Abstract—The propagation equation of a Lorentz-Gauss (LG) vortex **beam** in biological tissues is derived. The inﬂuences of the **beam** parameters and the biological tissues on the spreading properties of a LG vortex **beam** are investigated. The obtained results are interpreted numerically and shown that the LG vortex **beam** propagating through biological tissues with the stronger turbulence strength will lose the dark hollow center and evolve into the **Gaussian**-**like** **beam** more rapidly.

To study the inﬂuences of refractive index structure constant of atmospheric turbulence C n 2 on the evolution properties of FPLG **beam**, the cross lines of an FPLG **beam** propagating through atmospheric turbulence and free space for the diﬀerent C n 2 are illustrated in Figure 5. It is found that FPLG **beam** propagating through stronger atmospheric turbulence (larger C n 2 ) will evolve into the **Gaussian**-**like** **beam** faster (Figure 4(a)), and the **beam** propagating through stronger atmospheric turbulence will have a larger **beam** spot at the longer propagation distance. Thus, the atmospheric turbulence will accelerate the spreading of FPLG **beam**.

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Most popular implementation of the refractive **beam** shapers is telescopic optical system transforming collimated **Gaussian** or **Gaussian**-**like** **beam** to collimated **beam** with uniform intensity. The design technique allows also creating collimating Shaper realizing transformation of divergent **Gaussian** input **beam** to collimated flattop output; this type of **beam** shapers is important for more and more popular fiber lasers as well as fiber-coupled diode and solid-state lasers. There is one more important feature of the refractive field mapping **beam** shapers – their operational principle presumes the input **beam** has a certain size - usually defined as diameter at 1/e 2 intensity level, and a certain intensity profile - **Gaussian** or similar profiles with peak intensity in the centre. If an input **beam** size differs from the pre-determined one the resulting profile deviates from the flattop as well, for example, when an input **beam** is essentially smaller, say 2-3 times less than a specified value, the **beam** shaper operates as an ordinary **beam**-expander, so the output **beam** is about 1.6 times expanded but the resulting profile stays almost the same **like** at the entrance i.e. **Gaussian**. This effect is demonstrated on Fig. 1. It can be used, for example, to generate a Roof-**like** **beam** profile with uniform intensity in one direction and **Gaussian** in another one – this is easily achieved when an elliptic input **beam** with a long axis of proper length (according to a Shaper design), Fig. 1. With using the effect of dependence of output **beam** profile and shape from the input **beam** size it is possible to build various optical system realizing various shapes and intensity profiles of final laser spots.

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Carrying the orbital angular momentum, the hollow vortex **Gaussian** **beam** has many potential applications in optical trapping, optical micro-manipulation, nonlinear optics, and quantum information processing [19–22]. When the hollow vortex **Gaussian** **beam** interacts with microscopic particles, the orbital angular momentum in the hollow vortex **Gaussian** **beam** can be exchanged to microscopic particles. Therefore, here we investigate the distribution of the orbital angular momentum density of a hollow vortex **Gaussian** **beam**. Moreover, the starting point to describe a hollow vortex **Gaussian** **beam** is the Maxwell equations in free space. To obtain the exact solution of the Maxwell equations, we use the method of vectorial angular spectrum. By using the electromagnetic ﬁeld of a hollow vortex **Gaussian** **beam** beyond the paraxial approximation, the expression of the orbital angular momentum density of a hollow vortex **Gaussian** **beam** propagating in free space is derived. The eﬀects of the **beam**

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The electromagnetic features of a wide class of one- and two- dimensional periodical structures in the case of the plane electromag- netic waves excitation are now quite well studied. However, in real de- vices the electromagnetic field usually has the form of the wave beams. The transmitted and reflected fields have also a form of the beams. To date, there are a large number of publications in which the peculiari- ties of scattering of two-and three-dimensional beams on different types of structures [1–12] are studied. In them the homogeneous dielectric slabs, one-dimensional periodic structures, two-dimensional periodic arrays of magnetodielectric layers are considered. A result of these studies is the knowledge that the pattern configuration, amplitude and phase distributions of the transmitted and reflected fields of **beam** can be different from that ones of plane wave and some distinctive effects **like** lateral shift, focal shift, angular shift, **beam** splitting appear in the scattered field of the **beam** [13–18]. Therefore, it is necessary to take into consideration this circumstance in the designing quasi-optical devices and particularly in the phased antenna system in the form of two-dimensional apertures array [19]. Additionally, it is important for

