Paraxial wave equation

Summary

The paraxial wave equation describes a light beam that travels mostly along one axis and spreads only slowly sideways. It comes from the Helmholtz equation when the field is written as a fast plane wave along the axis times a slowly varying envelope. It has the form of the free Schrödinger equation in two dimensions, with the distance along the beam playing the role of time. Its solutions include the Gaussian beam and the higher-order laser modes.