Wavefront distortion of the reflected and diffracted beams produced by the thermoelastic deformation of a diffraction grating heated by a Gaussian laser beam

It may be advantageous in advanced gravitational-wave detectors to replace conventional beam splitters and Fabry-Perot input mirrors with diffractive elements. In each of these applications, the wavefront distortions produced by the absorption and subsequent heating of the grating can limit the maximum useful optical power. We present data on the wavefront distortions induced in a laser probe beam for both the reflected and diffracted beams from a grating that is heated by a Gaussian laser beam and compare these results to a simple theory of the wavefront distortions induced by thermoelastic deformations.     

Relative phase shifts of apertured Gaussian beams and transformation of a Gaussian beam through a phase aperture

When a Gaussian beam is apertured, it undergoes a focal shift as well as a phase shift. The focal shift has been investigated extensively although the phase shift has seldom been discussed. We analyze the phase shift of the apertured Gaussian beam. Furthermore we point out that the phase aperture may be used to transform the intensity distribution of the Gaussian beam to obtain a more concentrated beam, to realize uniformity of the Gaussian beam, and to obtain a ring beam.     

Shear design of reinforced concrete beams with FRP longitudinal and transverse reinforcement

The shear resisting mechanisms of reinforced concrete (RC) beams with longitudinal and transverse FRP reinforcement can be affected by the mechanical properties of the FRP rebars. This paper presents a mechanical model for the prediction of the shear strength of FRP RC beams that takes into account its particularities. The model assumes that the shear force is taken by the un-cracked concrete chord, by the residual tensile stresses along the crack length and by the FRP stirrups. Failure is considered to occur when the principal tensile stress at the concrete chord reaches the concrete tensile strength, assuming that the contribution of the FRP stirrups is limited by a possible brittle failure in the bent zone. The accuracy of the proposed method has been verified by comparing the model predictions with the results of 112 tests. The application of the model provides better statistical results (mean value V_test/V_pred equal to 1.08 and COV of 19.5%) than those obtained using the design equations of other current models or guidelines. Due to the simplicity, accuracy and mechanical derivation of the model it results suitable for design and verification in engineering practice.     

Significant deformations and propagation variations of Laguerre-Gaussian beams reflected and transmitted at a dielectric interface

We observe TM and TE Laguerre-Gaussian (LG) light beams reflected and transmitted at a dielectric interface near critical incidence. The intensity distribution of the reflected beam is transversely deformed near the beam waist, and that of the transmitted beam is similar to that of a diagonal Hermite-Gaussian beam. The former rotates around the optical axis by approximately pi/2 with propagation, and the latter returns to that of the incident LG beam. These observations agree well with numerical calculations based on an angular spectral analysis and are attributable to the helical wavefront of the LG beams, the sharp incidence-angle dependence of the Fresnel reflection and transmission coefficients, and the Gouy phase.     

Degradation of an image by Gaussian longitudinal motion

The effect of random longitudinal motion of an image is discussed. Numerical results are given for systems with circular and annular pupils. It is shown that, for a given value of the image motion, the time-averaged Strehl ratio is larger for a larger value of the obscuration ratio of an annular pupil. We also show that the time-averaged image irradiance distribution near its center and the corresponding encircled power can be obtained from their aberration-free values by multiplying them by the Strehl ratio.     

Approximate method for the analysis of stability of beams under the action of a system of longitudinal and transverse forces

We propose an approximate method for the analysis of stability of uniplanar bending of beams under the action of a complex system of longitudinal and transverse forces, obtain formulas for the determination of the critical values of total longitudinal and transverse forces and the factor of stability of flange and rectangular beams that are convenient for practical applications, and present examples of the numerical analysis of actual beams. The critical values of the total forces obtained by the proposed method are compared with known results. The difference between the exact and approximate critical values does not exceed 2–7%. The experimental data enable us to recommend these approximate formulas for practical calculations of the stability of uniplanar bending of beams subjected to the combined action of complex systems of longitudinal and transverse forces. Translated from Problemy Prochnosti, No. 3, pp. 69–77, May–June, 1998.     

