Gaussian Beam Wave Research Articles

A modification to the extended Rytov theory

This paper proposes a heuristic modification to the extended Rytov theory of strong scintillation [Andrews L, Phillips R. Laser beam propagation through random media. 2nd ed., Washington, USA: SPIE Press; 2005, Andrews LC, Al-Habash MA, Hopen CY, et al. Theory of optical scintillation: Gaussian-beam wave model. Waves Random Media. 2001;11(3):271–291]. This is done by dividing the large and small scales in the extended Rytov theory into further sub-scales. Expressions for the induced irradiance variance, and log-irradiance, due to each sub-scale are presented. The modified theory is used to derive and justify recent results in irradiance fluctuation modeling and hence answer a question initially proposed in [Shishter YM, Young RC, Ali FH. Irradiance probability density function for turbulence induced fading in free space optics. JOSA A. 2022;39(7):1267–1274, Shishter YM, Young RC, Ali FH. General statistical model of irradiance fluctuations in free space optics. JOSA A. 2023;40(1):53–63]. Plots of the irradiance pdf under the modified theory are in support of the theory. The validity of the theory presented would result in modifications to the classical scintillation analysis of waves in random media, with applications to the design of optical systems. Moreover, it is observed that the mathematical framework developed also follows from the assumption of variations in the turbulence along a horizontal path. The work presented in this paper suggests the need of further theoretical and experimental investigations into the effect of variations in atmospheric turbulence characteristics along horizontal paths in the received signal irradiance distribution.

Impacts of Aerosol Scattering Attenuation on Free-Space Optical Communication in Owerri, Nigeria

In spite of the several benefits of using free-space optical (FSO) communication systems as complementary platforms for next-generation networks, the existence of atmospheric disturbances such fog and scintillations are key sources of signal impairment that affect system performance. Thus, it is crucial to learn about the specific weather patterns of the areas where FSO lines will be installed. The purpose of this work is to estimate the availability performance of FSO lines broadcasting at both 850 nm and 1550 nm by performing a statistical analysis of meteorological visibility data gathered for Owerri in Nigeria over a 21-year period (2000-2021). The results shows that the visibility during the most common fog events in Owerri is 100 meters. The probabilities of encountering and exceeding the scattering attenuations associated with Owerri’s most common fog event are 0.0002 and 0.0229, respectively. This research could be expanded in the future by exploring the effects of varying localized climatic conditions on the many forms of optical signals, such as plane, spherical, and Gaussian beam waves.

Design and experimental results of a 28 GHz, 400 kW gyrotron for electron cyclotron resonance heating

A high-power 28 GHz gyrotron has been successfully developed at the Institute of Applied Electronics, China Academy of Engineering Physics. This gyrotron was designed for electron cyclotron resonance heating (ECRH) in the spherical tokamak XL-50. A diode magnetron injection gun was designed to produce the required gyrating electron beam. The gyrotron operates in the TE8,3 mode in a cylindrical open cavity. An internal quasi-optical mode converter was designed to convert the operating mode into a fundamental Gaussian wave beam and separate the spent electron beam from the outgoing microwave power. A tube has been built and successfully tested. The operational frequency of the tube is 28.1 GHz. For beam parameters at an accelerating voltage of 71 kV and beam current of 16 A, the gyrotron has delivered an output power of 400 kW, with a pulse length of 5 s. The output efficiency is about 50% with a single-stage depressed collector. The gyrotron has been installed on the XL-50 and has played an important role in the ECRH experiments.

Aperture-averaged scintillation for a weak underwater turbulence-affected Gaussian beam using the OTOPS model.

The calculation of optical system performance for laser beam propagation in optical turbulence, such as bit error rate (BER), signal-to-noise ratio, and probability of fade, requires the knowledge of scintillation. In this paper, we show the analytical expressions of the aperture-averaged scintillation using a new recently introduced power spectrum of the refractive index fluctuations for underwater turbulence, the oceanic turbulence optical power spectrum (OTOPS). In addition, we use this main result to investigate the impact of weak oceanic turbulence on free-space optical system performance for a propagating Gaussian beam wave. Similar to the atmospheric turbulence case, results show that aperture averaging can reduce the mean BER and the probability of fade several orders of magnitude if the receiver aperture is chosen with a diameter larger than the Fresnel zone, L/k. Being valid for weak turbulence regime in any natural waters, results present the variations of irradiance fluctuations and the performance of underwater optical wireless communication systems depending on the practical values of average temperature and average salinity concentration that can be encountered in any world's waters.

