Modeling the Thermoelastic Sample Response for Subdiffraction Infrared Spectroscopic Imaging

There is significant and increasing interest in using the photothermal effect to record infrared (IR) absorption spectra localized to volumes that are considerably smaller than the wavelength of excitation, i.e., subdiffraction imaging. As opposed to conventional IR microscopy, in which absorption and scattering of the illuminating light is measured, subdiffraction imaging can be achieved through detection of the sample’s thermal response to IR absorption-induced heating. While this relationship has been examined by a variety of coarse-grained models, a generalized analysis of the dependence of temperature and surface deformation arising from an absorber below the surface has not been reported. Here, we present an analytical model to understand a sample’s thermoelastic response in photothermal measurements. The model shows important dependence of the ability to record subdiffraction data on modulation frequency of exciting light, limitations imposed by optical sensing, and the potential to discern location of objects ultimately limited by noise and sharpness of the detecting mechanism. This foundational analysis should allow for better modeling, understanding, and harnessing of the relationship between absorption and sample response that underlies IR photothermal measurements.