On the Occurrence of Caustics in the Drawdown Zone of Silica Fibers

The drawdown zone of a silica fiber manufactured in a laser furnace has a cross section that varies rapidly along its axis. When this zone is internally illuminated with a collimated beam parallel to the axis, a region of high-intensity radiation is observed (see Fig. 1). The radiation is the result of multiple internal reflections and a refraction of the beam caused by the rapidly varying boundary of the glass. The locus where the rays of geometrical optics form an envelope is known as a caustic. Along such a surface the luminous intensity is a maximum. 1 Normal to the caustic, the intensity is characterized mathematically by an Airy function, decaying exponentially on one side, the shadow region, and varying harmonically in the opposite direction. For simple geometries, the techniques used to calculate the caustics are straightforward; e.g., a collimated beam reflected from a semicircular concave mirror forms a caustic which is part of an epicycloid. When the reflecting boundaries 535