3
$\begingroup$

I am trying to understand the basic principles of scalar diffraction theory and came across the sentence "E and H obey the Helmholtz equation", what does that mean? Does that mean that each component of E and H field obey the same equation?

$\endgroup$
1
4
$\begingroup$

Yes. First, $E$ and $H$ (each separately) obey the same wave equation which says nothing else that the $E$ wave travels with the speed of light and has the same wavelength as the $H$ wave which, too, travels with the speed of light. The Helmholtz equation is obtained from the wave equation when one separates space and time variables to find particular solutions.

Maxwell Vacuum Equations

Helmholtz Equation

$\endgroup$
1
  • $\begingroup$ With E you probably mean each component of E vector field obeys the Helmholtz equation. But dont forget that there is also a constraint on the solution which is div E=0. $\endgroup$
    – lalala
    Jun 26 at 11:17

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.