Variable antennas positions solution to reduce pointing errors due to wind speed and temperature coupled effects during free space optical link using matrix Rician pointing error model

Pointing errors (PE) during free space optical (FSO) transmission can be caused by laser beam wander due to thermal and wind dynamic instability. The aim of this work is to study the coupled effects of temperature and wind speed on PE using matrix Rician pointing error (MRPE) model; then show how variable antennas height can reduce PE due to wind speed and temperature coupled effects. To achieve this purposes, average PE expression was established using MRPE model. Then considering a Gaussian beam wave and Monin–Obukhov similarity functions for the structure parameters of temperature, explicit relationship was established between average PE, temperature and wind speed. It comes out of this study that under dynamic turbulence, one can appropriately modify temperature to reduce PE due to dynamic instability and reciprocally. Depending on turbulence large cells or frozen turbulence eddies distribution, PE can be reduced by appropriately modified antennas height or the distance between transmitter and receiver. That is why this work suggests to install variable or dynamic antennas (rather than fixed ones) which could intelligently modify its positions according to laser beam wander created by atmospheric turbulence.

Scattering of a Gaussian Beam Wave by Multiple Homogeneous Anisotropic Cylinders

Scattering of a Gaussian Beam Wave by Multiple Homogeneous Anisotropic Cylinders

Performance evaluation of aeronautical uplink/downlink free-space optical communication system with adaptive optics over gamma–gamma turbulence channel

In this study, we analyze the effect of adaptive optics corrections on the performance of an aeronautical free-space optical (FSO) system with bidirectional slant path uplink and downlink communication channels. The aeronautical FSO communication (FSOC) system operates in a gamma–gamma atmospheric turbulence channel and employs adaptive optics corrections for the distorted wave front of the Gaussian beam wave. The modulation type of the aeronautical FSOC system is chosen to be M-ary phase-shift-keying-subcarrier intensity modulation and the type of the employed photodetector is positive-intrinsic-negative. In analysis, the effect of system parameters such as zenith angle, the height of transmitter/receiver on the ground, M-ary level, filter bandwidth, link distance, and the adaptive optics correction modes on bit-error-rate are demonstrated.

Analysis of wander and spreading of an optical beam by using the oceanic turbulence optical power spectrum

Variance of beam displacement and short-term and long-term spreading of a Gaussian beam propagating in the presence of underwater turbulence are examined by using the oceanic turbulence optical power spectrum (OTOPS). Analytical expressions for both beam wander displacement variance and beam spreading are presented. Results show that the underwater turbulent channel causes deflection from the on-axis mean irradiance and brings significant wander and spreading effects to the propagating Gaussian beam wave. The variations of beam wander and short- and long-term spreading are obtained depending on the underwater medium parameters such as the average temperature, average salinity concentration, temperature-salinity gradient ratio, and temperature and energy dissipation rates. In particular, the real values of the average temperature and salinity concentration of turbulent water are used to obtain the results. In addition, the effects of propagation distance, Gaussian beam source size, and wavelength are shown. The results demonstrate that the underwater turbulent channel brings displacements in the centroid and spreading of the optical beam.

Performance of a free-space optical communication system employing receive diversity techniques in anisotropic atmospheric non-Kolmogorov turbulence

In this paper, bit error rate (BER) performance of a free-space optical communication (FSOC) system operating in anisotropic non-Kolmogorov weak turbulence is investigated together with the spatial diversity techniques. The spatial diversity techniques are implemented as maximum ratio combining (MRC), equal gain combining (EGC), and selection combining (SC) and applied to the receiver. The propagating beam is the Gaussian beam wave, and the modulation scheme is binary phase-shift keying (BPSK). Results are obtained for various parameters such as the anisotropy factor, non-Kolmogorov power law exponent, photodetector responsivity, equivalent load resistor, electronic bandwidth, Gaussian beam radius, wavelength, propagation distance, and turbulence structure constant. It is found that the spatial diversity technique used at the receiver causes significant improvement in the performance of an FSOC system under the conditions of anisotropic non-Kolmogorov atmospheric turbulence. It is also observed that BER performance improves as the atmospheric turbulence becomes more anisotropic. Among the spatial diversity techniques, SC is inferior to EGC and EGC is inferior to MRC in terms of BER performance.

