The transformation by a lens of a polychromatic laser beam composed of on-axis superposed monochromatic TEM<sub>00</sub> Gaussian modes in the paraxial approximation is studied. The chromatic aberrations are described by allowing the waist position on the <i>z</i> axis and the Rayleigh range to depend on wavelength. The beam radius, the far-field divergence, the Rayleigh range, the beam product, the beam propagation factor, and the kurtosis parameter are calculated. The relationship between the fourth-order and the second-order moments of Hermite–Gaussian and Laguerre–Gaussian modes is obtained and is used for calculating kurtosis parameter. The results are generalized to polychromatic modes of higher orders. It is shown that the on-axis superposition of monochromatic TEM<sub>00</sub> modes with no chromatic aberration is leptokurtic.
© 2001 Optical Society of America
Luis Martí-López, Omel Mendoza-Yero, and José A. Ramos-de-Campos, "Propagation of polychromatic Gaussian beams through thin lenses," J. Opt. Soc. Am. A 18, 1348-1356 (2001)