Parameterization of the Tilted Gaussian Beam Waveobjects

Abstract

Abstract-Novel time-harmonic beam fields have been recently obtained by utilizing a non-orthogonal coordinate system which is a priori matched to the field's planar linearly-phased Gaussian aperture distribution. These waveobjects were termed tilted Gaussian beams. The present investigation is concerned with parameterization of these time-harmonic tilted Gaussian beams and of the wave phenomena associated with them. Specific types of tilted Gaussian beams that are characterized by their aperture complex curvature matrices, are parameterized in term of beam-widths, waist-locations, collimationlengths, radii of curvature, and other features. Emphasis is placed on the difference in the parameterization between the conventional (orthogonal coordinates) beams and the tilted ones.

Scattering of Gaussian Beam by a Spheroidal Particle

“…Figure 3 shows that, with the increase of the angle between the propagation direction of the incident Gaussian beam and the major axis of the spheroid, i.e., the increase of the absolute value of β in 1, the curve shows fewer oscillations. According to the concept of geometrical shadow adopted by Asano and Yamamoto [24,25], the geometrical shadow of the spheroidal particle is πb 2 (a 2 2 sin 2 β + b 2 2 cos 2 β) 1/2 and that of the spherical inclusion is πa 2 1 . It is obvious that, with the increase of the absolute value of β, the ratio of the geometrical shadow of the spherical inclusion to that of the spheroidal particle becomes smaller, and then the interference effects decrease of light diffracted and transmitted by the spherical inclusion with light by the spheroidal particle, thus leading to a smoother curve with fewer oscillations.…”

“…The generalized Lorenz-Mie theory (GLMT) developed by Gouesbet et al is effective for describing the interaction of a shaped beam with a spherical particle by relying on the separability of variables [1][2][3], and has been extended by so many researchers to multilayered spheres [4,5], spheroids [6] and infinite cylinders [7][8][9]. Various applications of focused beam scattering include optimizing the rate at which morphology-dependent resonances (MDRs) are excited, laser trapping, particle manipulation, and the analysis of optical particle sizing instruments [10,11].…”

Pulsed Beam Expansion of Electromagnetic Aperture Fields

“…Finally by applying the convolution theorem to (A8) we obtain the result in (38) and applying the inverse operator S −1 to both sides of (A6) yields the result in (37).…”

“…The expansion propagating elements have been termed phase-space (spectral) Green's functions, as they link induced sources in the configuration-space to phase-space distributions of scattered fields, as well as phasespace distributions of incident fields to phase-space distributions of scattered fields [7,21]. Recently a novel beam-type waveobjects were obtained [22,37,38] by applying a non-orthogonal coordinate system which is a priori matched to localized aperture field distributions. These waveobjects which were termed tilted Gaussian beams, are suitable for planar beam-type expansions and exhibit enhanced accuracy over the commonly used paraxial solutions.…”

TE and TM beam decomposition of time-harmonic electromagnetic waves

“…Several electromagnetic beam scattering and diffraction problems have been solved for rough surface scattering [18,19], dielectric interfaces [20], surfaces of perfectly electric conductor [21,22], stratified [23] and negative isotropic media [24], and more. Recently, novel time-harmonic [25][26][27] beam-type wave objects were obtained by applying a nonorthogonal coordinate system that is a priori matched to localized aperture field distributions. These wave objects, which were termed tilted Gaussian/pulsed beams, are suitable for planar beam-type expansions and exhibit enhanced accuracy over the commonly used paraxial solutions.…”