The potential for coherent addition of laser channels is both interesting and impor­tant. Coherent addition methods known from the literature are based on the injec­tion of the radiation of one channel into another and subsequent separation of a specific field distribution using various selection methods.

For sets of lasers with periodic arrangements of elements, there is an opportunity for coherent phasing due to the effect of the self-reproduction of the periodic structure of the monochromatic field at some distance (Talbot optical coupling) [33]. Individual lasers may also be coupled on a common nonlinear cell in the laser cavity (mirror based on stimulated Brillouin scattering) [34].

Hereafter, as we examine a large number of optically coupled lasers, we will assume that, during independent lasing, each laser operates in a single transverse mode. If the dimensions of the active medium of an individual laser grow, the selection of a specific transverse mode turns into a problem. It can be solved using unstable cavities. Thus, the synchronization of lasers having individual independent cavities presents difficulties.

From a technical point of view, it is convenient to create sets of lasers with periodically arranged elements. Optical coupling in such sets can be implemented using external mirrors deflecting a small portion of the radiation into neighboring lasers. It is sufficient to simply use a flat mirror as the coupling element which is placed at some distance from the aperture of the set of lasers. Radiation reflected from the mirror leads to optical coupling between elements due to diffraction “spreading.” However, the efficiency of this coupling remains rather low. To increase the portion of radiation coming from one laser to another, the mirror must be moved aside. Due to diffraction, the radiation spreads along the whole aperture, and losses increase in the coupling channel. With a periodic arrangement of the set of lasers, this consideration is incorrect, because it does not take into account the reproduction effect of the periodic structure of the monochromatic field at a specific distance (Talbot diffraction coupling).

If the mirror is placed at half the reproduction distance of the periodic structure (Fig. 10.8), the image of the face plane of the channel, if it is emitted in phase, is projected onto the very same face plane. At the same time, because there is a contribution from the radiation of many channels to the image of each spot, coupling between individual lasers is sufficiently high. Without in-phase radiation of individual channels, the diffraction image breaks up, and losses increase sharply. Thus, this effect leads to selection of a phase-synchronization mode. It has been shown in study [33] that the distance z at which the mirror should be placed is equal to half of the “Talbot” distance ZT = ра2Д, where a is the lattice pitch and p is a numerical coefficient that is a function of the geometry of the lattice.

As exemplified by a multi-beam waveguide CO2 laser with periodically arranged elements, there was experimental confirmation [35, 36] of the potential for effective phase synchronization by Talbot diffraction coupling. It was shown that the graph of the laser power as a function of z can be divided into three parts. The first part relates

to independent lasing. In this case, the field distribution in the far-field region is determined by the aperture of a single channel, and the laser power is at a maximum. The second part represents a region with a partially coherent mode, with spots corresponding to interference orders are visible in the far-field and the total power drops by approximately twofold. In the third part, the radiation of each channel is highly coherent. However, the power is ~20 % the power of independent lasing.

A method that uses a spatial intra-cavity filter (Fig. 10.9) does not add up to optical coupling between lasers. The concept of a spatial filter consists of the selection of a specific configuration of the generated field that has minimal losses in the filter. If this configuration corresponds to an in-phase mode, it can be selected [36]. It was experimentally confirmed that with the use of an intra-cavity filter, there is absolutely no incoherent lasing, and complete synchronization is possible even with rough positioning of the filter. The total laser power in the principal maximum is 12 % with respect to the power of independent lasing. To enhance synchroniza­tion, it is recommended that the lengths of the laser cavities be increased and varied between themselves.

The first experiments [37] studying the coherent addition of NPL channels were performed by VNIITF researchers on reactor EBR-L. These experiments used the spatial filter method to realize an in-phase operation mode for a NPL package consisting of three parallel 60-cm long tubes with an internal diameter of 11 mm. The parameters of the laser medium, including the laser wavelength, are not given in study [37]. Diaphragms 1-2 mm in diameter were used as the spatial filters. The experiments showed that the use of a laser cavity including a telescope with a spatial filter reduces the laser radiation divergence due to phase synchronization of individual channels.

Fig. 10.10 Optical coupling in a nonlinear cell

Individual lasers may also be coupled by redistributing the beams on a common nonlinear cell in the laser cavity. SBS mirror can be used as this cell The nonlinear cell based on stimulated Brillouin scattering (SBS). This method is especially useful for NPLs that make it possible to obtain the significant laser power necessary to reach the SBS threshold. The schematic of a laser with SBS mirror is simple (Fig. 10.10). The laser radiation is somehow focused in the cell with a transparent medium. When a certain threshold power is exceeded, the radiation due to SBS is reflected back and returns to the laser cavity. If the radiation of two or more lasers is focused on one nonlinear cell, they will be synchronized due to redistribution of the energy.

To maintain a steady SBS process, the threshold radiation power Wthr, which corresponds to the threshold energy Ethr« Wthr x т (where т is the pulse duration) and is inversely proportional to the gain increment of the medium g, should enter the nonlinear medium. The energy released in the medium leads to the development of processes that compete with SBS. Therefore, when exceeding some critical energy Ecr, the effectiveness of SBS falls sharply. Thus, the determining criterion for the choice of a SBS medium is that the critical energy Ecr exceeds the threshold energy, that is, the product gEcr, which only depends on the properties of the medium. Values for the gain increment and critical energy of different media are given in Table 10.6 [34]. It follows from the table that high-purity xenon is preferred as the SBS medium.

The experiments [34] performed by VNIIEF researchers studied the effect of SBS within the range 0.69-4.2 qm. They demonstrated the potential to:

• Compensate for aberrations and increase the radiation brightness.

• Phase the radiation of a large number of laser channels (up to 1,000).

• Obtain high-frequency (>1 MHz) pulsed-periodic lasing.

In pulsed power NPLs, the pulse length is 10~3-1 s. This significantly increases the time for pressure equalization in the focal region. This means that the efficiency of SBS may be influenced by a change in refraction coefficient due to electrostriction and heating of the medium. Experiments on xenon (at 46 atm) with a wavelength X = 1.315 pm gave values determined by electrostriction: Wcr = 3.2 x 105 W and Ecr = 5 J.

An experimentally obtained a laser beam divergence for a single laser channel of ~0.5 x 10~3 rad, close to that of a diffraction one. Linear methods (serial and parallel addition, telescoping, etc.) make it possible to obtain laser beam diver­gences of up to ~10 5 rad. Use of coherent addition methods brings the beam divergence up to values no worse than 10~6 rad.