Two-dimensional axisymmetric opto-thermal phosphor modeling based on fluorescent radiative transfer equation

Remote phosphor plate excited by the light-emitting diode (LED) or laser diode (LD) has been widely applied in solid-state lighting. The light propagation properties within the phosphor have been analytically characterized based on the one-dimensional assumption. However, this may be not feasible in some cases, e.g., the excitation spot diameter is comparable to the plate thickness or the incident irradiance is not uniform along the horizontal direction. In this work, we extend the one-dimensional model to a two-dimensional axisymmetric opto-thermal model based on the fluorescent radiative transfer equations (FRTEs) for the cylindrical phosphor plate excited by a collimated beam with a small spot diameter and Gaussian irradiance distribution. The radiances of the blue and yellow lights are iteratively calculated by solving FRTEs in the cylindrical coordinate system using the discontinuous spectral element method. By inputting the obtained heat generation density from FRTEs, we calculate the three-dimensional temperature distribution by solving the heat diffusion equation (HDE). In addition, the opto-thermal interaction between FRTEs and HDE is achieved by introducing the temperature-dependent phosphor quantum efficiency. Using the model, we evaluate the optical, thermal and opto-thermal interacted performances of the phosphor. Finally, the model is validated by comparing the measured output optical power and surface temperature distribution with the calculated results.