Showing papers on "Gaussian beam published in 1995"
TL;DR: The vacuum beat wave accelerator (VBWA) concept is proposed and analyzed, and acceleration by two crossed beams is correctly described by the Lawson-Woodward theorem, and single-particle simulations confirm that substantial energy gains are possible and that optical components are not needed near the focal region.
Abstract: Several features of vacuum laser acceleration are reviewed, analyzed, and discussed, including electron acceleration by two crossed laser beams and acceleration by a higher-order Gaussian beam. In addition, the vacuum beat wave accelerator (VBWA) concept is proposed and analyzed. It is shown that acceleration by two crossed beams is correctly described by the Lawson-Woodward (LW) theorem, i.e., no net energy gain results for a relativistic electron interacting with the laser fields over an infinite interaction distance. Finite net energy gains can be obtained by placing optical components near the laser focus to limit the interaction region. The specific case of a higher-order Gaussian beam reflected by a mirror placed near focus is analyzed in detail. It is shown that the damage threshold of the mirror is severely limiting, i.e., substantial energy gains require very high electron injection energies. The VBWA, which uses two copropagating laser beams of different frequencies, relies on nonlinear ponderomotive forces, thus violating the assumptions of the LW theorem. Single-particle simulations confirm that substantial energy gains are possible and that optical components are not needed near the focal region.
264 citations
TL;DR: The relativistic dynamics of electrons subjected to the electromagnetic field of an intense, ultrashort laser pulse in vacuum is studied theoretically and the relation between the scattering angle and the escape energy is derived analytically from the conservation of canonical momentum and energy in the photon field.
Abstract: The relativistic dynamics of electrons subjected to the electromagnetic field of an intense, ultrashort laser pulse in vacuum is studied theoretically. The effects of both finite pulse duration and beam focusing are taken into account. It is found that when the quiver amplitude of the electrons driven by the laser field exceeds the focal spot radius of a Gaussian beam, the restoring force acting on the charge decays exponentially, and the electrons are scattered away from the focus. This physical process, known as ponderomotive scattering, effectively terminates the interaction within a laser wavelength, and the electrons can escape with very high energy, as the normalized laser field is of the order of or greater than unity. The relation between the scattering angle and the escape energy is derived analytically from the conservation of canonical momentum and energy in the photon field. For a linearly polarized laser field, the interaction produces two jets of high energy electrons. The theory is supplemented by detailed two-dimensional computer simulations.
194 citations
TL;DR: Some numerical results that describe the scattering patterns and the radiation-pressure behavior when an incident Gaussian beam or a plane wave impinges on a multilayered sphere are presented.
Abstract: A solution is given for the problem of scattering of an arbitrary shaped beam by a multilayered sphere. Starting from Bromwich potentials and using the appropriate boundary conditions, we give expressions for the external and the internal fields. It is shown that the scattering coefficients can be generated from those established for a plane-wave illumination. Some numerical results that describe the scattering patterns and the radiation-pressure behavior when an incident Gaussian beam or a plane wave impinges on a multilayered sphere are presented.
159 citations
TL;DR: Good agreement between theory and experiment is obtained, and it is found that the terahertz beam can be represented by a Gaussian beam emitted from a circular aperture equal to the diameter of the lens.
Abstract: We report on investigations of the angular distribution of the radiation emitted from a terahertz antenna system equipped with a truncated spherical silicon lens. The pattern is calculated by wide-angle interference principles and Huygens-Fresnel diffraction theory. Experimental determination of the radiation pattern is performed by spatially resolved terahertz time-domain spectroscopy. Good agreement between theory and experiment is obtained, and we find that the terahertz beam can be represented by a Gaussian beam emitted from a circular aperture equal to the diameter of the lens.
132 citations
TL;DR: In this article, the authors reported the generation of three-dimensional bright spatial solitary waves by the breakup of an optical vortex in a saturable self-focusing nonlinear medium, where an elliptical Gaussian beam from a Ti:sapphire laser containing a singly charged on-axis vortex was passed through a non-linear medium consisting of rubidium vapor at low concentrations.
