Free-space propagation of an aberrating Gaussian beam

Approximate solutions of the wave equation are investigated, which can be considered as Gaussian beams affected by third-order spherical aberration. In practical cases, such beams are good approximations to the beams emerging from media whose square refractive index is described by a fourth-degree polynomial of the transverse coordinate. The measure of their spherical aberration could be a means for the determination of the coefficient of the fourth-order term in the expression of the square refractive index of the gradedindex medium.