Attenuation of light in fiber light guides

It is shown experimentally and theoretically that the dependence of the attenuation of light on the length L of straight cylindrical light guides (fiber diameter d >> λ) does not obey the Bouguer law: The extinction coefficient per unit length decreases with increasing L and decreasing d. It is demonstrated that the deviation from the Bouguer law is due to the filtration of the rays in respect of their angular distribution and closeness to the axis. A modified form of the Bouguer equation is given and problems encountered in comparisons of the transmission of light by fiber guides with different values of L and d are discussed.