We perform numerical simulations on a model describing a Brillouin based temperature and strain sensor, testing its response when probed with relatively short pulses. Experimental results were recently published that showed a broadening of the Brillouin loss curve when the probe pulse duration is reduced, followed by a sudden and rather surprising reduction of the linewidth when the pulse duration gets shorter than the acoustic relaxation time. Our study reveals the processes responsible for this behavior. We give a clear physical insight into the problem, allowing us to define of the best experimental conditions required to take advantage of this effect
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