Nonparaxial propagation of a partially coherent dark hollow beam
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Based on the generalized Raleigh-Sommerfeld diffraction integral, an analytical nonparaxial propagation formula of a partially coherent dark hollow beam (DHB) in free space is derived. The paraxial approximation is dealt with as a special case of our general result. By using the derived formula, the nonparaxial propagation properties of DHBs are studied and are compared with the paraxial results. It is shown that the nonparaxiality properties of a partially coherent DHB are closely related to its initial beam parameters (i.e., beam waist size, wavelength, coherence length, dark size) and the propagation distance.
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