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