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?
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1$\begingroup$ Since you mention wanting to understand scalar diffraction theory, my question received some good answer (although not 100% satisfying), have a look: physics.stackexchange.com/questions/311102/… $\endgroup$– lalalaJun 26, 2021 at 11:19
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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.
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$\begingroup$ 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. $\endgroup$– lalalaJun 26, 2021 at 11:17