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We address propagation of paraxial Gaussian-type beam modes in longitudinally inhomogeneous axisymmetric lens-like media, with a specific case of a transition of waveguide into antiwaveguide. Higher-order modes are described in a unified manner using a so-called secondary parabolic equation. Analyzing a linear transition from waveguide to antiwaveguide where beams are described in terms of Airy functions, we conclude that the width of a localized Gaussian-type beam in inhomogeneous media can dramatically grow. This fact should be taken into account in numerical procedures employing summation of Gaussian beams.

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