Laser Beam Propagation Research Articles

Optical design of the laser launch telescope via physical optics theorem for laser guide star facility

The Laser Guide Star Facility (LGSF), as the most important part of the adaptive optics system of the large ground-based telescope, is aimed to generate multiple laser guide stars at the sodium layer. Laser Launch Telescope is employed to implement this requirement by projecting the Gauss beam to the sodium layer with a small beam size in LGSF system. As the diffraction and interference effects of laser’s long-distance transmission, the conventional optical design based on the geometrical optics mechanism cannot achieve the expected laser propagation. In this paper, we propose a method to design optical system for laser launch telescope based on the physical optics theorem to generate an acceptable light spot at the sodium layer in the atmosphere. Besides, a tolerance analysis method based on physical optics propagation is also demonstrated to be necessitated to optimize the system’s instrumentation performance. The numerical results show that the optical design considering physical optics propagation is highly rewarding and even necessitated in many occasions, especially for laser beam propagation systems.

Propagation of laser beams through curved interfaces of transparent media

Mathematical models of propagation of Gaussian, collimated and structured laser beams in transparent optically homogeneous media in the presence of curved interfaces are presented. Experimental techniques which are used for reconstruction of the interfaces profiles are described.

Synthesis of spherical zinc sulfide nanoparticles produced by femtosecond laser ablation and deposited on a silicon substrate under the action of an electrostatic field

In this paper we consider the synthesis of spherical zinc sulfide (ZnS) nanoparticles (NPs) deposited on a silicon substrate by femtosecond laser ablation of ceramic target under the action of an electrostatic field in argon gas atmosphere. The use of an electrostatic field in the process of ablative synthesis of NPs allows, in addition to capturing particles, to carry out predicted deposition of nanomaterials on the substrate, while carrying out the ablation products from the region of laser beam propagation. The morphology and structural characteristics of synthesized ZnS NPs were investigated using scanning electron microscopy and X-ray diffraction analysis. The size distribution of ZnS NPs were studied using dynamic light scattering technique. Obtained NPs have a spherical shape and are characterized by a hexagonal phase of wurtzite ZnS.

Strong instability of solitary waves for inhomogeneous nonlinear Schrödinger equations

This paper studies the inhomogeneous nonlinear Schrödinger equations, which may model the propagation of laser beams in nonlinear optics. Using the cross‐constrained variational method, a sharp condition for global existence is derived. Then, by solving a variational problem, the strong instability of solitary waves of this equation is proved.

Second-harmonic generation of hollow Gaussian laser beams in inhomogeneous plasmas in the presence of wiggler magnetic field

Second-harmonic generation of hollow Gaussian laser beams (HGLBs) in inhomogeneous plasmas is investigated in the presence of an external wiggler magnetic field. The wiggler magnetic field and electric field of the laser pulse exert a ponderomotive force on electrons deriving electron velocity. Electron velocity, wiggler magnetic field and magnetic field of the laser pulse beat to exert a nonlinear ponderomotive force on electrons at the second-harmonic frequency. The nonlinear ponderomotive force can derive a nonlinear current density. Using linear and nonlinear current densities and wave equation in cylindrical coordinates, two equations obtaining different components of the electric field of second-harmonic wave (SHW) are derived. Results indicate that by increasing the external wiggler magnetic field, order of HGLB, rippled electron density, rippled wave number and initial intensity of the laser pulse, the amplitude of the excited SHW increases. Finally, it is found that by decreasing the initial width of the laser beam, the amplitude of SHW increases, attains a maximum and then decreases.

Optical Kerr effect field measurements and ad hoc engineering model comparisons.

