Gaussian Beam Propagation Research Articles

Random optical beam propagation in anisotropic turbulence along horizontal links.

Considerable amount of data has been collected in the past asserting that atmospheric turbulence has regions where it exhibits anisotropic statistics. For instance, it is known that the fluctuations in the refractive index within the first meter above the ground are typically stronger in the vertical direction compared with those in the horizontal directions. We have investigated the second-order statistical properties of a Gaussian Schell-model (GSM) beam traversing anisotropic atmospheric turbulence along a horizontal path. Analytical expression is rigorously derived for the cross-spectral density function of a GSM beam. It is shown that the spread of the beam and its coherence properties become different in two transverse directions due to anisotropy. In the limiting case when the source coherence width becomes infinite our results reduce to those for Gaussian beam propagation. Source partial coherence is shown to mitigate anisotropy at sub-kilometer distances.

Propagation of specular and anti-specular Gaussian Schell-model beams in oceanic turbulence

On the basis of the extended Huygens-Fresnel principle and the unified theory of coherence and polarization of light, we investigate the propagation properties of the specular and anti-specular Gaussian Schell-model (GSM) beams through oceanic turbulence. It is shown that the specularity of specular GSM beams and the anti-specularity of anti-specular GSM beams are destroyed on propagation in oceanic turbulence. The spectral density and the spectral degree of coherence are also studied in detail. The results may be helpful for underwater communication.

Effects of finite inner and outer scales on the scintillation index of turbulent slant path

In this paper, the effects of nonzero inner scales and finite outer scales are investigated, in the context of Gaussian beam propagation along a slant path under general turbulence conditions. Theoretical expressions for the cut-off spatial frequencies are derived with an approach method, and thereby a modified scintillation model is developed to incorporate inner scale and outer scale parameters in the analysis. Then, inner and outer scale effects on the downlink are analysed with respect to the zenith angle, the altitude of the transmitter, the initial beam radius, as well as the turbulence strength. Numerical results indicate that the effects of a finite outer scale mainly influence transmission that occurs at large zenith angles or high altitudes, while the inner scale effects are more prevalent. This study may be helpful to improve the accuracy of calculation of slant-path scintillation index, and thus benefit the characterization and optimization of space/air-ground laser communication systems.

Propagation of Gaussian Beams in the Presence of Gain and Loss

We consider the propagation of Gaussian beams in a waveguide with gain and loss in the paraxial approximation governed by the Schrodinger equation. We derive equations of motion for the beam in the semiclassical limit that are valid when the waveguide profile is locally well approximated by quadratic functions. For Hermitian systems, without any loss or gain, these dynamics are given by Hamilton's equations for the center of the beam and its conjugate momentum. Adding gain and/or loss to the waveguide introduces a non-Hermitian component, causing the width of the Gaussian beam to play an important role in its propagation. Here, we show how the width affects the motion of the beam and how this may be used to filter Gaussian beams located at the same initial position based on their width.

Influence of non-Kolmogorov atmospheric turbulence on the beam quality of vortex beams.

Based on the extended Huygens-Fresnel principle and the definition of second-order moments of the Wigner distribution function (WDF), the analytical expressions for the propagation factors (M2-factors) and Strehl ratio SR of the Gaussian Schell-model (GSM) vortex beams and GSM non-vortex beams propagation through non-Kolmogorov atmospheric turbulence are derived, and used to study the influence of non-Kolmogorov atmospheric turbulence on beam quality of the GSM vortex beams. It is shown that the smaller the generalized structure constant and the outer scale of turbulence are, and the bigger the inner scale of turbulence is, the smaller the normalized propagation factor is, the bigger the Strehl ratio is, and the better the beam quality of GSM vortex beams in atmospheric turbulence is. The variation of beam quality with the generalized exponent α is nonmonotonic, when α = 3.11, the beam quality of the GSM vortex beams is the poorest through non-Kolmogorov atmospheric turbulence. GSM vortex beams is less affected by turbulence than GSM non-vortex beams under certain condition, and will be useful in long-distance free-space optical communications.

