We study the quasienergy band structure of a potential consisting of a periodic array of harmonically oscillating $\delta$ functions. The perturbative and non-perturbative regimes are investigated using Floquet-Bloch states and the Floquet translation matrix whose eigenvalues and eigenvectors are given in terms of continued fractions. We study the structure of these eigenstates and relate it to the structure of the quasibound state of a single $\delta$-function potential. We also study the dynamics of the bands as a function of the strength of the oscillating potential and find that the collapse of one of the quasienergy bands is related to the quenching of the transmission through a single $\delta$-function potential.

• Received 26 July 2002

DOI:https://doi.org/10.1103/PhysRevB.66.174306