Frequency up-conversion and arbitrary sum arithmetic of lights with orbital angular momentum

Frequency sum of two light beams carrying orbital angular momentum (OAM) in quasi-phase matching crystals was reported for the first time. The situations in which one light carried OAM and the other is in Gaussian mode and both beams carried OAM were studied in detail. An arbitrary sum arithmetic of lights with OAM was demonstrated in the conversion process. Our study is very promising in constructing hybrid OAM-based optical communication networks and all optical switching.