Rayleigh range and the M2 factor for Bessel-Gauss beams

摘要

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 M2 for large values of k↓(t)w↓(o). For small values of k↓(t)w↓(o), the half-intensity axial position of the J↓(o) Bessel-Gauss beam is the Rayleigh range divided by M2. Also, the ratio of the half-intensity lengths of J↓(o) 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↓(o), the values of peak intensity times effective range for J↓(o) Bessel-Gauss beams is a constant and is a factor of 1.3 larger than the corresponding product for the comparable simple Gaussian beam. #1998 Optical Society of America OCIS codes: 050.1940, 350.5500.