Small Dielectric Spheres Research Articles

Second-harmonic generation from spherical particles

We calculate the nonlinear dipole and quadrupole moments induced at the second-harmonic (SH) frequency $2\ensuremath{\omega}$ in a small dielectric sphere by an inhomogeneous monochromatic electric field of frequency $\ensuremath{\omega}.$ We neglect finite-size effects and assume that the selvedge region of the sphere is thin enough so that the surface may be considered locally flat. The second-order dipole displays resonances corresponding to the excitation of dipolar and quadrupolar plasmons at $\ensuremath{\omega}$ and a dipolar plasmon at $2\ensuremath{\omega},$ besides the resonances in the nonlinear surface response parameters a, b, and f. The second-order quadrupole, on the other hand, has resonances corresponding to those of a, b, and f, and to the excitation of dipolar surface plasmons at $\ensuremath{\omega}$ only. Depending on the relation between the size of the sphere and the spatial scale of variation of the field, the SH radiation may be dominated by either dipolar or quadrupolar scattering, with a crossover region. As an application, we calculate the SH scattering of a Si sphere lying at various distances above a dielectric substrate.

Multiple-scattering approach to Mie scattering from a sphere of arbitrary size

The classic Mie scattering problem is revisited via an integral-equation formalism. Our approach consists in resumming the multiple-scattering Born series in terms of which the solution can be formally expressed. For small dielectric spheres, the resummation can be done exactly without invoking the full apparatus of multipoles. For a large dielectric sphere with a small refractive-index discontinuity relative to the surrounding medium, the Born series may be approximately resummed to generate correctly a description of the phenomenon of anomalous diffraction. For spheres of arbitrary size, the Born series for each excited electric or magnetic multipole has a complicated structure, but one that is shown to be exactly equivalent to the celebrated Mie results. A significant advantage over the usual differential approach is the implicit inclusion of the electromagnetic boundary conditions at the scattering surface in the integral approach, a feature that may provide valuable insights into scattering from arbitrarily shaped particles.

Resonant Frequencies in an Electromagnetic Rectangular/Cylindrical/Spherical Cavity With an Inner Off-Axis Small Dielectric Sphere

Analytical expressions for the resonant frequencies of an electromagnetic rectangular/cylindrical/spherical cavity with an off-axis electrically small lossless dielectric sphere are obtained in a very simple and immediate manner, for both TE and TM modes. The walls of the cavities are perfectly conducting. Rectangular/cylindrical/spherical vector wave functions are used in our analysis. The results are useful for cavities containing small inhomogeneities, as well as for the determination of permittivities or permeabilities of various materials, from the measurement of the resonant frequency shifts caused by introducing small samples of them inside cavities.

Optical coherence propagation and imaging in a multiple scattering medium

We present a formal, microscopic, solution of the wave propagation problem for an inhomogeneity embedded in an isotropically disordered, multiple scattering, homogeneous background. The inhomogeneity is described by a local change in the complex, dielectric autocorrelation function B(r,r8) [v4/c4^e*(r)e(r8)&ensemble for a wave of frequency w and velocity c. For the homogeneous background, we consider a dielectric autocorrelation function Bh(r−r8) arising from a colloidal suspension of small dielectric spheres. This autocorrelation function can be determined using a newly developed technique called phase space tomography for optical phase retrieval. This technique measures the optical Wigner distribution function I(R,k) defined as the Fourier transform, with respect to r, of the electric field mutual coherence function ^E*(R+r/2)E(R −r/2)&ensemble. The Wigner distribution function is the wave analog of the specific light intensity, Ic(R,k ˆ ), in radiative transfer theory which describes the number of photons in the vicinity of R propagating in direction k ˆ. The Wigner function describes coherence properties of the electromagnetic field which can propagate much longer than the transport mean-free-path l* and which are not included in radiative transfer theory. Given the nature of the homogeneous background, repeated light intensity measurements, which determine the optical phase structure at different points along the tissue surface, may be used to determine the size, shape, and internal structure of the inhomogeneity. In principle, this method improves the resolution of optical tomography to the scale of several optical wavelengths in contrast to methods based on diffusion approximation which have a resolution on the scale of several transport mean-free-paths.

