  We report on studying the dynamic evolution of orbital angular momentum (OAM)
carrying light in sum frequency generation (SFG). Dynamic evolution of the SFG
beam is studied in different cases, in which the two pump beams are either a
single OAM mode or OAM superposition mode. For the cases when the two pumps are
both in superposition mode, two kinds of spatial patterns and evolution
behaviors are observed, one set of spatial pattern is non-diffractive and
unchanged with propagating. In addition, SFG of two pump beams with opposite
OAM will evolve into a kind of quasi-Gaussian mode. These observations show
that the pumps phases are coherently transferred to SFG beam in the conversion
process. Our findings give insights to physical picture of OAM light
transformation in nonlinear processes, which can be used in OAM mode
engineering and de-multiplexing of different OAM modes.
