Wave Equation Approach Research Articles

Dominance of polarization modes and absorption on self-focusing of laser beams in collisionless magnetized plasma

This work investigates the polarization modes i.e., Extraordinary (E-mode) and Ordinary (O-mode) on self-focusing of higher-order mode of elegant Hermite-cosh-Gaussian (EHChG) laser beams within collisionless magnetized plasma medium. In this study, the authors have taken transverse electromagnetic ([Formula: see text]) mode with mode indices (0, 4) and explored. The ponderomotive force is primarily responsible for the dielectric constant’s nonlinearity in this context. Also, WKB and paraxial approximations via the parabolic wave equation approach are used to establish the general form of differential equations for beam-width parameters in both transverse dimensions of the beam. In this paper, the authors have theoretically investigated the dominance of polarization modes and absorption coefficient on self-focusing. The final results show good enhancement of laser propagation through collisionless plasma medium.

Self-focusing/defocusing of skew-cosh-Gaussian laser beam for collisional plasma

The inverse relationship between the linear increase in skewness parameter s and the domain’s width of the order of skewness n plays a vital role in both critical beam radius and propagation dynamics of skew-cosh-Gaussian (skew-chG) laser beams. The interplay between the skewness parameter s and the order of skewness n is explored analytically and graphically in the current study to unveil the complexity of the propagation dynamics of the skew-chG laser beam. Naturally, the intensity’s complexity considerably affects the dielectric constant of the medium. Basically, the nonlinearity in the dielectric function of collisional plasma is attributed to the non-uniform heating of energy carriers along the wavefront of the laser beam, which becomes important and is used in the current study. By following Akhmanov’s parabolic wave equation approach under Wentzel–Kramers–Brillouin and paraxial approximations, the nonlinear differential equations are set up for the beam width parameters f 1 and f 2 and solved numerically. The present work analytically investigates the domains of the order n of skew-chG laser beams for a given set of skewness parameter s to investigate their effects on the self-focusing and defocusing of skew-chG laser beams. The critical curve also gets affected significantly due to the choice of domains for n. Finally, the numerical results are presented in the form of graphs and discussed in this study.

Improved least-squares migration through double-sweeping solver

Based on a recently developed approximate wave-equation solver, we have developed a methodology to reduce the computational cost of seismic migration in the frequency domain. This approach divides the domain of interest into smaller subdomains, and the wavefield is computed using a sequential process to determine the downward- and upward-propagating wavefields — hence called a double-sweeping solver. A sequential process becomes possible using a special approximation of the interface conditions between subdomains. This method is incorporated into the least-squares migration framework as an approximate solver. The associated computational effort is comparable to one-way wave-equation approaches, yet, as illustrated by the numerical examples, the accuracy and convergence behavior are comparable to that of the full-wave equation.

Analytical Study of Skew-cosh-Gaussian Laser Beam Propagation through Collisionless Plasma

In the present theoretical investigation the domains of the order of skew-cosh-Gaussian (skew-chG) laser beams for agiven set of skewness parameters and its significant effect on the self-focusing/defocusing in collisionless plasma has beenstudied. The nonlinearity in the dielectric function of collisionless plasma is mainly due to the ponderomotive force. Byfollowing parabolic wave equation approach under Wentzel-Kramers-Brillouin (WKB) and paraxial approximations,nonlinear coupled differential equations are established for the beam width parameters. These equations have been solvednumerically by using fourth-order Runge-Kutta method. The results obtained are presented graphically and discussed.

