It is well known that as the diameter of a dielectric waveguide decreases, more energy of the supported modes is conducted outside the guide. Thus the absorption coefficient of the waveguide material becomes only partially effective and the “effective absorption coefficient” is a function of the surrounding medium also. The effective absorption coefficient can be determined by calculating the fractions of energy conducted inside and outside the guide and applying the absorption coefficients of the two media. The results of such calculations for several low-order modes in fibers of small diameter and n. a. are presented. The effective absorption coefficient is plotted as a function of the fiber characteristic term R=πd/λ (the fiber n. a.). Experimental measurements have been made in low-n. a. fibers of absorbing core and transmitting coating of different R values, and photometric results in support of the theory are included.
N. S. KAPANY, J. J. BURKE, and C. C. SHAW, "Fiber Optics. X. Evanescent Boundary Wave Propagation," J. Opt. Soc. Am. 53, 929-934 (1963)