Theory of Scattering by Finite Dielectric Needles Illuminated Parallel to Their Axes

I derive the angular distribution of light scattered by parallel-illuminated dielectric needles (i.e., cylinders of radius r≪λ) of finite length L≫λ. The scattered light is found to be strongly peaked in the near-forward direction. As the needles get longer, they scatter more light, and the angular half-width decreases. The total light scattered at all angles is proportional to Lr4/λ3. This theory was developed to help interpret measured scattered-light distributions from low-loss optical-fiber waveguides.