Numerical approximation of light scattering from tenuous cylindrical membranes at normal incidence

A numerical method has been developed to calculate the scattered field from a complex matrix of cylindrical membranes that are thin relative to wavelength with a refractive index close to that of the medium. The membranes are broken into a collection of adjacent parallel thin fibers, each fiber is assigned an internal field, and vector summation of the fields scattered by each fiber is used to calculate the total scattered field. For an incident wave in the TM mode the internal field of each membrane fiber is chosen to be equal to the incident field (the Born approximation). For the TE mode the internal field is determined by the local membrane orientation (φ) and relative refractive index (m) according to A sin 2φ for the component in the direction of incidence and 1 - A(1 - cos 2φ)for the transverse component, where A = (m(2) - 1)/2m(2). The method has application to light scattering by cell membranes in bundles of nerve axons.