Raman scattering from small spherical particles.

Raman coupling coefficients are calculated for the acoustic vibrations of a small dielectric sphere. The mean components of the strain tensor are calculated for the symmetric and quadrupolar Raman-active vibrational modes, within a continuum approximation which considers a vibrating homogeneous sphere. The Raman coupling coefficient depends on the crystalline structure and on the microscopic scattering mechanism. For cubic Bravais lattices and for a dipole-induced dipole scattering mechanism, the coupling coefficient of the symmetric vibrations vanishes. The Raman intensity of the inner modes is found to be small with respect to that of surface modes. The scaling law, which gives the Raman coupling coefficient as a function of the particle size, has been derived. The coupling of the sphere with a surrounding elastic medium has been considered and found to cause shift and broadening of the lines. This effect can alter significantly the estimated mean value and distribution of particle sizes.

Trapping and levitation of a dielectric sphere with off-centred Gaussian beams. II. GLMT analysis

For pt. I see ibid., vol. 2, p.261, (1993). We study the forces exerted by a Gaussian laser beam on a small dielectric sphere in water as a function of beam-off centring, i.e. the distance between the beam axis and the sphere centre. Our experimental data are from the first part work of Angelova and Pouligny who studied the levitation of polystyrene latex spheres, a few micrometres in radius, by a couple of vertical laser beams in water. We also report on newly acquired results, particularly the observation of sustained oscillations of the levitated sphere in water. These data are analysed from the viewpoint of radiation pressure forces, which we calculate using the generalized Lorenz-Mie theory (GLMT). We find that calculated equilibria fit those experimentally recorded with beams of unequal intensities. Experiments with equally intense beams lead to instabilities in the levitated particle position. This is also well explained by GLMT, but the instability threshold is found to be very sensitive to uncontrolled water convection around the particle.

Scattering by a small object close to an interface III Buried object

Exact-image theory is applied to the problem of electromagnetic-wave scattering from a small object below the interface separating two isotropic and homogeneous media. The object is assumed to be electrically small so that it can be approximated by an electric dipole with known dyadic polarizability. Scattering from a buried small dielectric sphere is considered as an example of the theory.

A Characterization of Light Scattering by Small Dielectric Spheres

Abstract While using the standard Mie formulae to calculate the intensity distribution of light scattered by a small dielectric sphere, we have noticed some new qualitative results which suggest a boundary between a scattering regime qualitatively similar to the well known Rayleigh scattering distribution and that observed for rather larger particles. This may be of practical use when considering the position of photodetectors in light scattering experiments, for example particle velocimetry. The reason for such a transition has been discovered, using an unusual approximation in which the diameter of a sphere is made very small and its refractive index very large, with their product and the wavelength held constant.

Resonant Frequencies in an Electromagnetic Cylindrical/Spherical Cavity with an Internal Off-Axis Small Dielectric Sphere

ABSTRACT Analytical expressions for the resonant frequencies in an electromagnetic cylindrical/spherical cavity with an off-axis inner electrically small dielectric sphere are derived, for both magnetic and electric modes. The walls of the cylindrical/spherical cavity are perfectly conducting. Cylindrical/spherical vector wave functions and related addition theorems, as well as expansion of cylindrical wave functions in terms of spherical ones, are used. Our results are useful in problems connected with resonant cavities containing small inhomogeneities, as well as in cases that we want to determine the permittivities or magnetic permeabilities of various materials, by measuring the resonant frequency shifts caused by the introduction of small samples of them, inside cavities. Graphical results for some of the lower order modes are given, for various values of the parameters and for both kinds of modes.

