Paraxial Formalism Research Articles

Quadruple Gaussian Laser Beam Profile Dynamics in Collisionless Magnetized Plasma

This paper presents an investigation of self-focusing of a quadruple Gaussian laser beam in collisionless magnetized plasma. The nonlinearity due to ponderomotive force which arises on account of nonuniform intensity distribution of the laser beam is considered. The nonlinear partial differential equation governing the evaluation of complex envelope in the slowly varying envelope approximation is solved using a paraxial formalism. The self-focusing mechanism in magnetized plasma, in the presence of self-compression mechanism will be analyzed in contrast to the case in which it is absent. It can be observed that, in case of ponderomotive nonlinearity, the self-compression mechanism obstructs the pulse self-focusing above a certain intensity value. The effect of an external magnetic field is to generate pulses with smaller spot size and shorter compression length. The lateral separation parameter and the initial intensity of the laser beam play a crucial role on focusing and compression parameters. Also, the three-dimensional analysis of pulse propagation is presented by coupling the self-focusing equation with the self-compression one.

Nonparaxial Cartesian and azimuthally symmetric waves with concentrated wavevector and frequency spectra

In this paper, we develop a theoretical analysis to efficiently handle superpositions of waves with concentrated wavevector and frequency spectra, allowing an easy analytical description of fields with interesting transverse profiles. First, we analyze an extension of the paraxial formalism that is more suitable for superposing these types of waves, as it does not rely on the use of coordinate rotations combined with paraxial assumptions. Second, and most importantly, we leverage the obtained results to describe azimuthally symmetric waves composed of superpositions of zero-order Bessel beams with close cone angles that can be as large as desired, unlike in the paraxial formalism. Throughout the paper, examples are presented, such as Airy beams with enhanced curvatures, nonparaxial Bessel–Gauss beams and circular parabolic-Gaussian beams (which are based on the Cartesian parabolic-Gaussian beams), and experimental data illustrates interesting transverse patterns achieved by superpositions of beams propagating in different directions.

Spin and orbital angular momentum propagation in anisotropic media: theory

This paper is devoted to a study of the propagation of light beams carrying orbital angularmomentum in optically anisotropic media. We first review some properties of homogeneousanisotropic media, and describe how the paraxial formalism is modified in order to proceedwith a new approach dealing with the general setting of paraxial propagation alonguniaxial inhomogeneous media. This approach is suitable for describing space-variantoptical-axis phase plates.

Relativistic laser pulse compression in plasmas with a linear axial density gradient

The self-compression of a relativistic Gaussian laser pulse propagating in a non-uniform plasma is investigated. A linear density inhomogeneity (density ramp) is assumed in the axial direction. The nonlinear Schrödinger equation is first solved within a one-dimensional geometry by using the paraxial formalism to demonstrate the occurrence of longitudinal pulse compression and the associated increase in intensity. Both longitudinal and transverse self-compression in plasma is examined for a finite extent Gaussian laser pulse. A pair of appropriate trial functions, for the beam width parameter (in space) and the pulse width parameter (in time) are defined and the corresponding equations of space and time evolution are derived. A numerical investigation shows that inhomogeneity in the plasma can further boost the compression mechanism and localize the pulse intensity, in comparison with a homogeneous plasma. A 100 fs pulse is compressed in an inhomogeneous plasma medium by more than ten times. Our findings indicate the possibility for the generation of particularly intense and short pulses, with relevance to the future development of tabletop high-power ultrashort laser pulse based particle acceleration devices and associated high harmonic generation. An extension of the model is proposed to investigate relativistic laser pulse compression in magnetized plasmas.

Use of a novel wide-angle FD-BPM for loss performance assessment in randomly perturbed photonic crystal fibers

A novel wide-angle finite-difference beam-propagation method is applied to the analysis of confinement losses in photonic crystal fibers (PCFs). The method is formulated in terms of the locally one-dimensional (LOD) technique and Pade polynomials. It was found that the wide-angle approach allows an acceleration of the convergence rate of up to 50% for the effective-index imaginary part when compared to paraxial formalism. In this framework, an important aspect of PCF structures, namely, the random structural variation of the hole radius and pitch, which occurs during the fabrication process of these devices, is investigated in this paper. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 45: 568–573, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20882

Derivation of a modified paraxial formalism for two-dimensional trajectories in electron and ion sources of non-simple geometries

A modified paraxial formalism has been developed which describes two-dimensional charged particle beam dynamics in electron and ion sources with pointed or needle-type geometries. A Hamiltonian formalism, and a more exact treatment of energy conservation is used to derive the modified paraxial equation for two-dimensional trajectories in systems with axially symmetric prolate-spheroidal beams. Calculations have been done for a gallium field emission liquid metal ion source modeled by a hyperboloid of revolution and planar extractor. Two important conclusions emerge from these calculations: i) The dominant effect of space-charge, for source geometries with small radii of curvature, occurs in the region close to the apex (<0.05 μn) and ii) beam divergence has a strong dependence on geometry. This latter effect is a consequence of large two-dimensional field gradients near the apex of sources with needle-type or pointed geometry.

Use of a modified paraxial formalism for particle beam dynamics: Application to liquid metal ion sources

A modified paraxial formalism has been developed and used to describe two-dimensional ion beam dynamics in liquid metal ion sources with pointed geometries. It has been shown that appreciable differences exist between first-order and modified paraxial theory in the calculation of beam dispersion. For a singly charged ion the effects of mass and initial energies on calculated trajectories in the modified theory are demonstrated. Finally, it is argued that only the modified theory can accurately describe within the paraxial approximation the ion trajectories close to the apex of needle-type liquid metal ion sources.