A quantitative treatment of the mechanism of phototropism in plants (directed growth caused by assymetrical illumination) implies the description of light propagation in both nonscattering and intensely scattering finite cylinders. We solve this problem for cylinders illuminated unilaterally by parallel and diffuse light applying the diffusion theory. As a first step, the complicated spatial distribution of the coherent intensity as caused by the jump of the refractive index and the nonzero curvature of the cylinder has been derived by means of differential geometry. This distribution (which is also the final solution for nonscattering objects) provides the source term in the diffusion equation (for isotropic scattering) for the turbid cylinder, which is then solved using a Green function.
© 1985 Optical Society of America
Alfred R. Steinhardt and Leonid Fukshansky, "Diffusion approximation for scattering in a cylinder: optics of phototropism," J. Opt. Soc. Am. A 2, 1725-1734 (1985)