Metal waveguide modeling of tapered graded-index media

Abstract

Graded-index media having quadratic radial variations of the index of refraction have several well-known advantages for transmission of optical signals. Tapered graded-index waveguides are also of interest as waveguide couplers, power concentrators, and image size reducers. Unfortunately, the experimental study of such z-dependent media may be difficult. Even If well-characterized tapered media could be constructed, the measurement of the parameters of a microscopic propagating beam would not be straightforward. We describe a metal waveguide technique for inexpensive modeling of tapered graded-index fibers. One finds that in some respects the modes of a certain class of concave curved metal waveguides are mathematically equivalent to the modes of quadratic index media. The focusing profiles (curvatures) of these waveguides can be made arbitrarily weak, so that even at optical frequencies the modes may be large and easily observed. We have constructed several tapered metal waveguides using a variety of materials and corresponding to a variety of taper functions. The performance characteristics and applications of these devices are discussed, and the results are compared to theoretical expectations.