Improved Gaussian beam-scattering algorithm.

The localized model of the beam-shape coefficients for Gaussian beam-scattering theory by a spherical particle provides a great simplification in the numerical implementation of the theory. We derive an alternative form for the localized coefficients that is more convenient for computer computations and that provides physical insight into the details of the scattering process. We construct a FORTRAN program for Gaussian beam scattering with the localized model and compare its computer run time on a personal computer with that of a traditional Mie scattering program and with three other published methods for computing Gaussian beam scattering. We show that the analytical form of the beam-shape coefficients makes evident the fact that the excitation rate of morphology-dependent resonances is greatly enhanced for far off-axis incidence of the Gaussian beam.

Theory of the observations made of high-order rainbows from a single water droplet.

Over a dozen rainbows have been observed in a single water droplet. They appear as glare spots on the water droplet which take on coloration at the appropriate rainbow angles. The appearance of rainbows as colored glare spots in this situation is understood in terms of the caustics created in the vicinity of the droplet by the refracting light rays. The angular positions of the glare spots are understood in terms of the Fourier transform of the geometric scattering amplitude. The rainbow glare spots are also found to appear numerically in the Fourier transform of the Mie scattered fields. An additional glare spot produced by rays at grazing incidence and not attributable to geometric optics also appears numerically in the Fourier transformed Mie fields.

Ray scattering by an arbitrarily oriented spheroid. I. Diffraction and specular reflection.

Diffraction and reflection of an arbitrarily polarized plane wave by an arbitrarily oriented spheroid in the short-wavelength limit are considered in the context of ray theory. A closed-form solution for both diffraction and reflection is obtained, and the polarization character of the diffracted plus reflected electric field is obtained. It is found that the magnitude of the reflected electric field is multivalued for forward scattering. This is interpreted in terms of the variation of the spheroid's Gaussian curvature at the points where grazing ray incidence occurs.

Ray scattering by an arbitrarily oriented spheroid. II. Transmission and cross-polarization effects.

Transmission of an arbitrarily polarized plane wave by an arbitrarily oriented spheroid in the short-wavelength limit is considered in the context of ray theory. The transmitted electric field is added to the diffracted plus reflected ray-theory electric field that was previously derived to obtain an approximation to the far-zone scattered intensity in the forward hemisphere. Two different types of cross-polarization effects are found. These are (a) a rotation of the polarization state of the transmitted rays from when they are referenced with respect to their entrance into the spheroid to when they are referenced with respect to their exit from it and (b) a rotation of the polarization state of the transmitted rays when they are referenced with respect to the polarization state of the diffracted plus reflected rays.

Role of multiple scattering in cross-correlated light scattering with a single laser beam.

Previous systems for measuring cross-correlated light scattering by small particles suspended in a liquid with multiple-scattering suppression have illuminated the particles with two laser beams. It is shown that multiple-scattering suppression should also occur in cross correlation for a system that employs a single laser beam and two closely spaced detectors with wide fields of view. The single-scattering, double-scattering, and single-double-scattering cross-term contributions to the intensity cross-correlation function are calculated. It is found that the two cross terms, when added together, are unimportant for both autocorrelation and cross correlation. The amplitude of the double-scattering term can be greatly diminished by judicious detector spacing because the spatial coherence area in the detector plane for double scattering is much smaller than that for single scattering.

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

When a laser beam scatters from a microparticle whose shape deviates from that of a sphere, a number of partial waves of the incident beam couple to a given partial wave of the scattered and interior fields. As a result, partial-wave coupling caused by small surface irregularities of a liquid droplet provides the mechanism for exciting low-radial-order morphology-dependent resonances.

Ray theory analysis of the shadow blister effect.

When an extended light source such as the Sun illuminates two objects so that their shadows lie close to each other, the shadow of one of the objects occasionally appears to bulge out toward the shadow of the other. This effect is caused by the overlap of the penumbras of the shadows and is analyzed here with ray theory. A laboratory demonstration of this phenomenon is performed and compared with theoretical predictions.

Interference enhancement of the internal fields at structural scattering resonances of a coated sphere.

We examine the interior electromagnetic energy density of a coated nonabsorbing sphere at a number of scattering resonances. As is the case for an uncoated sphere, the interior energy density becomes large at the a(p)(l) and b(p)(l) resonances. It becomes especially large for p - 1 values of the coating thickness at resonance. These p - 1 enhancements are analogous to the interference maxima that occur in the intensity reflectance of two thin films in contact.

Supernumerary spacing of rainbows produced by an elliptical-cross-section cylinder. I. Theory.

A sequence of rainbows is produced in light scattering by a particle of high symmetry in the short-wavelength limit, and a supernumerary interference pattern occurs to one side of each rainbow. Using both a ray-tracing procedure and the Debye-series decomposition of first-order perturbation wave theory, I examine the spacing of the supernumerary maxima and minima as a function of the cylinder rotation angle when an elliptical-cross-section cylinder is normally illuminated by a plane wave. I find that the supernumerary spacing depends sensitively on the cylinder-cross-section shape, and the spacing varies sinusoidally as a function of the cylinder rotation angle for small cylinder ellipticity. I also find that relatively large uncertainties in the supernumerary spacing affect the rainbow angle only minimally.

Electric field autocorrelation functions for beginning multiple rayleigh scattering.

The polarization-resolved electric field autocorrelation function for p-order scattering was derived from the order-of-scattering solution of the exact equations for electromagnetic multiple Rayleigh scattering and was calculated for 2

Semiclassical scattering of an electric dipole source inside a spherical particle.

