<title>Time-dependent numerical simulation of vertical cavity lasers</title>

To simulate vertical cavity surface emitting lasers (VCSELs), we are developing a 3D, time-dependent field-gain model with absorption in bulk dielectric regions and gain in quantum-well regions. Since the laser linewidth is narrow, the bulk absorption coefficient is assumed to be independent of frequency with a value determined by the material and the lattice temperature. In contrast, the frequency-dependent gain regions must be solved consistently in the time domain. Treatment of frequency-dependent media in a finite-difference time-domain code is computationally intensive. However, because the volume of the quantum-well regions is small relative to the volume of the multilayer dielectric (MLD) mirror regions, the computational overhead is reasonable. A key issue is the calculation of the fields in the MLD mirror regions. Although computationally intensive, good agreement has been obtained between simulation results and matrix equation solutions for the reflection coefficient, transmission coefficient, and bandwidth of MLD mirrors. We discuss the development and testing of the 2D field-gain model. This field- gain model will be integrated with a carrier transport model to form the self-consistent laser code, VCSEL.