Angle-resolved photoluminescence spectrum of a uniform phosphor layer

A photoluminescence spectrum depends on an emission angle due to self-absorption in a phosphor material. Assuming isotropic initial emission and Lambert-Beer’s law, we have derived simple expressions for the angle-resolved spectra emerging from the top and bottom surfaces of a uniform phosphor layer. The transmittance of an excitation light through the phosphor layer can be regarded as a design parameter. For a strongly-absorbing phosphor layer, the forward flux is less intense and more red-shifted than the backward flux. The red-shift is enhanced as the emission direction deviates away from the plane normal. When we increase the transmittance, the backward flux decreases monotonically. The forward flux peaks at a certain transmittance value. The two fluxes become similar to each other for a weakly-absorbing phosphor layer. We have observed these behaviors in experiment. In a practical application, self-absorption decreases the efficiency of conversion and results in angle-dependent variations in chromaticity coordinates. A patterned phosphor layer with a secondary optical element such as a remote reflector alleviates these problems.