Rayleigh range and the M2 factor for Bessel-Gauss beams

The M-2 factor of Bessel-Gauss beams derived by Borghi and Santarsiero [Opt. Lett. 22, 262-264 (1997)] is shown to predict the e(-2) axial position rather than the half-intensity position of the on-axis intensity as the Rayleigh range divided by M-2 for large values of k(t)w(0). For small values of k(t)w(0), the half-intensity axial position of the J(0) Bessel-Gauss beam is the Rayleigh range divided by M-2. Also, the ratio of the half-intensity lengths of J(0) Bessel-Gauss and comparable Gaussian beams having the same radial size of their central regions is shown to be M-2/1.3. For equal input powers and large k(t)w(0), the values of peak intensity times effective range for J(0) Bessel-Gauss beams is a constant and is a factor of 1.3 larger than the corresponding product for the comparable simple Gaussian beam. (C) 1998 Optical Society of America.