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Our work demonstrates the variation of donut-shaped depletion pattern under the combined influence of pri- mary optical aberration. The simulation is based on common STED system which utilizing **Gaussian** **beam**, vortex phase plate and aplanatic objective. In view of the particular designed objective and spherical aberration is insensitive to this kind of STED system, the effect of spherical aberration is ignored. The depletion patterns that affected by coma and astigmatism are presented in the assumption of the two factors contribute same mount to wavefront aberration. Through our study, the effects of multiple aberrations to donut-shaped depletion patterns are demonstrated visually, and the STED system is quite sensitive with primary aberrations. The simulation results are helpful guidelines for analyzing the aberration of depletion patterns in real situations.

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In the past decades, partially coherent beams have found important applications in inertial confinement fusion, laser scanning, optical imaging, free space optical communications, second harmonic generation and optical trapping [1–9]. **Gaussian** Schell-model (GSM) **beam** is a typical partially coherent **beam** whose spectral degree of coherence and the intensity distribution are **Gaussian** functions [1, 4, 10–12]. A more general partially coherent **beam** can possess a twist phase, which differs in many respects from the customary quadratic phase factor, and it exists only in partially coherent **beam** [13, 14]. Simon and Mukunda first introduced the twisted **Gaussian** Schell-model (TGSM) **beam** opening up “a new dimension” in the area of partially coherent fields [13, 14]. Unlike the

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Lasers are devices that amplify or increase the intensity of light to produce a highly directional, high-intensity **beam** that typically has a very pure frequency or wavelength. The beams come in sizes ranging from approximately one-tenth the diameter of a human hair to that of a very large building.[1] Since the generation of the first laser **beam** in 1960, the detection techniques have been developed in order to recognize and analyze properties of the **beam**. In general, the analysis of laser **beam** is based on energy measurement, the intensity distribution of the laser **beam**, **beam** divergence, waist parameter, number of modes and others [2]. In optics, a **Gaussian** **beam** is an example of electromagnetic wave whose transverse electric field and intensity distributions are well approximated by **Gaussian** functions. Many lasers emit beams that approximate a **Gaussian** profile, in which case the laser is said to be operating in the fundamental transverse mode. The **Gaussian** wave is commonly used in theoretical and experimental optics and its mathematical representation has successfully been applied by many workers, and the mathematical function that describes shape of the laser **beam** is approximate solution of Helmholtz equation. We get this approximation by solution of homogeneous wave equation, and wave equation can be derived from Maxwell's equations in empty space. Thus any solution of Maxwell's equations in empty space satisfies the wave equa- tion.[3]

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One of the most important requirements for the pilot’s cockpit is the type of display through which the most important flight information with the outdoor image is simultaneously provided for the pilot. Two types of dis- play instruments were used: Head-Up Displays or HUDs and Helmet Mounted Displays or HMDs. HUD is a type of display instrument mounted in the cockpit and the most important flight information, the image of out- side area, comes in its combiner-collimator **beam** splitter display surface and thus, a composite image of the out- side world with the flight information is available to the pilot. HMD has the same structure, but its main specifi- cation is the compactness structure of the projection mounted on the pilot’s helmet building the output image in its exit pupil [1] [2]. In this article, the HUD type has been designed. Creating high quality image is a common concern for optoelectronic designers. The image quality for this system is a function of: light source, image source and image projector’s optical design. Therefore, there are three fundamental challenges that must respond

