Optically realizable localized wave solutions of the homogeneous scalar wave equation

One of the most frequently discussed problems in construction of localized wave (LW) solutions of the homogeneous scalar wave equation has been their energy content--the LW's generally have infinite energy content and special methods have to be used to obtain physically realizable wave fields. So far the problem has mainly been addressed as a pure mathematical one and the proposed LW's can hardly be implemented in optics. In this paper we propose an approach for constructing physically realizable LW's that have a transparent interpretation in terms of optical setups. It will be shown that such LW's can be derived as finite aperture approximations of fundamental LW's, the focus wave modes.