Gaussian Beam Propagation in a Kerr Type Metamaterial Medium Using ABCD Matrix Method

In this paper, a split step ABCD matrix method is suggested to investigate Gaussian beam propagation in a Kerr type metamaterial medium. This method is based on dividing the medium interval into subsequent steps. Meanwhile, Gaussian beam profile in every step is obtained by finding the ABCD matrix of that particular step, and is used to find the ABCD matrix of the next step. Results of the suggested matrix method have been compared with the results of numerical split-step Fourier method for a Kerr medium, which indicates a good agreement. Then, we use the ABCD matrix to investigate Gaussian beams propagation in a Kerr type metamaterial, which is also in agreement with pervious results by other methods.

Propagation of Gaussian Schell-model Array beams in free space and atmospheric turbulence

Based on the extended Huygens-Fresnel principle, the evolution behavior of the spectral density and the spectral degree of coherence of the beam produced by a recently introduced novel class of Gaussian Schell-model Arrays (GSMA) source in free space and turbulence atmospheric are explored and comparatively analyzed. And the influence of the fractal constant of the atmospheric power spectrum and refractive-index structure constant on the spectral density and the spectral degree of coherence of beams are analyzed. It is shown that the optical lattice profile is stable when beams propagate in free space, but the spectral density eventually is suppressed and transformed into a Gaussian profiles when it passes at sufficiently large distances through the turbulent atmosphere. The distributions of the spectral degree of coherence in far field eventually transformed into a shrink Gaussian profile relative to free space which means that the degree of spatial coherence turns worse.

Energy parameters of CO2 laser radiation focused in a turbulent atmosphere under wind-dominated thermal blooming

Temporal dynamics of peak intensity and power in a finite-size aperture of focused radiation at a wavelength of 10.6 µm under thermal self-action in a clear turbulent atmosphere is analyzed by means of computer simulation. Propagation of Gaussian beams along paths up to 160 m long is considered. It is shown that there are time spans where the peak intensity of a sharply focused beam in the middle of the path is higher than in the focal plane at the end of the path under strong fluctuations of the refractive index.

Complex geometrical optics and nonlinear absorption/gain effects

The paper presents systematic analysis of the influence of nonlinear absorption/gain phenomena on Gaussian wave field evolution in Kerr type medium with additional consideration of the initial light beam convergence and divergence. To perform efficient analysis of the joint contribution of the initial curvature of the wave front and nonlinear absorption/gain effects on self-focusing/self-defocusing phenomena I propose to apply the method of complex geometrical optics (CGO) which at once reduces Gaussian beam diffraction and self-action effects (including nonlinear absorption/gain) to domain of ordinary differential equations (ODEs), which are base (output) equations. Description in output ODEs causes that CGO possess great superiority over well known analytic methods of nonlinear optics such as: variational method and method of moments which every time demand to solve Nonlinear Schrodinger Equation (NLS) by applying integral variational procedure or virial theory to obtain resulting equations describing evolution of amplitude, beam width and wave front curvature which happen to be identical with those obtained by CGO method. CGO method dealing with output ODEs is time consuming physical approach comparing to the numerical methods of nonlinear and wave optics. CGO with output evolutionary ODEs enables one to apply basic mathematical computer software such as: Matlab/Octave, Mathcad and Mathematica commonly available on every University, Colleague and secondary school nowadays. Full Text: PDF References N. N. Akhmediev and A. Ankiewicz, Solitons. Nonlinear Pulses and Beams. (Chapman and Hall, London 1997). N. N. Akhmediev and A. Ankiewicz ed. Dissipative Solitons. Lecture Notes in Physics, Vol. 661, p. 1-443, ISBN: 978-3-540-23373-2, (Springer Berlin Heidelberg, 2005). CrossRef E. Jaatinen and M. W. Jones, "Theoretical description of low divergence Gaussian fields in self-defocusing photorefractive media", Optics Communications, 281, p. 3201-3207 (2008). CrossRef P. Berczynski, and S. Marczynski. Book Chapter 1: Gaussian Beam Propagation in Inhomogeneous Nonlinear Media. Description in Ordinary Differential Equations by Complex Geometrical Optics , (Edited by: P. W. Hawkes) , Advances in Imaging and Electron Physics, 185, pages 1-111, ISBN 9780128001448, Elsevier New York, (2014). Y. Silberberg, "Solitons and two-photon absorption", Optics Letters, vol. 15, No. 18, p.1005-1007 (1990). CrossRef D. Ianetz, Yu. Kaganovskii, A. D. Wilson-Gordon, and M. Rosenbluh, "Propagation of an asymmetric Gaussian beam in a nonlinear absorbing medium", Phys. Rev. A 81, 53851, pages-1-6 (2010). CrossRef D. Mc Morrow, W. Lotshaw, J. Melinger, S. Buchner, and R. Pease, "Subbandgap laser-induced single event effects: carrier generation via two-photon absorption", IEEE Trans. Nucl. Sci., vol. 49, no. 6, pp. 3002 ? 3008 (2002). CrossRef

