Peter W. Barber

Spatial distribution of the internal and near-field intensities of large cylindrical and spherical scatterers

Spatial distributions of the near-field and internal electromagnetic intensities have been calculated and experimentally observed for dielectric cylinders and spheres which are large relative to the incident wavelength. Two prominent features of the calculated results are the high intensity peaks which exist in both the internal and near fields of these objects, even for nonresonant conditions, and the well-defined shadow behind the objects. Such intensity distributions were confirmed by using the fluorescence from iodine vapor to image the near-field intensity distribution and the fluorescence from ethanol droplets impregnated with rhodamine 590 to image the internal-intensity distribution.

Near-resonance excitation of dielectric spheres with plane waves and off-axis Gaussian beams

Modes haυing high-Q morphology-dependent resonances (MDR’s) can dominate the internal energy distribution in spheres eυen when excited by many linewidths from the resonant location.

Frequency splitting of degenerate spherical cavity modes: stimulated Raman scattering spectrum of deformed droplets

High-resolution interferometric spectra of the stimulated Raman scattering (SRS) spectra from flowing ethanol droplets are presented. The linewidths of the SRS peaks are less than 0.005 cm(-1), and the equal frequency spacings of the SRS peaks are an order of magnitude smaller than the spacings for morphology-dependent resonances of a perfect sphere. The observed results from droplets that are deformed by inertial effects are consistent with T-matrix and perturbation predictions of frequency splitting into the various azimuthal modes of a (2n + 1)-degenerate morphology-dependent resonance with angular momentum n in a perfect sphere.

Energy-density distribution inside large nonabsorbing spheres by using Mie theory and geometrical optics

Mie theory and geometrical-optics ray tracing are used to obtain the distribution of electric energy density inside a nonabsorbing micrometer-sized sphere illuminated by a polarized plane wave. The Mie solution shows the multiply reflected geometrical-optics rays inside a sphere having a diameter of ~ 150 free-space wavelengths (size parameter = circumference/wavelength = 500). The geometrical-optics result shows the major features of the Mie solution and provides a physical interpretation of the electromagnetic interactions that result in the observed energy-density distributions. Both solutions show internal on-axis energy-density maxima inside the shadow surface of the sphere. The region of greatest enhanced energy density is approximately one internal wavelength in diameter and approximately twenty internal wavelengths in length.

Morphology-dependent resonances in radially inhomogeneous spheres

Resonant frequencies and quality-factor (Q’s) of the morphology-dependent resonances of radially inhomogeneous spherical particles are computed with a Runge–Kutta method. In one type of inhomogeneity the refractive index of the sphere decreases smoothly from a core value of 1.5 to a value of 1.0(0.1)1.4 at the surface. The fraction of the radius over which the refractive index rolls off varies from 0.01 to 0.25. As the refractive index near the surface is decreased, the resonant frequencies shift to higher values and the Q’s decrease. Numerical results for modes with Q’s in the range of 500–1016 show that, when the change in refractive index occurs in only the outer few percent of the droplet radius, the change in the Q is less than 20%. Calculated resonant frequencies and Q’s simulating a refractive index that increases near the surface are also shown.

Time dependence of internal intensity of a dielectric sphere on and near resonance

Transient intensities inside a large dielectric sphere (circumference/incident wavelength > 50) are computed for excitation with plane-wave pulses having a Gaussian time dependence. The center frequency of the pulse is either on or near a morphology-dependent resonance (MDR). For each internal point considered, the time dependence of the electric field is determined from the frequency spectrum of the field at that point. The frequency spectrum is the product of the incident field spectrum and the transfer function at that point. In a sphere both the internal spectrum and the associated time dependence vary with spatial location, particularly when the incident frequency is near a MDR. The time dependence of the intensity at an internal location near the surface shows an exponential tail with a time constant of 1/Δωr, where Δωr is the resonant linewidth of the MDR, so long as the incident spectrum overlaps the MDR significantly, i.e., when Δω ≤ Δω0 and Δω0 ≥ Δωr, where Δω0 is the width of the incident pulse spectrum and Δω is the detuning, the difference between the MDR frequency and the center frequency of the incident Gaussian pulse.

Light scattering by two parallel glass fibers

Angular- and spectral-light-scattering measurements have been made for a glass fiber parallel to and at varying distances from a mirror. Scattering calculations have been made for two parallel fibers. The multiple-scattering effects between a fiber and its mirror image or between two fibers are shown to be quite similar, even for an imperfectly conducting mirror. The multiple scattering becomes less important when one fiber is not in the shadow of the other and when the separation is large. Also, the morphology-dependent resonances shift, and the line shapes change as the separation decreases. In the fiber–mirror configuration, the evanescent fields of the fiber couple to propagating surface plasmons of the metal mirror for TE polarization, greatly damping the scattered intensity.

Multiple scattering by two parallel dielectric cylinders

The solution of the multiple-scattering problem for two parallel infinite dielectric cylinders is considered for plane wave illumination perpendicular to the cylinder axes. Numerical results show the coupling effect with respect to cylinder size, separation, and orientation of the cylinder axes with respect to the incident wave. The coupling effect is illustrated by calculations of the internal and near-field intensity for end-on and broadside incidence. Results for circular cylinders with a size/wavelength ratio corresponding to a particular morphology-dependent resonance (size parameter = 45.329) show that the local effect of the resonance is completely damped when the two cylinders touch.

Information content of the scattering matrix for spheroidal particles

The T-matrix method is shown to be an efficient and accurate procedure for calculating the scattering matrix for randomly oriented nonspherical particles. Calculated scattering matrix elements for spheroidal particles are identical to those obtained by the spheroidal harmonic approach. T-matrix calculations for a randomly oriented finite length cylinder agree well with microwave scattering measurements. Analysis of the information content of the angular variation of the matrix elements for a set of moderately sized absorbing spheroidal particles is presented. It is found that the Fourier spectrum of the phase function and a parameter related to the depolarization ratio contain particle size and shape information, respectively.

Time-resolved shadowgraphs of large individual water and ethanol droplets vaporized by a pulsed CO 2 laser

Carbon dioxide laser-induced explosive vaporization of water and ethanol droplets at high laser fluence has been observed with time-resolved shadowgraphs. The asymmetry seen in the droplet vaporization can be qualitatively explained by comparison to the internal-field intensity distribution. A central green spot observed in the shadowgraph is attributed to the near-field distribution just outside the shadow face of the droplet when the droplet is illuminated by a visible laser. This spot can be used to probe the shape deformation and optical inhomogeneity of the droplet. The energy dependence of the explosive vaporization of water was also studied. Increasing the CO(2) laser fluence increases the rate of explosive vaporization.