I remember once, a long time ago, wondering what a photon would look like if I could freeze one, or better yet, if I could catch up to one and travel with it. I also recall being completely flummoxed by the question and the answers my professors gave me (when they didn't roll their eyes and kick me out of their offices.)
|Stylized map showing the probaility that a photon will be detected at various locations. Image courtesy of M. Bellini/National Inst. of Optics|
Our good friends over at Physics (the publication, not the subject) have finally explained it in a way that I can understand - a photon doesn't have a shape. However, you can map out a region where you could find the photon if you placed a detector at various places and took a measurement. That is, you can map out the probability that a photon would appear at any given place. It's a lot like the orbital maps of electrons around the Hydrogen atom.
|Hydrogen orbitals. Image courtesy of FlorianMarquardt|
|C. Polycarpou, K. N. Cassemiro, G. Venturi, A. Zavatta, and M. Bellini, Physical Review Letters|