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Abstract A key challenge in millimeter-wave and terahertz wireless networks is blockage of the line-of-sight path between a base station and a user. User and environmental mobility can lead to blockage of highly directional beams by intervening people or objects, yielding link disruptions and poor quality of service. Here, we propose a solution to this problem which leverages the fact that, in such scenarios, users are likely to be located within the electromagnetic near field of the base station, which opens the possibility to engineer wave fronts for link maintenance. We show that curved beams, carrying data at high bit rates, can realize a link by curving around an intervening obstacle. We develop a model to analyze and experimentally evaluate the bandwidth limitations imposed by the use of self accelerating beams. We also demonstrate that such links employ the full aperture of the transmitter, even those portions which have no direct line of sight to the receiver, emphasizing that ray optics fails to capture the behavior of these near-field wave fronts. This approach, which is ideally suited for use at millimeter-wave and terahertz frequencies, opens vast new possibilities for wave front management in directional wireless networks.