The dynamic focusing characteristics of linearly polarized ultrashort pulses are studied. Both the complex source-sink model (CSSM) and the Richards-Wolf diffraction integral theory (RWT) are used to study the focusing phenomena. For the central focus spot, the descriptions of both the CSSM and the RWT are well consistent. Also, the CSSM can describe the super-resolution focused spot very conveniently, and only the beam waist parameters need to be changed. The dynamic convergence and divergence focusing phenomena of linearly polarized ultrashort pulse are studied by both the CSSM and RWT. The numerical simulation results of both the CSSM and the RWT are not consistent. In the convergent focusing process, there are dynamic focusing phenomena transitions from the halo to two light lobes to the elliptical focus spot. In the divergent defocusing process, the phenomena are the inverse process of the phenomena in the focusing process. The peak power of halos versus the beam convergence angles are studied. The specific angles corresponding to the significantly reduced peak powers of halos are given. These studies may be applied in the field of particle manipulation and acceleration.
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