Laser Beam Propagation Research Articles

Stability of bound states for regularized nonlinear Schrödinger equations

AbstractWe consider the stability of bound‐state solutions of a family of regularized nonlinear Schrödinger equations which were introduced by Dumas et al. as models for the propagation of laser beams. Among these bound‐state solutions are ground states, which are defined as solutions of a variational problem. We give a sufficient condition for existence and orbital stability of ground states, and use it to verify that ground states exist and are stable over a wider range of nonlinearities than for the nonregularized nonlinear Schrödinger equation. We also give another sufficient and almost necessary condition for stability of general bound states, and show that some stable bound states exist which are not ground states.

Theoretical Study on Transverse Mode Instability in Raman Fiber Amplifiers Considering Mode Excitation.

Raman fiber lasers (RFLs), which are based on the stimulated Raman scattering effect, generate laser beams and offer distinct advantages such as flexibility in wavelength, low quantum defects, and absence from photo-darkening. However, as the power of the RFLs increases, heat generation emerges as a critical constraint on further power scaling. This escalating thermal load might result in transverse mode instability (TMI), thereby posing a significant challenge to the development of RFLs. In this work, a static model of the TMI effect in a high-power Raman fiber amplifier based on stimulated thermal Rayleigh scattering is established considering higher-order mode excitation. The variations of TMI threshold power with different seed power levels, fundamental mode purities, higher-order mode losses, and fiber lengths are investigated, while a TMI threshold formula with fundamental mode pumping is derived. This work will enrich the theoretical model of TMI and extend its application scope in TMI mitigation strategies, providing guidance for understanding and suppressing TMI in the RFLs.

Nonlinear parametric generation and optical vortex transfer in graphene ensemble under Landau quantization

We explore the dynamics of nonlinear parametric generation and light beam propagation in a Landau-quantized graphene structure with three energy levels interacting with two laser pulses, utilizing the Maxwell-Bloch equations. By applying a laser field to one transition of the graphene sample while keeping the second beam initially absent, the distinctive preparation of the graphene sample, coupled with its weak interaction with laser radiation, results in the parametric generation of a new laser beam in a different transition. We investigate the influence of diverse system parameters on both the efficiency of the generated beam and the propagation dynamics of both beams. Our findings reveal that manipulating these parameters can induce oscillations in the intensity of propagated beams, mitigate absorption losses during propagation allowing for earlier relaxation, and enhance the efficiency of energy transfer from the initial to the generated beam. Additionally, we demonstrate the transfer of optical vortices within the graphene ensemble by introducing an optical vortex to the initial beam. This scheme holds promise for applications in high-dimensional quantum information processing.

Soliton solutions of cubic quintic septimal nonlinear Schrödinger wave equation with conformable derivative by two distinct algorithms

This paper investigates the cubic-quintic-septimal nonlinear Schrödinger wave equation with a conformable derivative, which governs the evolution of light beams in a weak nonlocal medium. The analysis utilizes the Kudryashov method and the enhanced modified tanh expansion method. By utilizing these analytical integration schemes, various optical wave solutions are derived within the present conformable model. The paper demonstrates the significance of these optical soliton solutions by illustrating different soliton solutions, including kink-type, bell-shaped, singular, dark, and wave soliton solutions, depicted via contour, three-dimensional, and two-dimensional representations. Moreover, it is crucial to emphasize the importance of analyzing the cubic-quintic-septimal nonlinear Schrödinger wave equation, which finds utility across a spectrum of fields including optics, quantum mechanics, and the study of nonlinear wave propagation. Moving forward, these approaches hold promise for investigating diverse sets of differential equations within multiple domains of applied sciences. This governing equation also has numerous applications in nonlinear optics, such as describing the propagation of laser beams through materials with nonlinear optical properties. The inclusion of these nonlinearities illustrates the interaction and behavior of light beams in weakly non-local media.

Self-focusing of skew cosh gaussian laser beams propagation in absorbing collisionless and collisional plasmas

Self-focusing of skew cosh gaussian laser beams propagation in absorbing collisionless and collisional plasmas

Second harmonic generation of high power cosh-gaussian laser beam in collisional magnetized plasma

Second harmonic generation of high power cosh-gaussian laser beam in collisional magnetized plasma

Investigation of self-focusing of Gaussian laser beams within magnetized plasma via source-dependent expansion method

Self-focusing emerges as a nonlinear optical phenomenon resulting from an intense laser field and plasma interaction. This study investigates the self-focusing behavior of Gaussian laser beams within magnetized plasma environments utilizing a novel approach, source-dependent expansion. By employing source-dependent expansion, we explore the intricate dynamics of laser beam propagation, considering the influence of plasma density and external magnetic fields. The interplay between the beam's Gaussian profile and the self-focusing mechanism through rigorous mathematical analysis and numerical simulations, particularly in the presence of plasma-induced nonlinearities, is elucidated here. Our findings reveal crucial insight into the evolution of laser beams under diverse parameters, including the ponderomotive force, relativistic factors, plasma frequency, polarization states, external magnetic field, wavelength, and laser intensity. This research not only contributes to advancing our fundamental understanding of laser–plasma interactions but also holds promise for optimizing laser-driven applications.

