Abstract

Naturally produced icicles can be approximately symmetrical about a vertical axis. Some icicles are only weakly tapered so that approximating the icicle as a circular cylinder gives insight into ray optics of die scattering. Several features of the scattering are evident when viewing a sunlit icicle with the unaided eye. These include (i) the specular reflection and (ii) the merging and disappearance of the two-chord "rainbow rays" as the scattering angle to the observer's eye is varied. As described below, other information about the scattering process is manifested by viewing the scattering through a camera focused on the farfield scattering. The dominant direction of the incident wave vector k_i is ordinarily tilted by a angle γ relative to a plane perpendicular to the symmetry axis z of the icicle. Consequently the ray evolution differs from the well known case of a circular cylinder at normal incidence. An analysis summarized here shows how the conditions for the Airy caustic evolves with γ such that the Airy caustics from opposite sides of the cylinder merge and disappear at a critical tilt angle γ_c. These phenomena were simulated in laboratory observations of scattering by a clear tilted PMMA polymer fiber illuminated by a laser beam as summarized below. While our observations and analysis are intended to give insight into naturally occurring processes, the problem of the ray-optics of tilted dielectric cylinders may also be of general interest [1,2]. Furthermore, the Airy caustic features of laser-illuminated fibers at normal incidence have been used in the testing of optical fibers (for communication applications) so that is reasonable to inquire how the rainbow features evolve with tilt [3]. During the course of this investigation, we became aware of a closely related investigation by Lock et al. [4,5] of the ray optics of a large glass cylinder.

© 1997 Optical Society of America