Fundamental Gaussian Beam Research Articles

Forward-scattering analysis in a focused-beam system

The forward scattering from an arbitrarily shaped cylinder is characterized by its induced field ratio (IFR). This paper describes how a focused-beam system is used to determine the scattering characteristics of an arbitrary-shaped cylinder. The fields of the transmitting and receiving antennas, as well as the scattered field from the cylinder, are described by equivalent fundamental Gaussian beams. An analytical procedure based on the computation of the coupling between the Gaussian beams in the focused-beam system is used to determine the IFR of the cylinder. The results obtained by this method verify well with the scattering characteristics computed analytically or numerically by the method of moments or finite-elements method.

Second-harmonic generation in biaxial crystals for a focused fundamental Gaussian laser beam: application to ()2-α-(methylbenzylamino)- 5-nitropyridine single crystals

The second-harmonic nonlinear optical susceptibility tensor of (-)2-α-(methylbenzylamino)-5-nitropyridine single crystals has been calculated from electric-field-induced second-harmonic generation (SHG) data and the oriented-gas model. From this tensor the calculated value of the maximum effective nonlinear optical susceptibility deff for phase-matched SHG was found to be 6.5 pm V-1. Calculations along the whole of the phase-matching locus show that the highest value of deff is in the region of the lowest values of the second-harmonic wave beam walk-off angle. The walk-off angle of the fundamental is approximately five times smaller. A theory necessary for the optimization of SHG efficiency in biaxial crystals is developed and it is shown that, for the range of crystal lengths and beam walk-off angles available, the criteria for the selection of the parameters w0,z0, and Δk for optimization of the second-harmonic signal are the same in biaxial and uniaxial crystals. The optimal configuration for the highest second-harmonic efficiency on the phase-matching locus has been determined. The maximum SHG figure of merit, P2ω(l)/Pω2(0), is found to be 3.7×10-3 W-1 for a 50-mm-long crystal.

Scattering analysis of arbitrarily shaped cylinders in a focused beam system

The scattering from an arbitrarily shaped cylinder is characterised by its induced field ratio (IFR) and its scattering pattern. The paper describes how a focused beam system is used to determine the scattering characteristics of an arbitrarily shaped cylinder. The fields of the transmitting and receiving antennas are described by equivalent fundamental Gaussian beams. An analytical procedure based on the computation of the coupling between the Gaussian beams in the focused beam system and the scattered field is used to determine the IFR and the scattering pattern of the cylinder. The results obtained by this method verify well with the scattering characteristics computed analytically or numerically by the method of moments or finite element method.

Theoretical and experimental investigation of a quasi-optical mode converter for a 110-GHz gyrotron

A quasi-optical mode converter has been designed to transform the TE/sub 22,6/ mode at 110 GHz to a Gaussian beam in free space. The converter consists of a rippled-wall waveguide launcher and two toroidal focusing reflectors. A full vector diffraction theory was developed to simulate the converter operation and predict the characteristics of the output beam. The simulation results were used to modify and improve the reflector design. The converter was built and tested on a 3-/spl mu/s pulsed gyrotron operating in the TE/sub 22,6/ mode at 110 GHz. Beam expansion and calorimetric efficiency measurements agreed well with diffraction theory predictions. Greater than 95% of the TE/sub 22,6/ power generated by the gyrotron was converted to a fundamental Gaussian beam and coupled into a corrugated waveguide. Four additional reflectors were built to transform the fundamental Gaussian beam into two similar Gaussian-like beams of approximately equal power level. The vector diffraction theory analysis suggested that simple sinusoidal and toroidal shaping mirrors can achieve high-efficiency beam splitting. Experiments showed that the beam splitting mirror relay successfully converted the fundamental Gaussian beam, produced by the launcher and two mirror relay, to two Gaussian-like beams. Calorimetric measurements indicated that 94% of the total power leaving the gyrotron was converted to the dual beam output with 52% of the power in the upper beam and 42% in the lower beam. The measured beam patterns and expansions were in good agreement with predictions of vector diffraction theory.

