Effect of quartic-phase aberrations on the focal switch of Hermite-Gaussian beams

The focal switch of Hermite-Gaussian beams diffracted at an aperture and subsequently focused by a spherically aberrated lens is studied. Our main attention is focused on the effect of quartic-phase aberrations on the behavior of the focal switch. It is shown that quartic-phase aberrations affect the relative focal shift Δzf, turning position s1,t, and relative transition height Δzsw. Apart from a critical maximum truncation parameter αc,max, there is a critical minimum truncation parameter αc,min. Within the region αc,min<α<αc,max the focal switch can take place, but quartic-phase aberrations give rise to a decrease of αc,max-αc,min in comparison with the aberration-free case.