We study a statistical ensemble of multimode laser beams. Each beam is made up of an incoherent superposition of off-axis polychromatic Hermite–Gaussian modes. We obtain analytic expressions for the squared beam radius, the waist position, the Rayleigh range, the skewness parameter, the kurtosis parameter, and the squared beam-propagation factor. We demonstrate that the squared beam radius has a quadratic dependence on the distance from the waist plane. The skewness parameter may be different from zero in the near-field zone, but it tends to zero in the far-field zone. The kurtosis parameter in the far-field zone coincides with the kurtosis parameter of the incoherent superposition of on-axis modes.
© 2002 Optical Society of America
Original Manuscript: August 24, 2001
Revised Manuscript: December 5, 2001
Manuscript Accepted: March 7, 2002
Published: August 1, 2002
Luis Martı́-López, Omel Mendoza-Yero, and Joris J. J. Dirckx, "Incoherent superposition of off-axis polychromatic Hermite–Gaussian modes," J. Opt. Soc. Am. A 19, 1572-1582 (2002)