Twist phase is a nontrivial second‐order phase that only exists in a partially coherent beam. Such twist phase endows the partially coherent beam with orbital angular momentum (OAM) and has unique applications such as in super‐resolution imaging. However, the manipulation and the detection of the twist phase are still far from easy tasks in experiment. In this work, we present a flexible approach to generate a famous class of twisted Gaussian Schell‐model (TGSM) beam with controllable twist phase by the superposition of the complex field realizations using a single phase‐only spatial light modulator. The precise control of the amplitude and phase of the field realizations allows one to manipulate the strength of the twist phase easily. In addition, we show that the twist factor, a key factor that determines the strength of twist phase and the amount of OAM, can be measured by extracting the real part of the complex degree of coherence of the TGSM beam. The experiment is carried out with the help of the generalized Hanbury Brown and Twiss experiment as the generated TGSM beam obeys Gaussian statistics. The flexible control and detection of the twist phase are expected to find applications in coherence and OAM‐based ghost imaging.

A new kind of partially coherent vector beam named vector Hermite-Gaussian correlated Schell-model (HGCSM) beam is introduced as a natural extension of recently introduced scalar HGCSM beam. The realizability and beam conditions for a vector HGCSM beam with uniform state of polarization (SOP) or non-uniform SOP are derived, respectively. Furthermore, analytical formulae for a vector HGCSM beam propagating in free space are derived, and the propagation properties of a vector HGCSM beam with uniform SOP or non-uniform SOP in free space are studied and analyzed in detail. We find that the behaviors of a vector HGCSM beam on propagation are quite different from those of a conventional vector partially coherent beam with uniform SOP or non-uniform SOP, and modulating the structures of the correlation functions cannot only modulate the intensity distribution, but also the state of polarization, the degree of polarization and the polarization singularities of a partially coherent vector beam on propagation. Furthermore, we report experimental generation of a radially polarized HGCSM beam for the first time. Our results provide a novel way for polarization modulation.

Propagation properties of a scalar twisted Gaussian Schell-model (TGSM) beam in turbulent atmosphere has been studied in detail. In this paper, we explore the propagation properties of a radially polarized TGSM beam in turbulent atmosphere. Analytical formulae for the elements of the cross-spectral density matrix of a radially polarized TGSM beam propagating in turbulent atmosphere are derived based on the extended Huygens–Fresnel integral. We find that the atmospheric turbulence induces degeneration of the intensity distribution and depolarization of a radially polarized TGSM beam on propagation, while the twist phase plays a role in anti-degradation and anti-depolarization. Furthermore, we also find that the twist phase induces not only the rotation of the beam spot but also changes of the state of polarization on propagation, which are caused by the fact that the twist phase imposes orbital angular momentum on the beam. Thus, the twist phase can be used to control the propagation properties of radially polarized partially coherent beam. Our results will be useful in some applications, such as optical trapping and free-space optical communications.

The analytical expression of the cross-spectral density function of a twisted anisotropic Gaussian Schell-model (TAGSM) beam transmitting in turbulent ocean is derived by applying a tensor method. The statistical properties, including spectral density, the strength of twist and beam width of the propagating beam are studied carefully through numerical examples. It is demonstrated that the turbulence of ocean has no effect on the rotation direction of the beam spot during propagation. However, the beam shape will degrade into a Gaussian profile under the action of oceanic turbulence with sufficiently long propagation distance, and a beam with a larger initial twist factor is more resistant to turbulence-induced degeneration. As oceanic turbulence becomes stronger, the beam spot spreads more quickly while the twist factor drops more rapidly upon propagation. The physical mechanisms of these phenomena are addressed in detail. The obtained results will be helpful in optical communication systems underwater.

We introduce a new kind of partially coherent source whose cross-spectral density (CSD) function is described as the incoherent superposition of elliptical twisted Gaussian Schell-model sources with different beam widths and transverse coherence widths, named twisted elliptical multi-Gaussian Schell-model (TEMGSM) beams. Analytical expression for the CSD function propagating through a paraxial ABCD optical system is derived with the help of the generalized Collins formula. Our results show that the TEMGSM beam is capable of generating a flat-topped elliptical beam profile in the far field, and the beam spot during propagation exhibits clockwise/anti-clockwise rotation with respect to its propagation axis. In addition, the analytical expressions for the orbital angular momentum (OAM) and the propagation factor are also derived by means of the Wigner distribution function. The influences of the twisted factor and the beam index on the OAM and the propagation factor are studied and discussed in detail.

Propagation properties in the turbulence atmosphere of the optical coherence vortex lattices (OCVLs) are explored by the recently developed convolution approach. The evolution of spectral density distribution, the normalized $M^2$ -factor, and the beam wander of the OCVLs propagating through the atmospheric turbulence with Tatarskii spectrum are illustrated numerically. Our results show that the OCVLs display interesting propagation properties, e.g., the initial Gaussian beam distribution will evolve into hollow array distribution on propagation and finally becomes a Gaussian beam spot again in the far field in turbulent atmosphere. Furthermore, the OCVLs with large topological charge, large beam array order, large relative distance, and small coherence length are less affected by the negative effects of turbulence. Our results are expected to be used in the complex system optical communications.