In this paper, the propagation properties of a vortex cosh-Gaussian beam (vChGB) in turbulent atmosphere are investigated. Based on the extended Huygens–Fresnel diffraction integral and the Rytov ...method, the analytical expression for the average intensity of the vChGB propagating in the atmospheric turbulence is derived. The effects of the turbulent strength and the beam parameters on the intensity distribution and the beam spreading are illustrated numerically and analyzed in detail. It is shown that upon propagating, the incident vChGB keeps its initial hollow dark profile within a certain propagation distance, then the field loses gradually its central hole-intensity and transformed into a Gaussian-like beam for large propagation distance. The rising speed of the central peak is demonstrated to be faster when the constant strength turbulence or the wavelength are larger and the Gaussian width is smaller. The obtained results can be beneficial for applications in optical communications and remote sensing.
Context. Over the past 40 years, helioseismology has been enormously successful in the study of the solar interior. A shortcoming has been the lack of a convincing detection of the solar g modes, ...which are oscillations driven by gravity and are hidden in the deepest part of the solar body – its hydrogen-burning core. The detection of g modes is expected to dramatically improve our ability to model this core, the rotational characteristics of which have, until now, remained unknown. Aims. We present the identification of very low frequency g modes in the asymptotic regime and two important parameters that have long been waited for: the core rotation rate, and the asymptotic equidistant period spacing of these g modes. Methods. The GOLF instrument on board the SOHO space observatory has provided two decades of full-disk helioseismic data. The search for g modes in GOLF measurements has been extremely difficult because of solar and instrumental noise. In the present study, the p modes of the GOLF signal are analyzed differently: we search for possible collective frequency modulations that are produced by periodic changes in the deep solar structure. Such modulations provide access to only very low frequency g modes, thus allowing statistical methods to take advantage of their asymptotic properties. Results. For oscillatory periods in the range between 9 and nearly 48 h, almost 100 g modes of spherical harmonic degree 1 and more than 100 g modes of degree 2 are predicted. They are not observed individually, but when combined, they unambiguously provide their asymptotic period equidistance and rotational splittings, in excellent agreement with the requirements of the asymptotic approximations. When the period equidistance has been measured, all of the individual frequencies of each mode can be determined. Previously, p-mode helioseismology allowed the g-mode period equidistance parameter P0 to be bracketed inside a narrow range, between approximately 34 and 35 min. Here, P0 is measured to be 34 min 01 s, with a 1 s uncertainty. The previously unknown g-mode splittings have now been measured from a non-synodic reference with very high accuracy, and they imply a mean weighted rotation of 1277 ± 10 nHz (9-day period) of their kernels, resulting in a rapid rotation frequency of 1644 ± 23 nHz (period of one week) of the solar core itself, which is a factor 3.8 ± 0.1 faster than the rotation of the radiative envelope. Conclusions. The g modes are known to be the keys to a better understanding of the structure and dynamics of the solar core. Their detection with these precise parameters will certainly stimulate a new era of research in this field.
Based on the extended Huygens–Fresnel diffraction integral, the analytical expression of the average intensity for a vortex cosine hyperbolic-Gaussian beam (vChGB) propagating in oceanic turbulence ...is derived in detail. From the derived formula, the propagation properties of a vChGB in oceanic turbulence, including the average intensity distribution and the beam spreading, are discussed with numerical examples. It is shown that oceanic turbulence influences strongly the propagation properties of the beam. The vChGB may propagate within shorter distance in weak oceanic turbulence by increasing the dissipation rate of mean-square temperature and the ratio of temperature to salinity fluctuation or by increasing the dissipation rate of turbulent kinetic energy per unit mass of sea water. Meanwhile, the evolution properties of the vChGB in the oceanic turbulence are affected by the initial beam parameters, namely the decentered parameter
b
, the topological charge
M
, the beam waist width
ω
0
and the wavelength λ. The obtained results can be beneficial for applications in optical underwater communication and remote sensing domain, imaging, and so on.