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finding the direction of incoming laser radiation on combat vehicles. This finds application in warning the crew of combat vehicles about incoming laser threats. The design is based on a linear array of photo-detectors and a Plano- convex cylindrical lens. The incoming laser radiation is focused by the lens on to linear array of photo-detectors and **Gaussian** curve fitting is used to find the position of center or peak of **Gaussian**, which in turn is calibrated to calculate the Angle of Arrival (A-o-A). Basic idea behind the design is the displacement of centroid of **Gaussian** **beam** with the change in angle-of-arrival. The system is able to measure the angle-of-arrival with the very high angular resolution, depending upon the number of sampling instants in the **Gaussian** fitted curve. The designing of the cylindrical lens and its simulation with laser **beam** is performed, at different angle-of-arrival using OSLO designer. The curve fitting and error analysis of the samples collected by the detector on being illuminated by the laser **beam** is performed using MATLAB curve fitting tool.

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means higher power density but the welds may become narrower than necessary or even not fully fused [26]. Laser welding seams are usually less than one quarter of the width of a tungsten-arc inert gas weld (TIG) for the same material thickness. Joint fit-up and **beam** alignment are more critical for a small spot size as small spot size may also lead to more loss of elements by vaporization causing undercut and under fill defects due to high power density. Thus small spot size cannot ensure good welding performance for Nd: YAG laser **beam**. The position of focal points has an important influence on welding process and quality. The focal plane should be set where the maximum penetration depths or best process tolerances are produced. Focal position on the work piece surface produces smallest weld width while any deviation (above or below the surface) leads to wider welds [15].

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Along with the rapid evolution of fiber optics, integrated optics and application of laser in both medicine and technology, there has been a growing interest in the study of **Gaussian** **beam** propagation. This is based on the fact that **Gaussian** **beam** has to do with focusing and modifi- cation of shape of propagating electromagnetic wave or laser **beam**. From the earlier finding on the research on laser **beam**, it has been found that laser **beam** propagation can be approximated by an ideal **Gaussian** **beam** intensity profile [1,2]. Understanding of the basic properties of **Gaussian** **beam** has been specifically found to be very vital. I select the best optics for practical application [3]. Sequel to this, lots of scientists had worked on **Gaussian** **beam** applications in electromagnetic wave propagation and in optics. For instance, a work has been carried out on nonspecular phenomena for **beam** reflection at mono- layer and multilayered dielectric interface respectively from where it has revealed that under various conditions nonspecular **beam** phenomena is more realizable [4-6]. Tamir on his own presented a unified and simplified analysis of the lateral and longitudinal displacement with

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Abstract—In this work, a novel family of Finite Airy array beams have been produced by an optical Airy transform system illuminated by **Gaussian** Array beams. Based on the generalized Huygens- Fresnel integral, an analytical expression is developed to describe the pattern properties of the **beam** generated at the output plan of the optical system. The well-known Finite Airy **beam** generated from the fundamental **Gaussian** **beam** using an optical Airy transform system is deduced, here, as a particular case of the main result of the actual study. Numerical calculations are performed to show the possibility to create a multitude of Finite Airy array beams with controllable parameters depending on the number of beamlets, the distance between the adjacent modules and the positions and orientations of the beamlets.

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Abstract : In this paper, we propose a robust time-frequency decomposition (RTFD) model to suppress of impulse noise mixed with small dense **Gaussian** noise in VoIP systems. Mixed **Gaussian**-impulse noise may appear during transmission over cordless phones, in VoIP systems and during the acquisition stage of old-time audio recordings. Voice over IP (VoIP) is a methodology and group of technologies for the delivery of voice communications and multimedia sessions over Internet Protocol (IP) networks. The transmission mechanism uses the IP protocol with an IP address. Special equipment must be used to convert the analog signal into a digital one. VoIP systems employ session control and signaling protocols to control the signaling, set-up, and tear-down of calls. Noise is an interference with the quality of the signal. Noise can be caused by a variation in the signal, packet loss, reduction in the signal strength, or by having additional users on the system such as the Internet. For this we develop 2 algorithm fidelity-oriented algorithm and articulation oriented with RTFD model. By this technique we can remov the noise from the VoIP systems.