The effect of the external magnetic field on the power of the laser passing through the magnetized plasma and the calculation of the radius of convergence and the investigation of the condition of the beam's filamentation in the Medium

In this article, the power of a laser passing through a magnetized plasma medium which is affected by an external magnetic field is calculated.The change in the intensity of the magnetic field and its rotation around the axis of laser beam propagation in the plasma, on the power of the passing beam is investigated.This work is done based on the indirect effect of the magnetic field on the density distribution of electrons in the plasma, which we can consider the density changes as changes in the refractive index of the medium, so the laser power in this case is different from the case where there is no magnetic field. Also, the condition of beam filamentation has been researched as one of the third-order nonlinear phenomena, and the convergence radius has been calculated under these conditions.

Mitigation of laser plasma filamentation by rotating beam smoothing scheme

The propagation of intense laser beams in plasma inevitably gives rise to laser plasma instabilities, which have a significant impact on the illumination uniformity of the focused spot on the target in inertial confinement fusion (ICF) facilities. Here we propose an ultrafast smoothing scheme using a rotating beam (RB) to mitigate the laser plasma filamentation. Using the propagation model of the rotating beam in plasma for the laser-plasma self-focusing (SF) and filamentation, the filamentation characteristics of laser spots were analyzed. The results indicate that the rotating beam smoothing scheme, operating at picosecond timescale, exhibits superior mitigation effect of laser plasma filamentation.

Analysis of speckle-beacon size impact on wavefront sensing and closed-loop control in deep turbulence conditions

The impact of the laser beacon size on the performance of an ideal phase-conjugation-type adaptive optics (AO) system is analyzed using wave-optics-based numerical simulation. The analysis includes wavefront aberration sensing and closed-loop control for laser beam propagation both in vacuum and in distributed (volume) atmospheric turbulence with the beacon beam scattering off a flat extended target with Lambertian surface roughness. For mitigation of the impact of target-induced speckle effects on the performance of AO systems, speckle-average wavefront sensing and control approaches are introduced and analyzed. The results demonstrate that proposed speckle-average phase conjugation control algorithms enable partial mitigation of turbulence-induced aberrations in presence of strong speckle modulations.

Phase-tuned acousto-optic spatial filter.

An acousto-optic (AO) tunable filter with a phase-controlled dual-section piezoelectric transducer is designed and created for laser beam shaping (LBS). Owing to the acoustic beam steering effect, we experimentally observe splitting of the two-dimensional transfer function. As a result, we demonstrate generation of tunable bottle laser beams and dual-ring intensity distributions for the diffracted beam.

Simultaneous measurements of temporal evolutions of the voltage and the current on the load of the Seoul National University X-pinch device using the optics-based systems.

Optics-based measurement systems have been developed to measure the voltage and the current on a load of the Seoul National University X-pinch device [Ryu etal., Rev. Sci. Instrum. 92, 053533 (2021)]. A lithium niobate crystal that changes the polarization state of the propagating laser beam due to the Pockels effect induced by the electric field across the crystal, thus capable of measuring the voltage, is located next to the load. For the current measurement, an optic fiber is wound around the load to detect the change in the polarization state of the propagating laser beam due to the Faraday rotation induced by the magnetic field. As both voltage and current measurement systems utilize optical effects, the sensors, i.e., the lithium niobate crystal and the optic fiber, do not require any electrical grounds, in contrast to circuit-based probes, such as voltage dividers or Rogowski grooves. This facilitates an easy access to shield other required electronic devices, such as lasers and photodetectors, from the electromagnetic interference generated by the X-pinch power system. In addition, the sensors can be placed in close proximity to the load with fewer concerns on the electrical insulation. Temporal evolutions of the simultaneously measured voltage and current on the load of the X-pinch are successfully obtained and discussed.

Properties of focused combined modes of terahertz laser

Physical features of spatial-energy characteristics of linearly polarized THz laser beams at sharp and moderate focusing in free space are analyzed both theoretically and experimentally. The Rayleigh–Sommerfeld vector theory is used to model propagation of laser beams excited by quasi-optical waveguide resonator modes in free space. Well-known methods of measuring spatial-energy characteristics of laser beams in the THz range are used in the experimental study. It is shown that the intensity of the total electric field of both combined TE0n + EH2n and EН–1n + EH3n modes (n = 1, 2, 3) in the focal region is defined by all three components and has a dip on the axis for both focusing types. The central maxima of the field of these modes become significantly shifted from the geometric foci of the lenses used as the order n of these modes increases. The EН–11 + EH31 mode has the smallest diameter (2.94λ) of the focal spot in the maximum intensity region at sharp focusing. The TE01 + EH21 mode has the smallest diameter (13.65λ) of the focal spot at moderate focusing.

