Time-dependent model for vertical-cavity surface-emitting laser

Two models have been developed to simulate a vertical-cavity surface-emitting laser (VCSEL). The first model is a two-dimensional time-dependent solution of Maxwell`s equations, with frequency-independent bulk dielectric and absorption coefficients. These bulk coefficients depend upon the material, lattice temperature, and carrier concentration. This field model is coupled with a frequency-dependent gain model that describes the quantum well regions in the time domain. Treatment of frequency-dependent media in a finite-difference time-domain code is computationally intensive. On the other hand, because the volume of the active region is small relative to the volume of the distributed laser cavity, the computational overhead is reasonable. A semi-empirical transport model is used to describe the bulk transport, which drives the quantum well transport. In addition, the semi-empirical model provides a spatial distribution for the lattice temperature and carrier concentrations. The second model is a three-dimensional solution of Maxwell`s equations. The three-dimensional model can be used for cold-cavity calculations. The two-dimensional code generates the dielectric and absorption coefficients assuming azimuthal symmetry, providing the initial conditions for the three-dimensional calculation