Demonstration of a fiber-optical light-force trap

We demonstrate a fiber-optical version of a stable three-dimensional light-force trap, which we have used to hold and manipulate small dielectric spheres and living yeast. We show that the trap can be constructed by use of infrared diode lasers with fiber pigtails, without any external optics.

Reflection of light by a slab containing electrically small dielectric spheres

Theoriginal and theenhanced Maxwell-Garnett estimates for the permittivity of a particulate medium are applied to the reflection of light by a composite dielectric slab. The reflection coefficients for incident s and p polarizations are calculated and some curves are plotted and discussed.

Spectral lines of symmetrically shaped particles or clusters with internal disorder

We have investigated the spectral properties of light scattering by small dielectric spheres whose resonant modes are perturbed by disordered static scatterers placed inside. We show that: (a) A narrow peak in the scattering spectrum, which is associated with a highly degenerate Mie resonance with a surface mode, can be broadened into a nearly semicircular curve. (b) Two such adjacent peaks can become overlapping, and the resulting curve differs from the linear superposition of the two curves. (c) The scattering cross section of a resonant mode can be increased by several orders of magnitude.

Electrostatic image theory for the dielectric sphere with an internal source

The electrostatic image theory for a point charge next to the conducting sphere, originally discovered by Lord Kelvin, was recently generalized to the dielectric sphere with external sources by one of the present authors. This article treats the corresponding problem of a source located inside the dielectric sphere, thus completing the theory. Image expressions corresponding to potentials both outside and inside the sphere are worked out and their validity is checked with numerous tests. The present theory can be applied for small dielectric spheres with internal sources or scatterers. © 1992 John Wiley & Sons, Inc.

Interaction of a small eccentrically stratified sphere with an electromagnetic field

The optical response of a system consisting of a small dielectric sphere containing a smaller eccentrically embedded sphere of different dielectric properties is investigated. By employing bispherical coordinates the problem is reduced to the solution of a system of linear equations. The results of numerical calculations are presented illustrating the dependence of the infrared absorption spectrum of a CdTe-CdO system on the degree of eccentricity.

Weak localization and enhanced backscattering of light in dilute suspensions

The differential scattering cross-section of light from a cluster of two small dielectric spheres is calculated exactly and it has been shown that after averaging over cluster orientations a backscattering peak emerges. The height and the width of this peak depend on the polarization state of the incoming and the outgoing waves and for a linearly polarized incident wave the peak is anisotropic, in agreement with existing experimental data. It is predicted that a giant backscattering peak will be observed for light in an appropriate frequency range if metal instead of dielectric spheres are used in the experiment. Fluctuations of the scattered intensity are also calculated.

Absolute calibration of acoustic sensors utilizing electromagnetic scattering from in situ particulate matter

The present paper initiates a study to understand the errors inherent to a laboratory technique similar to that used by K. J. Taylor [J. Acoust. Soc. Am. 70, 939–945 (1981)] for absolute calibration of microphones. Considered here is the idealized situation when a plane-polarized monochromatic plane electromagnetic wave is incident on a finite scattering volume containing dispersed small dielectric spheres that oscillate under the joint influence of a plane transient acoustic wave and Brownian motion. Any component of the scattered and Doppler-shifted electromagnetic signal at a distant farfield point in an obliquely backward direction is a sum of N terms, each of the generic form An cos(ω0t) + Bn sin(ω0t), where An and Bn depend on the instantaneous position of the nth scatterer. Since these positions change with time, the coefficients also vary, although slowly over intervals comparable to 1/ω0. Statistical properties of the time varying sum functions A(t) and B (t) are studied analytically and with numerical simulations for various models of the sound wave and the Brownian motion. A principal problem adressed is that of determining the statistics of the time interval Δt over which a fixed number K of zero crossings occur for the sum A(t) cos(ω0t) + B(t) sin(ω0t), given that this interval is centered at a particular time, the pertinent quantity of interest being the relative error in the accumulative phase difference 2 π K / Δt − ω0 per unit time. The results support the general conclusions that smaller errors are expected for higher amplitude sound waves and for sound waves of lower frequency. [Work supported by ONR.]

