Statistical properties of a radially polarized twisted Gaussian Schell-model beam in an underwater turbulent medium

Correlation and polarization singularities of a radially polarized Gaussian Schell-model vortex beam propagating in oceanic turbulence

The correlation and polarization singularities as the important parameters of a radially polarized Gaussian Schell-model vortex beam propagating in oceanic turbulence have been investigated in detail. On the one hand, the correlation singularity of the beam will first split, and then generate new correlation singularities, and finally vanish in pairs. The longer the propagating distance, the larger the rate of dissipation of mean-square temperature, and the lower initial correlation lengths reduce the stability of correlation singularities. On the other hand, polarization singularities also split during transmission. The different initial correlation lengths cause the uneven distribution of polarization singularities, and the high order topological charge leads to the generation of new polarization singularities at short distances. Our numerical findings may be of great significance for detection and imaging of the oceanic optical telecommunication links.

Effect of oceanic turbulence on the propagation behavior of a radially polarized Laguerre-Gaussian Schell-model vortex beam

Optical wireless communications applications are restricted by oceanic media-induced beam quality degradation. However, modulating the coherence and polarization structures of the laser beams can effectively diminish the negative influence of oceanic turbulence on the beams. The average intensity of a radially polarized Laguerre-Gaussian Schell-model vortex (RPLGSMV) beam propagating through oceanic turbulence is explored by employing the extended Huygens-Fresnel principle. We found that the average intensity of an RPLGSMV beam is greatly affected by oceanic turbulence with a large rate of dissipation of the mean-square temperature and a large relative strength of the temperature and salinity fluctuations as well as the small rate of dissipation of the turbulent kinetic energy per unit mass of fluid and small Kolmogorov microscale. It was also found that a RPLGSMV beam with a larger radial index, topological charge, initial coherent length, and beam waist has a stronger anti-turbulence ability. Our numerical findings may be of great significance for the detection and imaging of oceanic optical telecommunications links.

Polarization and coherence properties in self-healing propagation of a partially coherent radially polarized twisted beam

With the help of generalized Huygens-Fresnel integral, an analytical expression for the self-healing of a partially coherent radially polarized twisted (PCRPT) beam is derived. The coherence and polarization properties of the PCRPT beam in self-healing propagation are studied in detail. It shows that the existence of the twist phase is a double-edged sword for the self-healing properties of the beam. With the increase of the twist factor, the self-healing ability of beam intensity distribution decreases. However, the anti-disturbance performance of beam polarization improves at the same time. Besides, the polarization and coherence distribution of the beam are proved that own a slight self-healing ability when the obstacle is small. Our results will be helpful to the fields of optical tweezers, microscopy, optical communication, and so on.

Twisted electromagnetic elliptical multi-Gaussian Schell-model beams and their transmission in random media

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.

Progress on Studies of Beams Carrying Twist

Optical twist has always been a hot spot in optics since it was discovered in 1993. Twisted beams can be generated by introducing the twist phase into partially coherent beams, or by introducing the twisting phase into anisotropic beams, whose spectral density and degree of coherence will spontaneously rotate during propagation. Unlike conventional beams, twisted beams have unique properties and can be used in many applications, such as optical communications, laser material processing, and particle manipulation. In this paper, we present a review of recent developments on phase studies of beams carrying twist.

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.

Propagation of twisted EM Gaussian Schell-model array beams in anisotropic turbulence

The behavior of the twisted electomagnetic (EM) Gaussian Schell-model array beams in anisotropic random turbulence is investigated. An example illustrates that a twisted EM source can produce lattice-like patterns in degree of polarization with rotation or not, which depends on the setting of the initial twist phase. One also finds that the anisotropy of the medium leads to an anisotropic beam spreading, and we can effectively limit such turbulence-induced effects by optimizing the initial twist and source correlation widths. Moreover, after transmitting through the turbulence for sufficiently long distances, the intensity and coherence are mainly affected by turbulence statistics; however, for the case of polarization, the initial twist plays a dominant role in determining its distribution profile.

