal with color centers at elevated temperatures, i.e., Thus, the hologram decay occurs simultaneously with its recording. With a decrease and increase in the center concentration in the interference field maxima and minima, respectively, the rates of recording and decay processes equalize, so that the diffraction efficiency of recorded hologram, DE, reaches saturation. As seen, such situation differs from that for media in which the laser radiation produces the irreversible modification (modulation) of the optical constants. This results in a decrease in DE, after passing a maximum, with an increase in exposure because of occurrence of the scattered radiation.

In **Figure 5**, the recording kinetics for the first diffraction order of the hologram read out at 980 nm is presented. The readout beam was switched on, each 10 s, for 0.1 s. The absorption spectra of the crystal registered before and after hologram recording are shown in **Figure 6**.

The hologram may be considered as the phase one with only minor amplitude contribution. However, this is the case only at the initial stage of the formation of the holographic planes. Let us consider this stage in more detail.

**Figure 5.** Diffraction efficiency measured at 980 nm vs. exposure time in the course of hologram recording with 532 nm laser emission.

**Figure 6.** Absorption spectra of additively colored sample of CaF<sup>2</sup> crystal before (solid line) and after (dotted line) recording the "saturated" hologram.

The first (small) maximum of kinetic curve is related to the local center transformation in the maxima of the fringe pattern. The simultaneously occurring process of center drift from the maxima to the minima restricts an increase in DE due to the local transformation and is the reason for the appearance of the first minimum (an analogous local maximum was observed under hologram recording in KCl crystals with color centers [12]). At this point, the amount of anion vacancies/electrons is a bit larger in the minima of the fringe pattern; however, this increase is compensated by center transformation in the maxima.

A subsequent increase in the center concentration in the minima implies DE to increase up to the second maximum. The time (exposure) at which this maximum is reached corresponds to the completion of holographic plane formation.

To explain the existence of two very pronounced minima at the kinetic curve, it is necessary to assume that the minima are connected to the process of center transformation in the holographic planes. Probably, there is a variety of color center types in the formatted holographic planes; however, the distribution of these types varies with time (exposure) in accord with a scheme as follows: simple → long‐wavelength quasi‐colloidal → short‐wavelength quasi‐colloidal → colloidal centers. In the process of this conversion, the mass center of the absorption bands crosses twice the readout wavelength when moving to the larger wavelengths and backward. The points of these crossing correspond, according to Kramers‐ Kronig relation

$$
\delta n(\nu\_1) = \frac{c\_0}{2\pi^2} \int\_0^\nu \frac{\delta \alpha(\nu) \, d\nu}{\nu^2 - \nu\_i^2} \tag{1}
$$

(where *c*<sup>0</sup> is the light speed in vacuum, *δn*(*ν*) and *δ*α(*ν*) are the modulations of the refractive index and absorption coefficient, respectively), to the second and the third minima. In these points, the hologram is a purely amplitude one.

One should note that the above scheme of center transformation shows only a general trend rather than the details of this process. Actually, there are several types of color centers/electron traps in the holographic planes. Electrons released from these traps and anion vacancies recombine with both the formation of *F*‐centers and complication of the existing center structures. The recombination can occur on the colloidal centers with an increase in their size. Simultaneously, the colloidal centers decay with the formation of quasi‐colloidal, in particular, short‐wavelength quasi‐colloidal centers, that absorb at the readout wavelength. This consideration explains the amplitude nature of the hologram in the second minimum.

When passing the third maximum, the hologram has the amplitude‐phase nature. At the third minimum, the hologram becomes the amplitude one again because of overlapping the readout wavelength with the quasi‐colloidal absorption bands.

After passing the third minimum, the hologram is gradually converted from the amplitude‐ phase into the predominantly phase one and its DE increases. Some decrease in DE after *~*80000 seconds down to a certain saturation value is connected to the short‐wavelength quasi‐colloid → colloid transformation (moving away the absorption band from the readout wavelength).

**Figure 6.** Absorption spectra of additively colored sample of CaF<sup>2</sup>

**Figure 5.** Diffraction efficiency measured at 980 nm vs. exposure time in the course of hologram recording with 532 nm

recording the "saturated" hologram.

laser emission.

412 Holographic Materials and Optical Systems

crystal before (solid line) and after (dotted line)
