Gaussian Beam Propagation Research Articles

Propagation of Sine hyperbolic Gaussian vortex beam (ShGvB) in vertical anisotropic oceanic turbulence with adaptive optics correction

The propagation of Sinh Gaussian vortex beam (ShGvB) along vertical anisotropic oceanic turbulence is established using the spatial power spectrum which depends upon the depth of the ocean. The average intensity of the beams has been derived. For 100 m depth, the average intensity has been plotted and studied using the measured salinity and temperature from the ocean in both isotropic and anisotropic oceanic turbulence systems. The average transmittance of the ShGvB is studied and found that the beam degrades faster in anisotropic media than in isotropic media. To mitigate the aberrations adaptive optics (AO) correction is incorporated in the study along the vertical link. Quantitative estimates of the Bit error rate (BER) have been made to evaluate the beam's performance for vertical underwater optical communication and found that by improving the signal-to-noise ratio and incorporating AO, the ShGvB performs effectively in vertical underwater optical communication.

Near-field propagation of a flat-topped gaussian beam: analysis in weakly ‎turbulent atmospheres

We investigate the analysis of optical communication employing the shape beams, definitely concentrating on the effect of factors on the physical characteristics of a Flat Top Gaussian (FTG) beam. The propagation of a beam of laser light in the atmosphere layer is disposed to being affected by many optical phenomena such as scattering, absorption, and turbulence. These phenomena arise from differences in the scintillation index and the intensity modes realized in the source and receiver planes. This work is a numerical investigation of the FTG laser beam as it beams trekking through a zone of low turbulence using open-source software. This simulation will be conducted using a mathematical model derived from the split-step beam propagation technique. The intensity distributions of the source plane and the average intensity is received in air turbulence are computed, with an extra contour at the transducer plane. The Rytov approach to develops the scintillation index, structural constant, source size, and supplementary parameters to measure the weak turbulent model. Furthermore, these factors are studied in the context of near-field propagation. Also, the impression of the scintillation and wander of the beam is assessed. All simulated results are analyses and contrasted with the TEM00 Gaussian beam. At last, these discoveries are compared with the data obtained in the experimental piece of the study, additionally by applied in laser applications.

Generalized Ince–Gaussian beams propagation through oceanic medium

Generalized Ince–Gaussian beams propagation through oceanic medium

Scaling laws for high energy Gaussian beams propagation through the atmosphere

In order to meet the requirements of rapid evaluation of high-energy lasers for practical applications, this paper constructs scaling laws for Gaussian beams propagation through the atmosphere. Firstly, the beam spreading due to single effects including diffraction, optical turbulence and thermal blooming is scaled to identify suitable scaling factors. Then, the scaling functions of the effective radius with multi-effect interaction are established step by step, and the scaling exponents are fixed by genetic algorithm. Finally, the scaling laws of the far-field mean intensity of high-energy laser propagating through atmosphere are constructed. Comparison with the simulations in given scenarios reveals the mean relative error of the scaled mean intensity.

Gold Nanoparticles at a Liquid Interface: Towards a Soft Nonlinear Metasurface

Optical second-harmonic generation (SHG) is achieved using adsorbed gold nanoparticles (AuNPs) with an average diameter of 16 nm at the aqueous solution–air interface in reflection. A detailed analysis of the depth profile of the SHG intensity detected shows that two contributions appear in the overall signal, one arising from the aqueous solution–air interface that is sensitive to the AuNP surface excess and one arising from the bulk aqueous phase. The latter is an incoherent signal also known as hyper-Rayleigh scattering (HRS). The results agree with those of an analysis involving Gaussian beam propagation optics and a Langmuir-like isotherm. Discrepancies are revealed for the largest AuNP concentrations used and indicate a new route for the design of soft metasurfaces.

The analysis of the non-Kolmogorov turbulence effect on the performance of uplink coherent DPSK laser satellite communication system in the presence of tilt-corrected beam wander

