Discrete Bessel transform and beam propagation method for modeling of vertical-cavity surface-emitting lasers

An efficient matrix formulation combining a discrete Bessel transform and a beam propagation method for the modeling of vertical-cavity surface-emitting lasers is presented. Devices with circular symmetry are considered. The theory generalizes the concepts of field reflection and transmission coefficients, and generates a round-trip matrix that characterizes the entire structure. The model yields, among other things, the threshold current and intensity distribution at threshold and higher-order mode profiles. We apply the model to the threshold analysis of a gain-guided device. Our theoretical results agree very well with experimental observations on the temperature-dependent threshold characteristics. The optical modal reflection behavior of distributed Bragg reflectors based on our discrete Bessel transform approach is also analyzed and compared to other models. The importance of coupling loss for devices with oxide confinement layers is also discussed.