Propagation properties of radially polarized multi-Gaussian Schell-model beams in oceanic turbulence

By utilizing the extended Huygens-Fresnel principle, we derive the analytical formulas for the cross-spectral density matrix elements of a radially polarized multi-Gaussian Schell-model (RPMGSM) beam propagating in oceanic turbulence. Effects of beam parameters and oceanic turbulence parameters on the propagation properties of RPMGSM beams are investigated in detail by numerical simulation. Our results show that the RPMGSM beam with larger beam order M has an advantage over the radially polarized Gaussian Schell-model beam for reducing turbulence-induced degradation. Compared with temperature-induced turbulence fluctuation, the salinity-induced turbulence fluctuation makes a greater contribution to the influence on propagation properties of RPMGSM beams.

Ghost Imaging with a Partially Coherent Beam Carrying Twist Phase in a Turbulent Ocean: A Numerical Approach

Ghost imaging (GI) is an indirect imaging approach that can retrieve an object’s image even in a harsh environment through measuring the fourth-order correlation function (FOCF) between the signal and idle optical paths. In this paper, we study lensless GI with a partially coherent beam carrying twist phase, i.e., twisted Gaussian Schell-model (TGSM) beam, in the presence of oceanic turbulence. Explicit expression of the FOCF is derived based on the optical coherence theory and Rytov approximation, and the effects of the twist phase and the oceanic turbulence on the quality and visibility of image are investigated in detail through numerical examples. Our results show that the simulated oceanic turbulence strongly affects the GI. The quality of image decreases monotonously with an increase of the strength of turbulence whereas the visibility increases. When the illumination light carries a twist phase, the visibility of the image is improved while the quality of the image is reduced in contrast to those without a twist phase. By properly selecting the strength of the twist phase, the image can still be maintained at an acceptable level of quality with high visibility. Furthermore, it is found that the quality and visibility of the ghost image are less affected by the oceanic turbulence using a TGSM beam with larger twist factor. Our findings will be useful for the application of GI in an oceanic turbulent environment.

Statistical properties of partially coherent radially and azimuthally polarized rotating elliptical Gaussian beams in oceanic turbulence with anisotropy

A new class of partially coherent radially and azimuthally polarized rotating elliptical Gaussian (PCRPREG and PCAPREG) beams is introduced. The analytical expressions of the PCRPREG and PCAPREG beams propagating through anisotropy oceanic turbulence are derived based on the extended Huygens-Fresnel principle and the spatial power spectrum of oceanic turbulence. The effects of beam waist size w₀, coherence width σ₀, propagation distance z and oceanic turbulence parameters on the evolution statistics properties of PCRPREG and PCAPREG beams are studied in detail by numerical simulation. Our results indicate that with the increase of the propagation distance in the far field region, the normalized initial profile with a doughnut-like distribution of PCRPREG and PCAPREG beams gradually converts into a flat-topped one, and finally evolves into a Gaussian-like beam profile. We also find that the salinity-induced turbulence fluctuation makes a greater contribution to the decrease of beam quality compared with the temperature-induced turbulence fluctuation. Furthermore, the full width at half maximum becomes wider for the larger propagation distance z and wavelength λ or the smaller dissipation rate ε. Our work will pave the way for the development of underwater optical communication and underwater laser radar in oceanic environment.

Twisted Gaussian Schell-model array beams

We introduce, to the best of our knowledge, a new class of twisted partially coherent sources for producing rotating Gaussian array profiles. The general analytical formula for the cross-spectral density function of a beam generated by such a novel source propagating in free space is derived, and its propagation characteristics are analyzed. It is shown that both the irradiance profile of each element of the array and the degree of coherence rotate during propagation, but in opposite directions. Further, the twist effects of the spectral density and the degree of coherence are quantified. It is shown that the direction of rotation is changeable upon propagation. Our results may provide new insight into the twist phase and may be applied in optical trapping.

Beam wander of a partially coherent Airy beam in oceanic turbulence

The beam wander of a partially coherent Airy beam in oceanic turbulence is investigated with the help of the extended Huygens-Fresnel integral formula. Analytical expression for the second-order moment and the beam wander of a partially coherent Airy beam propagating in oceanic turbulence is derived. From the numerical results based on the analytical formula, we find that increasing the dissipation rate of turbulent kinetic energy or decreasing the dissipation rate of mean-square temperature and relative strength of temperature and salinity fluctuations of oceanic turbulence tends to decrease the wander effect of a partially coherent Airy beam. Moreover, it is found that increasing the transverse scale factor and wavelength or decreasing the coherent length and exponential truncation factor of a partially coherent Airy beam decreases beam wander in oceanic turbulence. Our results will be useful in optical underwater communications and laser defense.

