Abstract : We have investigated and determined how the tensor properties of an impedance surface can be shaped to control and steer surface waves in a very general way, all the while preserving phase information. Two findings made this possible. First, it was discovered through eigenvalue analysis that a TM or TE surface bound wave tends to favor strongly propagation along one of the principal axes of its tensor impedance matrix. This is illustrated by the series of simulations shown in Figure 1 for the case of a TM wave, which favors propagation along the shorter principal axis.