Multi-wavelength phosphor model based on fluorescent radiative transfer equation considering re-absorption effect

The light propagation properties within the phosphor layer in phosphor-converted light-emitting diodes (pcLEDs) have been extensively described by the two-wavelength model, in which two individual excitation and emission wavelengths are selected. The ignorance of the wavelength-dependence may cause deviation and cannot return the spectrum. In this paper, we extended the two-wavelength model to a multi-wavelength model based on fluorescent radiative transfer equation (FATE) to characterize the overall light propagation behavior in the phosphor layer. In addition to the light absorption, forward scattering, and fluorescence characteristics, the re-absorption effect was further considered. The spectral radiance at any spatial location and angular direction for each wavelength was iteratively solved using the spectral element method (SEM). The model was validated by comparing the calculated spectrum and angular correlated color temperature (CCT) with experiments and good agreement was achieved with the corresponding maximum deviations of 7.6% and 3.6%, respectively. We also conducted a comparison between the multi-wavelength model with the two-wavelength model. We found that the two-wavelength model may underestimate or overestimate the optical power in the blue region and yellow region, respectively. It was attributed to assuming the peak absorption coefficient and quantum efficiency for all excitation wavelengths in the two-wavelength model.