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    Materials which posses unique macroscopic properties due to finer scale repetition have been recently termed Metamaterials.  This amorphous term encompasses many different research topics, one of which is periodic, composite dielectrics. These periodic dielectrics may be used in two regimes, the effective medium regime in which the periodicity is small relative to a wavelength (Fig. 1), or in the regime where the period is an appreciable amount of the wavelength and constructive and destructive interference occur (Fig. 2).  This latter scenario, where the periodic spacings are an appreciable amount of the wavelength, gives rise to Electromagnetic Bandgaps (EBG's), also previously called Photonic Bandgaps (PBG's).
    Fig. 1 - Micro scale porosity which allows for graded, low-loss, or anisotropic dielectrics.

    The EBG is a material in which periodic inclusions inhibit wave propagation due to destructive interference from scattering from the periodic repetition.  Propagation through a periodic lattice was seminally discussed by Brillouin [1], though he cites periodic structures and band diagrams for waves dating even back to Kelvin.  Periodic structure research was later reintroduced by Yablonovitch [2] with a new perspective focusing on the inhibition of field propagation from a source embedded inside the material.  The newer work recast the problem and redefined much of the focus of the periodic structure research.  Much of the newer periodic structures research uses Yablonovitch's  perspective to show that

    Fig. 2 - Mesoscale porosity formed by internal patterning of ceramic layers allowing to create a synthesized dielectric.

    two-dimensional and three-dimensional fields can be inhibited by the correct combination of two and three-dimensional periodic lattices.

    Alternatively we can use structured porosity or fine scale periodicity to create effective medium. Overshadowed by the more exotic left handed materials, these finely periodic "effective" medium materials can greatly impact materials resarch.   The materials can have vastly better loss tangents than naturally occuring materials.  This effect has been used for a variety of filter applications.

    [1] L. Brillouin, Wave Propagation in Periodic Structures (Dover, New York, 1953).
    [2] E. Yablonovitch, Inhibited Spontaneous Emission in Solid-State Physics and Electronics, Phys. Rev. Lett., Vol. 58, 2059, (1987).

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