The asymptotic behaviour of the light power at large distance in a random waveguide system with a short correlation length and a mathematical mechanism of the asymptotic behaviour are clarified. The discussion is based on the coupled mode theory. First, for the light propagation in an ordered waveguide system a new description in terms of the light power is presented. A solution of the integro-differential equation describing the light power is expressed as a contour integral in the Laplace transform domain. Singularities of the integrand are branch points and the branch cut integral determines the asymptotic behaviour of the solution. The light power decreases in inverse proportion to the distance. Secondly the description is extended to the case of a random waveguide system. The differential equation of the recurrence type describing the incoherent power is reduced to the integro-differential equation and it is shown that the kernel is the product of the kernel for an ordered system and the damping term. The equation is solved by using the same procedure as that for an ordered system and a contour integral representation of the solution is obtained. Singularities of the integrand are poles and branch points. The poles arise from the damping term of the kernel and the residues of the poles determine the asymptotic behaviour of the solution. The incoherent power decreases in inverse proportion to the square root of the distance.

The power coupling coefficients between cores of waveguide systems with random geometrical imperfections along the fiber axis are determined by comparing numerical solutions of the coupled mode equations with numerical solutions of the coupled power equations and the dependence of the power coupling coefficient on the correlation length with respect to the propagation constants of modes is clarified. When the correlation length D is small the power coupling coefficient is proportional to κ 2 D where κ is the mean mode coupling coefficient and is independent of the fluctuation of the propagation constants. For sufficiently large D the power coupling coefficient dc decreases in proportion to D-1 with increasing D and when D , dc 0. Then the dependence of the power coupling coefficient on the mode coupling coefficient and the fluctuation of the propagation constants δ β is expressed as a function of a single variable κ /δ β .

Random fluctuations of the propagation constants of modes along the fiber axis are taken into consideration and the power coupling coefficient between cores of an image fiber is theoretically derived. For the fiber used for the measurement in the previous paper (A. Komiyama, IEICE, vol.E79-C, no.2, pp.243-248, 1996) it is verified that the coupling coefficient can be described in terms of statistical properties of the propagation constants in the cross-section of the fiber.

One of coupling coefficients appearing in the coupled power equations describing the crosstalk in an image fiber is derived based on the coupled mode theory. Cores arranged in the cross-section of the fiber differ randomly to the degree of several percent in size and consequently modes propagating along the cores differ randomly. Random fluctuations of the propagation constants of modes cause the random transfer process of power between the cores, whereas contributions of the random fluctuations of the mode coupling coefficients to the statistical process can be neglected. The coupling coefficient is described as the ratio of the power transfer ratio to the coupling length for two cores with slightly different radii characterizing the random cores. The theoretical results are in good agreement with measurement results except near cutoff.

In an image fiber containing a large number of cores, a certain class of crosstalk has been found to decrease with the distance along the fiber axis. This crosstalk is absolutely distinguished from the usual crosstalk that increases with the distance. A theoretical model is presented based on the power transfer between three groups of modes supported by each core. The process of power transfer is described by coupled power equations. Values of the coupling coefficients can be determined from the measurement of the crosstalk. The equations are solved numerically for the transmission of a point image. The results are in good agreement with measurement results.