The field propagates in all directions, i.e. the field distribution in one place at one time depends on all places on its Light Cone at another time. (The light "cone" may become a very complicated surface when you take inhomogeneous media into consideration)

Another way to ask this might be to ask to what extent is it possible to localize a single photon.

When you examine electrons in the vicinity of an atomic nucleus, you have to resort to the wave equation, and the probability of finding an electron at any given point depends on its set of quantum numbers, and all those do is narrow the possibilities to one peculiar shaped region in preference to another.

But now with an EM wave, you have to think about photons. Presumably any single photon travels in a straight line, and along that line the variations in the E (and M) fields have definite large scale features. The E fields in the radio wave bringing you an FM broadcast reverse every 3 meters or so, yet surely this is a single particle with a quantum nature. Or, think about lasers, where you have atoms, on the order of 0.1nm or less in diameter emitting photons of visible light at 638 nm, these packets of E-M thousands of times larger than themselves.

It's a good question, to ask 'how big are photons, at right angles to their direction of propagation'. +1 for asking it.