Second-order moments of a twisted Gaussian Schell-model beam in anisotropic turbulence

Changes in orbital angular momentum distribution of a twisted partially coherent array beam in anisotropic turbulence

Based on the generalized Huygens Fresnel integral, we derive the analytical formula of the cross-spectral density of a twisted partially coherent array beam propagating in non-Kolmogorov anisotropic turbulence, and investigate the changes in orbital angular momentum (OAM). The results show that the anisotropy of the turbulence causes different effects in horizontal and vertical directions. The spectral density distribution of twisted partially coherent array beam in turbulence presents self-splitting and rotation, which combines the interesting effects of the twist phase and coherent structure. Although OAM is conserved, the spatial distribution of OAM flux density can be changed by changing the propagation distance, power and anisotropy of turbulence, and the modulation of the twist phase affects not only the magnitude of OAM but also its distribution. Our work is helpful for exploring new forms of OAM sources, and promote the application of free-space optical communications and optical field modulation.

Customizing twisted Schell-model beams

Since the celebrated twist phase was proposed by Simon and Mukunda, despite the tremendous progress made in theory over the past decades, developing a simple and flexible experimental method to customize this novel phase has long been a tricky challenge. In this Letter, we demonstrate a general experimental method for generating twisted Schell-model beams by implementing the continuous coherent beam integral function in a discrete form. Experimental results based on rigorous Laguerre-Gauss modes superposition are also demonstrated, indicating that our method is more convenient and of higher quality. The twist factor is also measured using the rotation characteristics during propagation, and the results agree well with the theoretical prediction. The method could serve as a general way for customizing bona fide twisted cross-spectral densities while facilitating certain applications.

Propagation of orbital angular momentum modes carried by hollow vortex Gaussian beams in anisotropic atmospheric turbulence

We establish the propagation model of orbital angular momentum (OAM) modes carried by hollow vortex Gaussian (hvG) beams propagating in anisotropic atmospheric turbulence. Effects of light source parameters and atmospheric conditions on the OAM mode propagation performance are investigated in detail. The findings indicate the hvG beam with a smaller OAM quantum number, a larger beam order, or a longer source wavelength has more robust resistance to atmospheric turbulence interference. The waist width of the light source has different influences on the OAM mode propagation at different propagation distances. Atmospheric turbulences with larger values of anisotropy, inner-scale factor, non-Kolmogorov power spectrum index, and altitude are favorable for the OAM mode propagation. These research results are conducive to optimizing the design of light sources and space wireless communication systems with hvG beams.

Statistical properties of an electromagnetic Gaussian Schell-model beam propagating in uniaxial crystals along the optical axis

Within the angular-spectrum representation, we study the partially coherent beam propagating in uniaxial crystals along the optical axis. By a method of vortex expansion, we derive the analytical solution for the cross-spectral density (CSD) function of an electromagnetic Gaussian Schell-model (EGSM) beam. We demonstrate that the analytical expression of CSD function can be written into a quasi-coherent-mode representation, whose basis vectors are constructed by the elegant Laguerre-Gaussian (eLG) functions. Several limits of the analytical solution are examined and good agreements with previous theories are obtained. Moreover, we calculate the energy density and degree of polarization (DOP) of the EGSM beam, from which the effects of coherent degree on the propagating properties are revealed. It is found that the energy conversion between circularly polarized components becomes rapid when the degree of coherence is decreasing. For all degree of coherence, the energy density and DOP exhibit a similar saturated behavior in the far field.

Statistical Characteristics of a Twisted Anisotropic Gaussian Schell-Model Beam in Turbulent Ocean

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.

Twisted elliptical multi-Gaussian Schell-model beams and their propagation properties

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.

Rectangular Hermite non-uniformly correlated beams and its propagation properties

We introduce a new class of non-uniformly correlated beams that are called rectangular Hermite non-uniformly correlated (RHNUC) beams, which possess rectangular symmetry in their degree of coherence. It is shown that, in free space and in turbulence, these beams possess self-focusing properties and that the position of the focus can be adjusted in 3-D space by manipulating the correlation properties of the source. Furthermore, it is demonstrated that, by choosing different mode orders and correlation lengths along two transverse directions, one creates astigmatic beams that can be designed to have a high and near-constant intensity over an extended propagation range.

Twisted partially coherent array sources and their transmission in anisotropic turbulence

A new class of twisted Schell-model array correlated sources are introduced based on Mercer's expansion. It turns out that such sources can be expressed as superposition of fully coherent Laguerre-Gaussian modes, and the twistable condition is established. Furthermore, on the basis of a stretched coordinate system and a quadratic approximation, analytical expressions for the mutual coherence function of an anisotropic non-Kolmogorov turbulence and the cross-spectral density of a twisted Gaussian Schell-model array beam are rigorously derived. Due to the presence of the twist phase, the beam spot and the degree of coherence rotate as they propagate, but their rotation centers are different. It is shown that the anisotropy of turbulence causes an anisotropic beam spreading in the horizontal and vertical directions. However, impressing a twist phase on source beams can significantly inhibit this effect. For an anticipated atmospheric channel condition, a comprehensive selection of initial optical signal parameters, receiver aperture size and receiver capability, etc., is necessary. Our work is helpful for exploring new forms of twistable sources, and promotes guidance on optimization of partial coherent beam applications.

Propagation Characteristics of a Twisted Cosine-Gaussian Correlated Radially Polarized Beam

Recently, partially coherent beams with twist phases have attracted growing interest due to their nontrivial dynamic characteristics. In this work, the propagation characteristics of a twisted cosine-Gaussian correlated radially polarized beam such as the spectral intensity, the spectral degree of coherence, the degree of polarization, the state of polarization, and the spectral change are investigated in detail. Due to the presence of the twisted phase, the beam spot, the degree of coherence, and the state of polarization experience rotation during transmission, but the degree of polarization is not twisted. Meanwhile, although their rotation speeds closely depend on the value of the twist factor, they all undergo a rotation of π / 2 when they reach the focal plane. Furthermore, the effect of the twist phase on the spectral change is similar to the coherence, which is achieved by modulating the spectral density distribution during transmission. The twist phase opens up a useful guideline for manipulation of novel vector structure beams and enriches potential applications in the field of beam shaping, optical tweezers, optical imaging, and free space optical communications.