Optical Kerr effects induced by the propagation of high peak-power laser beams through real atmospheres have been a topic of interest to the nonlinear optics community for several decades. This paper proposes a new analytical model for predicting the filamentation/light channel onset distance in real atmospheres based on modulation instability model considerations. The normalized intensity increases exponentially as the beam propagates through the medium. It is hypothesized that this growth can be modeled as a weighted ratio of the Gaussian beam diameter at range to the lateral coherence radius and can be used to set the power ratio for an absorbing, turbulent, nonlinear media to estimate the beam collapse distance. Comparison of onset distance predictions with those found from computer simulation and deduced from field experiments will be presented. In addition, this model will be used with an analytical approach to quantify the expected radius of light channels resulting from self-focusing both with and without the production of a plasma filament. Finally, this paper will describe a set of 1.5-micron, variable focal length USPL field experiments. Comparisons of theoretical radius calculations to measurements from field experiments will be presented.

Optical guiding of intense Hermite–Gaussian laser beam in preformed plasma channel and second harmonic generation

This work presents the scheme of optical channeling of the intense Hermite Gaussian laser beam and second-harmonic generation in plasma having the preformed plasma channel, where relativistic nonlinearity is operative. Excitation of the electron plasma wave at the incident beam frequency leads its coupling with the latter produces the second harmonics of the beam. For the formulation of differential equations for the beam waists of the Hermite Gaussian laser beam propagating through the channel, the method of moments has been used. The solutions of the coupled differential equations are found using Runge Kutta fourth-order numerical method. Perturbation theory has been applied to find the equation governing the excitation of electron plasma wave and hence the source term for the second-harmonic yield. It has been observed that the preformed plasma channel helps to optically guide the laser beam and enhances the efficiency of second-harmonic generation of various modes of the Hermite Gaussian laser beam in plasma.

Laser Beam Atmospheric Propagation Modelling for Aerospace LIDAR Applications

Atmospheric effects have a significant impact on the performance of airborne and space laser systems. Traditional models used to predict propagation effects rely heavily on simplified assumptions of the atmospheric properties and their interactions with laser systems. In the engineering domain, these models need to be continually improved in order to develop tools that can predict laser beam propagation with high accuracy and for a wide range of practical applications such as LIDAR (light detection and ranging), free-space optical communications, remote sensing, etc. The underlying causes of laser beam attenuation in the atmosphere are examined in this paper, with a focus on the dominant linear effects: absorption, scattering, turbulence, and non-linear thermal effects such as blooming, kinetic cooling, and bleaching. These phenomena are quantitatively analyzed, highlighting the implications of the various assumptions made in current modeling approaches. Absorption and scattering, as the dominant causes of attenuation, are generally well captured in existing models and tools, but the impacts of non-linear phenomena are typically not well described as they tend to be application specific. Atmospheric radiative transfer codes, such as MODTRAN, ARTS, etc., and the associated spectral databases, such as HITRAN, are the existing tools that implement state-of-the-art models to quantify the total propagative effects on laser systems. These tools are widely used to analyze system performance, both for design and test/evaluation purposes. However, present day atmospheric radiative transfer codes make several assumptions that reduce accuracy in favor of faster processing. In this paper, the atmospheric radiative transfer models are reviewed highlighting the associated methodologies, assumptions, and limitations. Empirical models are found to offer a robust analysis of atmospheric propagation, which is particularly well-suited for design, development, test and evaluation (DDT&E) purposes. As such, empirical, semi-empirical, and ensemble methodologies are recommended to complement and augment the existing atmospheric radiative transfer codes. There is scope to evolve the numerical codes and empirical approaches to better suit aerospace applications, where fast analysis is required over a range of slant paths, incidence angles, altitudes, and atmospheric conditions, which are not exhaustively captured in current performance assessment methods.

Dynamics of resonant self‐focusing on second harmonic generation of Gaussian laser beam in a rippled density plasma

AbstractResonant second harmonic generation by a Gaussian laser beam in a rippled density plasma is studied using the moment theory approach. The nonlinearity arises through the relativistic mass effect and ponderomotive forces. The laser beam creates a plasma channel and gives rise to electron density perturbation at the laser frequency. The density perturbation beats with electron quiver velocity to produce second harmonics. The ripple provides phase matching and makes the process a resonant one. The second harmonic power efficiency is increased effectively with density ripple. Self‐focusing causes enhancement in the efficiency of harmonic generation.

