Rayleigh Range of Hermite–Gaussian Array Beams

Abstract

An analytical expression for the Rayleigh range of Hermite–Gaussian (H-G) array beams is derived. It is shown that under the non-phase-locked case the Rayleigh range zR increases monotonously with the increasing beam number M, the beam separation distance xd and the beam waist width w0, and with decreasing the beam order m. However, under the phase-locked case there exists oscillatory behavior of zR versus m and xd. For Gaussian array beams, under the phase-locked case, zR is always larger than that under the non-phase-locked case. However, it holds true only when xd is small enough or w0 is large enough for H-G array beams. In addition, zR of Gaussian array beams is always larger than that of H-G array beams.