  Chirped Bessel waves are introduced as stable (non-diffracting) solutions of
the paraxial wave equation in optical antiguides with a power-law radial
variation in their index of refraction. Through numerical simulations, we
investigate the propagation of apodized (finite-energy) versions of such waves,
with or without vorticity, in antiguides with practical parameters. The new
waves exhibit a remarkable resistance against the defocusing effect of the
unstable index potentials, outperforming standard Gaussians with the same full
width at half maximum. The chirped profile persists even under conditions of
eccentric launching or antiguide bending and is also capable of self-healing
like standard diffraction-free beams in free space.