In the present study, a model for analyzing the performance of laser-based satellite uplinks that account for beam wander and atmospheric turbulence is presented. The developed scintillation index model is a continuation of the recent works considering the effects of non-Kolmogorov turbulence on the propagation of Gaussian beams across turbulent media. We specifically concentrate on the specific regime under the tilt-corrected beam wander. The on-axis scintillation index is developed assuming an isotropic non-Kolmogorov spectrum model where the power law exponent (PLE) effective value, α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document}, is taken to be 3 < α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document} < 4. Within that regime, effective irradiance models for tilt-corrected beam wander are presented, using the Gamma and Gamma-Gamma distributions. Closed-form expressions of the average bit error rate (BER) are derived to evaluate the performance of the optical communication system considering coherent detection of differential phase shift keying. The obtained numerical results show the impact of the Gaussian beam radius at the transmitter, the PLE effective value, and the zenith angle on the on-axis scintillation index and the average BER of the system under consideration. Due to beam wander, the link performance in terms of scintillation index and average BER depends on the beam radius at the transmitter. With tilt-corrected beam wander the link performance becomes best at an intermediate value of beam radius. With the non-Kolmogorov turbulent medium model, the PLE effective value has a major effect on the beam radius with the best performance. The obtained results guide the choice of the optimum beam radius for best performance for each PLE effective value.

A hybrid variational method for beam propagation and interaction in a graded-index nonlinear waveguide

The hybrid variational method can be used to simplify multidimensional numerical simulations. We examine the applicability of this method to study the nonlinear propagation of a single beam and the interference of two spatial soliton beams in a graded-index optical waveguide governed by a two-dimensional nonlinear Schrodinger equation. We classified three distinct regimes of the dynamics that emerge during single Gaussian beam propagation, corresponding to beam decay, breather formation, and self-focusing. When two spatial soliton beams were set up to interfere in the waveguide, we identified the boundary where the nonlinear interaction during the interference led to excitation or self-focusing. These quite involved dynamics were used to test the predictive power of our variational models by comparing them with direct numerical simulations, obtaining good agreement.

Exact wave solver for nonparaxial laser beam propagation

Simulations of inertial confinement fusion (ICF) experiments require high-fidelity models for laser beam propagation in a nonuniform plasma with varying index of refraction. We describe a new numerical wave solver that is applicable to centimeter-scale length plasmas encountered in indirect drive ICF applications. The one-way Helmholtz equation (OHE) generalizes the time-harmonic paraxial wave equation to large angles. Here, we present a methodology to numerically evaluate the exact solution to the OHE. This solution is computed by analytically advancing eigenfunctions of the one-way Helmholtz operator along a propagation direction and is applicable to any given index of a refraction profile. We compare our exact method with a commonly used approximate split-step technique for solving the OHE. As a test problem, we consider nonparaxial propagation of Gaussian and speckled beams in a plasma density channel with internal reflection. We find that the split-step approach incurs significant errors compared to the exact solution computed using the novel algorithm.

Propagation of auto-focusing hypergeometric Gaussian beams along a slant path in oceanic turbulence

Compared to horizontal transmission, the oceanic dissipation rate and temperature-salinity distribution ratio are no longer constant but vary with depth, imposing greater complexity on oceanic turbulence when beams propagate through a slant path and resulting in more limitations on the performance of underwater wireless optical communication (UWOC) links. This study focuses on investigating the performance, especially the auto-focusing characteristic, of auto-focusing hypergeometric Gaussian (AHGG) beams propagating along slant paths in oceanic turbulence. We theoretically derive the spatial coherence radius and the relative probability of the orbital angular momentum (OAM) mode for AHGG beams passing through such links. Numerical simulations reveal that AHGG beams exhibit superior propagation performance compared to hypergeometric Gaussian beams. Lower beam orders and OAM numbers contribute to improved performance, while careful selection of auto-focusing length can tangibly enhance detection performance as well. Additionally, tidal velocities and wind speeds have nonnegligible effects on OAM signal probability. Our results further demonstrate that surface buoyancy flux, temperature gradients, and waterside friction velocity significantly affect beam transmission under varying wind conditions. These findings, particularly controlling the auto-focusing length of AHGG beams to match the transmission distance, provide valuable insights for enhancing the quality of UWOC links.

Rayleigh length extension in long-distance free-space optical communications based on lens group optimization

In the field of high-speed data transmission, wireless optical communications provide a paradigm shift from the conventional tethered connections, offering promising bandwidth and minimal latency. The cornerstone of such systems lies in their ability to precisely control the propagation of Gaussian beams, which are favored due to their inherent properties of minimal divergence and high spatial coherence over long distances. Efficient transmission hinges on the proper manipulation of these beams’ spatial characteristics, particularly the waist radius and the associated Rayleigh length, which together delineate the beam’s diffraction and spread. This manuscript methodically explores the theoretical and practical aspects of Gaussian beam focusing through lens systems, aiming to elucidate the pivotal relationship between the optimally adjusted focal parameters and the resultant augmentation of the Rayleigh length. Through rigorous diffraction integral simulations and a keen analysis of constraints posed by finite apertures, the study articulates strategies to considerably enhance the Gaussian beam’s propagation characteristics, thereby bolstering the reliability and efficacy of wireless optical communication systems.

