Scattering of a spheroidal particle illuminated by a gaussian beam

An approach to expanding a Gaussian beam in terms of the spheroidal wave functions in spheroidal coordinates is presented. The beam-shape coefficients of the Gaussian beam in spheroidal coordinates can be computed conveniently by use of the known expression for beam-shape coefficients, g(n), in spherical coordinates. The unknown expansion coefficients of scattered and internal electromagnetic fields are determined by a system of equations derived from the boundary conditions for continuity of the tangential components of the electric and magnetic vectors across the surface of the spheroid. A solution to the problem of scattering of a Gaussian beam by a homogeneous prolate (or oblate) spheroidal particle is obtained. The numerical values of the expansion coefficients and the scattered intensity distribution for incidence of an on-axis Gaussian beam are given.     

Levelling the focal spot intensity of the focused gaussian beam

Abstract

It is experimentally and numerically shown that a simple binaryphase optical element can be used for levelling the light energy in the focal plane of the focused Gaussian beam, generating a square-shaped focal beam, and transforming the Gaussian beam into a uniform beam which preserves its radius at a definite length of its path.     

Scattering of a tightly focused beam by an optically trapped particle

Near-forward scattering of an optically trapped 5-mum-radius polystyrene latex sphere by the trapping beam was examined both theoretically and experimentally. Since the trapping beam is tightly focused, the beam fields superpose and interfere with the scattered fields in the forward hemisphere. The observed light intensity consists of a series of concentric bright and dark fringes centered about the forward-scattering direction. Both the number of fringes and their contrast depend on the position of the trapping beam focal waist with respect to the sphere. The fringes are caused by diffraction that is due to the truncation of the tail of the trapping beam as the beam is transmitted through the sphere.     

Scattering of a plane wave by an anisotropic ferrite-coated conducting sphere

On the basis of the three-dimensional spherical vector wave functions in ferrite anisotropic media, and the fact that the first and second spherical vector wave functions in ferrite anisotropic media satisfy the same differential equations, the electromagnetic fields in homogeneous ferrite anisotropic media can be expressed as the addition of the first and second spherical vector wave functions in ferrite anisotropic media. Applying the continue boundary condition of the tangential component of electromagnetic fields in the interface between the ferrite anisotropic medium and free space, and the tangential electric field vanishing in the interface of the conducting sphere, the expansion coefficients of electromagnetic fields in terms of spherical vector wave function in ferrite medium and the scattering fields in free space can be derived. The theoretical analysis and numerical result show that when the radius of a conducting sphere approaches zero, the present method can be reduced to that of the homogeneous ferrite anisotropic sphere. The present method can be applied to the analyses of related microwave devices, antennas and the character of radar targets.     

Scattering of a gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation: numerical results

We present numerical results concerning the properties of the electromagnetic field scattered by an infinite circular cylinder illuminated by a circular Gaussian beam. The cylinder is arbitrarily located and arbitrarily oriented with respect to the illuminating Gaussian beam. Numerical evaluations are provided within the framework of a rigorous electromagnetic theory, the generalized Lorenz-Mie theory, for infinite cylinders. This theory provides new insights that could not be obtained from older formulations, i.e., geometrical optics and plane-wave scattering. In particular, some emphasis is laid on the waveguiding effect and on the rainbow phenomenon whose fine structure is hardly predictable by use of geometrical optics.     

Scattering of a plane harmonic SH wave by a completely embedded corrugated scatterer

Anti‐plane‐strain model for steady‐state scattering of elastic waves by a rough inclusion or a cavity embedded in a half space is considered by using a direct boundary integral equation method. The roughness of the scatterer is assumed to be periodic with arbitrary amplitude and period. Detailed testing of the numerical results is presented. The motion along the half‐space surface is evaluated for different corrugations, frequencies and impedance contrast of the materials. The importance of the scatterer roughness upon the displacement field is clearly demonstrated. It was shown that larger corrugation amplitudes, shorter corrugation periods and higher frequencies may produce significant change in the displacement field when compared with the corresponding smooth scatterer result. This effect strongly depends upon the impedance contrast of the materials. Copyright © 2008 John Wiley & Sons, Ltd.     

Fiber-diameter measurement by occlusion of a gaussian beam

The amount of light occluded by a fiber as it passes through alaser beam can be used as the basis for fiber-diametermeasurement. This technique is analyzed with a two-dimensionalrigorous model. The occlusion seen for dielectric fibers as afunction of their diameter is highly oscillatory owing to interferencebetween the light transmitted by the fiber and the rest of thediffracted field. Scalar diffraction theory is shown to be adequatein modeling this effect. The oscillation sets a limit to theaccuracy of simple diameter measurement systems and is confirmedexperimentally for glass fibers. However, wool fibers are found tobe better treated as an absorbing material. The effect of beampolarization is investigated and found to be negligible for dielectricfibers but significant for metal fibers of small diameter.     

Spatial beam shaping of ultrashort laser pulses: theory and experiment

We studied the spatial intensity profile of an ultrashort laser pulse passing through a laser beam shaping system, which uses diffractive optical elements to reshape a Gaussian beam profile into a flat-topped distribution. Both dispersion and nonlinear self-phase modulation are included in the theoretical model. Our calculation shows that this system works well for ultrashort pulses (approximately 100 fs) when the pulse peak intensity is less than 5 x 10(11) W/cm2. Experimental results are presented for 136 fs pulses at 800 nm wavelength from a Ti:sapphire laser with a 6 nJ pulse energy. We also studied the effects of lateral misalignment, beam-size deviation, and defocusing on the energy fluence profile.     

