How Does a Plane Electromagnetic Wave Exist in Three Dimensions?

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j-lee00
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A simple question

How can one talk of a Plane Electromagnetic wave, when it moves within 3 dimensions, i.e. E and B?
 
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A "plane wave" is taken to mean a propagating electromagnetic wave that has flat planes as surfaces of constant phase. This implies that the direction of propagating is in a single direction (normal to the planes). As such, a plane wave is a nonphysical idealization of real electromagnetic waves which diffract.