Beam quality characterization of a radial laser array

Abstract

With the Hermite-Gaussian mode used to describe radial laser arrays and the M²-factor and power in the bucket (PIB) chosen as criteria for characterizing beam quality, a detailed study of beam quality of coherent and incoherent radial laser arrays is made. The closed-form expression for the M²-factor of incoherent radial arrays, which depends upon the Hermite-Gaussian order m, inverse radial fill factor r' and aspect ratio w _0x /w _0y , is derived. Numerical examples are given to illustrate and compare beam quality of coherent and incoherent radial arrays.     

Beam propagation properties of radial laser arrays

A detailed study of phase-locked and non-phase-locked radial laser arrays is presented. The closed-form propagation expressions for the beamlets and the resulting beam are given, which enable us to study beam propagation properties of radial laser arrays for both phase-locked and non-phase-locked cases. Numerical calculation examples are given to illustrate the application of our analytical results and the differences between phase-locked and non-phase-locked radial arrays.     

Dynamics of laser bullet propagation in carbon nanotube array with metal inhomogeneities

The problem of the propagation of a solitary wave—a two-dimensional analog of the so-called laser (light) bullet—in an array of carbon nanotubes with metal inhomogeneities (defects) has been considered. An effective equation for the vector potential of this wave is obtained and numerically studied. It is established that the scattering of a laser bullet on a pair of metal inhomogeneities is accompanied by characteristic “beats” of the electromagnetic field.     

Beam quality after propagation of Nd:YAG laser light through large-core optical fibers

Laser beam characteristics are altered during propagation through large-core optical fibers. The distribution of modes excited by the input laser beam is modified by means of mode coupling on transmission through the fiber, leading to spatial dispersion of the profile and, ultimately and unavoidably, to degradation in the quality of the delivered beam unless the beam is spatially filtered with consequent power loss. Furthermore, a mismatch between the intensity profile of a typical focused high-power laser beam and the profile of the step-index fiber gives rise to additional beam-quality degradation. Modern materials processing applications demand ever higher delivered beam qualities (as measured by a parameter such as M(2)) to achieve greater machining precision and efficiency, a demand that is currently in conflict with the desire to utilize the convenience and flexibility of large-core fiber-optic beam delivery. We present a detailed experimental investigation of the principal beam-quality degradation effects associated with fiber-optic beam delivery and use numerical modeling to aid an initial discussion of the causes of such degradation.     

Study of radial basis collocation method for wave propagation

A numerical method based on radial basis functions and collocation method is proposed for wave propagation. Standard collocation and weighted boundary collocation approaches yield significant errors in wave problems. Therefore, a new method based on explicit time integration scheme that can correct the inaccuracy in the solutions and the errors accumulated in time integration is developed. This method can be easily applied for low and high dimensional wave problems. The stability conditions are obtained and the relationships between control parameters and stability are evaluated. Requirement of collocation points in numerical dispersion is studied and nondispersion condition is formulated. Eigenvalue analysis is investigated to evaluate the effectiveness of radial basis collocation method for solving wave problems. Eigenvalue study with and without imposing the boundary conditions are compared. The influences of shape parameters and distribution of collocation points and source points are presented. Numerical examples are simulated to examine and validate the proposed method.     

Flow-velocity measurements with a laser diode array

To measure flow velocity, a new technique, laser diode array velocimetry, generates multiple laser spots (four or more) separated by short distances (20-100 mum) at the probe volume. Particles that pass through the probe volume generate a signal that is analyzed by a digital signal processor for frequency content. The product of frequency and laser-to-laser spot separation determines the velocity. Rotating wire and wind-tunnel experiments confirm the performance of the new technique. An error analysis showed that the uncertainties in the processed diode array velocimetry signal frequency were less than 0.3%, and uncertainties in the beam-to-beam separation were less than +/-0.05%.     

Beam combination of a linear array: Hermite-Gaussian superposition model

Abstract

Starting from the generalized Huygens-Fresnel diffraction integral and using a Hermite-Gaussian superposition model, an analytical propagation equation of the beam emitted from a linear array is derived and illustrated numerically. Furthermore, the beam quality of the resulting beam in terms of the M ²-factor and power in the bucket (PIB) is analysed. Interestingly, the M ²-factor in the × direction is dependent upon the separation distance of beamlets, but the PIB is not, because the latter is determined by the irradiance distribution in the far field and the bucket size chosen.     

Optimal control of laser beams for propagation through a turbulent medium

Concerning the problem of transmitting a laser beam from one telescope to another telescope through a turbulent medium, it is established that using an adaptive optical system on both telescopes to precompensate an outgoing laser beam based on the aberrations measured on the received laser beam leads to an iteration that maximizes the transmission (neglecting attenuation losses) of laser power between the telescopes. Simulation results are presented demonstrating the effectiveness of this technique when the telescopes are equipped with either phase-only or full-wave compensation systems. Simulation results are shown that indicate that for a uniform distribution of the strength of turbulence, 95% transmission of laser power is attained when both telescopes can achieve full-wave compensation provided that the aperture diameter D of the two telescopes is greater than twice the Fresnel length square root of lambdaL, where A is the wavelength of propagation and L is the distance between the two telescopes.     