Abstract: We report the generation of three-dimensional bright spatial solitary waves by the breakup of an optical vortex in a saturable self-focusing nonlinear medium. An elliptical Gaussian beam from a Ti:sapphire laser containing a singly charged on-axis vortex was passed through a nonlinear medium consisting of rubidium vapor at low concentrations. The modulational instability resulted in the formation of a pair of out-of-phase solitonlike beams, which spiraled away from each other during propagation as a result of the repulsive nature of their interaction. The rate of rotation and separation of the two soliton beams could be controlled by the parameters of the medium and the laser intensity. Numerical analysis of the propagation based on a model nonlinearity corresponding to a strongly saturated two-level system showed good quantitative agreement with the experimental data.
120 citations
TL;DR: In this paper, a simulation tool based on the finite-difference time-domain (FDTD) technique is developed to model the electromagnetic interaction of a focused optical Gaussian beam in two dimensions incident on a simple model of a corrugated dielectric surface plated with a thin film of realistic metal.
Abstract: A simulation tool based on the finite-difference time-domain (FDTD) technique is developed to model the electromagnetic interaction of a focused optical Gaussian beam in two dimensions incident on a simple model of a corrugated dielectric surface plated with a thin film of realistic metal The technique is a hybrid approach that combines an intensive numerical method near the surface of the grating, which takes into account the optical properties of metals, with a free-space transform to obtain the radiated fields A description of this technique is presented along with numerical examples comparing gratings made with realistic and perfect conductors In particular, a demonstration is given of an obliquely incident beam focused on a uniform grating and a normally incident beam focused on a nonuniform grating The gratings in these two cases are coated with a negative-permittivity thin film, and the scattered radiation patterns for these structures are studied Both TE and TM polarizations are investigated Using this hybrid FDTD technique results in a complete and accurate simulation of the total electromagnetic field in the near field as well as in the far field of the grating It is shown that there are significant differences in the performances of the realistic metal and the perfect metal gratings
116 citations
TL;DR: In this article, the authors extend the Gaussian beam migration (GBM) method to work for 2-D migration in generally anisotropic inhomogeneous media, which is based on the solution of the wave equation in ray-centered coordinates.
Abstract: Gaussian beam migration (GBM), as it is implemented today, efficiently handles isotropic inhomogeneous media. The approach is based on the solution of the wave equation in ray‐centered coordinates. Here, I extend the method to work for 2-D migration in generally anisotropic inhomogeneous media. Extension of the Gaussian‐beam method from isotropic to anisotropic media involves modification of the kinematics and dynamics in the required ray tracing. While the accuracy of the paraxial expansion for anisotropic media is comparable to that for isotropic media, ray tracing in anisotropic media is much slower than that in isotropic media. However, because ray tracing is just a small portion of the computation in GBM, the increased computational effort in general anisotropic GBM is typically only about 40%. Application of this method to synthetic examples shows successful migration in inhomogeneous, transversely isotropic media for reflector dips up to and beyond 90°. Further applications to synthetic data of lay...
115 citations
TL;DR: The analytical form of the beam-shape coefficients makes evident the fact that the excitation rate of morphology-dependent resonances is greatly enhanced for far off-axis incidence of the Gaussian beam.
Abstract: The localized model of the beam-shape coefficients for Gaussian beam-scattering theory by a spherical particle provides a great simplification in the numerical implementation of the theory. We derive an alternative form for the localized coefficients that is more convenient for computer computations and that provides physical insight into the details of the scattering process. We construct a FORTRAN program for Gaussian beam scattering with the localized model and compare its computer run time on a personal computer with that of a traditional Mie scattering program and with three other published methods for computing Gaussian beam scattering. We show that the analytical form of the beam-shape coefficients makes evident the fact that the excitation rate of morphology-dependent resonances is greatly enhanced for far off-axis incidence of the Gaussian beam.
115 citations
TL;DR: The modified localized approximation to evaluate these coefficients for a focused Gaussian beam is presented and a new description of Gaussian beams, called standard beams, is introduced.
Abstract: In the framework of generalized Lorenz-Mie theory, laser beams are described by sets of beam-shape coefficients. The modified localized approximation to evaluate these coefficients for a focused Gaussian beam is presented. A new description of Gaussian beams, called standard beams, is introduced. A comparison is made between the values of the beam-shape coefficients in the framework of the localized approximation and the beam-shape coefficients of standard beams. This comparison leads to new insights concerning the electromagnetic description of laser beams. The relevance of our discussion is enhanced by a demonstration that the localized approximation provides a very satisfactory description of top-hat beams as well.
