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We report on experiments on the interaction of a gigawatt femtosecond laser pulse train with hanging isolated millimeter-sized water droplets. A transparent droplet experienced explosive boiling-up and emitted light in the visible spectrum as a result of laser-induced plasma formed inside the droplet volume. The droplet emission spectra showed remarkable broadening, depending on the laser power. The role of pulse self-phase modulation in measured spectral broadening when the pulse propagates through the droplet is discussed.