Calculations of Photonic Band Structure

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There has been great progress recently in the creation of artificial three-dimensional dielectric structures which are to photon waves as semiconductor crystals are to electron waves. That is, these photonic crystals have a photonic bandgap, a band of frequencies in which electromagnetic waves are forbidden, irrespective of propagation direction in space. A face-centered-cubic photonic crystal has recently been introduced, fabricated, and studied experimentally and theoretically. The experimental findings for the photonic band structure and for the attenuation length within the band gap are in excellent agreement with our calculated results. Photonic bandgap materials inhibit the spontaneous absorption and emission of photons of the frequencies concerned and have many potential applications in device physics. Examples are zero- threshold semiconductor lasers, highly efficient heterojunction bipolar transistors and highly reliable light-emitted-diodes. Moreover, very compact high- Q resonators can be made with these materials for applications from millimeter to ultraviolet wavelengths by introducing defects into the structure. We will continue to search for photonic band gap materials with specific photonic band gap structures tailored to particular applications. We will also calculate the effects of these materials on a variety of optical, atomic and chemical processes.