**2. Holographic laser on the basis of dye-doped cholesteric liquid crystal (DD CLC)**

A new type of CLC laser with the transversely distributed excitation was realized first time in the DD CLC. The interference pattern of two coherent pumping beams of the second harmonic of a Q-switched Nd:YAG laser (532 nm) was used for the pumping. The interference pattern was located in the plane of the laser active layer [21, 25]. The laser radiation of the DD CLC layer was observed perpendicular to the laser cell from the opposite side of the incidence of the pumping light. Emitted laser field is modulated spatially. The periodical character of the modulation of intensity along cross section of the lasing depends and corresponds to the parameters of the interference pattern of the pumping, and the pattern of the emitted light field qualitatively looks like a diffraction from an elementary hologram.

Periodical spatial modulation of such a picture of lasing is connected with characteristics of coherence of obtained DD CLC laser. Particularly, the interference pattern of the pumping beams creates periodical distribution of intensity in the plane of the DD CLC laser layer for its excitation, forming a laser structure representing a periodical set of microlasers. The total interference pattern of emission from these microlasers forms the lasing picture which looks like a diffraction from a periodical structure. So, obtained laser can be considered as a laser and, at the same time, as an elementary hologram simultaneously.

**Figure 1** shows the scheme of the experimental setup of the double-beam pumping of the laser cell. The second harmonic (*λ***p** = 532 nm) of the Q-switched **Nd3+:YAG** laser is divided into two mutually coherent beams of equal intensity with the help of beam splitter. The beam splitter was composed of two laser mirrors with reflectance of 50% (1) and 99.9% (2) for the wavelength of 532 nm. The distance of 15 mm between the mirrors (1) and (2) of the beam splitter provided a stable interference pattern. The duration of the pulses was 15–20 ns. The excited, by the pumping laser, spot on the DD CLC layer has a size 1–2 mm.

Such an experimental setup (**Figure 2**) ordinarily is used for the recording of the holographic gratings and for the pumping of the dye distributed feedback (DFB) lasers. So, the pumping light field in this case represents oneself the interference pattern as a periodically arranged bright and dark strip (**Figure 3**). The period *d* of the interference pattern of the pumping light is determined by the well-known formula [4, 29, 30]:

**Figure 2.** Scheme of double-beam coherent pumping.

**Figure 3.** Formation of the interference pattern of the pumping in the DD CLC layer.

$$d = \frac{\lambda\_p}{s \sin(\%)}\tag{1}$$

where *λ***p** is the wavelength of pumping and *θ* is the convergence angle of the pumping beams.

As a result, an array of microlasers was obtained which emit light simultaneously in perpendicular direction regarding to DD CLC laser layer. The picture of the array of microlasers was observed by microscope and was fixed by digital camera (**Figure 4**). **Figure 4(a)** and **(b)** corresponds to the convergence angles of **1.8**° and **0.6**° for the pumping beams accordingly. Thus, microlasers were formed as a separate strips of lasing the width of which depends on the angle between pumping beams.

**Figure 4.** Array of microlasers in the DD CLC layer.

*<sup>d</sup>* <sup>=</sup> *<sup>λ</sup>* \_\_\_\_\_\_ *<sup>p</sup>*

**Figure 3.** Formation of the interference pattern of the pumping in the DD CLC layer.

**Figure 2.** Scheme of double-beam coherent pumping.

466 Holographic Materials and Optical Systems

where *λ***p** is the wavelength of pumping and *θ* is the convergence angle of the pumping beams. As a result, an array of microlasers was obtained which emit light simultaneously in perpendicular direction regarding to DD CLC laser layer. The picture of the array of microlasers

*<sup>s</sup>* sin(*θ*⁄2) (1)

The DD CLC laser cell was prepared by conventional, well-known technology. For the active laser medium, dye DCM exciton was used, which was introduced in the CLC matrix.

A mixture of nematic liquid crystal BL-036 and optically active component MLC-6247 (both from Merck) was used as a CLC matrix where 0.4% of DCM (exciton) was added. The period of the helix of the CLC mixture was about 370 nm. The thickness of the obtained plane parallel layer of the CLC was approximately 40 μ. Glass plates for the windows of the CLC laser cell were precoated with thin layers of polyvinyl alcohol (PVA) and are oriented by rubbing.