Propagation of Gaussian beam through a uniaxial anisotropic slab

An exact analytical solution to the reflection and transmission of an incident Gaussian beam by a uniaxial anisotropic slab is obtained in terms of the rectangular vector wave function expansion form. In the uniaxial anisotropic slab, the optical axis is parallel to the interface. For a localized beam model, numerical results of the normalized field intensity distributions are presented, and the propagation characteristics are analyzed concisely.

SU‐F‐SPS‐05: Experimental Validation of Peripheral Dose Distribution of Electron Beams for Eclipse Electron Monte Carlo Algorithm

Purpose:In this study, the two available calculation algorithms of the Varian Eclipse treatment planning system(TPS), the electron Monte Carlo(eMC) and General Gaussian Pencil Beam(GGPB) algorithms were used to compare measured and calculated peripheral dose distribution of electron beams.Methods:Peripheral dose measurements were carried out for 6, 9, 12, 15, 18 and 22 MeV electron beams of Varian Triology machine using parallel plate ionization chamber and EBT3 films in the slab phantom. Measurements were performed for 6×6, 10×10 and 25×25cm2 cone sizes at dmax of each energy up to 20cm beyond the field edges. Using the same film batch, the net OD to dose calibration curve was obtained for each energy. Films were scanned 48 hours after irradiation using an Epson 1000XL flatbed scanner. Dose distribution measured using parallel plate ionization chamber and EBT3 film and calculated by eMC and GGPB algorithms were compared. The measured and calculated data were then compared to find which algorithm calculates peripheral dose distribution more accurately.Results:The agreement between measurement and eMC was better than GGPB. The TPS underestimated the out of field doses. The difference between measured and calculated doses increase with the cone size. The largest deviation between calculated and parallel plate ionization chamber measured dose is less than 4.93% for eMC, but it can increase up to 7.51% for GGPB. For film measurement, the minimum gamma analysis passing rates between measured and calculated dose distributions were 98.2% and 92.7% for eMC and GGPB respectively for all field sizes and energies.Conclusion:Our results show that the Monte Carlo algorithm for electron planning in Eclipse is more accurate than previous algorithms for peripheral dose distributions. It must be emphasized that the use of GGPB for planning large field treatments with 6 MeV could lead to inaccuracies of clinical significance.