Generation of tunable chain of three-dimensional optical bottle beams via focused multi-ring hollow Gaussian beam

We report here the generation of a chain of three-dimensional (3-D) optical bottle beams by focusing a π-phase shifted multi-ring hollow Gaussian beam (HGB) using a lens with spherical aberration. The rings of the HGB of suitable radial (k(r)) and axial (k(z)) wave vectors are generated using a double-negative axicon chemically etched in the optical fiber tips. Moving the lens position with respect to the fiber tip results in variation of the semi-angle of the cones of wave vectors of the HGBs and their diameter, using which we demonstrate tunability in the size and the periodicity of the 3-D optical bottle beams over a wide range, from micrometers to millimeters. The propagation characteristics of the beams resulting from focusing of single- and multi-ring HGBs and resulting in a quasi-non-diffracting beam and a chain of 3-D optical bottle beams, respectively, are simulated using only the input beam parameters and are found to agree well with experimental results.     

Shift and shape of grating diffracted beams

Abstract

The grating diffraction of beams is theoretically investigated by applying an electromagnetic method (the Integral Equation System Method with Parametrization of the grating profile = IESMP) to their plane wave components. For the first time, explicit values for the displacement of grating diffracted Gaussian beams are calculated with this method. For total reflection this displacement of beams is known as the Goos-Hänchen shift. A maximum shift of 36 μm has been found for the investigated sinusoidal grating near an anomaly which is much greater than the known Goos–Hänchen shift of about 1 μm for the total reflection case. The replacement of the angular spectrum of plane waves with constant wavelength by a wavelength spectrum of plane waves of constant direction allows an analogous treatment of short-time pulses. Surprisingly, the above anomaly causes a maximum temporal shift of 80 fs for the pulse diffraction. These temporal shifts and additional effects like pulse deformations can influence ultra short-time pulse experiments. Furthermore, the behaviour of temporally and spatially Gaussian shaped light pulses (TSG pulses) by grating diffraction are studied considering the diffraction of an angular and wavelength dependent spectrum of plane waves. The diffraction of a short TSG pulse at the above grating deforms the pulse and creates an additional smaller satellite pulse. All described effects occur only at positions of the space–time complex filtering function in the angular-wavelength frequency space with high gradient of the phase.     

Vector propagation of radially polarized Gaussian beams diffracted by an axicon

On the basis of the vectorial Rayleigh diffraction integrals and stationary-phase method, the analytic expression describing the vectorial field distribution of radially polarized Gaussian beams diffracted by an axicon is derived. The theoretical analysis and simulation calculation show that the radial component of the diffraction field is the propagation-invariant first-order Bessel beam when the radially polarized Gaussian beam illuminates the axicon. However, the longitudinal component possesses no such behavior because of its intrinsic r dependence, and its central intensity is the maximum. The longitudinal component is related to the open angle and index of the axicon, which has to be considered when the open angle and index are large. For a small open angle and index, the longitudinal component can be neglected, and the scalar approximation is valid.     

Propagation of elliptical Gaussian beams modulated by an elliptical annular aperture

An analytical propagation expression for a generalized astigmatic elliptical Gaussian beam (EGB) modulated by an elliptical annular aperture and passing through an axially nonsymmetrical optical system is obtained by the use of vector integration. The derived analytical results provide more convenience for studying the propagation and transformation of EGBs than the usual method of using the diffraction integral directly, and the efficiency of the numerical calculation is significantly improved. Some numerical simulations are illustrated for the propagation properties of EGBs passing through a free space with an elliptical annular aperture, an elliptical screen, or an elliptical aperture. Further extensions are also pointed out.     

