GENERALIZED SIEGMAN FORMULA AND COMMENTS ON THE INEQUALITY M²≥1 FOR LIGHT-BEAM QUALITY

An generalized version of the Siegman formula which comes directly from Helmholtz equation is reported in this paper. Based on this formula, a comparison between the two definitions of the light beam far-field divergence angle is made. It is discovered the Siegman's moment definition for divergence angle would not make sense if the light beam could not be approximated to the slowly varying one. The proof of inequality M²≥1 given by Chen and Qiu would fail if the evanescence wave effects are considered.