Power spectrum of refractive-index fluctuations in turbulent ocean and its effect on optical scintillation

Recent simulations and experiments have shown that the viscous-range temperature spectrum in water can be well described by the Kraichnan spectral model. Motivated by this, a tractable expression is developed for the underwater temperature spectrum that is consistent with both the Obukhov-Corrsin law in the inertial range and the Kraichnan model in the viscous range. In analogy with the temperature spectrum, the formula for the salinity spectrum and the temperature-salinity co-spectrum are also derived. The linear combination of these three scalar spectra constitutes a new form of the refractivity spectrum. This spectral model predicts a much stronger optical scintillation than the previous model.

Average intensity and beam quality of optical coherence lattices in oceanic turbulence with anisotropy

Based on the extended Huygens-Fresnel principle, we have derived the analytical expression of the average intensity of optical coherence lattices (OCLs) in oceanic turbulence with anisotropy, and then the beam quality parameters including the Strehl ratio (SR) and the power-in-the-bucket (PIB) are obtained. One can find that the OCLs will eventually evolve into Gaussian shape with the periodicity reciprocity gradually breaking down when propagating through the anisotropic ocean water, and that the trend of evolving into Gaussian can be accelerated for increasing the ratio of temperature and salinity contributions to the refractive index spectrum ω, the lattice constant a and the rate of dissipation of mean square temperature χT or decreasing the anisotropic factor ξ and the rate of dissipation of turbulent kinetic energy per unit mass of fluid ε. Further, the SR and PIB in the target plane under the effects of oceanic parameters are discussed in detail, and the SR and PIB can be increased for the larger ξ and ε or the smaller χT and ω, namely, the beam quality becomes better. Our results can find potential application in the future optical communication system in an oceanic environment.

Devising genuine twisted cross-spectral densities

Sticking a twist to a partially coherent source cannot be done at will, since the result can violate the definiteness property of the corresponding cross-spectral density. As a matter of fact, the study of twisted sources has been mainly concentrated on the original case proposed by Simon and Mukunda [J. Opt. Soc. Am. A10, 95 (1993)JOAOD60740-323210.1364/JOSAA.10.000095] of circularly symmetric Gaussian Schell-model sources. Here, we discuss a modeling procedure that can be used to generate numberless genuine twisted sources without symmetry constraints. As geometrically simple examples, two cases of non-Gaussian twisted sources endowed with circular or rectangular symmetry are explicitly worked out.

Practical approximation of the oceanic refractive index spectrum

Oceanic turbulence is described by the oceanic refractive-index spectrum (ORIS), which considers several important hydrodynamic parameters. Based on ORIS, many optical oceanic quantities can be calculated using numerical integration. However, it is difficult to calculate the analytical solutions. In this paper, an approximate oceanic temperature spectrum is obtained by multiplying the non-Kolmogorov spectrum with a correction factor. By analogy with the obtained temperature spectrum, an approximate salinity spectrum and an approximate coupling spectrum are obtained. A linear summation of these three approximate spectra forms the approximate form of ORIS. The approximate form of ORIS we obtained helps calculate the analytical solutions of the relevant oceanic optical quantities.

Self-focusing of a partially coherent beam with circular coherence

In a recent publication [Opt. Lett.42, 1512 (2017)OPLEDP0146-959210.1364/OL.42.001512], a novel class of partially coherent sources with circular coherence was introduced. In this paper, we examine the propagation behavior of the spectral density and the spectral degree of spatial coherence of a beam generated by such a source in free space and in oceanic turbulent media. It is found that the beam exhibits self-focusing, which is dependent on the initial coherence and the parameters of oceanic turbulence. The self-focusing phenomenon disappears when the initial coherence is high enough or the oceanic turbulence is strong. The area of high coherence appears in the center and along two diagonal lines. With increasing turbulence, the coherence area reduces gradually along one diagonal line and is retained along the other one. A physical interpretation of the self-focusing phenomenon is presented, and potential applications in optical underwater communication and beam shaping are considered.