Suitable state bases for nonlinear optical mode conversion protocols

By considering parity-defined Laguerre-Gaussian (LG) and Hermite-Gaussian (HG) beams as input modes, we present arguments through experimental and theoretical results in order to affirm that using HG modes as bases is more suitable for optical mode conversion than using LG modes. By analyzing the normalized overlap integral and the generated modes, we determine a clear rule for the dominant mode for nonlinear mixing of HG beams, while the same is not possible for LG beams. In addition, examples of optical modal conversion using both HG and LG modes as input beams are demonstrated.