104 citations
TL;DR: A theoretical procedure in which a spheroidal coordinate separation-of-variables solution is used is developed for the determination of the internal and the near-surface electromagnetic fields for an arbitrary monochromatic field that is incident upon a homogeneous spheoidal particle.
Abstract: A theoretical procedure in which a spheroidal coordinate separation-of-variables solution is used is developed for the determination of the internal and the near-surface electromagnetic fields for an arbitrary monochromatic field that is incident upon a homogeneous spheroidal particle. Calculations are presented for both the prolate and the oblate geometries, demonstrating the effects of particle size, particle axis ratio, and the orientation and character (plane-wave and focused Gaussian beam) of the incident field on the resultant internal and near-surface electromagnetic-field distributions.
89 citations
TL;DR: The aim of this Letter is to show experimentally that a simple nonlinear Goos-Hanchen effect can be isolated in the case of total reAection at the interface between a linear and a negative Kerr-type nonlinear medium, without any visible deformation of the incident Gaussian beam.
Abstract: The nonlinear Goos-H\"anchen effect is experimentally isolated for the total reflection of a Gaussian beam at an interface between a linear medium and a negative Kerr-type nonlinear medium. The evolution of this nonlinear spatial shift versus light intensity is measured for both TE and TM polarizations. The results are in good agreement with a simple model based on nonlinear Artmann's formulas.
TL;DR: Analytical expressions for the width, far-field divergence, crossed moment, and generalized beam-quality parameter of a coherent, lowest-order Gaussian beam propagating through hard-edged slits are given in terms of the size of the opening and of the position of the aperture plane with respect to the beam waist.
Abstract: Analytical expressions for the width, far-field divergence, crossed moment, and generalized beam-quality parameter of a coherent, lowest-order Gaussian beam propagating through hard-edged slits are given in terms of the size of the opening and of the position of the aperture plane with respect to the beam waist. Some optimization criteria of these beam-shape parameters are also inferred.
TL;DR: In this paper, a 3 × 3 transfer-matrix method is developed to propagate off-axis Gaussian beams in astigmatic optical systems that may include tilted, displaced, or curved optical elements.
Abstract: A novel 3 × 3 transfer-matrix method is developed to propagate off-axis Gaussian beams in astigmatic optical systems that may include tilted, displaced, or curved optical elements. Unlike in a previous generalized ray matrix formalism, optical elements that possess gain or loss such as Gaussian apertures, complex lenslike media, and amplifiers are included; and a new beam transformation is found. In addition, a novel exponential variable-reflectivity mirror, which displaces a Gaussian beam without changing its spot size, and a complex prismlike medium are introduced.
TL;DR: A generalization of the Gaussian beam is obtained by introducing a complex-valued shift in the transverse dimension, which has a Gaussian intensity distribution with width varying as an ordinary Gaussianbeam, but whose peak traces an inclined linear trajectory.
Abstract: A generalization of the Gaussian beam is obtained by introducing a complex-valued shift in the transverse dimension. The resulting beam has a Gaussian intensity distribution with width varying as an ordinary Gaussian beam, but whose peak traces an inclined linear trajectory. The wave fronts are displaced laterally in a sheared fashion. This generalized beam preserves its form after passing through arbitrary paraxial optical components, even if they are decentered. The peak-intensity line is modified by such systems as if it were a ray.
TL;DR: An analytical treatment for the propagation of astigmatic Gaussian beams in Kerr media is presented in this article, which allows us to calculate in closed form the nonlinear variations of the spot size and the radius of curvature.
Abstract: An analytical treatment for the propagation of astigmatic Gaussian beams in Kerr media is presented. This method, which is valid to the first order in the beam power, allows us to calculate in closed form the nonlinear variations of the spot size and the radius of curvature. This formalism is applied to the calculation of the self-consistent Gaussian mode of an astigmatic resonator with a Kerr medium, such as those used for Kerr-lens mode-locked lasers. Theoretical predictions are confirmed by the experimental results obtained with a femtosecond Ti:sapphire laser. In particular, the design of an optimized resonator permits self-starting of the mode-locking mechanism.