Propagation and focusing of Gaussian beams generated by Gaussian mirror resonators

The propagation and focusing properties of a class of Gaussian beams generated by optical resonators with Gaussian reflectivity mirrors are investigated. Attention is concentrated on the following two beams in this class: (a) the annular Gaussian beam (the Gaussian doughnut mode) and (b) the flat-topped Gaussian beam. A class of flat-topped Gaussian beams is introduced. All analysis is limited to a coherent superposition scheme of the lowest-order Gaussian modes (TEM00) that have different parameters.     

Jones matrices of a quarter-wave plate for Gaussian beams

The Jones matrix of a quarter-wave plate is studied theoretically and experimentally, taking into account internal reflections, the ellipsoid of the indices, geometric defects, the tilt angle, and the characteristics of the incident Gaussian beam. The influence of the different parameters is isolated, and large discrepancies are observed with respect to results obtained from the Jones matrix that are usually given in textbooks. It is shown that the effective Jones matrix of the plate does not depend on the longitudinal position of the plate on the Gaussian beam but only on the beam-waist size. This leads to a method of characterization of the defects of a quarter-wave plate that is more precise than the usual methods. Different procedures to optimize the efficiency of a given plate are discussed, taking the plate defects into account. In all cases, a good agreement between experiments and theory is obtained.     

ABCD matrix for reflection and refraction of Gaussian beams at the surface of a parabola of revolution

We report the formulation of an ABCD matrix for reflection and refraction of Gaussian light beams at the surface of a parabola of revolution that separate media of different refractive indices based on optical phase matching. The equations for the spot sizes and wave-front radii of the beams are also obtained by using theABCD matrix. With these matrices, we can more conveniently design and evaluate some special optical systems, including these kinds of elements.     

Optics for modulating multiple beams using an asymmetric multilevel phase grating and a multichannel acousto-optic modulator

Asymmetric multilevel phase gratings for generating even numbered beams have been designed, assuming that their phase patterns are formed by overlapping plural binary-phase patterns, each of which has an arbitrary phase height. The grating for four beams, which produces uniform and high intense diffraction orders of the minus first to the plus second order, is fabricated. The efficiency is 75.5%, although the theoretical efficiency is 79.9%. It is also demonstrated that the optics in which the beams from the grating are fed into a multichannel acousto-optic modulator through a Fourier-transform lens makes their successful modulation possible for pulse signals of 20-ns pulse duration.     

Experimental study of focused ultrasonic beams reflected at a fluid-solid interface in the neighborhood of the Rayleigh angle

A technique for measuring the lateral and axial displacements of the focal point of an acoustic focused beam reflected at a water-aluminum interface in the neighborhood of the Rayleigh angle incidence is presented together with a qualitative representation of other nonspecular phenomena, based on the cartography of the reflected beam. A study of the feasibility of the experiment and the choice of the transducer is carried out. The results obtained are in agreement with theoretical predictions.     

Propagation characteristics of Gaussian beams through a paraxial ABCD optical system with an annular aperture

By introducing a hard aperture function into a finite sum of complex Gaussian functions, an approximate analytical expression for a Gaussian beam passing through a paraxial ABCD optical system with an annular aperture has been derived. The results could be reduced to the case of circular black screen or circular aperture. Some numerical simulations are also performed and illustrated for the propagation characteristics of a Gaussian beam through a paraxial ABCD optical system with an annular aperture, a circular black screen or a circular aperture.     

Dependence of transverse and longitudinal resolutions on incident Gaussian beam widths in the illumination part of optical scanning microscopy

We studied both theoretically and experimentally the intensity distribution of a Gaussian laser beam when it was focused by an objective lens with its numerical aperture up to 0.95. Approximate formulas for full width at half-maximum (FWHM) of the intensity distribution at focus were derived for very large and very small initial beam waists with respect to the entrance pupil radius of the objective lens. In experiments, the energy flux through a 0.5 microm pinhole was measured for various pinhole positions. It was found in theoretical analysis and confirmed in experiments that the FWHMs at focus in the transverse and longitudinal directions do not increase much from the ultimate FWHMs until the input beam waist is reduced below half of the entrance pupil radius.