The propagation properties of a vortex Hermite-cosh-Gaussian beam (vHChGB) in atmospheric turbulence are investigated based on the extended Huygens–Fresnel diffraction integral and Rytov method. The ...analytical formula for the average intensity of a vHChGB propagating in turbulent atmosphere is derived in detail. The influence of the turbulence strength on the intensity distribution under the change of beam parameters conditions is illustrated numerically and discussed. Results show that the profile of the initial vHChGB remains unchanged within small propagation distance range, and at certain propagation distance a central peak intensity appears, and finally the beam evolves into Gaussian profile–like in far-field. The rising speed of the central peak intensity is faster when the turbulence strength is larger or the beam parameters such as the beam order, the vortex charge and the Gaussian waist width are smaller. With a small decentered parameter b, the beam profile changes faster as the wavelength is larger, whereas the reverse behavior occurs when b is large. The obtained results may be useful for the practical applications of vHChGB in optical communications and remote sensing.
The propagation of a Circular cosh-Gaussian beam (CiChGB) through a paraxial ABCD optical system in a turbulent atmosphere is investigated based on the extended Collins formula and Rytov theory. In ...particular, the analytical expression for the on-axis average intensity of a CiChGB focused by a thin lens in a turbulent atmosphere is derived in detail. From the obtained formula, the on-axis intensity distribution of the output beam is discussed numerically with a comparison to direct propagation in free space. The influences of the turbulence strength and initial beam parameters on the on-axis intensity are examined. It is found that the on-axis intensity near the focus region is less affected by atmospheric turbulence compared to the free space.
The properties of a linearly polarized cosine-hyperbolic-Gaussian beam (ChGB) propagating in a chiral medium are investigated theoretically by using the Huygens-Fresnel diffraction integral. Beam ...intensity distribution characteristics in the chiral medium are discussed with numerical examples. The linearly polarized ChGB is found to split into a superposition of left and right circularly polarized Gaussian components, and its intensity pattern exhibits a variable shape depending on the chirality factor and decentered parameter b. The output beam can exhibit a richer intensity pattern compared to the Gaussian beam. The results could be beneficial for the application of ChGB in beam shaping and optical micromanipulation.
In this work, the propagation properties of a partially coherent vortex cosh-Gaussian beam (PCvChGB) have been investigated. Within the framework of the extended Huygens–Fresnel diffraction integral, ...an analytical formula for a PCvChGB propagating in a paraxial ABCD optical system is derived. Based on the obtained formula, the influences of the spatial coherence, decentered parameter and vortex charge on the propagation properties of a PCvChGB in free space are illustrated numerically and analyzed. The obtained results could be beneficial for applications of PCvChG beams in optical communications, remote sensing and atom optics.
In this paper, we investigate the focusing properties and focal shift of a partially coherent vortex cosine-hyperbolic-Gaussian beam (PCvChGB) passing through a lens system. Based on the extended ...Collins formula, the analytical expression for a PCvChGB propagating through a thin lens is derived in detail. By using the obtained formula, the influences of the spatial coherence length, the Fresnel number, and the initial beam parameters on the focusing properties and the focal shift of a PCvChGB are discussed numerically. It is shown that the average intensity distribution in the focal region and the focal shift of the focused PCvChGB are strongly affected by the above factors. The obtained results could be beneficial for applications of vortex cosine-hyperbolic-Gaussian beam (vChGB) beams in beam shaping and atom optics.
Based on the Huygens–Fresnel diffraction integral, the analytical expression for a vortex Hermite-cosh-Gaussian beam (vHChGB) propagating in a gradient-index medium (GIM) is derived. From the ...obtained expression, the evolution of the intensity and the phase distributions of the vHChGB through GIM are analyzed numerically as a function of the gradient-index parameter
β
and under the change of the incident beam parameters. The results show that the output beam evolves periodically versus the propagation distance, and the period of the self-repetition slows down as the parameter
β
is increased. It is found that the self-repetition of the intensity and phase distributions of the field in GIM is altered by the incident beam parameters. The results obtained may be beneficial for applications in fiber communications and beam shaping.
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