  Orbital angular momentum (OAM) of photons, as a new fundamental degree of
freedom, has excited a great diversity of interest, because of a variety of
emerging applications. Arbitrarily tunable OAM has gained much attention, but
its creation remains still a tremendous challenge. We demonstrate the
realization of well-controlled arbitrary OAM in both theory and experiment. We
present the concept of general OAM, which extends the OAM carried by the scalar
vortex field to the OAM carried by the azimuthally varying polarized vector
field. The arbitrary OAM has the same characteristics as the well-defined
integer OAM: intrinsic OAM, uniform local OAM and intensity ring, and
propagation stability. The arbitrary OAM has unique natures: it is allowed to
be flexibly tailored and the radius of the focusing ring can have various
choices for a desired OAM, which are of great significance to the benefit of
surprising applications of the arbitrary OAM.