TL;DR: Numerical simulations of beam propagation in polydiacetylene para-toluene sulfonate (PTS) are reported, and stable self-trapping is demonstrated and a new phenomenon in which a Gaussian input beam evolves into an expanding spatial ring is demonstrated.
Abstract: Numerical simulations of two-dimensional beam propagation in polydiacetylene para-toluene sulfonate measured values for n2 > 0 and n3 < 0, where Δn = n2I + n3I2, predict stable self-trapping and a new phenomenon in which a spatial ring evolves from a Gaussian input beam. We interpret the numerical results theoretically, using the variational model of nonlinear Gaussian beam propagation.
TL;DR: In this article, the authors report the state of the art in the development of high power millimetre wave sources and windows and discuss the components and the characteristics of TEM00 and HE11 transmission systems and antennas.
TL;DR: In this paper, the authors investigated the scattering of an off-axis incident Gaussian beam by a homogeneous dielectric cylinder at normal incidence, based on the exact solution of the Helmholtz equation in circular cylindrical coordinates.
Abstract: For the development of new kinds of refractive-index sensors for capillary electrophoresis, we investigated the scattering of an off-axis incident Gaussian beam by a homogeneous dielectric cylinder at normal incidence. The numerical calculations are based on the exact solution of the Helmholtz equation in circular cylindrical coordinates. Contrary to the procedures with geometrical and paraxial models, this procedure gives accurate results even when the beam dimensions are of the order of the wavelength of light and when the beam diameter is greater than the diameter of the dielectric cylinder. This rigorous electromagnetic treatment is verified by experimental measurements for cylinders with diameters from 5 to 100 μm.
TL;DR: The evolution of a complex beam width parameter g describing focusing or defocusing of a paraxial Gaussian beam is considered as the cause of an additional topological phase of the electromagnetic field associated with the beam.
Abstract: The evolution of a complex beam width parameter g describing focusing or defocusing of a paraxial Gaussian beam is considered as the cause of an additional topological (Berry) phase of the electromagnetic field associated with the beam. It is pointed out that the well-known Gouy phase is a special case of such a phase that should arise in general in all symplectic systems.
TL;DR: Fast Fourier beam-propagation methods for simulating the roles of internal refractive effects and external propagation from nonlinear media are introduced in this article, which is applied to model picosecond Z-scan measurements for the induced absorber, the dye Chloro-Aluminum Phthalocyanine, at 532 nm.
Abstract: Fast Fourier beam–propagation methods (BPM’s) for simulating the roles of internal refractive effects and external propagation from nonlinear media are introduced. These techniques are applied to model picosecond Z-scan measurements for the induced absorber, the dye Chloro-Aluminum Phthalocyanine, at 532 nm. Within the thin-sample approximation an incident Gaussian beam is taken to experience a change in phase profile on propagation through the medium but remains of Gaussian amplitude profile. Outside this approximation one must determine both the phase and the amplitude profiles at the sample exit face that are due to the influence of nonlinear refraction (and nonlinear absorption) on the beam propagating through the medium. The BPM technique allows this to be achieved efficiently, and the external propagation technique enables a single discrete fast Fourier transform to be used to describe the subsequent external propagation of the non-Gaussian-shaped beams. The analysis is especially useful for such self-enhancing nonlinearities as one would wish to exploit in optical limiting.
TL;DR: In this article, the variance and the power spectral density of turbulence-induced log-amplitude fluctuations were derived for Gaussian-beam waves in the regime of weak scattering, including effects that are due to turbulence strength variations along the propagation path, offset of the observation point from the beam axis and sensitivity to focus and beam diameter.
Abstract: Expressions for the variance and the power spectral density of turbulence-induced log-amplitude fluctuations are derived for Gaussian-beam waves in the regime of weak scattering. This formulation includes effects that are due to turbulence strength variations along the propagation path, offset of the observation point from the beam axis, and sensitivity to focus and beam diameter. Comparison of theoretical results with observed scintillation during experiments with a laser-illuminated satellite reveals good agreement.
