Propagation-independent fields

Nondiffracting beams are solutions of the wave equation which keep their shape during free propagation. Because of this property, they are widely studied, both as mechanical and electromagnetic waves. Another scheme, however, can be devised in order to find beams that, even if do not maintain their shape upon propagation, are independent on the propagation distance, apart from a phase factor. In this sense it can be said that these beams are also nondiffracting. In this work, the scheme leading to this different kind of nondiffracting fields, which we term propagation-independent beams, is presented. Closed-form expressions for a few of these fields, for 1-D sources, are found. A method, which in principle is able to produce beams of this type, is given. This also clarifies some of their properties. Finally, the item of finite realizations of these beams, which in principle require infinite-dimension sources, is analyzed through numerical simulations. It is also shown that the practical feasibility of these fields poses some limitations on the bandwidth they can present.