Comparison of photothermal responses under spatial and temporal modulations of CW Gaussian beam excitation: A numerical study

Obtaining stronger photothermal response of optical materials is of great interest in the measurement of optical losses using the photothermal tools, in particular the thermal mirror. In our previous work, we experimentally demonstrated a more effective method of thermal mirror detection employing the spatial modulation (SM) of a continuous wave Gaussian beam excitation instead of the conventional temporal modulation (TM). A complete analytical model is presented to describe the laser-induced three-dimensional dynamic thermal fields in a semi-infinite sample and the time-dependent thermal mirror due to the thermoelastic response of the material as well as the evolution of the intensity distribution of a probe beam after interacting with the thermal mirror, in both the SM and TM schemes under the low absorption and exponentially-decaying absorption cases. With the model, we obtained the variations of temperature, surface displacement, and diffraction intensity giving rise to the photothermal response of the material. The results of the comparison between the two schemes reveal that the SM scheme is more sensitive than the TM scheme originating from a large variation range of the temperature in the SM scheme. We also explained the complex relation between the surface displacement and the diffraction intensity of the probe beam at the center of the detection plane on the basis of the phase shift caused by the thermal mirror. The presented model and the results of comparison are of great importance to gain a deeper insight into the photothermal characterization in both the SM and TM schemes.Obtaining stronger photothermal response of optical materials is of great interest in the measurement of optical losses using the photothermal tools, in particular the thermal mirror. In our previous work, we experimentally demonstrated a more effective method of thermal mirror detection employing the spatial modulation (SM) of a continuous wave Gaussian beam excitation instead of the conventional temporal modulation (TM). A complete analytical model is presented to describe the laser-induced three-dimensional dynamic thermal fields in a semi-infinite sample and the time-dependent thermal mirror due to the thermoelastic response of the material as well as the evolution of the intensity distribution of a probe beam after interacting with the thermal mirror, in both the SM and TM schemes under the low absorption and exponentially-decaying absorption cases. With the model, we obtained the variations of temperature, surface displacement, and diffraction intensity giving rise to the photothermal response of th...