I was trying to solve an exercise in classical optics, consisting in finding the type polarization of certain field profiles. And, by analyzing this one: $$E_x(z,t) = |E|sin(kz-\omega t)\\ E_y(z,t)=|E|sin(kz-\omega t +\frac{\pi}{4})$$ I first found that it was the superposition of a elliptical polarization and a linear one by splitting the $sin$ in two, then I plotted it and discovered that in fact it's an inclined ellipse. It brought me to the conclusion that superposing a defined longitudinal and an elliptical gives another elliptical one. Now, I recall hearing that the elementary polarization are the two circular ones, which should imply that any elliptical or longitudinal can be decomposed into a sum of circular polarization, am I right? Because formally it's not evident to me.
ps: Also, what do the terminology TM and TE labeling the polarization of single photons refer to? I encountered them a few times, but they were never defined.