Efficient light propagation algorithm using quantum computers

Quantum algorithms can potentially overcome the boundary of computationally hard problems. One of the cornerstones in modern optics is the beam propagation algorithm, facilitating the calculation of how waves with a particular dispersion relation propagate in time and space. This algorithm solves the wave propagation equation by Fourier transformation, multiplication with a transfer function, and subsequent back transformation. This transfer function is determined from the respective dispersion relation, which can often be expanded as a polynomial. In the case of paraxial wave propagation in free space or picosecond pulse propagation, this expansion can be truncated after the quadratic term. The classical solution to the wave propagation requires O(NlogN) computation steps, where N is the number of points into which the wave function is discretized. Here, we show that the propagation can be performed as a quantum algorithm with OlogN2 single-controlled phase gates, indicating exponentially reduced computational complexity. We herein demonstrate this quantum beam propagation method (QBPM) and perform such propagation in both one- and two-dimensional systems for the double-slit experiment and Gaussian beam propagation. We highlight the importance of the selection of suitable observables to retain the quantum advantage in the face of the statistical nature of the quantum measurement process, which leads to sampling errors that do not exist in classical solutions.

Robust autofocusing propagation in turbulence

Turbulence in complex environments such as the atmosphere and biological media has always been a great challenge to the application of beam propagation in optical communication, optical trapping and manipulation. To overcome this challenge, this study comprehensively investigates the robust propagation of traditional Gaussian and autofocusing beams in turbulent environments. In order to select stable beams that exhibit high intensity and high field gradient at the focal position in complex environments, Kolmogorov turbulence theory is used to simulate the propagation of beams in atmospheric turbulence based on the multi-phase screen method. We systematically analyze the intensity fluctuations, the variation of the coherence factor and the change in the scintillation index with propagation distance. The analysis reveals that the intensity fluctuations of autofocusing beams are significantly smaller than those of Gaussian beams, and the coherence of autofocusing beams is better than that of Gaussian beams under turbulence. Moreover, autofocusing beams exhibit less oscillation than Gaussian beams, indicating that autofocusing beams propagate in complex environments with less distortion and intensity fluctuation. Overall, this work clearly demonstrates that autofocusing beams exhibit higher stability in propagation compared with Gaussian beams, showing great promise for applications such as optical trapping and manipulation in complex environments.

A receiver intensity for Super Lorentz Gaussian beam (SLG) propagation via the moderate turbulent atmosphere using a novelty mathematical model

Abstract First of all, the beam propagation of Super Lorentz Gaussian (SLG) profile is propagated via space, the recent research dealt extensively with the investigation of the propagation of SLG in a level of specified atmospheric. In a turbulent atmosphere of intensity and receiver field, models were derived from a new mathematical expression of intensity and analyzed. Also, to find the power scintillation indicators for the SLG beam in a random turbulence of receiver plane. The equations are obtained for the average receiver-aperture. The new beam of SLG systems generated a modified model when compared with the receiver-aperture averaging. When we revisions the parameters, firstly is started the factor source size, this affected the profile for the power propagation and the analysis proved that the average of the aperture is affected by increasing the distance of propagation length. The enhancement of the average power of the aperture effect reliably with the source size of the initial beam source depends on several factors, including the structure constant, the beam order and static value of source size. Finally, the target of this article is detected a novel of mathematical expression of the receiver intensity is applied in the system of optical communications.

Ince–Gaussian beams propagation through turbulent atmospheric medium

Ince–Gaussian beams propagation through turbulent atmospheric medium

Performance of Orbital Angular Momentum Communication for a Non-Uniformly Correlated High-Order Bessel–Gaussian Beam in a Turbulent Atmosphere

We derived the formula for the detection probability, signal-to-noise ratio (SNR), and average bit error rate (BER) for the signal orbital angular momentum (OAM) state carried via non-uniformly correlated high-order Bessel–Gaussian beam propagation in a turbulent atmosphere. The wavelength, receiver aperture, beam width, strength of the turbulent atmosphere, and topological charge effect on detection probability, SNR, and average BER of the signal OAM state were demonstrated numerically. The results show that the signal OAM state with low topological charge, a small receiver aperture, a narrow beam width, and a long wavelength can improve the performance of optical communications systems under conditions of weak atmospheric turbulence. Our results will be useful in long-distance free space optical (FSO) communications.

