## 1 Introduction  
Understanding interactions between light and medium is a longstanding issue in biomedical imaging [1, 2], as it has fundamental importance to imaging techniques such as photoacoustic imaging [3, 4, 5, 6]. Optical resolution photoacoustic microscopy (ORPAM) is a photoacoustic imaging modality, which has demonstrated diffraction-limited lateral resolution on the surface [7], subwavelength-resolution label-free imaging [8], and sub-diffraction label-free imaging [9], despite typically limited penetration depth of 1-2 mm due to the tight optical focus of ballistic photons [10]. Photoacoustic tomography (PAT) showed penetration depths down to 7 cm in phantom [11, 12]. Most photoacoustic imaging utilizes water or ultrasound gel as an acoustic coupling medium to make contact between the phantom and ultrasonic transducers. Noncontact methods for acoustic wave sensing are always favorable in photoacoustic imaging. The photoacoustic pressure can be observed or detected with interferometry, such as low-coherence interferometry ((LCI); optical coherence tomography (OCT) hardware) [13]and stroboscopic polarization selective imaging [14]. These methods are often sensitive to small vibrations around the phantom. However, a recently reported noncontact photoacoustic modality, called deep photoacoustic remote sensing (dPARS) microscopy, has demonstrated insensitivity to external vibration via the contact-free detection of photoacoustic signals [15; 16]. In dPARS microscopy, the detection of photoacoustically induced sound pressure relies on the interaction process between light and the phantom, in which only the photoacoustic pressure effect was considered, and the photothermal effect was ignored. Although the induced effect caused by the photothermal effect, such as the perturbation of refractive index, is weak compared with photoacoustic pressure, it cannot be ignored in certain scenarios. In this paper, a theoretical model was used to describe the whole energy conversion process when pulsed light was absorbed by the medium, which is the fundamental signal generation mechanism in most photoacoustic modalities. The photothermal effect was considered together with the photoacoustic effect in both the theoretical model and finite element method (FEM) simulations. A model is presented to describe the local modulation of the refractive index induced by both photoacoustic pressure and photothermal effect, by showing the whole process of absorbed energy conversion analysis (wAEC). The transient refractive index perturbation produced by the incident pulsed light when combined with an existing refractive index step at the interface of two different mediums can provide significant modulations to the local reflectivity from the interface. The absorbed energy from the light source causes a temperature increase in the specimen, which changes its refractive index and thus optical path length via the thermo-optic effect [17]. For crystal and liquid materials, the change in refractive index caused by the thermal effect can be calculated by a thermo-optic coefficient. The photoacoustic pressure-induced refractive index change can also be calculated through initial pressure [18; 19; 20]. An analytical description was made to demonstrate the progress on a planar surface, which was illuminated by a pulsed beam for excitation and a continuous beam for interrogation. The temporal evolution of the temperature, displacement changes, and temporal evolution of the outward propagating photoacoustic waves were calculated, and an analysis was carried out on how these processes affect the reflectivity intensity between the interface and when it was sensed by the probe beam. To verify the accuracy of the model, FEM-based COMCOL software was employed for the simulation of the temporal temperature variation and photoacoustic signal in a silicon sample.