Permittivity Gradient Induced Depolarization: Electromagnetic Propagation With the Maxwell Vector Wave Equation

Recent interest in 3-D vectorial sensors requires the development of vectorial propagation methods, rather than scalar wave equation approaches. We derive a vector wave equation from Maxwell’s equations for a medium which has an inhomogeneous dielectric permittivity dominated by variation along one dimension. It is well known that the electric field components decouple for homogeneous media. However, 1-D permittivity variations yield an upper triangular system of scalar wave equations with the wave polarization component parallel to the inhomogeneous direction/axis acting as a forcing term for the orthogonal components. The main implication is that waves with polarization oriented parallel to the permittivity gradient will act as a forcing term and excite other polarization components and, thus, induce depolarization. Contemporary studies treat the permittivity as a constant when deriving a wave equation or paraxial approximation, and then re-introduce via inhomogeneous wave speed, variable permittivity, thus missing important terms and physical mechanisms in their resulting equations. Contemporary studies neglect the term in the Maxwell vector wave equation responsible for this effect. Application of the electromagnetic propagation depolarization effect is demonstrated numerically for an air–sea interface evaporation duct with a 500 MHz source.

Self-Focusing of Hermite–Cosh–Gaussian Laser Beams in a Plasma Under a Weakly Relativistic and Ponderomotive Regime

In the theoretical investigation of the self-focusing of elegant Hermite–Cosh–Gaussian (EHChG) beams, the crucial role of decentered parameters has been explored thoroughly in the case of the weak relativistic and ponderomotive regime of interaction. In the present study, the Cartesian coordinate system has been employed, which enables us to study the evolution of two transverse beam-width parameters simultaneously. The differential equations for the beam-width parameters are set up through the parabolic wave equation approach by following WKB and paraxial approximations.

Self-focusing of higher-order asymmetric elegant Hermite-cosh-Gaussian laser beams in collisionless magnetized plasma

In the present paper, we have explored the complexity in self-focusing of asymmetric elegant Hermite-cosh-Gaussian (EHChG) laser beams in magnetized plasmas. We have studied transverse electromagnetic (TEM) mode indices (m, n) of laser with distinct values (0, 0), (0, 2) and (0, 4). The nonlinearity in dielectric constant considered herein is mainly due to the ponderomotive force. General form of differential equations for beam-width parameters in both transverse dimensions of the beam are established by using WKB and paraxial approximations through parabolic wave equation approach. The behaviour of beam-width parameters with dimensionless distance of propagation is studied at different parameters of plasma and those of the considered beams family.

Relativistic self-focusing of finite Airy-Gaussian beams in collisionless plasma using the Wentzel‐Kramers‐Brillouin approximation

In this paper, we present a preliminary study of relativistic self-focusing of finite Airy-Gaussian beams in collisionless plasma taking into consideration the relativistic nonlinearity in the dielectric constant. The differential equation for the beam width parameter of the finite Airy-Gaussian beam is derived by using Wentzel-Kramers-Brillouin (WKB) and paraxial approximations through parabolic wave equation approach. The behavior of beam width parameter with distance of propagation is investigated at different parameters of plasma and those of the considered beams family. Our results detect that the beam is more focused at higher values aperture coefficient and higher intensity parameter. Furthermore, a strong oscillatory behavior of the beam width parameter and better focusing during laser propagation in plasma is apparent.

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.

Investigation of relativistic self-focusing of Hermite-cosine-Gaussian laser beam in collisionless plasma

Relativistic self-focusing of Hermite-cosine-Gaussian (HcosG) laser beam in plasma has been investigated. The distribution of HcosG laser field in the plasma is closely related to decentered parameter. The differential equation for the beam width parameter is derived by following Wentzel–Kramers–Brillouin (WKB) and paraxial approximation through parabolic wave equation approach. The behavior of beam width parameter with distance of propagation is investigated at different values of plasma density, decentered parameter and intensity parameter. Our results reveal that the laser beam is more focused at lower values of decentered and intensity parameter. Further, a strong oscillatory behavior of the beam width parameter during laser propagation in collisionless plasma is seen.

Density Transition Based Self-Focusing of cosh-Gaussian Laser Beam in Plasma with Linear Absorption* *Supported by a Financial Grant from CSIR, New Delhi, India, under Project No. 03(1277)/13/EMR-II

Density transition based self-focusing of cosh-Gaussian laser beam in plasma with linear absorption has been studied. The field distribution in the plasma is expressed in terms of beam width parameter, decentered parameter, and linear absorption coefficient. The differential equation for the beam width parameter is solved by following Wentzel–Kramers–Brillouin (WKB) and paraxial approximation through parabolic wave equation approach. The behaviour of beam width parameter with dimensionless distance of propagation is studied at optimum values of plasma density, decentered parameter and with different absorption levels in the medium. The results reveal that these parameters can affect the self-focusing significantly.