01 May 1995
TL;DR: In this article, the state of the art in gyrotron, window, transmission line and antenna development and discusses possibilities of ECH systems cost reduction, which can be achieved by a closed, highly overmoded, circumferentially corrugated or dielectrically lined tubular HE 1,1 -hybrid mode waveguide and open quasi-optical TEM 0,0 transmission through a gaussian beam waveguide using focusing reflectors as phase-correcting elements.
Abstract: Electron cyclotron heating (ECH) is one of the major candidates for heating and current drive on ITER (170 GHz) and W7-X (140 GHz). ECH is extremely attractive from physics and reactor engineering points of view, offering start-up assist, efficient and localized power deposition, simple and compact launching structures with high injected power density, and a simple interface with shielding and blanket. High unit power (1 MW or greater) and high efficiency (35% or greater) single-mode continuous-wave (CW) gyrotron oscillators are under development in order to reduce significantly the systems costs by reducing the size of the auxiliary support systems. 140 GHz gyrotrons with 0.55 MW output power in the Gaussian free-space TEM 0,0 mode with a pulse length τ up to 3.0 s and efficiency η of 42% are already commercially available (Gycom). Improved internal quasi-optical mode transducers generate the TEM 0,0 output mode with efficiencies of 90–95% and separate the electron beam from the r.f. beam, thus allowing the use of large CW relevant depressed collectors for energy recovery. Tube efficiencies around 50% have been already achieved at JAERI and KfK. Face cooled double-disk sapphire windows, cryogenically edge-cooled single-disk sapphire windows (liquid-nitrogen, liquid-neon or liquid-helium cooling), distributed windows (metal or ceramics) as well as diamond and silicon windows are under investigation in order to solve the window problem. Long-distance high-power millimeter wave transmission from the source to the plasma device with very low ohmic losses and high mode purity can be accomplished by (1) a closed, highly overmoded, circumferentially corrugated or dielectrically lined, tubular HE 1,1 -hybrid mode waveguide and (2) open quasi-optical TEM 0,0 transmission through a gaussian beam waveguide using focusing reflectors as phase-correcting elements. This paper reports the state of the art in gyrotron, window, transmission line and antenna development and discusses possibilities of ECH systems cost reduction.
TL;DR: In this article, it was shown that the optical theorem is not valid when an electromagnetic wave with some degree of amplitude rolloff in the transverse direction is scattered by a spherical particle, and the extinction cross section may be written as an infinite series in powers of the reciprocal of the beam width.
Abstract: It is shown that when an electromagnetic wave with some degree of amplitude rolloff in the transverse direction is scattered by a spherical particle, the optical theorem is not valid. For such shaped beams the extinction cross section may be written as an infinite series in powers of the reciprocal of the beam width. The imaginary part of the forward-scattering amplitude is shown to be the first term in this series. Two approximations to the extinction cross section are presented for the special case of Gaussian-beam scattering. The first one is based on the dominance of diffraction in the forward direction for w0 ≳ a, where w0 is the beam half-width and a is the target particle radius. The second approximation, valid for w0 ≲ a, is based on transmission-compensating field interference.
TL;DR: In this paper, a periodic domain structure in a 0.5 mm thick slab of LiTaO3 crystal was fabricated by applying an external pulsed field at room temperature, and a third-order quasi-phase matched second-harmonic blue-light generation was demonstrated by free propagation of a 862.6 nm fundamental Gaussian beam in a 4 mm long LTAO3 slab, with a single pulse energy of 0.072 mJ and an energy conversion efficiency of 5.7%.
Abstract: We fabricated a periodic domain structure in a 0.5 mm thick slab of LiTaO3 crystal by applying an external pulsed field at room temperature. Using a pulse dye laser with a pulsewidth of 8 ns and a repetition rate of 10 Hz, third‐order quasi‐phase‐matched second‐harmonic blue‐light generation is demonstrated by free propagation of a 862.6 nm fundamental Gaussian beam in a 4 mm long LiTaO3 slab, with a single pulse energy of 0.072 mJ and an energy conversion efficiency of 5.7%.
TL;DR: In this paper, the effects of a birefringent rod on the beam quality of a Gaussian TEM00 laser beam were studied and analytical expressions for the beam parameters at the output plane of a rod amplifier were derived.