Far-field diffraction of truncated higher-order Laguerre-Gaussian beams

A simple analytic expression for the far-field diffraction pattern of a general high-order Laguerre-Gaussian mode from a circular aperture is derived. Aperturing of the fundamental Gaussian beam is shown as a special case, where in the limit of waist size much larger than the aperture the Airy pattern is recovered and in the opposite limit we get a Gaussian intensity pattern. The diffraction pattern is shown to be an infinite series of Bessel functions and is strongly dependent on the ratio of the aperture area to the beam waist area (also known as the truncation parameter). This formulation leads to a more intuitive understanding of the far field of these modes, and the effect of the aperture as a spatial filter is discussed.

Location and profile of phase conjugate image with gaussian beam pumping

AbstractWhen applying phase conjugate waves to various types of image processing, the characteristics of the wavefront, generated by the nonlinear optical medium, are an important research problem. The characteristics of a phase conjugate mirror with plane wave pumping have been investigated in previous research. To perform more realistic analysis, we derive equations describing the image location of the phase conjugate mirror with fundamental mode Gaussian beams as the pumping light and calculate the phase conjugate images numerically. The relationship between the probe light and the phase conjugate image using the Fresnel diffraction formula will be formulated first. Then the image location and the image magnification factor in consideration of the wave‐front curvature of the pump light is derived. Then the characteristics of the image location are analyzed considering the change of the curvature radius of the Gaussian beam in the thickness direction of the nonlinear optical medium. The image profile of the phase conjugate mirror is found by numerical calculation. The results show for the first time the effects of wavefront curvature of the pump light on the image reconstruction capability, which is an important characteristic of the phase conjugate mirror.

Second-harmonic generation of blue light in bulk periodically poled LiTaO3

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%.

Experiments with narrow movable beams of pulsed sound waves at 35 GHz

AbstractOnly the study of absorption and angular dependent scattering of GHz and THz sound can give us detailed information about interaction processes of acoustical phonons. Therefore, the necessary techniques of sound generation, detection and undisturbed transmission to the target must be improved or to a large extent must still be developed. Corresponding attempts at 35 GHz are described. Sound‐beam topography allowed to study crystal defects and also showed us where transmission without scattering occurred. For the piezoelectric generation a reflex klystron was used feeding a planar Hertzian resonator. The needle‐like sound beams appeared as a double beam, each showing a minimum diameter of 35 μm for longitudinal polarized sound at an acoustic wavelength of 165 nm in X‐cut quartz and 320 nm in a‐cut sapphire. To obtain the smallest possible beam diameter for high resolution work, model calculations are presented for an excited fundamental Gaussian sound beam in an isotropic medium.

Second harmonic generation in field poled, quasi-phase-matched, bulk LiNbO/sub 3/

Field induced periodic poling is used to create >10 micron period structures in /spl sim/250 micron thick slabs of LiNbO/sub 3/. Third order quasi-phase-matched second harmonic blue light generation is demonstrated by free propagation of a 937 nm fundamental Gaussian beam in periodically poled LiNbO/sub 3/, with a conversion efficiency of 0.2%/W cm.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Generation of millimeter wave Gaussian beams and their propagation in a dielectric waveguide

Linearly polarized fundamental mode Gaussian beams were generated and coupled to a hollow circular oversized dielectric waveguide by placing the waist of the beam at the guide entrance. The transmission properties of the waveguide were characterized as a function of frequency for a variety of coupling conditions. These conditions included changes in the input beam waist radius, angle of incidence, and displacement perpendicular and parallel to the guide axis. It has been found that: 1.) power transmission is maximized when the waist of the input beam is centered at the guide input, injected normally, and has a radius of 0.43 times the waveguide radius, 2.) power transmission decreases rapidly with increasing angle of incidence and the rate of that loss increases with frequency, 3.) the waveguide preserves the linear polarization of the input beam, 4.) power transmission in the fundamental waveguide mode is not greatly affected by moderate displacements in the input beam position, and 5.) upon exit from the waveguide the launched EH11 mode propagates as a fundamental mode Gaussian beam in the quasi-far field. The results compare favorably to the transmission theory of Belland and Crenn and approximately to the near and far field mode pattern theory of Degnan.