Self-Focusing of Hermite-Cosh-Gaussian Laser Beams in Plasma under Density Transition

Self-focusing of Hermite-Cosh-Gaussian (HChG) laser beam in plasma under density transition has been discussed here. The field distribution in the medium is expressed in terms of beam-width parameters and decentered parameter. The differential equations for the beam-width parameters are established by a parabolic wave equation approach under paraxial approximation. To overcome the defocusing, localized upward plasma density ramp is considered, so that the laser beam is focused on a small spot size. Plasma density ramp plays an important role in reducing the defocusing effect and maintaining the focal spot size up to several Rayleigh lengths. To discuss the nature of self-focusing, the behaviour of beam-width parameters with dimensionless distance of propagation for various values of decentered parameters is examined by numerical estimates. The results are presented graphically and the effect of plasma density ramp and decentered parameter on self-focusing of the beams has been discussed.

A level set two-way wave equation approach for Eulerian interface tracking

We present a new approach to perform Eulerian level set interface tracking. It consists in advecting the level set function using a second-order two-way wave equation instead of the standard one-way wave advection equation. The resulting numerical schemes are simple to implement, more stable, and significantly less prone to dissipation errors than popular (e.g., WENO) discretizations of the one-way advection equation of higher order, in particular for long advection times. While both the two-way wave advection and the associated numerical schemes were derived previously, these approaches have never been combined with level set advection. Since the level set function to advect is smooth by construction, this ensures the stability of the solution when using the two-way advection equation discretized using centered finite difference schemes. Our numerical tests show that the two-way wave equation approach yields more accurate results than the standard one-way wave equation for the level set advection, at a considerably smaller computational cost.

The One-Way Wave Equation: A Full-Waveform Tool for Modeling Seismic Body Wave Phenomena

The study of seismic body waves is an integral aspect in global, exploration and engineering scale seismology, where the forward modeling of waves is an essential component in seismic interpretation. Forward modeling represents the kernel of both migration and inversion algorithms as the Green’s function for wavefield propagation and is also an important diagnostic tool that provides insight into the physics of wave propagation and a means of testing hypotheses inferred from observational data. This paper introduces the one-way wave equation method for modeling seismic wave phenomena and specifically focuses on the so-called operator-root one-way wave equations. To provide some motivation for this approach, this review first summarizes the various approaches in deriving one-way approximations and subsequently discusses several alternative matrix narrow-angle and wide-angle formulations. To demonstrate the key strengths of the one-way approach, results from waveform simulation for global scale shear-wave splitting modeling, reservoir-scale frequency-dependent shear-wave splitting modeling and acoustic waveform modeling in random heterogeneous media are shown. These results highlight the main feature of the one-way wave equation approach in terms of its ability to model gradual vector (for the elastic case) and scalar (for the acoustic case) waveform evolution along the underlying wavefront. Although not strictly an exact solution, the one-way wave equation shows significant advantages (e.g., computational efficiency) for a range of transmitted wave three-dimensional global, exploration and engineering scale applications.

Comparison of 2D and 3D Electromagnetic Approaches to Predict Tropospheric Turbulence Effects in Clear Sky Conditions

Two-dimensional electromagnetic simulations are often used to evaluate the atmospheric turbulence effects on radiowave propagation in clear sky conditions. However, turbulence is clearly a three-dimensional atmospheric process. Therefore, errors potentially introduced by 2D propagation schemes to predict 3D scintillation effects have to be quantitatively assessed. On the one hand, as part of an analytical approach and starting from the Kolmogorov-von Karman turbulent spectrum, 2D formulations for log-amplitude and phase variances and for log-amplitude and phase temporal power spectra are derived from the 2D scalar propagation equation. They are compared asymptotically to their classical 3D counterparts. On the other hand, as part of a numerical approach, the scintillation effects are evaluated from 3D and 2D parabolic wave equation (PWE) approaches associated with 2D and 1D multiple phase screen (MPS), respectively. It is then shown that 2D propagation schemes underestimate by a factor 1.86 the log-amplitude variances in Fresnel regime and can lead to significant errors in predicting log-amplitude and phase temporal spectra at low frequencies. It is then suggested that the dimensional reduction should be limited to the prediction of log-amplitude and phase variances in Fraunhofer configurations, or to the evaluation of log-amplitude and phase power spectra at high frequencies.

