Multiphoton Wannier-Stark effect in semiconductor superlattices

Interband optical transitions in a semiconductor superlattice induced by an intense optical wave in the presence of a uniform electric field are analyzed. Both the oscillating electric field of the optical wave and the uniform electric field are directed perpendicular to the heterolayers. The superlattice potential barriers are modeled by a periodical chain of {δ} functions. Quasienergetic time-dependent states are used. The explicit dependence of the coefficient of the multiphoton absorption on the frequency and magnitude of the oscillating electric field, the superlattice parameters, and on the magnitude of the uniform electric field is obtained. The importance of a sufficiently strong uniform electric field, which causes Wannier-Stark localization of the electrons and holes, is emphasized. It has been shown that this localization increases with the magnitude of both the uniform and oscillating electric fields. The main influence of the intense oscillating field is found to be in the narrowing of the energy minibands. Under localization conditions, the electroabsorption multiphoton spectrum consists of a sequence of intense steps such that the number of steps depends upon the number of photons and increases with this number. The effective red boundary of the spectrum shifts towards longer wavelengths as the magnitude of the uniform electric field increases. The form of the spectrum is shown to depend upon the parity of the number of photons involved. Estimates for the GaAs/Ga_1-x{Al}ₓ$As superlattice are given.