Evaluating Laguerre-Gaussian beams with an invariant parameter

We define a new parameter about Laguerre-Gaussian (LG) beams, named $Q^{l}_{p}$, which is only related to mode indices $p$ and $l$. This parameter is able to both evaluate and distinguish LG beams. The $Q^{l}_{p}$ values are first calculated theoretically and then measured experimentally for several different LG beams. Another mode quality parameter, $M^{2}$ value, is also measured. The comparison between $Q^{l}_{p}$ and $M^{2}$ shows same trend for the quality of LG mode, while the measurement of $Q^{l}_{p}$ is much easier than $M^{2}$.