New X-wave solutions of free-space scalar wave equation and their finite size realization

Based on the method proposed by Donnelly and Ziolkowski [1], [2], a new gen eral solution has been obtained for the isotropic/homogenous scalar wave eq uation in cylindrical coordinates. It is shown that cell-known limited diff raction beams such as Durnin's Bessel beams [4], Lu and Greenleaf's X-wave [15], localized waves of Donnelly and Ziolkowski [1], [2], and limited-diff raction, band-limited waves of Li and Bharath [19], [20] can be obtained fr om this generic solution as particular cases. In addition, we have obtained new X-wave solutions and have calculated the field characteristics for one of them using a finite aperture realization. It is shown that with a prope r choice of the free parameter values, well-behaved X-waves with narrow bea mwidths and large depths of held can be achieved. For similar source spectr a, the results are compared with Lu and Greenleaf's zeroth-order X-wave, an d it is shown that the depth of held and beamwidth are very comparable.