Generation of hollow laser beam with adjustable profile distribution by using tapered fiber

We present a method to produce a hollow laser beam with adjustable profile distribution using a tapered optical fiber. The dependence of the dark spot size (DSS), hollow beam width (HBW), and transverse field intensity distribution of the hollow beam on the incidence angle of the laser beam, cone angle of the tapered fiber, and working distance are analyzed theoretically and experimentally. The study shows that a high-power hollow laser beam with excellent propagation properties can be achieved by using a tapered fiber with certain parameters. The proposed technique is simple, flexible, and easy to control and operate.

Improving the performance of a laser-driven flyer with a diffractive optical element of high wavefront distortion tolerance

To improve the performance of a laser-driven flyer (LDF), we design and fabricate a diffractive optical element (DOE) to convert a laser pulse with nonuniform energy into a flat-topped beam, with 77.05% diffraction efficiency and 55.45% mean square error (MSE). The DOE has a high tolerance for wavefront distortion. Within the maximum 3λ phase fluctuation, the diffraction efficiency of the flat-topped spot maintains around 77.05% and the MSE is 57.47%. In the experiment, the designed DOE has been well achieved through the photolithography and the reactive ion etching technique, and the DOE displays a diffraction efficiency of 75.15% and a MSE of 64.78%. When combining with the LDF, a flyer with high velocity and integrity has been demonstrated experimentally, where the flyer velocity is increased by about 1.16 ∼ 1.52 times due to the generation of high-uniform laser beam from DOE.

Correct measurement methodology spatial-energy characteristics of laser beams

A methodology for correct measurements of the spatial and energy characteristics of a laser beam is considered, based on the determination of the initial moments of the spatial intensity distribution in the beam cross section. The classification of radiation fields participating in the measuring process is given: emitted, measured and measured. It is shown that ISO 11146:2005 “Lasers and laser-related equipment. Test methods for laser beam widths, divergence angles and beam propagation ratios, Part 1-3” for measuring the spatial and energy characteristics of laser beams leads to incorrect measurements. This is due to the fact that the recommendations for the application of ISO 11146:2005 do not take into account the dynamic range of the used matrix radiation detectors, and the characteristics of the emitted field of interest to the user turn out to be diverging, which violates the uniformity of measurements. Moreover, the conditions ensuring the convergence of the results are practically impracticable. To solve these problems, it is proposed to establish and regulate the lower level of the dynamic range of measurements of the intensity of the used matrix receivers and to consider the spatial and energy characteristics of the emitted field of interest to the user, depending on the set value of the lower level. It is shown that measurements with this methodology become correct and make it possible to compare the characteristics of laser beams obtained by different array detectors. Formulas are given that take into account the effect of the lower level of the dynamic range of the matrix radiation detectors on the measurement result. These formulas should be recommended for inclusion in the updated edition of the national standard GOST R ISO 11146-2008 “Lasers and laser installations (systems). Methods for measuring widths, divergence angles and propagation coefficients of laser beams. Parts 1-3”.

Fluctuations of the orbital angular momentum of a laser beam registered by a finite-size receiver aperture after propagation through a turbulent atmosphere

The fluctuation characteristics of the orbital angular momentum (OAM) are studied numerically in the computer experiment simulating the propagation of an OAM-carrying laser beam through a turbulent atmosphere and OAM registering by a finite-size receiver aperture. The wave-optics numerical simulation employs the conventional split-operator method (with phase screens) and the Monte Carlo averaging technique. OAM statistical characteristics in the turbulent medium are compared for two employed definitions of the specific (normalized) orbital angular momentum. For the non-vortex Gaussian beam, the correlation between OAM fluctuations and intercepted power is found to be negligibly small at arbitrary size of the receiver aperture. For the vortex Laguerre—Gaussian beam, the correlation between OAM fluctuations and intercepted power is significant (the correlation coefficient can achieve 0.7). In this case, the values of OAM variance for these definitions differ almost twice. It is shown that the OAM value averaged over realizations of the turbulent medium for the aperture size intercepting almost the entire beam power becomes equal to that in the homogeneous medium. As the aperture size decreases, the average OAM value decreases, and when the aperture size tends to zero, it tends to zero as well. The results obtained in the paper can be used in development and improvement of methods for optical transmission of information by optical beams with OAM, as well as in development of optical means for manipulating micron-sized particles.

