The power of the trapped modes on a semi-infinite optical fiber illuminated by an incoherent source is determined. All possible modes are excited, each with approximately the same power when V→∞, V = 2πρ (n21 - n22)½ /λ, where ρ is the fiber radius, λ the wavelength of light in vacuum, and n1, n2 are the refractive indices of the fiber and its surround, respectively. A ray-optical interpretation is given for the summed power of the modes. For V=∞, the power corresponds to that found from classical geometric optics, treating all rays as if they are meridional. This result is independent of the degree of coherence of the source. The per cent error of meridional ray optics is 100/V when V is large. The total power within the fiber is the combined power of the trapped modes and the radiation field. In the limit V=∞, the total power within the fiber at any position z along its axis is that given by classical geometric optics, i.e., that found by tracing all rays, skew and meridional. At the point z = ∞ for arbitrary V, the total power is that due to the trapped modes only.
Allan W. Snyder and Colin Pask, "Incoherent illumination of an optical fiber," J. Opt. Soc. Am. 63, 806-812 (1973)