Semiconductor optics in length gauge: A general numerical approach

We present a numerical method for studying electron dynamics in semiconductor crystals interacting with electromagnetic fields. The approach employs the length gauge and is consequently free of the unphysical divergences that arise in the velocity gauge as omega -> 0. The topology of the electronic structure of the Brillouin zone is taken into account by the discretization employed, and the computational method is invariant under local gauge symmetry of the Bloch functions. Arbitrary electronic structures and any temporal dependence of the fields can be handled within this approach. We give some illustrative calculations to compare and contrast numerical results of velocity and length gauges for subgap excitations of semiconductors.