There is a difference in the definitions of the Green's functions for the Helmholtz equation and the paraxial equation. This difference is removed by the introduction of an appropriate excitation constant for the solution obtained from the Helmholtz equation. Then, the paraxial approximation of the exact solution found from the Helmholtz equation is the same as the paraxial approximation deduced from the paraxial equation.

Chapter Contents:

• C.1 Paraxial approximation
• C.2 Green's function Gp (x,y,z)
• C.3 Fourier transform G̅p (px,py,z )
• C.4 Bessel transform G̅p (η,z)
• References

Inspec keywords: Green's function methods; Helmholtz equations; electromagnetic wave propagation

Other keywords: appropriate excitation constant; Green function; Helmholtz equation; paraxial approximation; paraxial equation

Subjects: Mathematical analysis; Electromagnetic wave propagation