Density of states for a dielectric superlattice. II. TM polarization

We present an analysis of the band structure, the equifrequency surfaces, a nd the density of states (DOS) for the transverse magnetic (TM) polarizatio n mode of the dielectric superlattice, modeled by means of Dirac-delta func tions. This complements a recent article [Phys. Rev E 59, 3624 (1999)] that analyzes the case of transverse electric (TE) polarization. Unfortunately, for this simple model, there is no manifestation of the Brewster effect in the band structure for the TM modes. For large values of the frequency or the grating strength, the equifrequency surfaces essentially degenerate int o a set of concentric, hollow, and narrow cylinders centered on the superla ttice axis. The DOS is enhanced relative to foe space for any frequency and it exhibits discontinuities in the slope at the band edges. These results are relevant to the spontaneous emission by an atom or to dipole radiation in one-dimensional periodic structures. The differences between TE and TM m odes an discussed. We take the opportunity to correct an error in the DOS c alculation for TE polarization in the article referred above.