Abstract
For a long time, there was this idea that it is impossible to mode lock a laser on a pure high-order transverse mode. Recently, it has been demonstrated experimentally the generation of femtosecond pulses by a Kerr-Lens-Mode-Locking (KLM) laser operating on a vortex LG0m mode. At the best of our knowledge, there is no studies on lensing effect induced by a doughnut laser beam inside a Kerr medium which is fundamental for modelling accurately the behaviour of a KLM laser and optimising its parameters. We have shown that the doughnut Kerr lens can be view as a ring-lens, or eccentric lens, showing two combined lensing effects. The first one is equivalent to a pure converging lens, and the second one to a diverging axicon. Both lensing effects have been analytically modelled, and provide values for the best focus position which are in a good agreement with the focal position calculated numerically by using a diffraction integral.
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