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Laser-induced fluorescence spectroscopy (LIFS) is actively used for remote sensing of atmospheric aerosols and is currently one of the most sensitive and selective techniques for determining small concentrations of substances inside particles. The use of high-power femtosecond laser sources for LIFS-based remote sensing of aerosols contributes to the development of new-generation fluorescence atmospheric lidars since it makes it possible to overcome the energy threshold for the nonlinear-optical effects of multiphoton absorption in particles and receive the emission signal at long distances in the atmosphere. Our study is aimed at the development and experimental demonstration of the technique of nonlinear laser-induced fluorescence spectroscopy (NLIFS) based on the remote excitation of aerosol fluorescent emission stimulated by a spatially structured high-power femtosecond laser pulse. Importantly, for the first time to our knowledge, we demonstrate the advances in using stochastically structured plasma-free intense light channels (postfilaments) specially formed by the propagation of femtosecond laser radiation through a turbulent air layer to improve NLIFS efficiency. A multiple increase in the received signal of two-photon-excited fluorescence of polydisperse-dyed aqueous aerosols by the structured postfilaments is reported. [ABSTRACT FROM AUTHOR]