Spectral anomalies of diffracted Hermite-Gaussian beams in the neighborhood of focus

The spectral behavior of spatially coherent polychromatic Hermite-Gaussian (H-G) beams focused by an aperture lens is studied by using the propagation law of the cross-spectral density function. An analytical expression for the spectrum of focused H-G beams is derived, which is related to the original spectrum and spectral modifier, and the spectral modifier is dependent on the truncation parameter, Fresnel number, and position parameter. Detailed numerical results are given to illustrate the spectral anomalies of diffracted H-G beams in the neighborhood of focus.