Diffraction-free beams remain diffraction free under all paraxial optical transformations

Abstract

We point out that the nondiffracting ${\mathrm{J}}_0$ beams of Durnin, Miceli, and Eberly are subgroup-reduced basis functions for the group of paraxial (symplectic, linear) transformations of optical phase space. This allows the action of the group on such and similar beams to be computed through 2×2 matrix algebra.