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

We present an analysis of the band structure, the equifrequency surfaces, and the density of states (DOS) for the transverse magnetic (TM) polarization mode of the dielectric superlattice, modeled by means of Dirac-delta functions. 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 into a set of concentric, hollow, and narrow cylinders centered on the superlattice axis. The DOS is enhanced relative to free 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 modes are discussed. We take the opportunity to correct an error in the DOS calculation for TE polarization in the article referred above.