Transition from the paraxial approximation to exact solutions of the wave equation and application to Gaussian beams

Two related basic transition operators, T1 and T2, are found that transform arbitrary solutions of the parabolic equation of the paraxial approximation into exact monochromatic solutions of the scalar wave equation or of the corresponding Helmholtz equation. The operators realize different boundary conditions. The operator T1 preserves the transverse field distribution of the paraxial approximation in the plane z = 0 for the obtained exact solution. The method is applied to calculate the complete corrections to the paraxial approximation of the fundamental Gaussian beam solutions of the n-dimensional wave equation. The lowest-order correction to the paraxial approximation in the three-dimensional case is found to be in agreement with the result of Agrawal and Pattanayak [ J. Opt. Soc. Am.69, 575 ( 1979)]. The complete series of corrections on the axis is summed up to a transcendental function and discussed for the three-dimensional case.

Beam-mode expansion applied to focal-region fields

Propagation properties of elementary beam modes are derived and used to examine the structure of the focal region of a focused aperture. Some general features of the field structure are obtained by approximating the field with a suitable fundamental Gaussian beam. The parameters governing the beam are found to be closely related to the Fresnel number of the system. It is then shown how the equations describing the fundamental mode are also applicable to a complete set of modes. The relationship between an analysis based on beam modes and a Fourier treatment is shown. Numerical results are presented which show the accuracy of field reconstruction for finite numbers of modes.

Dye laser transverse mode control using capillaries

We propose and demonstrate the use of a hollow circular dielectric waveguide for laser transverse mode control. A capillary inserted in a conventional transversely pumped pulse dye laser is shown to effectively promote the fundamental gaussian beam oscillation. It is shown by direct comparison that capillary dye lasers are superior to pinhole dye lasers in that the beam far-field divergence is small, the power conversion of the pump to TEM 00 mode output is high. Capillary dye lasers are also superior to waveguide dye lasers in that the design is simple and flexible. It is suggested that the use of capillaries for transverse mode control be applicable to other types of lasers.

Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam

Fifth-order corrected expressions for the electromagnetic field components of a monochromatic fundamental Gaussian beam (i.e., a focused TEM00 mode laser beam) propagating within a homogeneous dielectric media are derived and presented. Calculations of relative error indicate that the fifth-order Gaussian beam description provides a significantly improved solution to Maxwell’s equations in comparison with commonly used paraxial (zeroth-order) and first-order Gaussian beam descriptions.

Generalized Gaussian beam solutions of paraxial optics and their connection to a hidden symmetry

It is shown that the Hermite–Gauss- and Laguerre–Gauss-type solutions of paraxial optics whose corresponding Hermite and Laguerre polynomials have complex arguments are closely related to a hidden symmetry in the parabolic equation. These solutions are generated from the fundamental Gaussian beam solution by applying the powers of the infinitesimal operators of this symmetry group. The Fourier spectrum of these solutions is obtained from the Fourier spectrum of the fundamental Gaussian beam solution in a similar manner. The Gaussian beam solutions containing Hermite polynomials with complex arguments that were derived by Siegman [ J. Opt. Soc. Am.63, 1093 ( 1973)] represent a limiting case of the more-general solutions considered here. The generalized Gaussian beam solutions show a sharp mode picture with exact zeros in the field distribution only in the focal or waist plane. Unconventional applications of the parabolic approximation in optics including focus wave modes are demonstrated.