A new study of turbulence effects in the marine environment on the intensity distributions of flat-topped Gaussian beams

In this study, we investigate the effects of maritime atmospheric turbulence on the propagation of flat-topped Gaussian beams within the regime of weak fluctuations. Based on the paraxial approximation and the Rytov theory, the statistical moments, the scintillation index, the probability of fade, and the duration of fade are studied analytically and numerically. The numerical results show that these parameters depend on the beam order, the beam waist, the refractive-index structure parameter, the inner scale of the turbulence and the wavelength.

Gaussian beam propagation in anisotropic turbulence along horizontal links: theory, simulation, and laboratory implementation.

Experimental and theoretical work has shown that atmospheric turbulence can exhibit "non-Kolmogorov" behavior including anisotropy and modifications of the classically accepted spatial power spectral slope, -11/3. In typical horizontal scenarios, atmospheric anisotropy implies that the variations in the refractive index are more spatially correlated in both horizontal directions than in the vertical. In this work, we extend Gaussian beam theory for propagation through Kolmogorov turbulence to the case of anisotropic turbulence along the horizontal direction. We also study the effects of different spatial power spectral slopes on the beam propagation. A description is developed for the average beam intensity profile, and the results for a range of scenarios are demonstrated for the first time with a wave optics simulation and a spatial light modulator-based laboratory benchtop counterpart. The theoretical, simulation, and benchtop intensity profiles show good agreement and illustrate that an elliptically shaped beam profile can develop upon propagation. For stronger turbulent fluctuation regimes and larger anisotropies, the theory predicts a slightly more elliptical form of the beam than is generated by the simulation or benchtop setup. The theory also predicts that without an outer scale limit, the beam width becomes unbounded as the power spectral slope index α approaches a maximum value of 4. This behavior is not seen in the simulation or benchtop results because the numerical phase screens used for these studies do not model the unbounded wavefront tilt component implied in the analytic theory.

Nonlinear propagation of Gaussian laser beam in an inhomogeneous plasma under plasma density ramp

Nonlinear propagation of Gaussian laser beam in an inhomogeneous plasma under plasma density ramp is studied. The differential equation for beam width parameter is derived by parabolic wave equation approach under paraxial approximation. For different values of plasma density, laser intensity and initial beam width, the behavior of beam width parameter with the normalized propagation distance is examined. It is found that the beam width parameter decreases with a higher rate. The frequency of the oscillations increases while amplitude decreases and the laser beam focuses up to long distance. Further, increase in relative plasma density causes reduction in the amplitude of spot size of laser beam near the propagation axis.

Propagation of optical beams in two transverse gradient index media

We investigate the propagation of optical beams in two gradient index inhomogeneous media. The Green’s function for paraxial propagation in an inhomogeneous medium is derived as a Feynman path integral involving summation over real rays. We use a simple method based on discontinuous functions, which is similar to that used in General Relativity when studying metric discontinuities across an hypersurface, to study the propagation in two transverse refractive index gradients which are coupled in the propagation direction. We show that this method is consistent with the geometric-optics ray theory, and then with the definition of the coupled Green’s function. The propagation of Gaussian beams in two homogeneous media with different refractive indices is analyzed. We also study the propagation of Airy beams in two media with different linear transverse refractive index gradients. We demonstrate that by controlling the gradient strength of the media it is possible to reduce to zero their acceleration, yielding an Airy beam that propagates linearly.

Moosh: A Numerical Swiss Army Knife for the Optics of Multilayers in Octave/Matlab

The aim of Moosh is to provide a complete set of tools to compute all the optical properties of any multilayered structure: reflection, transmission, absorption spectra, as well as gaussian beam propagation or guided modes. It can be seen as a semi-analytic (making it light and fast) solver for Maxwell’s equations in multilayers. It is written in Octave/Matlab, available on Github and based on scattering matrices, making it perfectly stable. This software is meant to be extremely easy to (re)use, and could prove useful in many research areas like photovoltaics, plasmonics and nanophotonics, as well as for educational purposes for the large number of physical phenomena it can illustrate.

