Theory of infrared nanospectroscopy by photothermal induced resonance

We present a theoretical investigation of the physics involved in a recently developed spectromicroscopy technique, called photothermal induced resonance (PTIR). With this technique, one measures the local infrared absorption spectrum of a sample shined with a tunable infrared laser pulse, and detects the induced photothermal expansion with the tip of an atomic force microscope (AFM). Simple physical assumptions allow us to describe analytically the heating and expansion of the sample, the excitation of the vibration modes of the AFM cantilever, and the detected signal. We show that the signal depends on the thermal expansion velocity rather than on the absolute displacement of the tip, and we investigate the influence of the laser pulse length. Eventually, we express the PTIR signal in terms of relevant parameters, and prove its proportionality to the sample absorbance. This analytical approach complement our experimental results and validates the PTIR method as a technique of choice for infrared spectroscopy of nanoscopic samples, getting around optical artifacts like reflectance perturbation.