Behavior of the Central Intensity of Generalized Humbert-Gaussian Beams Against the Atmospheric Turbulence

Based on the generalized Huygens-Fresnel integral in the paraxial approximation and on the Rytov theory, the analytical expression of the axial intensity distribution for the Generalized Humbert-Gaussian beams (GHGBs) propagating through a turbulent atmosphere is derived in this work. The results for the special cases of GHGBs are deduced from our study and illustrated numerically. The influence of the turbulent strength and the incident beam parameters on the propagation of these beams in the atmospheric turbulence is investigated and discussed in detail.

Propagation Properties of an Astigmatic Cos-Gaussian Beam through Turbulent Atmosphere

We use the extended Huygens-Fresnel integral to investigate the propagation properties of a cos-Gaussian beam (cosGB) with astigmatism in atmospheric turbulence. The intensity distribution behaviour along the propagation distance for an astigmatic cosGB in atmospheric turbulence are analytically and numerically demonstrated. Some novel phenomena are presented graphically, indicating that the intensity distribution and the on-axial intensity closely depend on the astigmatic parameter and the turbulent structure constant of the cosGBs in the atmospheric turbulence.

Propagations of Sin-Gaussian Beam with Astigmatism through Oceanic Turbulence

The propagation behaviours of a sin-Gaussian beam (SiGB) with astigmatism in oceanic water is analysed. The analytical expressions for the average intensity of such a beam are derived by using the extended Huygens-Fresnel integral. Its average intensity and on-axial intensity distributions in oceanic water are numerically examined. Then, we mainly focus on the effect of the beam parameters and the medium structure constant on the propagation behaviours for the astigmatic SiGBs in oceanic water, revealing that the evolutions of the intensity distributions can be effectively modulated by adjusting the astigmatic parameter, coherence length and the atmosphere turbulence strength.

Fraunhofer Diffraction

We will develop a simple derivation of the Huygens-Fresnel integral based on an application of Huygens’ Principle and on the addition of waves to calculate an interference field starting with two apertures as in Young’s two slit experiment extending to N apertures and then a continuum distribution. A detailed look is made of the obliquity factor and a constant value is derived to be used in the simple derivation. We use one dimensional theory for most of the discussion but do present the results of diffraction from a circular aperture as it will be needed in our later discussion of imaging. A second description of the propagation of light, useful when using laser light sources, the gaussian wave, is introduced and examples are given of the use of the theory in geometrical optics and laser design.

Goos-Hänchen effect on a one transverse dimensional Hermite-Gaussian Beam

We study the lateral displacement (Goos-H\"{a}nchen effect) of a Hermite-Gaussian beam incident on a dielectric interface of lower index of refraction than the incident media. Unlike previous results on the same subject, the present result can be applied to an infinite family of higher order solutions (or modes) of the Huygens-Fresnel integral. The final theoretical expression is valid for values that are close to the critical angle $\theta_{c}$. Discussion is made for the behavior of the lateral displacement for different modes of the Hermite-Gaussian beam.

PROBLEMS OF DIGITAL HOLOGRAMS SYNTHESIS DUE TO MASS DATA

The problems of digital synthesis of holograms due to big data and integral calculations of mass data are analyzed. Methods and algorithms are discussed and some examples of how to overcome these problems are given. A method of using symmetry in the cores of the Fresnel integral transform to reduce the amount of computation is proposed. Examples of the appearance of bands in a hologram arising from the discrete representation of the frame are given, and limitations that prevent their appearance are proposed.