Dynamics of electromagnetic pulses with wide spectra in semiconductor superlattices

We considered the Maxwell equations for electromagnetic-field propagation in a solid with a one-dimensional semiconductor superlattice of quantum dots in the case where the spectral width of the electromagnetic pulse is sufficient to excite transitions between different minizones. A phenomenological equation was obtained in the form of the classical one-dimensional sine-Gordon equation with the perturbation caused by quantum transitions between the minizones. Quantum behavior of electrons was considered using the microscopic Hamiltonian, in the assumption that the pulse duration is small enough for the phonon effects to be neglected. The equation obtained was analyzed numerically, and cases where the adiabatic perturbation theory for the sine-Gordon equation can be used were found. Numerical solutions were obtained, and the domain where transitions between the minizones play a significant role in the electromagnetic-pulse dynamics was found.