Propagation Properties of Vortex Cosine-Hyperbolic-Gaussian Beams Through Oceanic Turbulence

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 in the turbulent medium. 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 ω0 and the wavelength λ. The obtained results can be beneficial for applications in optical underwater communication and remote sensing domain, imaging, and so on.

Comparative Analysis of Some Schell-Model Beams Propagating Through Turbulent Atmosphere

In this paper, we investigate a comparative analysis of some Generalized Laguerre-Gaussian Schell-model beams through a paraxial ABCD optical system in a turbulent atmosphere. Based on the extended Huygens-Fresnel diffraction integral, analytical expressions for the spectral density in the receiver plane of the studied beams are derived in detail. By studying the effects of the source coherence parameters and the atmospheric turbulence strength, the numerical results indicate that the profile of these Schell-model beams takes different shapes during their propagation.

Lensless Reflection Imaging of Obliquely Illuminated Objects I: Choosing a Domain for Phase Retrieval and Ptychography

Ptychography is a lensless imaging technology that is validated from hard X-rays to terahertz spectral range. It is most attractive for extreme ultraviolet (EUV) and X-rays as optical elements are expensive and often not available. Typically, the set up involves coherently illuminated object that directs the scattered radiation normally to detector which is parallel to the object plane. Computer processing of diffraction patterns obtained when scanning the object gives the image, more precisely, the distribution of intensity and phase on its surface. However, this scheme is inefficient for EUV and X-rays due to poor reflectivity and low penetration in all materials. Reflection mode ptychography solves the problem if illumination angles do not exceed the critical angle of object material. Changing the geometry of experiment changes physical and mathematical model of image formation. Including: diffraction integral describing beam propagation from object to detector, inverse problem, optimization of object illumination angle, position and orientation of detector, choosing size and grid of coordinate and frequency computer domains. This paper considers the wavefield scattered to detector by obliquely illuminated object and determines a domain for processing of obtained scans. Solution of inverse problem with phase retrieval and resulting numerical images will be presented in the next paper.

Diffraction integrals and the Kirchhoff approximation

“Diffraction integrals and the Kirchhoff approximation” gathers together theorems concerned with diffraction. The diffraction integral may be put into Dirichlet and Neumann forms. Back-diffraction is exactly zero (not relying on a Kirchhoff approximation or an obliquity factor). We discuss the limits on Kirchhoff's approximation, complementary apertures (Babinet's principle), the Fraunhofer limit, and the case of a long slit.

Effects of Turbulent Atmosphere on the Propagation Properties of Vortex Hermite-cosine-hyperbolic-Gaussian Beams

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 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.

Focusing properties and focal shift of a vortex cosine-hyperbolic Gaussian beam

In this paper, we investigate the focusing properties of a vortex-cosh-Gaussian (vChG) beam passing through a converging thin lens. Based on the Huygens-Fresnel diffraction integral, we derived the analytical propagation equation as well as the beam width expression of a focused vChGB. It is shown that the focusing properties including the focal shift of the focused vChGB are crucially dependent on the incident beam parameters namely the decentered parameter and the topological charge in addition to the Gaussian Fresnel number\({N_F}\). From typical numerical examples, it is found that the focused vChGB is transformed into a multi-lobes structure shape at the real focus plane, and the principal maximum intensity of the beam is located away from the axis. The amount of focal shift, which is determined from the minimum spot size criterion, is strongly dependent on the Fresnel number, the decentered parameter and the vortex charge m. The obtained results may be useful for the applications of the vChGBs in beam shaping and beam focusing.

Propagation of Vortex Cosine-hyperbolic-gaussian Beams in Atmospheric Turbulence

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.

Soil particle size distribution – comparison between laser diffraction, integral suspension pressure and sedimentation (pipette) methods

<p>The sedimentation (pipette) (SP) method has been in use for a long time as a solid reference method to estimate particle size distribution (PSD) in soil. The procedure is demanding, not the least concerning the manual extraction of soil fractions at given depth and time intervals during the sedimentation process and their subsequent drying and weighing. The more recent laser diffraction (LD) and integral suspension pressure (ISP) methods are promising alternatives. They have the advantage that the extraction-drying-weighing procedure for the finer soil fractions (clay and silt) is replaced by automatic registration of particle volumes (for LD) and pressures at given depth during the sedimentation process (for ISP). Due to these differences in measurement technics, PSD:s determined with LD and ISP methods often deviate more or less from PSD:s by SP method, which have implications for the matching with historical SP soil databases. We present some draft results of studies comparing the three methods on samples from agricultural soils in Sweden. The results show that there is still a need for further fine-tuning in the methodologies to align PSD composition from one method to the other.</p>