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The degree of paraxiality (DOP) of an electromagnetic fractional multi-Gaussian Schell-model (EM-FMGSM) beam is discussed, and the effect of the properties of the light source on its DOP is also studied. It is shown from the numerical results that the DOP of an EM-FMGSM beam is determined by the rms widths of the auto-correlation functions, the truncated parameter, the degree of polarization, and the boundary characteristics of its source. Moreover, the far-field divergence angle of the beam source is also investigated to illustrate the behaviors of the DOP.

The definition of the degree of paraxiality (DOP) for a stochastic electromagnetic field is applied to a twist stochastic electromagnetic field. As an illustrative example, DOP for a wide class of model stochastic fields, i.e., twist electromagnetic Gaussian Schell-model (TEGSM) fields, is discussed. The dependence of the DOP of the light source on its properties is also studied in detail. The numerical results show that the DOP of a TEGSM beam is determined by the rms widths of auto-correlation functions and the twist factor as well as by the degree of polarization. To explain the behavior of DOP, the far-field divergence angle of this beam source is also discussed.

Degree of paraxiality (DOP) of an anisotropic hollow multi-Gaussian Schell-model (HMGSM) beam is discussed, and the influence of parameters of the beam source on its DOP is studied. It is shown that the parameters of the beam source, including the anisotropy, boundary characteristic, beam waist width, and beam coherence width, may play an important role in its DOP. Moreover, in order to illustrate the behaviors of DOP, the far-field divergence angle of this beam source has also been investigated.

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