  Electromagnetic metasurfaces enable the advanced control of surface-wave
propagation by spatially tailoring the local surface reactance. Interestingly,
tailoring the surface resistance distribution in space provides new, largely
unexplored degrees of freedom. Here, we show that suitable spatial modulations
of the surface resistance between positive (i.e., loss) and negative (i.e.,
gain) values can induce peculiar dispersion effects, far beyond a mere
compensation. Taking inspiration from the parity-time symmetry concept in
quantum physics, we put forward and explore a class of non-Hermitian
metasurfaces that may exhibit extreme anisotropy mainly induced by the
gain-loss interplay. Via analytical modeling and full-wave numerical
simulations, we illustrate the associated phenomenon of surface-wave
canalization, explore nonlocal effects and possible departures from the ideal
conditions, and address the feasibility of the required constitutive
parameters. Our results suggest intriguing possibilities to dynamically
reconfigure the surface-wave propagation, and are of potential interest for
applications to imaging, sensing and communications.
