With the help of the Fast Fourier Transform (FFT) method, a formula is given to study the pulsed spherical beams with the truncated cross section propagating in free space, where the paraxial approximation are also adopted in the derivation. As an application, a theoretical calculation of convergent isodiffracting pulsed beam propagation is presented as an approximation of spherical pulsed beam propagation. Simulation is also shown to illustrate the characteristics of focusing pulsed beam through several kinds of converging lens.
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