Transmission characteristics of Gaussian array beams in seawater-to-air propagating incorporating turbulence media and foam layer.

This paper investigates the propagation of Gaussian array beams (GABs) through seawater-to-air in the presence of oceanic turbulence, atmospheric turbulence, and wave foams. Specifically, we focus on the intensity distribution of diverse typical GAB structures (ring, multi-ring, and rectangle). Then, an innovative intensity analysis model to calculate the average intensity in each medium is proposed. Moreover, we experimentally verify the proposed method by examining the intensity fading characteristic of Gaussian beams in the seawater-to-air path. Our results show that the peak intensity is primarily affected by the refraction in the ocean and foam layer, rather than air layer. The difference of theoretical and experimental values are less than 0.13 for the peak intensity. Moreover, the intensity distributions are more significantly affected by ocean turbulence but less influenced by wind speed.

Adaptive focus beam migration method in visco-acoustic media

Abstract Owing to the prevalent viscosity in the subsurface medium, seismic waves experience amplitude attenuation effects during their propagation in visco-acoustic media. Therefore, it is crucial to develop a method that can compensate for wavelet amplitude attenuation and enhance imaging quality. In this paper, we derive an expression for corrected ray complex travel time by introducing the quality factor Q. Additionally, we modify the classical Gaussian beam propagation operator to an adaptive focus type propagation operator. Our research presents an adaptive focused beam migration imaging method specifically designed for viscous acoustic media, incorporating a combination of traditional Gaussian beam migration imaging methods. In comparison to traditional migration methods, the proposed approach achieves energy focusing along the phase axis and significantly improves imaging quality. The validity and effectiveness of our method are confirmed through the obtained imaging results.

Beam profile analysis in magnetoplasma medium

In the current study, electromagnetic fields produced by a point source in a magnetoplasma medium under the steady external magnetic field are derived by using Maxwell equations. To obtain the general Gaussian beams complex source point method is used. The radiated fields are Gaussian beams when the complex values are assigned to the source coordinates in the derived expressions. Due to the analytic continuation between real and imaginary source points being performed directly in the high frequencies no further calculations are required to convert ray solutions to beam solutions. Thus, the obtained beam solutions are valid outside the paraxial region therefore better representation of fields is obtained. The derived beam profiles are investigated for different set of parameters numerically.

Developing a misalignment model for folded optical resonators and designing a kilowatt-class disk laser resonator with a short effective length

In this article, a formulation was developed for designing a stable disk laser resonator and achieving a high power and a beam quality close to the fundamental mode with a short effective length. In this regard, by taking a matrix approach and using Gaussian beam propagation based on the ABCD law for Gaussian beams, the fundamental-mode spot size inside a resonator and its sensitivity to misalignment, as well as dynamic stability in multiple folded resonators, were analyzed in order to achieve a short effective length. In the presented method, the optimal geometrical parameters of the resonator were obtained by applying the length limits, permissible level of sensitivity to misalignment, and range of dynamic stability with the help of MATLAB software coding. Using this design algorithm, a Z-shaped resonator with the arm length of 50 cm and fundamental-mode spot size of 2.4 mm on the active media was designed, while the resonator had a good dynamic stability and low sensitivity to misalignment. Considering these specifications, it was possible to design a compact disk laser with a power of 1 kW, which had a beam quality close to the fundamental mode.To the best of our knowledge, the laser disk resonator described in this paper, which is resistant to misalignment and has a short effective length, has not been previously documented in the literature. The model developed in this research is a general model that can be used in much more complex structures with any numbers of optical elements in other lasers.

Laser beam blink propagation: Evaluation BER in free space resembled dual SLG

The laser beam blink propagation for Super Lorentz Gaussian (SLG) beam was calculated in free space (FSO) by using the Huygens Fresnel approximation method. In addition, the Scintillation index was articulated and evaluated BER (bit error rate) up to several kilometres for different parameters. Scintillation index variations in plan receiver point were treated in all states without turbulence in the atmosphere and using dual models. Our results were shown to be compatible with the results of earlier studies on Gaussian beam scintillation and propagation. Moreover, the Kolmogorov-spectrum function reduced the blink fluctuation. Also, the outcomes indicate that the small beam width of the dual SLG beam will bring a far distance by utilizing the same source size of the Gaussian beam. Better fallouts were achieved with decreased scintillation index that applied and changed a dual mode with a fixed structure constant factor. A low scintillation index, intensity, and receiver field were obtained. To this end, the scintillation index affects the circumstances depending on the magnitude of turbulence and control of the beam propagation factors.