Nonparaxial Dark-Hollow Gaussian Beams

The concept of nonparaxial dark-hollow Gaussian beams (DHGBs) is introduced. By using the Rayleigh--Sommerfeld diffraction integral, the analytical propagation equation of DHGBs in free space is derived. The on-axis intensity, far-field equation and, in particular, paraxial expressions are given and treated as special cases of our result. It is shown that the parameter f =1/kw₀ with k being the wave number and w₀ being the waist width determines the nonparaxiality of DHGBs. However, the parameter range, within which the paraxial approach is valid, depends on the propagation distance. The beam order affects the beam profile and position of maximum on-axis intensity.