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We extend the scalar elliptical multi-Gaussian Schell-model (EMGSM) beams with twist phase to the electromagnetic domain and obtain the analytical expression for the propagation of the electromagnetic twisted EMGSM beams through random media. The twist phase-induced changes of the spectral density and degree of polarization of such beams on propagation are studied numerically. Results show that by adjusting the twist factor and the correlated parameters of the source, both the spectral density and degree of polarization not only rotate around the propagation axis but also exhibit diverse shapes. The flattopped ellipse-like and diamond-like shape maintain over a relatively long propagation distance and finally involve into Gaussian-like shape due to stronger atmospheric turbulence. The results will be useful in optical trapping and optical communication.

A new class of pulse source with correlation being modeled by the convolution operation of two legitimate temporal correlation function is proposed. Particularly, analytical formulas for the Gaussian temporally modulated multi-sinc Schell-model (MSSM) pulses generated by such pulse source propagating in dispersive media are derived. It is demonstrated that the average intensity of MSSM pulses on propagation are reshaped from flat profile or a train to a distribution with a Gaussian temporal envelope by adjusting the initial correlation width of the Gaussian pulse. The effects of the Gaussian temporal modulation on the temporal degree of coherence of the MSSM pulse are also analyzed. The results presented here show the potential of coherence modulation for pulse shaping and pulsed laser material processing.

We numerically investigate the trapping effect of the focused generalized Multi-Gaussian Schell model (GMGSM) beam of the first kind which produces dark hollow beam profile at the focal plane. By calculating the radiation forces on the Rayleigh dielectric sphere in the focused GMGSM beam, we show that such beam can trap low-refractive-index particles at the focus, and simultaneously capture high-index particles at different positions of the focal plane. The trapping range and stability depend on the values of the beam index N and the coherence width. Under the same conditions, the low limits of the radius of low-index and high-index particles for stable trapping are indicated to be different.

We extend the scalar rectangular Gaussian Schell model (RGSM) beams to the electromagnetic domain and obtain the analytical expression for the propagation of the electromagnetic RGSM (EM RGSM) beams through an ABCD optical system. As a practical application, we illustrate how the spectral density, the spectral degree of polarization and the spectral degree of coherence of the EM RGSM beams through the fractional Fourier transform (FRFT) optical system depend on the FRFT order p and the value of beam profile M. It is found that the periods of the on-axis spectral density, the on-axis degree of polarization and the transverse degree of coherence for the FRFT order are all 2. In addition, it is of interest that the profiles of the transverse spectral intensity and the degree of polarization in the standard Fourier transform plane (i.e., p=1) are shown to form flat rectangular region which is wider for larger values of M.

The analytical expression for the propagation of a vortex Airy beam through ABCD optical systems is derived. As an example, the propagation of the beam in chiral medium is discussed. It is shown that the vortex will destroy the center lobe of the Airy beam at a critical position which is different for the left circularly polarized (LCP) and the right circularly polarized (RCP) vortex Airy beam. The intensity distribution exhibits novel features due to the existence of the vortex. In addition, the intensity distributions of the LCP beam and the RCP beam are more sensitive to the chirality parameter in far-zone than that in near-zone. The transverse shift of the center lobe of a vortex Airy beam during propagation is affected by the chiral parameter.

A class of random source for circular optical frame is generalized to electromagnetic domain. Analytical formulas for the propagation of the electromagnetic source for circular frames combinations through atmospheric turbulence are derived. As two examples, the statistic characteristics of a single circular frame and two nested frames are comparatively studied in free space and in non-Kolmogorov’s atmospheric turbulence. The evolutions of the degree of polarization and the degree of coherence of such circular frames exhibit unique features. The impacts, arising from the refractive-index structure constant, the fractal constant of the atmospheric spectrum and the upper index in the source degree of coherence, on the statistical characteristics are analyzed in detail.

We numerically investigate the radiation forces of multi-Gaussian Schell-model (MGSM) beams, in which the degree of coherence is modeled by the multi-Gaussian function, exerted on the Rayleigh dielectric sphere. By simulation of the forces calculation it is found that the steepness of the edge of the intensity profile (i.e., the summation index M) and the initial coherence width of the MGSM beams play important roles in the trapping range and stability. We can increase the trapping range at the focal plane by increasing the value of M or decreasing the initial coherence of the MGSM beams. It is also found that the trapping stability becomes lower due to the increase of the value of M or the decrease of coherence. Furthermore, the trapping stability under different conditions is explicitly analyzed. The results presented here are helpful for some possible applications.