Abstract
The coupled mode equation describing the propagation of light in a disordered waveguide system composed of randomly different cores in size is analytically solved by the perturbation method and the average amplitude of light is derived. In the summation of a perturbation series only successive scatterings from different cores are taken into account. The result obtained shows that the average amplitude behaves as if in an ordered waveguide system composed of identical cores at short distance and decreases exponentially with increasing distance at large distance. The result is compared with the result obtained by the coherent potential approximation and the both results are in good agreement with each other. The results are also compared with the results obtained by numerically solving the coupled mode equation.
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