Study on the time-varying and propagating characteristics of ultrashort pulse Laguerre-Gaussian beam

This work proposes a simple model of pulse Laguerre-Gaussian Beam (LGB) by chopping the incident continuous wave LGB into ultrashort: pulse. The pulse LGB is expanded into a series of LGBs with the same angular quantum number (AQN) but different radial quantum number (RQN). The expansion coefficients may show the time-varying and propagating characteristics of the pulse helical beam. Bigger RQN of the incident LGB will cause more serious mode dispersion. This work discusses emphatically the cases that the incident LGBs have zero RQN, in which the original mode, i.e. the same eigen-mode as the incident beam, can be used to approximate the pulse LGB in short propagating range, e.g. 2z_R. The original mode decreases, spreads and delays when propagating, and it's more evident for incident LGB with larger AQN. These conclusions are important for the optical communication that uses the orbital angular momentum division multiplexing (OAM-DM) technology.