A promising avenue in the development of high-energy pulsed chemical HF/DF lasers and amplifiers is the utilization of a photon-branched chain reaction initiated in a two-phase active medium, that is, a medium containing a laser working gas and ultradispersed passivated metal particles. These particles are evaporated under the action of IR laser radiation which results in the appearance of free atoms, their diffusion into the gas, and the development of a photon-branching chain process, which involves photons as both reactants and products. The key obstacle here is the formation of a relatively large volume (in excess of 10^3 cm^3) of the stable active medium and filling this volume homogeneously for a short time with a submicron monodisperse metal aerosol, which has specified properties. In this paper, results are presented for an extensive study of laser initiation of a photon-branched chain reaction in a gas-dispersed H2- F2 medium.