We present a new simulation method to predict the performance of various white LED packages with a planar phosphor layer using the extended Adding-Doubling method. In a phosphor converted white LED part of the incident and converted light is back-scattered from the phosphor layer towards the LED package. This light will be partly reflected back onto the phosphor layer by the LED package. When simulating the LED source with the extended Adding-Doubling method, the behavior of the LED package can be approximated by a reflection matrix. This matrix includes the directions in which the light is scattered from the LED package, as well as the efficiencies.
We found that, by using the extended Adding-Doubling method with the appropriate reflection matrix, it is possible to predict the total flux and the spectral angular intensity distribution of the light emitted from white LED packages with a planar luminescent layer. With this method we present a fast technique to predict the performance of phosphor converted white LEDs and optimize the optical parameters of the luminescent layer to obtain the best overall performance.