Density of states for a dielectric superlattice:: TE polarization

We present a calculation of the band structure and the density of states (DOS) for a dielectric one-dimensional superlattice (SL). It is modeled by means of a periodic array of Dirac delta functions, characterized by the grating strength parameter g [Tocci el nl., Phys. Rev. A 53, 2799 (1996)]. The band structure for TE or s-polarized modes is given by a simple, compact formula that reproduces well the qualitative features exhibited by a real SL. We make use of equifrequency surfaces in wave-vector space-a concept similar to the electron Fermi surfaces in solid state physics. This is helpful for deriving the DOS as a function of frequency and the g parameter. The slope of the DOS exhibits discontinuities at all the edges of the band gaps. However, the DOS is always finite, unlike the case that wave propagation is restricted to the SL axis (where the DOS vanishes in the band gap). In fact, surprisingly, the DOS is actually enhanced relative to free space for all values of the frequency and of g, and especially so at the lower edges of the band gaps. These results are relevant to the spontaneous emission by an atom, or to dipole radiation in one-dimensional periodic structures. [S1063-651X(99)11302-3].