Simulation of anharmonic Bloch oscillations: numerical problems and nonlinear effects

A stable and fast numerical method for calculating complex energies and wave functions of carriers in one-dimensional electrically biased periodic structures is presented. Optical transitions in a superlattice (Bloch oscillations) have been investigated using this method. It is shown that the transition probabilities depend nonlinearly on the applied (sufficiently strong) field. In this case, the transitions at the double and triple Bloch frequencies can be more intense than that at the fundamental frequency. A similar situation is observed in the superlattice with a split miniband (the nonlinearity is more pronounced at strong splitting).