High-resolution digital spatial control of a highly multimode laser

We developed a rapid and efficient method for generating laser outputs with arbitrary shaped distributions and properties that are needed for a variety of applications. It is based on simultaneously controlling the intensity, phase, and coherence distributions of the laser. The method involves a digital degenerate cavity laser in which a phase-only spatial light modulator and spatial filters are incorporated. As a result, a variety of unique and high-resolution arbitrary shaped laser beams were generated with either a low or a high spatial coherence and with a minimal change in the laser output power. By controlling the phase, intensity, and coherence distributions, a shaped laser beam was efficiently reshaped into a completely different shape after free space propagation. The generation of such laser beams could lead to new and interesting applications.

Analyses of Laser Propagation Noises for TianQin Gravitational Wave Observatory Based on the Global Magnetosphere MHD Simulations

Abstract TianQin is a proposed space-borne gravitational-wave (GW) observatory composed of three identical satellites orbiting around the geocenter with a radius of 105 km. It aims at detecting GWs in the frequency range of 0.1 mHz–1 Hz. The detection of GW relies on the high-precision measurement of optical path length at the 10−12 m level. The dispersion of space plasma can lead to the optical path difference (OPD, Δl) along the propagation of laser beams between any pair of satellites. Here, we study the OPD noises for TianQin. The Space Weather Modeling Framework is used to simulate the interaction between the Earth magnetosphere and solar wind. From the simulations, we extract the magnetic field and plasma parameters on the orbits of TianQin at four relative positions of the satellite constellation in the Earth magnetosphere. We calculate the OPD noise for single link, Michelson combination, and Time-Delay Interferometry (TDI) combinations (α and X). For single link and Michelson interferometer, the maxima of ∣Δl∣ are on the order of 1 pm. For the TDI combinations, these can be suppressed to about 0.004 and 0.008 pm for α and X. The OPD noise of the Michelson combination is colored in the concerned frequency range; while the ones for the TDI combinations are approximately white. Furthermore, we calculate the ratio of the equivalent strain of the OPD noise to that of TQ, and find that the OPD noises for the TDI combinations can be neglected in the most sensitive frequency range of TQ.

Discrete Nonlinear Schrödinger Systems for Periodic Media with Nonlocal Nonlinearity: The Case of Nematic Liquid Crystals

We study properties of an infinite system of discrete nonlinear Schrödinger equations that is equivalent to a coupled Schrödinger-elliptic differential equation with periodic coefficients. The differential equation was derived as a model for laser beam propagation in optical waveguide arrays in a nematic liquid crystal substrate and can be relevant to related systems with nonlocal nonlinearities. The infinite system is obtained by expanding the relevant physical quantities in a Wannier function basis associated to a periodic Schrödinger operator appearing in the problem. We show that the model can describe stable beams, and we estimate the optical power at different length scales. The main result of the paper is the Hamiltonian structure of the infinite system, assuming that the Wannier functions are real. We also give an explicit construction of real Wannier functions, and examine translation invariance properties of the linear part of the system in the Wannier basis.

Laser beam propagation simulations of long-path scintillation and fade with comparison to ground-to-aircraft optical link measurements

An analysis of optical scintillation and fade on long slant-path atmospheric channels is presented via a direct comparison between wave-optics-based numerical simulations and experimental flight data from a ground-to-aircraft optical communication link. In addition to physically modeling the propagation through slant-path atmospheric turbulence, the numerical simulations include simultaneously the effects of mechanical pointing jitter, aperture-averaging, and first-order scattering/absorption models. The power spectral density, fade probability, and mean fade time of the simulated power fluctuations are studied and validated against measurements taken at slant-path distances ranging from 60 to 113 km and aircraft speeds up to 70 m / s.

