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Mathematical and physical models have been suggested of the phenomenon, explaining the lowering of the damage threshold of a transparent dielectric by self-focusing of light energy on the refraction index dynamic inhomogeneity, arising in the compression wave which appears in transparent media around absorbing inhomogeneities in the process of their absorbing a part of light impulses. On the basis of this model the dependence have been obtained connecting parameters of light impulse, physical and chemical properties of the medium and absorbing inhomogeneity characteristics with the level of local concentration of light energy.
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Serguei Gribine, Boris Spesivtsev, "Mechanism of impulse-light self-focusing on shock lenses in transparent media," Proc. SPIE 2714, 27th Annual Boulder Damage Symposium: Laser-Induced Damage in Optical Materials: 1995, (27 May 1996); https://doi.org/10.1117/12.240390