Semiclassical scattering phenomena appearing in the far-zone scattered intensity of a point source of electromagnetic radiation inside a spherical particle are examined in the context of both ray theory and wave theory, and the evolution of the phenomena is studied as a function of source position. A number of semiclassical effects that do not occur for plane-wave scattering by the sphere appear prominently for scattering by an interior source. These include a series of scattering resonances and a new family of rainbows in regions of otherwise total internal reflection. Diffractive effects accompanying the semiclassical phenomena are also examined.

Mie theory model of the corona.

We performed a calculation of the corona colors that employed Mie theory to obtain the scattered light intensity. The scattered intensity was integrated over the visible spectrum for a number of different cloud droplet size distriubtions. The results were converted to chromaticity coordinates, convolved with the angular size of the sun, and plotted on the 1931 CIE chromaticity diagram. The results were compared to observations of multiple-ring coronas. It was found that, when using Mie theory to estimate cloud droplet sizes, water droplets with diameters in the 7-microm less, similar D less, similar 15-microm range produced the 13 multiple-ring coronas that were observed.

Light and color in the open air-introduction by the feature editors.

The natural environment is still rich in new observable phenomena despite centuries of scientific observation. Reflecting this fact, the papers in this feature issue of Applied Optics report the observation and analysis of both new and well-known naked-eye optical phenomena.

Correlated light scattering by a dense distribution of condensation droplets on a window pane.

An analytical model of the scattering structure factor for an assembly of noninteracting hard disks has recently appeared in the literature [Phys. Rev. A 42, 5978-5989 (1990)]. We employ this model to calculate correlated light scattering by monodispersions and binary mixtures of condensation droplets on a window pane. We find that an area fraction of ƒ ≥ 0.6 is required for producing the near-forward direction scattering suppression and that a moderately wide polydispersion of droplet sizes is capable of producing the experimentally observed bright ring of colored light.

Far-field scattering of an axisymmetric laser beam of arbitrary profile by an on-axis spherical particle.

Experimental laser beam profiles often deviate somewhat from the ideal Gaussian shape of the TEM(00) laser mode. In order to take these deviations into account when calculating light scattering, we propose a method for approximating the beam shape coefficients in the partial wave expansion of an experimental laser beam. We then compute scattering by a single dielectric spherical particle placed on the beam's axis using this method and compare our results to laboratory data. Our model calculations fit the laboratory data well.

Far-field scattering of a non-Gaussian off-axis axisymmetric laser beam by a spherical particle.

Experimental laser beam profiles often deviate somewhat from the ideal Gaussian shape of the axisymmetric TEM(00) laser mode. To take these deviations into account when calculating light scattering of an off-axis beam by a spherical particle, we use our phase-modeling method to approximate the beam-shape coefficients in the partial wave expansion of an experimental laser beam. We then use these beam-shape coefficients to compute the near-forward direction scattering of the off-axis beam by the particle. Our results are compared with laboratory data, and we give a physical interpretation of the various features observed in the angular scattering patterns.

Non-Debye enhancements in the Mie scattering of light from a single water droplet.

The glare spots usually seen on a single water droplet which has been illuminated by a plane wave are produced by geometrical rays which correspond to the different terms of the Debye series expansion of the Mie scattered field. Recently other glare spot enhancements have been predicted which correspond to scattering resonances coupling to the orbiting rays associated with high-order geometrical rainbows. We observed the non-Debye enhancement of the eleventh-order rainbow glare spot at an observation angle of 90 degrees on a 3.5-mm water droplet illuminated by polarized He-Ne laser light.

Partial-wave representations of laser beams for use in light-scattering calculations.

In the framework of generalized Lorenz-Mie theory, laser beams are described by sets of beam-shape coefficients. The modified localized approximation to evaluate these coefficients for a focused Gaussian beam is presented. A new description of Gaussian beams, called standard beams, is introduced. A comparison is made between the values of the beam-shape coefficients in the framework of the localized approximation and the beam-shape coefficients of standard beams. This comparison leads to new insights concerning the electromagnetic description of laser beams. The relevance of our discussion is enhanced by a demonstration that the localized approximation provides a very satisfactory description of top-hat beams as well.

Rainbow scattering by a coated sphere.

We examine the behavior of the first-order rainbow for a coated sphere by using both ray theory and Aden-Kerker wave theory as the radius of the core a(12) and the thickness of the coating δ are varied. As the ratio δ/a(12) increases from 10(-4) to 0.33, we find three classes of rainbow phenomena that cannot occur for a homogeneous-sphere rainbow. For δ/a(12) ≲ 10(-3), the rainbow intensity is an oscillatory function of the coating thickness, for δ/a(12) ≈ 10(-2), the first-order rainbow breaks into a pair of twin rainbows, and for δ/a(12) ≈ 0.33, various rainbow-extinction transitions occur. Each of these effects is analyzed, and their physical interpretations are given. A Debye series decomposition of coated-sphere partial-wave scattering amplitudes is also performed and aids in the analysis.

Rayleigh-Brillouin scattering to determine one-dimensional temperature and number density profiles of a gas flow field.

Rayleigh-Brillouin spectra for heated nitrogen gas were measured by imaging the output of a Fabry-Perot interferometer onto a CCD array. The spectra were compared with the theoretical 6-moment model of Rayleigh-Brillouin scattering convolved with the Fabry-Perot instrument function. Estimates of the temperature and a dimensionless parameter proportional to the number density of the gas as functions of position in the laser beam were calculated by least-squares deviation fits between theory and experiment.