 Paraxial approximation

The paraxial approximation describes waves whose propagation directions make small angles with a preferred axis. Factoring out a carrier $e^{ikx}$ and neglecting the envelope's second longitudinal derivative turns the Helmholtz equation into a parabolic wave equation and suppresses backward propagation.

The paraxial approximation is an assumption used in optics, particularly in the study of lenses and geometric optics. It simplifies the analysis of light rays when they travel through optical systems. The fundamental idea is that light rays make small angles with the optical axis (the central line of the optical system), allowing us to use certain mathematical simplifications. ### Key Points of the Paraxial Approximation: 1. **Small Angles**: The approximation assumes that the angles involved are small.