Focusing effect of radially power-law channel on an intense laser beam

• There exists a small critical region of the ratio of the initial laser spot size to the channel radius.
• The power-law channel effect becomes opposite when the ratio crosses the critical region.
• The power-law exponent of the channel affects the focusing significantly below the critical region.

To study the focusing effect of the power-law channel, the evolution equation of the laser spot size is derived for the laser propagation in a radially power-law channel by using variational method. It is found that there exists a small critical region of the ratio of the initial laser spot size to the channel radius. Below the critical region, the laser power for constant spot size varies dramatically with the increase of the power-law exponent of the channel and so do other focusing behaviors. Quite opposite behaviors are observed above the critical region.