The power density of an electromagnetic wave is proportional to the absolute square of the electric field |E|^2 (assuming a plane wave). Here, E is a vector so the absolute square involves all three of Ex, Ey, and Ez. In homogeneous, linear media, it's easy to show that each component of E follows its own Helmholtz equation. This decouples the three components and allows one to define a unified scalar wave (usually U) that can represent any of the field components. This is the foundation of scalar diffraction theory. In scalar diffraction theory, when people are interested in finding the intensity distribution at an image, they simply find |U|^2. A separate U is not found for Ex, Ey, and Ez. How is this an accurate representation of |E|^2, which includes all three field components? I have a Fourier optics book that claims these two quantities are directly proportional to each other, but I don't know how to show this. Doesn't polarization play an important role in interference? When we apply Huygen's principle, why don't we worry about the polarization of the spherical waves at a point?