The spectrums of transmission and fluorescence of the DD CLC laser cell are shown in **Figures 5** and **6**, respectively. **Figure 7** shows the lasing spectrum. Thus, according to results presented in **Figures 6** and **7** regarding the spectral characteristics of emission, this laser does not differ from the known DD CLC lasers with the single-beam pumping. However, the difference, caused by the excitation with the interference pattern of two mutually coherent beams, is manifested in the structure of the cross section of the emitted beam. In **Figure 8(a)** and **(b)**, the photos of the cross section of lasing for the angles **1.8**° and **0.6**° between the pumping beams are shown. It is seen that the intensity distribution along the cross section of lasing has the periodical character, which differs from distribution of intensity of lasing of conventional CLC lasers and looks like the diffraction from the diffractive grating.

The distance between the maximums (or minimums) of intensity of the pattern of lasing in **Figure 8(a)** and is approximately 2.3 mm (a) and 6.5 mm (b) accordingly, and the distance from the CLC layer to the screen is 20 cm. Thus, according to the calculation, the angles between the directions of propagation of the nearby maximums, from the excited spot of the CLC layer, have values **1.86**° and **0.66°** that closely enough agrees to angles of diffraction **1.81**° and **0.64**° from the diffractive grating calculated by the formula [4, 29, 30]:

$$\varphi = 2 \arcsin\left(\frac{\lambda\_p}{2d}\right) \tag{2}$$

where *λ***p** is the wavelength of lasing of the DD CLC laser cell and *d* is the period of the interference pattern of pumping. The modulation of the intensity of the emission pattern of lasing disappears when one of the pumping beams is shutting (**Figure 8(c)**).

**Figure 5.** The spectrum of optical transmission of the DD CLC cell along the cholesteric helical axis.

**Figure 6.** The spectrum of fluorescence of the DD CLC laser cell.

**Figure 7.** Lasing spectrum of the DD CLC cell.

where *λ***p** is the wavelength of lasing of the DD CLC laser cell and *d* is the period of the interference pattern of pumping. The modulation of the intensity of the emission pattern of lasing

disappears when one of the pumping beams is shutting (**Figure 8(c)**).

468 Holographic Materials and Optical Systems

**Figure 5.** The spectrum of optical transmission of the DD CLC cell along the cholesteric helical axis.

**Figure 6.** The spectrum of fluorescence of the DD CLC laser cell.

**Figure 8.** Picture of lasing from DD CLC laser cell at the pumping by interference pattern of two beams (a, b) and at the pumping by one beam (c). The convergence angles of the pumping beams are 1.8° (a) and 0.6° (b). The spatial period of the pumping interference patterns is 17 and 50 μ, respectively.

In author's opinion, the spatial modulation of laser emission field is a result of the mutual correlation between the emitting centers of the individual strips of radiation. Probably, correlation effects, in this case, are of the same nature that provides spatial coherence in the conventional lasers. Thus, the emitting area, of the described laser cell, represents a periodical structure of the mutually coherent microlasers. The total radiation of such a periodical structure, according to the Huygens-Fresnel principle, must form summary interference pattern similar to that shown in **Figure 8(a)** and **(b)**. This phenomenon is similar to the formation of the diffraction pattern from the diffractive grating of the corresponding periodical structure from the point of view of Huygens-Fresnel principle.

Probably, the main factor in reducing the contrast of the spatial modulation of the pattern of lasing is the significant value of the scattering of the light that is characteristic of liquid crystals (**Figure 8(a)** and **(b)**). The new type of a laser, which combines the properties of a laser and a hologram, was firstly realized on the basis of a DD CLC layer. The field of emission of this laser has a spatial modulation with the periodical distribution of the intensity, controlled by the transversely distributed excitation. Therefore, the spatial distribution of the emission intensity in this case carries out information about the interference pattern of the pumping that makes it similar to the elementary hologram, i.e., holographic diffractive grating. Thus, according to results presented in **Figures 6** and **7** regarding to the spectral.