Observations and parabolic wave modeling of underwater pile driving impact noise.

Pile driving in water produces extremely high sound levels in both surrounding air and underwater environments. In a companion work [Reinhall and Dahl] it is shown using finite element simulation that for underwater case the primary sound signal originates from a compression wave traveling down the pile at a speed in excess of Mach 3. In this work, we present measurements pile driving impact noise made from a marine construction site in Puget Sound using a vertical line array (VLA) positioned at ranges 8–15 m from full-scale impact pile driving. The measurements are modeled using the parabolic wave equation approach for which synthetic time series are generated (bandwidth 50–2050 Hz). The simulation is achieved by way of a phased array of point sources, representing one source traveling down the pile at supersonic speed. Pile end reflections are included and the process is repeated with both an up- and down-traveling time-delayed sources. With the field computed in this manner, excellent agreement is achieved between model and observations of peak pressure level, and the compression wave speed is also confirmed by way of arrival angle estimation using the VLA. Implications on transmission loss are also discussed. [Work supported by the Washington State Department of Transportation.]

Cross focusing of two coaxial cosh-Gaussian laser beams in a parabolic medium

In this paper authors have presented the cross focusing of two coaxial cosh-Gaussian laser beams of different frequencies in a parabolic medium. Starting from the expression for field distribution of cosh-Gaussian beams, differential equations for beam-width parameters of two beams have been established through parabolic wave equation approach and analytical solution for weak beam has been obtained. The effect of decentred parameter of strong beam on the behavior of beam-width parameter with the normalized distance of propagation for weak beam has been specifically considered. The results have been presented graphically and discussed.

Wave-equation migration in generalized coordinate systems

Month and year defended: March, 2009 Wave-equation migration using one-way wavefield extrapolation is commonly used to generate images of complex geologic structure from 3D seismic data. Most conventional wave-equation approaches restrict propagation to downward continuation, where wavefields are recursively depth extrapolated on Cartesian meshes. In practice, this approach exhibits limited high-angle accuracy and is restricted to down-going waves, which precludes using some steep-dip and all turning wave …

Fast free surface multiples attenuation workflow for three‐dimensional ocean bottom seismic data

ABSTRACTWater multiples can be very strong and contaminate the primary reflections. This can cause problems in the processing flow and the interpretation of the subsurface image. Hence, multiples suppression is an important part of the preprocessing flow. We present a fast workflow for attenuation of free surface related multiples for 2D and 3D ocean bottom seismic data based on the wave equation approach. Included in the workflow are: 1. Calibration of the pressure and vertical velocity components by using wavefield splitting. 2. Data interpolation by using offset projection. 3. Fast Radon transform by using fast fractional Fourier transform. Advantages of this workflow are that it is fast, efficient and the only requirements are the recording of both pressure and vertical particle components at some point below the source in the water column.

Self-focusing and defocusing of TEM 0p Hermite–Gaussian laser beams in collisionless plasma

The authors have investigated the self-focusing and defocusing of first six TEM 0 p Hermite –Gaussian laser beams in collisionless plasma. In case of collisionless plasma the nonlinearity in the dielectric constant is mainly due to the ponderomotive force. It is found that modes with odd p-values defocuses and that with even p-values exhibit oscillatory as well as defocusing character of beam-width parameters variation during their propagation in collisionless plasma. The entire theoretical formulation is established under parabolic wave equation approach. The numerical computation is completed by using fourth order Runge–Kutta method. Finally the behavior of beam-width parameters with the dimensionless distance of propagation is presented graphically.