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Normal modes and their propagation constants have been found for a two-dimensional lens-like medium in which the transverse refractive index varies essentially with quadratic law but has perturbing terms of higher order. In such a realistic guiding medium with aberrations, those modes are used to find the field configuration of a Gaussian beam of half width W entering off-axis. Close to the input the beam oscillates periodically with amplitude xias if the medium were aberration-free, but slowly the beam cross-section changes shape, breaking up in several maxima, and increases size, reaching a maximum approximately equal to 2(W + xi). Afterwards the beam slowly shrinks back to the starting field configuration and the process repeats again. These results are applicable to a sequence of lenses with aberrations and become important when the lenses are closely spaced. If redirectors are to be used to compensate for lens misalignments, the corrections must be made before a large break-up of the beam occurs.
E. A. J. Marcatili (1967) studied this question.