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In this paper, we use the techniques in [28], the altitude-dependent model of the ITU-R turbulence structure constant model, to develop a scintillation index model for a **Gaussian** Schell-model **beam** on the slant path that is applicable under weak-to-strong fluctuations. The result considers the focusing regime and also can be reduced to the result of the horizontal path when atmospheric structure constant is a fixed value. Finally, the numerical results are compared between the fully coherent **beam** and the partially coherent **beam**.

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From the analysis of the data presented in Figs. 5 and 6 one can see that in the case of oblique incidence of an elliptic **beam**, the effects of the pattern narrowing and the maximum shifting of the reflected and transmitted fields in far-field zone are also observed. These effects appear due to the amplitude-phase distribution variation on the screen surface on its both sides. The maximum shift of the field lobe in the pattern occurs at the frequency of total transmission of the electromagnetic field through the screen. There is another parameter, which can affect on the value of **beam** shifting and narrowing. It is the relation between the axes sizes of an ellipse in the cross-section of the **beam**. These effects are the most pronounced when the major axis of the ellipse is parallel to the y-axis.

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sources and detector technologies are relatively well developed on the component level, but there is little information available concerning the use of ocean water as an optical communication media compared to the other ones such as atmosphere [7, 8]. It is necessary to have a comparison between two media, water and atmosphere, to find similarities and dissimilarities. In this paper, first, analytical formula for intensity distribution of laser diode **Gaussian** **beam**, which propagates through optical path in seawater, is derived. In next step, quantitative effects of seawater scattering and absorption as an optical power attenuation factor (transmission function), in the fixed deep, is calculated. It is worth mentioning that the effects of ocean phenomena are classified in two groups: 1- Scattering and absorption, 2- Turbulence (The pressure and temperature gradient and sea waves cause oceanic turbulence and affect optical wave propagation). In this paper, the effects of scattering and absorption are investigated but the effect of turbulence is neglected. After the selection of appropriate wavelength for underwater propagation, the comparison between atmosphere and water attenuation is done. The detector's received power is calculated analytically. Based on the analytical formulae of intensity distribution and optical power, the effects of chlorophyll concentration, initial **beam** divergence and optical path on propagation behavior are investigated. The related results from calculation and simulation are illustrated by graphs and tables.

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envelope of the laser pulse. The e'"'^^’'' term contains all the radially uniform phase variations. As the radial phase variation calculations are the only concern specific to this report, A(^r), the Slowly Varying Envelope Approximation (SVEA) applies and all other phase changes that are uniform in r are ignored. The SVEA judges that the laser pulse envelope varies slowly in time and space compared to a period and wavelength of light. If the sample thickness is small so that changes in the **beam** diameter within the sample due to refraction and diffraction are negligible, we then can regard the medium as thin. This implies that for linear diffraction, the path length L « zo and for nonlinear refraction, the path length L « zo /A(j)(0). The second criterion is automatically met in most standard Z-scan experiments as is small. It has also been found experimentally that the first criterion for linear diffraction is more restrictive than necessary and the condition L<ndZo is sufficient. Thus the amplitude V7 and phase ([) o f the electric field as a function of z are now governed in the SVEA by a pair of simultaneous equations.

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It is suggested herein that, by properly selecting the parameters of a Gaussian beam, one can develop a simple theory which will describe, in a semi-quantitative fashion, the behavior of[r]

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Further development of acoustic methods may see more favourable results, given several limitations of the model used in this study. Horizontal refraction, reflection from the shore (a horizontally stratified medium is assumed), and sound scattering due to other factors (e.g. fish schools, sea surface roughness without a “mirror-**like**” 180 degree phase shift reflection, bubble clouds just below the sea surface, the effect of seaweed in aggregations rather than individuals and oxygen bubbles) can have large effects on sound propagation, and cannot be predicted by the simplified ray/**beam** theory model used here. It is probable that dynamic vertical mixing at the Fortescue Bay site means that the environment does not meet the simplifying assumptions of the ray-based model used here, or of our analysis of the environmental acoustic data obtained at the site. It is possible that further work, particularly in highly productive environments and using a more complex analysis of the acoustic data, may prove acoustics to be a useful tool for estimating the productivity of some seaweed communities over meaningful spatial scales.

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