We theoretically investigate the photonic band structure of one-dimensional superlattices composed of alternating layers of right-handed and left-handed materials (RHM and LHM). The dispersion curves are mainly studied by assuming that the dielectric permittivity and magnetic permeability are constant in each layer. It is shown that such structures can exhibit new types of electromagnetic modes and dispersion curves that do not exist in usual superlattices composed only of RHM. In particular, we emphasize the possibility of bands that originate from the interface modes localized at the boundary between a LHM and RHM or from confined modes in one type of layers. These waves are evanescent in both or in one constituent of the superlattice. One of the pass bands may lie below the light lines of the constituting material and go down to the static limit of a vanishing frequency omega, even at a value of the wave vector k(//) (parallel to the layers) that is different from zero. For a given value of the wave vector k(//), the dispersion curves omega versus k(z) (where k(z) is the Bloch wave vector of the periodic system along the axis of the superlattice) may exist only in a limited part of the superlattice Brillouin zone and exhibit a zigzag behavior instead of a monotonic behavior as in usual superlattices. With an appropriate choice of the parameters, we show that it is possible to realize an absolute (or omnidirectional) band gap for either transverse electric (TE) or transverse magnetic (TM) polarization of the electromagnetic waves. A combination of two multilayer structures composed of RHM and LHM is proposed to realize, in a certain range of frequency, an omnidirectional reflector of light for both polarizations.
We discuss two points related to the simultaneous existence of phononic and photonic band gaps in a two-dimensional crystal constituted by a square array of holes drilled in a matrix. In a first part, using the case of a sapphire sample in the microwave range, we show that in addition to the phononic gap, an absolute photonic gap may be obtained making use of the high values as well as the anisotropy of the dielectric matrix elements in the microwave regime. In a second part, using the case of silicon in the telecom frequency range, we demonstrate that absolute photonic and phononic gaps may be obtained by making a combination of two crystals having slightly different filling factors. The calculations of the band structures and transmission coefficients were mainly computed using the finite difference time domain method.
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