Coupled harmonic oscillators model with two connected point masses for application in photo-induced force microscopy

To comprehensively describe the operation of photo-induced force microscopy (PiFM), we have developed a model based on coupled harmonic oscillators. This model features two point masses connected by massless elastic wires, offering greater intuitiveness compared to existing PiFM models. It simplifies these models into a unified theoretical framework. By solving the equations of motion using adjusted oscillator parameters, we have successfully replicated all dynamic features from previous theories. These features include resonance frequencies and shapes of eigenmodes, as well as the responses to various external forces in the two PiFM modes: direct coupling and sideband coupling. Furthermore, by integrating our model with a recently developed photo-induced thermal expansion force model, which covers both tip-enhanced and global expansions, we have managed to uncover the underlying physical mechanism responsible for the unique signal behaviors observed in sideband coupling mode, where the signal plot, as a function of sample thickness, unexpectedly exhibits a peak followed by a valley, rather than a proportionally increasing signal. Our study has the potential to enhance the comprehension of various other physical phenomena associated with PiFM in the future.