Analytical study on the upward laser beam propagation in the turbulent atmosphere

The upward laser beam propagation in the turbulent atmosphere is studied analytically, where the nonlinear self-focusing, the atmospheric turbulence, and the atmospheric extinction effects are all taken into account. The analytical propagation expression of intensity is derived. The initial beam defocusing and the optimal beam power are two methods to improve the beam quality at the target. The analytical expressions of the focal length considering the initial beam defocusing and the corresponding target intensity are derived. Moreover, the analytical expressions of optimal beam power and the corresponding target intensity are also derived, and the target intensity is independent of the atmospheric extinction. In particular, the criterion for which method (the initial beam defocusing or the optimal beam power) to use is derived to optimize the target beam quality. The choice of the two methods depends on the laser beam parameters and the turbulent atmosphere parameters.

Effect of wavelength on propagation of high-power femtosecond laser pulses in diamond

Numerical modeling of the propagation of high-power femtosecond laser beams in a diamond crystal in the self-focusing mode is carried out. The wavelength of the modeled beams is varied in a wide range (400 nm, 532 nm, 800 nm, and 1064 nm), which covers the most common ultrashort laser systems. For all the wavelengths analyzed, a limitation in the growth of laser energy density inside the diamond crystal with increasing pulse energy is found. This effect has a certain similarity to the effect of optical limitation in laser filaments, but manifests itself outside the filament formation zone and is capable of equalizing the laser energy density, as well as the electron density, inside the extensive pre-focal region.

Single-Shot Diagnosis of Electron Energy Evolution via Streaked Betatron X Rays in a Curved Laser Wakefield Accelerator.

We report on an experimental observation of the streaking of betatron x rays in a curved laser wakefield accelerator. The streaking of the betatron x rays was realized by launching a laser pulse into a plasma with a transverse density gradient. By controlling the plasma density and the density gradient, we realized the steering of the laser driver, electron beam, and betatron x rays simultaneously. Moreover, we observed an energy-angle correlation of the streaked betatron x rays and utilized it in diagnosing the electron acceleration process in a single-shot mode. Our work could also find applications in advanced control of laser beam and particle propagation. More importantly, the angular streaked betatron x ray has an intrinsic spatiotemporal correlation, which makes it a promising tool for single-shot pump-probe applications.

Effect of self focusing on higher harmonic generation of q-Gaussian laser beam in graded index plasma channel

Effect of self focusing on higher harmonic generation of q-Gaussian laser beam in graded index plasma channel

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.

Simulation Method for the Impact of Atmospheric Wind Speed on Optical Signals in Satellite–Ground Laser Communication Links

To analyze the intensity of atmospheric turbulence in a satellite–ground laser communication link, it is important to consider the effect of increased atmospheric turbulence caused by wind speed. Atmospheric turbulence causes a change in the refractive index, which negatively impacts the quality and focusing ability of the laser beam by altering its phase front. To simulate the changes in amplitude and phase characteristics of laser beam propagation in atmospheric turbulence caused by wind speed, a transverse translation phase screen is used. To better understand and address the influence of atmospheric wind speed on the phase of optical signals in satellite–ground laser communication links, this paper proposes a Monte Carlo simulation method. This method utilizes the spatial and temporal variations in the refractive index in the atmosphere and integrates the principles of optical signal propagation in the atmosphere to simulate changes in the phase of optical signals under different wind speed conditions. By analyzing the variations in the received optical signal’s power, the Monte Carlo method is employed to simulate phase screens and logarithmic amplitude screens. Additionally, it models the probability density of the statistical behavior of received optical signal’s fluctuations, as well as the time autocorrelation coefficient of optical signals. This paper, under the coupling condition in satellite–ground laser communication links, conducted a Monte Carlo simulation experiment to analyze the characteristics of the optical signal’s fluctuations in the link and discovered that atmospheric wind speed affects the shape of the power spectral density model of the received optical signal. Increasing wind speed leads to a decrease in the time autocorrelation coefficient of the received optical signal and affects the coupling efficiency. The paper then used a cubic spline interpolation fitting method to verify the models of the power spectral density and the autocorrelation time coefficient of the optical signal. This provides a theoretical foundation and practical guidance for the optimization of satellite–ground laser communication systems.

Stochastic ray tracing for Fresnel diffraction

We propose stochastic ray tracing for laser beam propagation in Fresnel diffraction to find the duality between wave and ray representations. We transform from the Maxwell equations to the Schrödinger equation for a monochromatic laser beam in the slowly varying envelope approximation. The stochastic ray tracing method interprets this Schrödinger equation as a stochastic process, of an analogy of Nelson’s stochastic mechanics. It can illustrate the stochastic paths and the wavefront of an optical beam. This ray tracing method includes Fresnel diffraction effects naturally. We show its general theoretical construction and numerical tests for a Gaussian laser beam with diffraction, that stochasticity realizes the beam waist around the Rayleigh range.