FDTD calculations of the divergence angle of multi-mode VCSELs

We describe and demonstrate a method of decreasing the divergence angle of multi-mode VCSELs, and show how we can obtain a low and stable divergence angle. We first explain the relationship between the lateral wave-vectors of resonant modes and the divergence angle. Then we attempt to optimize the oxide aperture and the electrode structure. Here, we calculate the electro-magnetic field of the VCSELs by the Finite Difference Time Domain (FDTD) method and the far-field pattern by combining the diffraction integral and the FDTD. Finally, we compare the theoretical and experimental results of the divergence angle of the VCSELs.