Propagation properties of partially coherent dark hollow beams with rectangular symmetry through aligned paraxial optical systems

Propagation properties of partially coherent dark hollow beams with rectangular symmetry through aligned paraxial optical systems are investigated in this paper. Based on the unified theory of coherence and polarization, the analytical formulae for cross-spectral density both in source and reference plane are derived in tensor forms with the help of generalized paraxial Collins formula. By using the transmitting matrix law, we set up a general aligned ABCD optical system in order to analyze the propagation properties of beams passing through it. Numerical results show that intensity distribution in transversal output plane is easily influenced by coherence length in the source plane; oppositely it shows no variation by varying beam orders or dark-size adjusting parameter. We also investigate varying effects of two sorts of beam source parameters on degree of coherence in the transversal reference plane. Finally we show the relationship between dark-size adjusting parameter and paraxial transmitting intensity. Results show that when we decrease dark-size parameter to a certain number, the average intensity around the focal point disappear which is very different from ordinarily situation. All results in this paper may provide an effect way to describe and treat atom trapping and guiding by applying rectangular DHB.

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