Topological charge transfer in frequency doubling of fractional orbital angular momentum state

Nonlinear frequency conversion is promising for manipulating photons with orbital angular momentum (OAM). In this letter, we investigate the second harmonic generation (SHG) of light beams carrying fractional OAM. By measuring the OAM components of the generated second harmonic (SH) waves, we find that the integer components of the fundamental beam will interact with each other during the nonlinear optical process; thus, we figure out the law for topological charge transfer in frequency doubling of the fractional OAM state. Theoretical predictions by solving the nonlinear coupled wave equations are consistent with the experimental results.