Quasi-optical mode converter for a high power TE8,3-mode gyrotron

We successfully developed a Gyrotron HS-III (28-GHz/400-kW/5-s) for electron cyclotron resonance heating in a spherical tokamak EXL-50, which operated in the TE8,3 mode. An internal quasi-optical-mode converter was designed to separate the spent electron beam from the outgoing power and convert the operating mode to a fundamental Gaussian wave beam. The particle swarm optimization algorithm was used to reduce diffraction loss from the launcher in such a low-frequency band. This enabled us to optimize the perturbation distribution of the launcher and beam waist of the target function to obtain the largest possible scalar correlation coefficient. The launcher was followed by three mirrors: one quasi-parabolic mirror and two phase-correcting mirrors. These were also optimized based on the scalar diffraction theory and Katsenelenbaum–Semenov algorithm to allow us to change the beam direction and increase the purity of the Gaussian output beam. Simulation results revealed a transmission efficiency of 96% and vector Gaussian mode purity of 99.8% at the window plane.

Vector spherical harmonic analysis and experimental validation of spherical shells illuminated with broadband, millimeter wave Gaussian beams: applications to corneal sensing.

Coupling to longitudinal modes of thin spherical shells, under Gaussian-beam illumination, was explored with a theoretical method based on Fourier-optics analysis and vector spherical harmonics and was scrutinized with an experimental setup. For the theory part, the illumination frequency band was fixed between 100-600 GHz and the outer spherical shell radius of curvature and thickness are 7.5 mm and 0.5 mm, respectively. The shell material was either the lossless cornea or an aqueous effective media representing the cornea. Six different beam-target strategies were introduced being potential candidates for maximum coupling. Two dispersion-tuned beam ensembles with strongly frequency-dependent phase center location have been created with a fixed incident beam 1/e radius and radius of curvature called forward strategies. These computations of different alignments were continued with four beam ensembles of frequency-invariant phase center, constructed from fits to experimental data, oriented at four different axial locations with respect to the spherical shell center of curvature, they are called reverse strategies. Coupling efficiency for all strategies was calculated for different targets including perfect electrical conductor (PEC) sphere, PEC core covered by a cornea loss-free layer and cornea. All scattering strategies contrasted to scattering from equivalent planar targets as a reference with maximum coupling. The results show that, under an ideal calibration, forward strategies are a closer approximation to the plane-wave condition for the cornea. An experimental setup was assembled to explore the simulation approach in a frequency range between 220 GHz to 330 GHz. Two different quartz samples with permittivity of 4.1 were mounted on a water core, acting for a cornea. The first and second quartz radius and thickness were 7.5 mm and 0.5 mm and 8 mm and 1 mm, respectively. An adequate agreement between theory and experiment was confirmed. A particle optimisation swarm algorithm was applied to extract the thickness and permittivity of quartz from the measured back-scattered field for reverse strategies.

Laser Gaussian beam analysis of structure constant depends on Kolmogorov in turbulent atmosphere for a variable angle of wave propagation

Laser Gaussian beam propagation is important in optical communications; the challenges of the measured constant parameters are varied angle wave propagation, the receiver plan in the slant path of laser Gaussian beam (G) in Kolmogorov gauges, and the effect of the laser in a random medium. At this point, atmospheric turbulence is reputable based on laser Gaussian beam propagation. Moreover, the space propagation of Gaussian beam waves of higher-order Gaussian beam modes has been expanded from the effects of the scintillation index and with different zenith angles between the laser propagator and the detector (receiver) in the ramp path. Furthermore, in the Cartesian coordinate system, the scintillation index in the Kolmogorov standard is evaluated, and it employs two methods; first, Huygens–Fresnel fundamental and, second, random phase screen for work synchronization. Additionally, to analyze the contour parameters of constant construction, the intensity and receiver field is found to compute the high turbulent modes in the atmospheric deposition, which depends on propagation distances. These result in significant reserves in the matlab computation period and serve the imitation for enhancement of the link transmission; therefore, the zenith angle and scintillation index are pretentious by slant beam, and they enhance the performance that makes the comparisons found with fixed structure constant parameters C2n and the propagation distance against the scintillation index.