The coupling of submillimeter corner-cube antennas to Gaussian beams

We present calculations of a number of experimentally useful properties of the far-field of 90° corner-cube antennas. These are the orientation relative to the whisker and the waistsize of the best-matched fundamental Gaussian beam, the coupling efficiency to this beam, and the radiation resistance. Each of these is computed as a function of whisker length, L, and spacing from the corner-cube dihedral, d, using the standard far-field pattern obtained from an array of four traveling-wave current distributions, (one physical and three images). It is found that the conventional prescription for antenna length, L = 4 λ, and spacing, d = 1.2 λ, does not yield optimal coupling. This is obtained from shorter whiskers, spaced closer to the dihedral, namely L = 1.35 λ, d = 0.9 λ. An improvement of 1.5 dB in coupling efficiency, from 55% to 78%, is thereby obtained. This modification increases the width of the best fit Gaussian beam from W 0 λ = 1.82 ( FWHM = 12°) to w 0 λ = 1.24 ( FWHM = 17°) , and reduces the radiation impedance from 130 to 65Ω.

Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam

Theoretical expressions for the internal and external electromagnetic fields for an arbitrary electromagnetic beam incident upon a homogeneous spherical particle are derived, and numerical calculations based upon this theoretical development are presented. In particular, spatial distributions of the internal and near-surface electric field magnitude (source function) for a focused fundamental (TEM00 mode) Gaussian beam of 1.06 μm wavelength and 4 μm beam waist diameter incident upon a 5-μm-diam water droplet in air are presented as a function of the location of the beam focal point relative to the sphere center. The calculations indicate that the internal and near-surface electric field magnitude distribution can be strongly dependent upon relative focal point positioning and may differ significantly from the corresponding electric field magnitude distribution expected from plane-wave irradiation.

Excitation of higher order modes in optical fibers with parabolic index profile

A large number of modes can be supported by multimode fibers. There are applications where higher order modes are preferred. Microbend intensity sensors are good examples. The sensitivity of these sensors is greatly increased if higher order modes are excited. In this work, a simple method to excite higher order modes preferentially is suggested. It consists of thin-film gratings deposited directly onto the fiber end. By controlling the film thickness or transparency of the grating structure, a desired transmission coefficient T(r,Phi) is synthesized. The desired mode can be excited preferentially by incident Gaussian beams without the aid of additional optical components. Binary intensity and binary phase gratings have been studied. Numerical investigation reveals that the phase gratings are more effective for the preferential excitation of higher order modes than the intensity gratings. In fact, by using binary phase gratings and in optimal excitation conditions as much as 81.1, 76.9, 74.6, 73.3, and 72.3% of the power in the incoming, linearly polarized, fundamental Gaussian beam can be converted to LP(02), LP(03), LP(04), LP(05), and LP(06) modes, respectively, excluding Fresnel loss.

Design of phase plates for changing the wavefront of lasers

Using phase plates calculated by a two-dimensional discrete FFT with dimensionless parameters and a computer simulation method for the design, we can convert a fundamental mode gaussian beam into one of rectangular shape, or change an elliptical wavefront into one of circular symmetry. Formulae giving the relation between theoretical simulation and experimental parameters were introduced. The results demonstrated that the experimental equipement is simple using data obtained, and the efficiency of the energy transform is high.

Algebraic And Graphical Propagation Methods For Gaussian Schell-Model Beams

In many applications optical wavefields with reduced states of coherence are preferable to fully coherent fields. Gaussian Schell-model beams can be viewed as generalizations of the ordinary fundamental Gaussian laser beam by allowing a Gaussian variation of the transverse spatial coherence. Suitable propagation parameters for Gaussian Schell-model beams are stated, and their evolution in free space and through optical systems is analyzed. An illustrative geometrical approach, analogous to the propagation-circle method for laser beams, is also presented. Finally, the effects of spatial coherence on beam focusing are investigated, and applications of the algebraic and graphical methods to some particular problems are briefly discussed.