Let u(x, y, z, t ) be a monochromatic, Gaussian beam solution of the scalar wave equation in the paraxial approximation. The beam propagates in the z-direction. Use a suitably chosen Lorenz gauge vector potential to confirm the statement made in the text that the electric and magnetic fields of this beam in the same approximation can be written 

Confirm also that ∇ · E = 0 and ∇ · B = 0 within the paraxial approximation.

Transcribed Image Text:

і ди k ax E=ux+- «N and B = --V x E. (1)