Abstract
The problem of the propagation of a light ray in a lens-waveguide with arbitrarily bent axis is solved. The solution can conveniently be expressed in form of an integral if the waveguide is bent sufficiently gradually. In general, a ray which is incident on the axis of the straight lens-waveguide follows an undulating path after traversing the bend. The undulations can be kept arbitrarily small if the bend is tapered and if its curvature is sufficiently gentle. By properly dimensioning the bend, the undulations can be made to cancel out completely, so that a ray which follows the axis of the straight waveguide can be made to leave the bend on the axis of the outgoing straight waveguide. The cases of circular and tapered bends as well as tilts and offsets are discussed.
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