Theoretical Model And Propagation Properties Of A Partially Coherent Dark Hollow Beam

With the development of the laser optics, laser beams with special profiles, such as dark hollow beam (DHB), are required in many applications. DHBs with zero central intensity have important applications in laser optics, atomic optics, binary optics, optical trapping of particles, medical sciences and so on, more and more attentions are being paid to DHBs. In the past several years, coherent DHBs were extended to the partially coherent case, and many efforts were devoted to the generation and propagation properties of partially coherent DHBs. In this paper, we propose a theoretical model to describe a partially coherent beam with elliptical hollow beam profile. Nonparaxial propagation properties of a partially coherent DHB are also studied.First, we have proposed a new theoretical model named partially coherent elliptical dark hollow beam (EDHB) to describe a partially coherent beam with elliptical hollow beam profile. Analytical expressions for the propagation formula and the propagation factor are derived. Our numerical results show that the propagation factors and the propagation properties of a partially coherent EDHB are closely determined by the initial coherence width and the beam order. Our results agree well with the previous results reported on a partially coherent elliptical dark hollow beam, thus the partially coherent EDHB provides a reliable and alternative model for describing a partially coherent beam elliptical dark hollow beam.Second,when the beam waist size and wavelength are comparable or when the far-field divergence angle becomes large, the paraxial theory is no longer valid. In this paper, we study the nonparaxial propagation of a partially coherent DHB in free space. Analytical nonparaxial propagation formula for a partially coherent DHB is derived based on the generalized Raleigh-Sommerfeld diffraction integral. The far field expression and paraxial expression for a partially coherent DHB are also derived as special cases of our general results. Our numerical results show that the initial beam parameters and the propagation distance together determine the nonparaxiality properties of a partially coherent DHB on propagation. Our formulae provide a convenient way for studying the nonparaxial and paraxial propagation properties of a partially coherent DHB in free space.