Investigation of the influence of optical turbulence on DIRCM laser’s jamming effectiveness: A wave-optics approach

Due to their exceptionally large jam-to-signal ratios (J/S), Directed Infrared Countermeasure (DIRCM) systems are the most efficient means for defeating heat seeking missiles. Although many studies have investigated DIRCM systems, the influence of optical turbulence on the jamming code effectiveness is mostly ignored. However, due to optical turbulence caused by the exhaust plume of the air platform and the atmosphere, a DIRCM laser’s beam may be exposed to time-varying intensity fluctuations, which may dramatically reduce the effective J/S at the seeker’s aperture compared to the one at the platform. In addition, previous studies have generally focused on the signal processing stages of seeker heads while ignoring diffractive and aberrative properties of the missile optics. In this study, we employ a wave-optics approach for estimating the jamming code effectiveness under turbulence. Specifically, we investigate time-varying influence of several degrees of optical turbulence on DIRCM laser beams with specified beam quality factors (M2) that are modulated with various jamming patterns. In our model, the DIRCM laser beam first passes through a highly turbulent region, which is caused by the rotor downwash of the exhaust plume of a rotary-wing platform. Next, the DIRCM laser beam propagates in an atmospheric turbulence region for much longer distances (on the order of few km’s) until it reaches the missile. Laser beam propagation in both turbulence regimes is simulated using the split-step method. Subsequently, using the ZEMAX software and its wave-optics-based Physical Optics Propagation (POP) package, we employ a generic model for the optical system of a first-generation spin-scan seeker and obtain the time-dependent intensity profiles of the laser beam at the focal point. Generic models for an uncooled lead-sulfide detector and the following signal processing stages have also been included in the model.

Effect of laser beam propagation through the plasmonic nanoparticles suspension

Gold nanoparticles are excellent light absorbers at the surface plasmon resonance wavelength. This absorption process generates highly energetic electrons near the surface that enhances the local electric field on the gold nanoparticles surface, and results in modification of the refractive index. The present work focuses on interaction of the laser, both near and far from the resonance wavelength, with colloidal solution of plasmonic nanoparticles. For the laser beam interaction, we first prepared the gold nanoparticles by sol gel method and characterized the absorption spectrum in terms of particle size and morphology. The absorption peak in visible range confirmed to the formation of Au nanoparticles. Therefore, a laser at 532 nm was selected to study light matter interaction with Au nanoparticles in solution. The interaction produced diffraction rings, which changed shape over time due to convection of colloidal nanoparticles. In another experiment, a 405 nm laser with the same power produced only a laser spot on the screen. Thus, the 532 nm is closer to the surface plasmon excitation and is responsible for producing a pattern of diffraction rings in the far-field region. The produced diffraction rings provide a very simple and sensitive technique to find out induced nonlinear refractive index for the plasmonic nanoparticles. Finding plasmonic resonances holds importance for variety of applications in plasmonic sensing and these rings could be used to characterize the resonances.

Nanostructured active and photosensitive silica glass for fiber lasers with built-in Bragg gratings.

A nanostructured core silica fiber with active and photosensitive areas implemented within the fiber core is demonstrated. The photosensitivity, active and passive properties of the fiber can be independently shaped with this new approach. We show that discrete local doping with active ions in form of nanorods allow to obtain effective laser action as in case of continuous distribution of the ions in the core. Co-existing discrete photosensitive nanostructure of germanium doped silica determine single-mode performance and allow inscription of highly efficient Bragg grating over the entire core area. Each nanostructure do not degrade performance of other one since physical interaction between active and photosensitive areas are removed. As a proof of concept, we have designed and fabricated the nanostructured, ytterbium single-mode silica fiber laser with the Bragg grating inscribed in the entire core area. We demonstrated fiber laser with good quality of generated laser beam (M2=1.1) with lasing efficiency of 44% and inscribed Bragg grating with 98.5% efficiency and -18 dB contrast.