Average spreading of a radial gaussian beam array in non-Kolmogorov turbulence

The analytical expression for the rms beam width of the radial gaussian beam array propagating in non-Kolmogorov turbulence is derived, where the coherent combination is considered. The influences of the beam number, the generalized exponent, and the ring radius on the rms beam width are investigated. The results indicate that the rms beam width depends greatly on the generalized exponent and the beam number. Further, an optimum ring radius, which leads to a minimum beam width, is proved to exist within a certain traveling distance and the optimum ring radius increases when the beam number increases.     

Linewidth reduction in a large-smile laser diode array

We present theory and simulations for a spectral narrowing scheme for laser diode arrays (LDAs) that employs optical feedback from a diffraction grating. We calculate the effect of the so-called smile of the LDA and show that it is possible to reduce the effect by using a cylindrical lens set at an angle to the beam. The scheme is implemented on a 19-element LDA with smile of 7.6 microm and yields frequency narrowing from a free-running width of 2 to 0.15 nm. The experimental results are in good agreement with the theory.     

Beam propagation in an active planar waveguide with an angled bragg grating (α laser)

Abstract

In the angled Bragg grating semiconductor laser (α laser), light does not propagate at a right angle with respect to the two-dimensional corrugated grating of the planar waveguide. A closed-form solution of the coupled-wave theory is used to describe the propagation of both the wave fields with different directions. A constant gain is included. Some properties of the main wave and of the secondary wave are described, which are of interest for the α laser. Additional losses occur during facet reflection of the secondary wave.     

Simulation of laser propagation in a turbulent atmosphere

The split-step Fourier-transform algorithm for numerical simulation of wave propagation in a turbulent atmosphere is refined to correctly include the effects of large-scale phase fluctuations that are important for imaging problems and many beam-wave problems such as focused laser beams and beam spreading. The results of the improved algorithm are similar to the results of the traditional algorithm for the performance of coherent Doppler lidar and for plane-wave intensity statistics because the effects of large-scale turbulence are less important. The series solution for coherent Doppler lidar performance converges slowly to the results from simulation.     

Femtosecond laser pulse propagation in a uniaxial crystal

Abstract

The wave equation describing the vector propagation of a femtosecond laser pulse of a few optical cycles in a uniaxial crystal is solved numerically by the method of unidirectional waves. Propagation of the pulse in the direction normal to the optical axis is studied, taking into account both second- and third-order nonlinearities of the crystal. Conversion efficiency as a function of crystal length, pump intensity and pulse duration is studied. As an example, the propagation of femtosecond laser pulse of τ = 10 fs duration at λ = 810 nm in a LiNbO₃ crystal 12 μm thick is studied numerically.     

In-plane problem for wave propagation through elastic solids with a periodic array of cracks

Summary In the context of wave propagation in damaged (elastic) solids, an analytical method previously introduced for scalar problems, is now applied to study the (vector) problem for normal penetration of a longitudinal plane wave into a periodic array of collinear cracks. Reduced the problem to an integral equation holding over the openings, an approximation of one-mode type leads to analytical solutions and then to explicit representations for the wave fields and the scattering parameters. Some graphs will finally compare our results with the numerical ones by other authors.     

Beam profile measurement of a solar-pumped iodine laser

Beam profile measurements have been made as a function of time within the laser pulse and C2F5I pressure. Measurements indicate that the profile is determined directly by the optical excitation volume, produced by the solar simulator, and that media distortion plays a minor role compared to the build up of quenching species during the lasing pulse.     

Infrared optical constants for CO2 laser waveguide materials

The infrared optical constants of a number of commercially available glasses and ceramics have been determined by Kramers-Krönig analyses of the reflectance spectra of the materials at near normal incidence. The data derived, the refractive indexn, and extinction coefficientK, have been further analysed to provide an assessment of these materials as hollow waveguides at mid-infrared frequencies. The results demonstrate that the frequency dependence of waveguide transmission is a feature of anomalous dispersion. Furthermore, in the case of beryllia and alumina ceramics, the high transmissions predicted in straight guide at 10.6m can be attributed to the low refractive indices measured for these materials. Some experimental data are presented which substantiate the frequency characteristics of the predicted waveguide transmission.     

Interferometer for optical coupling and mode selection in a multichannel laser array

A theoretical consideration is presented of the optical coupling and selection of laser array modes by the use of a developed Lummer-Gehrcke interferometer as a resonator reflector. Control of the mirror reflection of the proposed interferometer permits laser power to be redistributed through channels on the outlet resonator mirror; in particular, it makes it possible to lead power out of the resonator by a single beam. In this way it is possible to diminish the sidelobes in the far-field radiation profile of multichannel lasers and to raise the efficiency of the optical coupling of the laser array with waveguides and fibers. This method may be used for the redistribution of laser power on the outlet mirror in striped lasers as well.     

Beam propagation in parabolically tapered graded-index waveguides

To a good approximation, the electromagnetic-propagation characteristics of graded-index waveguides can be written in terms of polynomial-Gaussian modes. For uniform quadratic-index waveguides the behavior of these modes is well known. However, there are sometimes practical reasons for using tapered waveguides, but detailed propagation solutions are known for only a few specific taper functions. The parabolic taper is perhaps the most important special case, and the solution-generating techniques that we generalize are used to obtain analytic solutions for this case.