  The Heisenberg uncertainty principle suggests that it is impossible to
determine the trajectory of a quantum particle in the same way as a classical
particle. However, we may still yield insight into novel behavior of photons
based on the average photon trajectories (APTs). Here we explore the APTs of
photons carrying spin angular momentum (SAM) and/or orbital angular momentum
(OAM) under the paraxial condition. We define the helicity and differential
helicity for unveiling the three-dimensional spiral structures of the APTs of
photons. We clarify the novel behaviors of the APTs caused by the SAM and OAM
as well as the SAM-OAM coupling. The APT concept is very helpful for profoundly
understanding the motion of trapped particles and for elucidating other
physical systems. Due to the presence of the helical path caused by the SAM
and/or the OAM, the actual traveling distance of the photons might be much
longer than the geometric distance.
