Characteristics of intense laser self-focusing in a plasma channel

Propagation of ultrashort intense laser pulses in a partially stripped pre-formed plasma channel, which is assumed to base a parabolic refractive index and to be unperturbed, is analyzed. The refractive index equation is derived and includes the effects of the third-order intensity-dependent nonlinearity, the self-guiding of the plasma channel, and the relativistic self-focusing. The envelope equation and the relation between the propagation distance and the laser spot size are derived based on the Hamilton-Jacobi equation and the refractive index equation. The potential well, including the effects of the diffraction, the third-order nonlinearity, the relativistic self-focusing, and the plasma channel, is discussed in detail.