Conversion and manipulation of radial quantum modes in second-harmonic-generation processes

The second-harmonic generation of Laguerre-Gaussian (LG) beams is investigated in this paper with a coupled equation set deduced from the nonlinear paraxial equations. Under the guidance of this coupled equation set, the conversion and propagation characteristics for individual LG modes in the second-harmonic (SH) generation process are studied quantitatively. Furthermore, we show that a periodic quasi-phase-matching crystal can be used as an integrated device to produce a controllable multimode SH source. By controlling the length or temperature of crystal each LG mode of the SH wave can be manipulated separately, instead of treating the SH wave as a whole. This method might be useful in mode division multiplexing system to expand the communication capacity, and thus has potential applications in optical communication.