Focused waves and the scalar wave equation

Abstract

New solutions of the free space wave equation are studied and particular forms of these new solutions lead naturally to the localized wave solutions that have recently been reported in the literature. Localized waves exhibit a high degree of spatial and temporal localization. Choosing the characteristic variables, (z−ct, z+ct), the Green’s function is constructed for the scalar wave equation. With this form for the Green’s function, it is shown how a relatively simple line source of infinite extent, aligned with the propagation axis, gives rise to a propagated field which exhibits a degree of transverse focusing.

The spatial distribution of the illumination of dynamic apertures and its effect on the decay rate of the radiated localized pulses

“…The time dependence of the radius of the investigated aperture reflects its dynamic character. Other suggestions to generate other FWM-like pulses are based on moving sources, the speeds of which are very close to the velocity of light [17][18][19][20]. Among such schemes the works of Borisov and Utkin [18,19] and that of Palmer and Donnelly [20] are prominent.…”

On Ignition of Thermonuclear Fuels Using Neutron-Nuclei Fusion Reactions

“…Other suggestions to generate other FWM-like pulses are based on moving sources, the speeds of which are very close to the velocity of light [17][18][19][20]. Among such schemes the works of Borisov and Utkin [18,19] and that of Palmer and Donnelly [20] are prominent. Such moving source schemes are derived from Green's function variables.…”

Periodic evolution of the Pearcey Gaussian beam under fractional effect

“…In recent years, special beams, where three important cases are the Airy beam [1], Gaussian beam [2] and Bessel beam [3], thanks to their advantages of being relatively simple to excite and their novel property characteristics, have gained a lot of public attention. Simultaneously, a great deal of research had been done on various aspects of the transmission characteristics of these special beams, such as diffracting-free [4], self-accelerating [5], self-healing [6] and self-focusing [7]. Furthermore, the Pearcey beam has also drawn attention similar to the Airy beam.…”