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The propagation of electromagnetic radiation in periodically stratified media is considered. Media of finite, semi-infinite, and infinite extent are treated. A diagonalization of the unit cell translation operator is used to obtain exact solutions for the Bloch waves, the dispersion relations, and the band structure of the medium. Some new phenomena with applications to integrated optics and laser technology are presented.

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of radiation coupling from the tapered fiber is based on a meridional-ray-propagation model which includes power flow calculation with the Poynting vector. The simple meridional-ray model without modification is able to predict propagation delay and pulse dispersion of a step-index, multimode fiber. 5 ' 6 By reciprocity, it appears possible to utilize such a conically tapered fiber as a means of coupling light from sources with high numerical apertures into a fiber of a relatively small numerical aperture by entering through the tapered zone. Of course, no improvement of intrinsic source brightness is possible. In our application of this fiber as a dispersing element, it was found to be much simpler than any other scheme. Fibers which are normally bundled together for the purposes of directing light into remote regions for illumination might benefit from such a tapered end in order to achieve wide-angle illumination.

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A generalized analysis of wave propagation in periodic layered media is applied to the special case of optical surface waves. These waves, confined to the interface between a periodic layered medium and a homogeneous medium, are formally analogous to electronic surface states in crystals. Single-mode surface-wave propagation along the surface of a GaAs-AlGaAs multilayer stack (grown by molecular-beam epitaxy) has been observed experimentally.

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