Wander of a Gaussian-Beam Wave Propagating through Kolmogorov and Non-Kolmogorov Turbulence along Laser-Satellite Communication Uplink

It is accepted that there exists two kinds of atmospheric turbulence in the Earth’s aerosphere—Kolmogorov and non-Kolmogorov turbulence; therefore, it is important to research their combined impacts on laser-satellite communications. In this paper, the exponential power spectra of refractive-index fluctuations for non-Kolmogorov turbulence in the free troposphere and stratosphere are proposed, respectively. Based on these two spectra, using the Markov approximation, beam wander displacement variances of a Gaussian-beam wave are derived, respectively, which are valid under weak turbulent fluctuations condition. On this basis, using a three-layer altitude-dependent turbulent spectrum model for vertical/slant path, the combined influence of a three-layer atmospheric turbulence on wander of a Gaussian-beam wave as the carrier wave in laser-satellite communication is studied. This three-layer spectrum is more accurate than a two-layer model. Moreover, the variations of beam wander displacement with beam radius, zenith angles, and nominal value of the refractive-index structure parameter on the ground are estimated. The theory of optical wave propagation through non-Kolmogorov atmospheric turbulence is further enriched and a theoretical model of a three-layer atmospheric turbulence beam wander for a satellite-ground laser communication uplink is established.

Atmospheric propagation of space-fractional Gaussian-beam waves in a FSO communication system.

We present a novel, self-consistent analytical model of Gaussian-beam propagation through the atmospheric turbulence by solving the paraxial wave equation in a fractional-dimension space of dimension D, in the range 2 < D ≤ 3, corresponding to the effective spatial dimension experienced by the beam under given turbulent conditions in a free space optical (FSO) communication system. The well-known refractive index structure parameter (C n2) has been mapped from D = 2.668 (C n2≈10-13, strong fluctuations) to D = 2.999 (C n2≈10-16, weak fluctuations) in our simple analytical model, whereas D = 3 corresponds to the ideal case of free-space propagation under zero turbulence. Finally, an optimization problem is developed to mitigate the effects of atmospheric turbulence, leading to efficient transceiver design for the FSO communication system to ensure the reliability of links under varying atmospheric turbulence.

Cyclotron Resonance Maser With Zigzag Quasi-Optical Transmission Line: Concept and Modeling

A microwave system in the form of a quasi-optical (QO) transmission line is proposed as an interaction circuit of an amplifier or an oscillator based on the cyclotron resonance maser (CRM) instability. The circuit consists of periodically spaced along the horizontal <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${z}$ </tex-math></inline-formula> -axis focusing mirrors, which transport the Gaussian wave beam along a zigzag path with vertical and inclined segments. A beam of electrons having sufficiently high perpendicular velocities is guided by a static B-field along the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${z}$ </tex-math></inline-formula> -axis so that the e-beam periodically crosses the wave beam. The CRM instability occurs in regions where an electromagnetic wave having a Bz-component, as in a gyrotron, propagates strictly across the e-beam resulting in the interaction with minimal sensitivity to particle velocity spread. Three-dimensional Particle-In-Cell (3-D PIC) simulations demonstrate the attractiveness of this “zigzag” CRM for the implementation of relatively broadband amplifiers or oscillators with unique (more than an octave bandwidth) frequency tunability at wavelengths of 1–2 mm.

Transformation of a Gaussian wave beam profile by an asymmetric ABCD system including a long path

The regularities of the transformation of the intensity profile of a collimated Gaussian wave beam formed by the control optical system at the exit of an long path are experimentally considered. A change in the symmetry of the beam cross section when controlling its tilt and change in shape and linear dimensions when controlling its area are considered. Based on the matrix model of the optical system, the limiting values of the targeting range of a two-lens system for a beam with a given diffraction length are established. The change scales size of the output beam waist under rearrangement the characteristics of a two-lens optical system is discussed.