On the ionization potential of small metal and dielectric particles

The ionization potential of small metal and dielectric spheres is considered in different frameworks: classical, semiclassical, and quantum mechanical density functional approach. Classical calculations give conflicting results, and the generally accepted result for the ionization potential of a metal sphere of radius R: WI(R)=bulk work function+(3/8)q2/R is shown to be wrong, resulting from the classical image potential too close to the metal surface. Using appropriate cutoff to the image potential, the result WI(R)=bulk work function+(1/2)q2/R (previously obtained from solvation energy considerations) is recovered. Experimental results on relatively large particles are in agreement with the latter result. For very small clusters, deviations of experimental results from this classical behavior are shown by a density functional calculation to arise from quantum mechanical effects. These are first the spilloff of the electronic wave functions beyond the cluster edge and secondly from exchange and correlation contributions.

Localization and absorption of waves in a weakly dissipative disordered medium.

The effect of a small imaginary part ${\ensuremath{\epsilon}}_{2}$ to the dielectric constant on the propagation of waves in a disordered medium near the Anderson localization transition is considered. The n\ensuremath{\rightarrow}0 replica-field representation of the averaged Green's function leads to a nonlinear \ensuremath{\sigma} model with a symmetry-breaking perturbation proportional to ${\ensuremath{\epsilon}}_{2}$. In d=2+\ensuremath{\epsilon}, the renormalized energy absorption coefficient is shown to increase anomalously with frequency \ensuremath{\omega} near the mobility edge ${\ensuremath{\omega}}^{\mathrm{*}}$ as \ensuremath{\alpha}\ensuremath{\sim}(${\ensuremath{\omega}}^{\mathrm{*}}$-\ensuremath{\omega}${)}^{\mathrm{\ensuremath{-}}(d\mathrm{\ensuremath{-}}2)\ensuremath{\nu}/2}$, \ensuremath{\nu}=1/\ensuremath{\epsilon}. It is shown that the wavelength ${\ensuremath{\lambda}}^{\mathrm{*}}$ below which localization occurs is related to the elastic mean free path l by (l/${\ensuremath{\lambda}}^{\mathrm{*}}$${)}^{d\mathrm{\ensuremath{-}}1}$\ensuremath{\sim}1/\ensuremath{\epsilon} (d>2). This may occur near the limit of attainable disorder from a quenched random array of small dielectric or metallic spheres.

A model for interstellar extinction

From an analysis of the interstellar extinction we conclude that interstellar grains are of three main kinds: graphite spheres of radii ∼0.02 μm making up ∼10% of the total grain mass, small dielectric spheres of radius about 0.04 μm making up ∼25% of the mass, and hollow dielectric cylinders containing metallic iron with diameters of ∼2/3 μm making up ∼45% of the mass. The remaining ∼20% consists of other metals and metal oxides. The main dielectric component of the grains appears to be comprised of organic material.

Inelastic light emission from spherical particles and cylindrical fibers

AbstractThe inelastic light‐scattering properties of molecules embedded in small dielectric spheres and cylinders are presented. The angular distribution of inelastically scattered radiation is shown to differ from that of elastically scattered radiation from the same dielectric particle. Furthermore, the inelastic emission spectra from the embedded molecules exhibit additional peaks which are not present for the same molecules embedded in a much larger dielectric object. The angular distribution, which is a complicated function of the size, shape and refractive index of the host dielectric particle and the internal molecular distribution, contains information needed to deduce the concentrations of the embedded molecules, as well as to characterize the morphology of the dielectric particle. The emission spectra contain the natural mode resonances of the particle in addition to the usual bulk‐observed spectral characteristics of the embedded molecules. Consequently, both angular and spectral distributions are important in the interpretation of inelastic scattering (spontaneous Raman or fluorescence) from molecules embedded in or coated on dielectric particles.