The M2 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 byM2 for large values of ktw0. For small values of ktw0, the half-intensity axial position of the J0 Bessel–Gauss beam is the Rayleigh range divided by M2. Also, the ratio of the half-intensity lengths of J0 Bessel–Gauss and comparable Gaussian beams having the same radial size of their central regions is shown to be M2/1.3. For equal input powers and largektw0, the values of peak intensity times effective range for J0Bessel–Gauss beams is a constant and is a factor of 1.3 larger than the corresponding product for the comparable simple Gaussianbeam.
© 1998 Optical Society of America
R. M. Herman and T. A. Wiggins, "Rayleigh Range and the M2 Factor for Bessel–Gauss Beams," Appl. Opt. 37, 3398-3400 (1998)