Internal fields of a spherical particle illuminated by a tightly focused laser beam: Focal point positioning effects at resonance

Abstract

The spherical particle/arbitrary beam interaction theory developed in an earlier paper is used to investigate the dependence of structural resonance behavior on focal point positioning for a spherical particle illuminated by a tightly focused (beam diameter less than sphere diameter), linearly polarized, Gaussian-profiled laser beam. Calculations of absorption efficiency and distributions of normalized source function (electric field magnitude) are presented as a function of focal point positioning for a particle with a complex relative index of refraction of n̄=1.33+5.0×10−6i and a size parameter of α≊29.5 at both nonresonance and resonance conditions. The results of the calculations indicate that structural resonances are not excited during the on-center focal point positioning of such a tightly focused beam but structural resonances can be excited by proper on-edge focal point positioning. Electric wave resonances were found to be excited by moving the focal point from on-center towards the edge of the sphere parallel to the direction of the incident beam electric field polarization. Magnetic wave resonances were found to be excited by moving the focal point from on-center towards the edge of the sphere perpendicular to the direction of the incident beam electric field polarization.

Angular scattering of light by a homogeneous spherical particle in a zeroth-order Bessel beam and its relationship to plane wave scattering

“…This problem has been studied extensively, in particular for light scattering involving spherical particles in a Gaussian beam, and has led to the development of two popular theories which extend LMT to the case of an arbitrarily shaped beam. [10][11][12][13][14][15][16][17] These theories are mathematically equivalent and in both cases beam-shape coefficients are used to decompose the incident beam into partial waves.…”

Comment on “A spectroscopic tour through the liquid aerosol interface: Implications for atmospheric chemistry” by J.‐X. Zhang, D. P. Aiello, and P. M. Aker

“…ZAA utilized instead a 130-p•m-diameter beam for edge excitation with the beam center positioned tens of microns distant from the droplet rim while making no provision to specifically achieve or avoid wavelength coincidence with edge or deeper lying modes, respectively. ZAA, in describing their pumping scheme, cite previous theory [Barton et al, 1989;Khaled et al, 1994]. However, these earlier works assumed (a) a tightly focused excitation beam of nominally 2 p•m diameter; (b) small droplets having size parameters (i.e., 2,ra/X, where a is the droplet radius) of less than 100; and (c) the highest Q nearsurface mode in near resonance with the excitation laser.…”

“…This is opposite to the trend depicted in Figures 1 and 3. ZAA may have confused the characteristic MDR field distributions with excitation coupling functions as described in cited theory [Barton et al, 1989;Khaled et al, 1994]. A function describing the efficiency of coupling into the first-order mode of small droplets can be plotted but even this is much broader than indicated.…”

“…For example, theory [Khaled, 1994] shows that the peak intensity within a first-order mode only falls a factor of 2 as the excitation beam is moved from 1.23a to a. It's also important to note that previous theories [Barton et al, 1989;Khaled et al, 1994] [Zhang and Chang, 1989]. In any event, we have observed spectra in our laboratory which clearly violate ZAA's hypothesis; i.e., SRS from several different azimuthal modes (each with different Lz) simultaneously where one specific n, l, m n MDR had been excited.…”

Excitation of morphology-dependent resonances and van de Hulst’s localization principle

“…Later, the localization principle was extended 2,3 to predict that a morphology-dependent resonance (MDR) of a partial wave l . ka is most efficiently excited when a focused incident beam, rather than a plane wave, passes the distance r 0 .…”