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Summary form only given.We work suggests a natural example of a one-index set of modes, for which the Talbot type effect must be quite pronounced. Consider first a tubular waveguide. One may think of it as of a planar waveguide of a small thickness d, which is rolled up into a circular pipe of the radius R, such that R is greater than or equal to d. The thickness d is assumed to be so small that the original planar waveguide supports only one transverse mode. Then, the field in this pipe has natural azimuthal periodicity. This results in the Talbot-type self-reproduction.