Evaluating Laguerre-Gaussian beams with an invariant parameter

We define a new parameter about Laguerre-Gaussian (LG) beams, named $Q_p^l$, which is only related to mode indices $p$ and $l$. This parameter is able to both evaluate and distinguish LG beams. The $Q_p^l$ 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 $Q_p^l$ and $M^2$ shows same trend for the quality of LG mode, while the measurement of $Q_p^l$ is much easier than $M^2$.