Optimal focusing conditions of lenses using Gaussian beams

By using the analytical equations of the propagation of Gaussian beams in which truncation exhibits negligible consequences, we describe a method that uses the value of the focal length of a focusing lens to classify its focusing performance. We show that for different distances between a laser and a focusing lens there are different planes where best focusing conditions can be obtained and we demonstrate how the value of the focal length impacts the lens focusing properties. To perform the classification we introduce the term delimiting focal length. As the value of the focal length used in wave propagation theory is nominal and difficult to measure accurately, we describe an experimental approach to calculate its value matching our analytical description. Finally, we describe possible applications of the results for characterizing Gaussian sources, for measuring focal lengths and/or alternatively for characterizing piston-like movements.

Green pulsed lidar-radar emitter based on a multipass frequency-shifting external cavity.

This paper investigates the radio frequency (RF) up-conversion properties of a frequency-shifting external cavity on a laser beam. We consider an infrared passively Q-switched pulsed laser whose intensity modulation results from the multiple round-trips in the external cavity, which contains a frequency shifter. The output beam undergoes optical second-harmonic generation necessary to reach the green wavelength. We model the pulse train using a rate-equation model to simulate the laser pulses, together with a time-delayed interference calculation taking both the diffraction efficiency and the Gaussian beam propagation into account. The predictions are verified experimentally using a diode-pumped Nd:YAG laser passively Q-switched by Cr4+:YAG whose pulse train makes multiple round-trips in a mode-matched external cavity containing an acousto-optic frequency shifter driven at 85 MHz. Second-harmonic generation is realized in a KTP crystal, yielding RF-modulated pulses at 532 nm with a modulation contrast of almost 100%. RF harmonics up to the 6th order (1.020 GHz) are observed in the green output pulses. Such a RF-modulated green laser may find applications in underwater detection and ranging.

Modelling Gaussian beam propagation through thick nonlinear refractive and absorptive media

A novel numerical finite difference beam propagation method developed for quadratic refractive index media is presented and applied to TEM00 Gaussian beams propagating through nonlinear optical media. The beam’s diffraction through the medium was calculated by using the nonlinear Schrodinger equation on small slices which proved to be effective for thick samples. The performance of the model was compared to experimental z-scan observations of colloidal ZnO particles at low cw and high pulsed peak powers at a wavelength of 532 nm. Different optical behaviours were observed in these two power regimes. Negligible nonlinear absorption and refraction were observed at low cw powers, with strong defocusing arising through thermal lensing in the colloidal solution. For the pulsed experiments with peak powers up to 43-kW and 7-ns pulses, values for the intensity-dependent absorption were determined to be \(\beta = 1.0 \times 10^{ - 10} \;{\text{m/W}}\) and \(n_{{2{\text{R}}}} = 2.0 \times 10^{ - 18} \;{\text{m}}^{2} /{\text{W}}\). Despite the very different nonlinear and thermal–optical behaviours in two power regimes, there was good agreement between the model and observations. This demonstrates the effectiveness of the approach in extracting the nonlinear properties of a medium even if it is not optically thin and in the case when a sample displays both strong nonlinear refraction and absorption.

Characteristics of Self-Focusing of a Gaussian Laser Pulse Under Lateral and Axial Plasma Density Variations

In this paper, we present a paraxial description of relativistic self-focusing of a Gaussian laser beam in a plasma channel with the density distribution as a function of radial and axial variations. We have derived the nonlinear dielectric permittivity of plasma due to ponderomotive force and relativistic effects. The effect of different conditions of the inhomogeneous plasma and the laser pulse on self-focusing and defocusing of Gaussian laser beam propagation in the plasma is studied. We find that with an increase in the value of intensity of the beam, self-focusing enhances and shifts toward lower values of normalized propagation distance. The self-focusing length also increases with an increase in channel width. When the density rapidly increases along the propagation distance, the nonlinearity increases and gives self-focusing at shorter values of $z$ .