Local Density of States in One-dimensional Photonic Crystals and Sinusoidal Superlattices

We have calculated the local density of states (LDOS) for four Brillouin zones of a superlattice for a plane source depending on its location relative to the change in the profile of dielectricpermeability ɛ(z) of the superlattice. It is shown that the LDOS for the cases of sinusoidal and rectangular profiles of ɛ(z) are close to each other in the first and second Brillouin zones, and sharp differences between them appear beginning with the third zone. Radical changes in the LDOS occur in a rectangular superlattice with different thicknesses of adjacent layers. In this case, the function LDOS has a sharp jump at the edges of the allowed bands in the transition from one layer to another. The effects studied theoretically in this paper, can be detected and studied experimentally by the intensively developing currently methods of nanooptics.