A filter or oscillator by a simple density hump for an intense laser propagating in a preformed plasma channel

Considering the relativistic self-focusing, the ponderomotive self-channel, and the preformed channel focusing, the effect of a density hump on the laser propagation in a preformed plasma channel is studied. The evolution equation of the laser spot size is derived by using the source-dependent expansion technique. It is found that the laser behavior after the hump strongly depends on the hump position and width and is also related to the hump altitude. For the incident laser with a constant spot size, the laser after the hump may oscillate or not change, only depending on the hump width under a certain hump altitude. For the incident laser with oscillation, the laser oscillation can be enlarged, decreased, unchanged, according to the hump width, position, and altitude. So, the density hump can play the role like a filter, or like an oscillator, or be ineffective by adjusting its width, position, and altitude. These results are well confirmed by the final numerical simulations.