Abstract: The effects produced by a birefringent rod on the beam quality factor,M
infr
sup2
, of a Gaussian TEM00 laser beam are studied. Analytical expressions for the beam parameters at the output plane of a rod amplifier are derived. The theory predicts that the beam quality degrades rapidly with the heat power dissipated in the rod.
TL;DR: In this article, the authors extend Sylvester's theorem to a broader class of optics-related matrices, such as lossy birefringent filters and misaligned lenses and mirrors.
Abstract: Sylvester’s theorem is often applied to problems involving light propagation through periodic optical systems represented by unimodular 2 × 2 transfer matrices. We extend this theorem to apply to broader classes of optics-related matrices. These matrices may be 2 × 2 or take on an important augmented 3 × 3 form. The results, which are summarized in tabular form, are useful for the analysis and the synthesis of a variety of optical systems, such as those that contain periodic distributed-feedback lasers, lossy birefringent filters, periodic pulse compressors, and misaligned lenses and mirrors. The results are also applicable to other types of system such as periodic electric circuits with intracavity independent sources, high-energy particle accelerators, and periodic computer graphics manipulations that may include object translation. As an example, we use the 3 × 3 form of Sylvester’s theorem to examine Gaussian beam propagation in a misaligned resonator.
TL;DR: The challenges and obstacles of typical optical profiles with regard to e-beam writing technology are described and different writing strategies for the fabrication of binary, multilevel and continuous surface profiles are demonstrated.
Abstract: The fabrication of surface profiles may become an interesting technology in the field of micromachining. Recently, surface profiles are known and widely used in optics, especially in diffractive optics. E-beam lithography is a suitable technology for the fabrication of such profiles. This paper gives an overview about the experiences and results achieved at the Friedrich-Schiller-University Jena, Germany, on this field for some years. At first we describe the challenges and obstacles of typical optical profiles with regard to e-beam writing technology. After introducing our two different e-beam writers ZBA 23H (variable shaped beam) and LION LV1 (high resolution gaussian beam) we demonstrate different writing strategies for the fabrication of binary, multilevel and continuous surface profiles. Variable energy writing is a new technology extending the abilities of the well-known variable dose writing. Some selected examples of interesting patterns and profiles, as holograms, gear wheels, lenses, gratings and encoder discs, demonstrate different aspects to be considered and the possible solutions for some problems.© (1995) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
TL;DR: The experimental observations reveal that the total intensity profile about the forward direction is quite sensitive to particle axial position within a Gaussian beam, which is significant when the ratio of the beam to the particle diameter is less than approximately 5:1.
Abstract: The forward scattering of a Gaussian laser beam by a spherical particle located along the beam axis is analyzed with the generalized Lorenz-Mie theory (GLMT) and with diffraction theory. Forwardscattering and near-forward-scattering profiles from electrodynamically levitated droplets, 51.6 µm in diameter, are also presented and compared with GLMT-based predictions. The total intensity in the forward direction, formed by the superposition of the incident and the scattered fields, is found to correlate with the particle-extinction cross section, the particle diameter, and the beam width. Based on comparison with the GLMT, the diffraction solution is accurate when beam widths that are approximately greater than or equal to the particle diameter are considered and when large particles that have an extinction efficiency near the asymptotic value of 2 are considered. However, diffraction fails to describe the forward intensity for more tightly focused beams. The experimental observations, which are in good agreement with GLMT-based predictions, reveal that the total intensity profile about the forward direction is quite sensitive to particle axial position within a Gaussian beam. These finite beam effects are significant when the ratio of the beam to the particle diameter is less than approximately 5:1. For larger beam-to-particle-diameter ratios, the total field in the forward direction is dominated by the incident beam.
TL;DR: In this article, a one photon photoensitivity process was used to create a channel waveguide within a uniform slab of germano-silicate glass from an incident Gaussian beam on the time scale of a few minutes.
TL;DR: The theory of scattering of a first-order Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation is presented in this paper, where a component of the theory is the use of the theories of distributions.
Abstract: The theory of scattering of a first-order Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation is presented. A component of the theory is the use of the theory of distributions.