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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?

Vahram Voskerchyan
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    Since you mention wanting to understand scalar diffraction theory, my question received some good answer (although not 100% satisfying), have a look: https://physics.stackexchange.com/questions/311102/scalar-wave-approximation-to-electrodynamic-wave-equation – lalala Jun 26 '21 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.

Maxwell Vacuum Equations

Helmholtz Equation

Kurt G.
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  • 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. – lalala Jun 26 '21 at 11:17