Fabrication of beam shapers in the bulk of fused silica by femtosecond laser pulses

We reported a new approach to the fabrication of three-dimensional refractive-index-modified microstructures inside transparent materials by combining two-dimensional writing by scanning the focus of the femtosecond laser pulse and by forming the long filament in the third dimension. In this way, embedded diffractive beam shapers of grid, square, and ring gratings were obtained in the bulk of fused silica by use of a femtosecond laser with a wavelength of 810 nm and a repetition rate of 1 KHz. These structures and their refractive efficiencies were optimized by selection of the appropriate fabrication parameters, including the pulse energy, grating period, scanning speed, and scanning repetition. The good performance of these devices indicates that, owing to its simple and flexible method for fabricating complex phase elements inside transparent materials, this technique has potential applications to integrated optics.     

Electromagnetic field for a tightly focused beam incident upon ordinary and layered plane surfaces

A solution procedure is developed for the determination of the electromagnetic field that results from the interaction of a tightly focused beam with a plane surface with and without a layer. The effects of angle of incidence, relative index of refraction, polarization, layer thickness, and incident beam profile on the resulting electromagnetic field distribution are demonstrated.     

Direct focusing modifications of elliptical gaussian beam by non-circular apertures

Abstract

For focusing the elliptical Gaussian beam directly, the effects of a non-circular aperture on the focusing properties are studied. The focusing properties for different shapes of apertures, which include a circle, an ellipse and a rectangle, are calculated and compared. Moreover, for different elliptical Gaussian beams, an empirical aperture selection rule that can be used to circularize the focusing spot is proposed. The energy transmission ratios are also considered in this paper.     

Diffraction of gaussian beams by plane apertures: A different approach

Abstract

We first develop an integral equation formalism to solve the boundary value problems of the paraxial scalar wave equation when data, of the Dirichlet or Neumann type, are given on a closed surface S, in particular when S is a plane. Then, we show how this formalism can be used to analyse the scattering by perfectly conducting planes of paraxial waves, specially of Gaussian beams, and how it may be applied to paraxial wave diffraction by plane apertures. Finally, the diffraction of Gaussian beams by slits, rectangular and circular apertures is investigated.     

Innovative methodologies of circuit edit by focused ion beam (FIB) on wafer-level chip-scale-package (WLCSP) devices

As packaging technology advances to wafer level chip scale packaging (WLCSP) to enable reduced chip size and manufacturing cost, circuit edit has become a critical issue for the fully packaged integrated circuits (ICs). These advanced package types cannot be rebuilt on a single chip; therefore, function testing after circuit edit of WLCSP faces challenges. Furthermore, there are routings at the redistribution layer of WLCSP ICs. Circuit edit was applied on both the chip and the package level. In this paper the focused ion beam was applied to mill the organic material of the package structure to expose underlying ICs, instead of chemically destroying the packaging. Metal line cutting and conductive path deposition were also developed by a beam-based technique. These new approaches make the direct edit of electrical circuitry possible not only in ICs but also at package level. Therefore, for the debug process and for failure analysis, the WLCSP ICs have negligible damage and negligible signal integrity loss by retaining the original packaging structure.     

Simulated dynamic behavior of single and multiple spheres in the trap region of focused laser beams

An enhanced photon propagation method is used to calculate the forces and torque present on each sphere of a system of particles located in the vicinity of focused laser-trapping beams. Infinitesimal trajectory displacements are computed through classical mechanics and the new particle position used to define the next trapping system geometry considered. Repeated applications of the process, implemented as a computer program, enables full trajectory plotting and the dynamic behavior of the systems to be explored as a function of time.     

Diffraction of a plane wave by a perfectly electromagnetic conducting (PEMC) slot

Using the duality transformations introduced by Lindell and Sihvola, an analytic theory for the electromagnetic diffraction from a perfect electromagnetic conductor (PEMC) slot is developed. Transformations have been applied to the diffracted field of a plane wave from a perfect electric conductor (PEC) slot. The problem was solved by using the Sommerfeld Green’s function and Fresnel integral.     

Filamentation of femtosecond laser pulses with amplitude modulation of a diffraction-free beam

Filamentation with the amplitude modulation of Mathieu beam in air is investigated numerically. Non-diffracting characteristic of Mathieu beam is partly maintained in the intense femtosecond laser area even though it is only an amplitude modulation. The amplitude modulation of Mathieu beam delays filament onset and the high intensity will be regenerated in the on-axis area when intensity clamping disappears. During the evolution process, the bunch of filaments merges into a single filament eventually only by the property of non-diffraction. Using an amplitude modulation of an invariable beam as an initial condition of intense femtosecond laser pulse offers a new way to control filaments’ onset, distribution and prolongation, which would be useful in their potential applications.     

Influence of spatiotemporal coupling induced by an ultrashort laser pulse shaper on a focused beam profile

4f pulse shapers have been widely used to temporally manipulate femtosecond optical pulses by spectral filtering. When the temporal waveform is manipulated with a spatial light modulator consisting of segmented pixels, the spatial profile of the output beam also varies because of diffraction at the pixel array, which is known as a spatiotemporal coupling effect. This effect produces a complicated spatio-temporal profile near the focus of the ultrashort pulses, which may affect the interpretation of experimental results obtained with shaped ultrashort pulses. We investigate the spatial intensity distribution at the focus of temporally shaped pulses through ablation experiments. The three-dimensional space-time beam profile is also numerically calculated.     

Material classification of nanoparticles by focused beam scattering

Advanced science and technology frequently encounters the need to detect particles in the micrometer and nanometer range of a given composition. While the scattering process of light by small particles is well documented, most conventional analytic methods employ wide illumination of large ensembles of particles. With such an approach, no information can be obtained about single particles due to their weak interaction. In this paper, we show that single particles can be classified with respect to their material composition by analyzing the scattering pattern of a focused Gaussian beam.