Extreme light intensities can be produced by high-power lasers, but the requirement for huge beam diameters to prevent damage to optical components prevents future development. Plasma can support extremely brilliant radiation and can be used to create and manipulate light without causing damage to solid materials. In order to create extremely high acceleration gradients for accelerators, relativistic plasma waves must be produced by powerful laser or electron beams in low-density plasmas. One of the methods is the wakefield accelerator. In this article, the basic characteristics of laser propagation and plasma wave excitation are discussed in the framework of laser-driven wakefield acceleration. The self-focusing behaviour of a Gaussian laser beam travelling through an inhomogeneous axial plasma is investigated.
