In this paper, we analyze in detail a new method of infrared micro-spectroscopy, which aims at performing "chemical mapping" of various objects with sub-wavelength lateral resolution by using the infrared vibrational signature characterizing different molecular species. Its principle consists in an atomic force microscope tip, probing the local transient deformation induced by an infrared pulsed laser tuned at a sample absorbing wavelength. The cantilever oscillates at resonant frequencies, which amplitudes can be correlated with local absorption. We show that the system acts as an amplifier of extremely small motions induced by optical absorption and that different frequencies provide different informations, leading to a full description of the sample deformation. We estimate also the influence of the light confinement in the sample and exemplify the accuracy of the method by mapping Escherichia coli bacteria at different cantilever frequencies.