Resonant Reflectors for Experimental Studies of the Reflected-Signal Influence on the Gyrotron Operation Regimes

Experimental study of the influence of resonant reflection of the operation mode on the gyrotron generation regimes is a topical problem of modern high-power vacuum electronics. In this work, we formulate the requirements for the external resonant reflection system and propose its development variants. We consider resonant reflectors of two types, which are intended for experiments with a gyrotron at the operation mode TE0, 2 at a frequency of 28 GHz. According to the initial requirements, the reflection coefficient of the gyrotron operation mode at the resonant frequency should amount to 5–10% with the reflector quality factor exceeding 15000 in the range 27998–28008 MHz of the gyrotron-frequency tuning by a magnetic field. The first variant of the reflector is a cylindrical cavity at the TE0, 3, 1 mode. The measured reflection coefficient amounted to 6% at a frequency of 27999 MHz with a quality factor of 15000. The tunable two-mirror resonator at the mode TEM0, 0, p (p >> 1) is the second variant. A number of the waveguide converters of the circular-waveguide mode TE0, 2 to the TE0, 1 mode, the TE0, 1 mode to the TE1, 1 mode, and the convertor of the TE1, 1 mode to the linearly polarized Gaussian wave beam are developed and manufactured for excitation of a two-mirror resonant reflector by the gyrotron radiation. During the frequency tuning in the band 27990–28010 MHz, the measured reflection coefficient amounted to 8% with a quality factor of about 40000. The calculated and measured converter characteristics are given along with the measured frequency characteristics of the developed resonant reflectors.

Wave Structure Function and Long-Exposure MTF for Gaussian-Beam Waves Propagating in Anisotropic Maritime Atmospheric Turbulence

The expressions of wave structure function (WSF) and long-exposure modulation transfer function (MTF) for laser beam propagation through non-Kolmogorov turbulence were derived in our previous work. In this paper, based on anisotropic maritime atmospheric non-Kolmogorov spectrum, the new analytic expression of WSF for Gaussian-beam waves propagation through turbulent atmosphere in a horizontal path is derived. Moreover, using this newly derived expression, long-exposure MTF for Gaussian-beam waves is obtained for analyzing the degrading effects in an imaging system. Using the new expressions, WSF and MTF for Gaussian-beam waves propagating in terrestrial and maritime atmospheric turbulence are evaluated. The simulation results show that Gaussian-beam waves propagation through maritime turbulence obtain more degrading effects than terrestrial turbulence due to the humidity and temperature fluctuations. Additionally, the degrading effects under anisotropic turbulence get less loss than that of isotropic turbulence.

Outer-Scale Effect of a Gaussian-Beam Wave Propagated Through Non-Kolmogorov Turbulent Atmosphere on the Beam Wander

To date, it is a common knowledge that there exists two kinds of turbulence in Earth’s aerosphere, the Kolmogorov turbulence and the non-Kolmogorov turbulence, which has been confirmed by both increasing experimental evidences and some results of theoretical investigations. Therefore, it is necessary to further develop theory of optical wave propagation through the atmospheric turbulence, namely, to study the propagation of laser beams in the non-Kolmogorov turbulence before analyzing the joint influence of the Kolmogorov turbulence and the non-Kolmogorov turbulence on satellite laser communication. Also it is well known that the beam wander results in the performance degradation of satellite laser communication systems and exert an influence on the achievement and stability of its links. In this paper, considering a non-Kolmogorov generalized exponential power spectrum of refractive-index fluctuations, we derive the variances of beam wander for a Gaussian-beam wave in weak turbulence for a horizonal path. This spectrum includes the inner and outer scales with a generalized power law; thus, we also analyze the effect of spectral power law and outer scale variations on the beam wander. It is important to note that the expression for the beam wander variance obtained is concise closed form and independent on the optical wavelength.

Design of master oscillator for frequency locking of a complex of megawatt level microwave sources

AbstractWe present the results of the development of a highly stable gyrotron (with long‐term stability of an operating frequency of 170 GHz being equal to 10−9) for experiments on frequency locking and control of megawatt power sources. The electron‐optical and electrodynamic systems of the gyrotron are calculated and optimized, including the magnetron‐injection gun, interaction space, collector, and quasioptical converter of radiation into a Gaussian wave beam. Main requirements for such systems are described along with their specific features, which allow one to develop a relatively simple, low cost, and reliable master generator for synchronization of a large number of continuous‐wave megawatt gyrotrons. This reveals new possibilities for creation of gyrotron complexes capable of generation coherent radiation of nearly unlimited power levels.