Rayleigh range and the m(2) 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 byM(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 largek(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 Gaussianbeam.