Charles L. Adler

Rainbow Scattering by a Cylinder with a Nearly Elliptical Cross Section

We both theoretically and experimentally examine the behavior of the first- and the second-order rainbows produced by a normally illuminated glass rod, which has a nearly elliptical cross section, as it is rotated about its major axis. We decompose the measured rainbow angle, taken as a function of the rods rotation angle, into a Fourier series and find that the rods refractive index, average ellipticity, and deviation from ellipticity are encoded primarily in the m = 0, 2, 3 Fourier coefficients, respectively. We determine these parameters for our glass rod and, where possible, compare them with independent measurements. We find that the average ellipticity of the rod agrees well with direct measurements, but that the rods diameter inferred from the spacing of the supernumeraries of the first-order rainbow is significantly larger than that obtained by direct measurement. We also determine the conditions under which the deviation of falling water droplets from an oblate spheroidal shape permits the first few supernumeraries of the second-order rainbow to be observed in a rain shower.

Exterior caustics produced in scattering of a diagonally incident plane wave by a circular cylinder: semiclassical scattering theory analysis.

We use the semiclassical limit of electromagnetic wave scattering theory to determine the properties of the exterior caustics of a diagonally incident plane wave scattered by an infinitely long homogeneous dielectric circular cylinder in both the near zone and the far zone. The transmission caustic has an exterior/interior cusp transition as the tilt angle of the incident beam is increased, and each of the rainbow caustics has a farzone rainbow/exterior cusp transition and an exterior/interior cusp transition as the incident beam tilt angle is increased. We experimentally observe and analyze both transitions of the first-order rainbow. We also compare the predictions of the semiclassical approximation with those of ray theory and exact electromagnetic wave scattering theory.

Twin-rainbow metrology. I. Measurement of the thickness of a thin liquid film draining under gravity

We describe twin-rainbow metrology, a new optical technique used to measure the thickness of thin films in a cylindrical geometry. We also present an application of the technique: measurement of the thickness of a Newtonian fluid draining under gravity. We compare these measurements with fluid mechanics models.

Experimental Observation of Rainbow Scattering by a Coated Cylinder: Twin Primary Rainbows and Thin-Film Interference

We experimentally examine the primary rainbow created by the illumination of a coated cylinder. We present a simple technique for varying the coating thickness over a wide range of values, and we see evidence for two different scattering regimes. In one, where the coating thickness is large, twin rainbows are produced. In the second, where the coating is thin enough to act as a thin film, a single rainbow is produced whose intensity varies periodically as the coating thickness varies. We find good agreement with previous theoretical predictions.

Supernumerary spacing of rainbows produced by an elliptical-cross-section cylinder. II. Experiment

We measured the supernumerary spacing parameter of the first- and second-order rainbows of two glass rods, each having an approximately elliptical cross section, as a function of the rods rotation angle. We attribute large fluctuations in the supernumerary spacing parameter to small local inhomogeneities in the rods refractive index. The low-pass filtered first-order rainbow experimental data agree with the prediction of ray-tracing-wave-front modeling to within a few percent, and the second-order rainbow data exhibit additional effects that are due to rod nonellipticity.

Amplification of high-order rainbows of a cylinder with an elliptical cross section

The intensity of high-order rainbows for normally incident light and certain rotation angles of a cylinder with an elliptical cross section is greatly amplified with respect to the intensity for a circular cross-sectional cylinder. The amplification is due to a number of the internal reflections occurring past the critical angle for total internal reflection, and the effect is especially strong for odd-order rainbows, beginning with the third order. Experimentally, the fourth- and the fifth-order rainbows of a nearly elliptical cross-sectional glass rod were observed and analyzed.

Twin-rainbow metrology

In this document, we describe twin-rainbow metrology, a non-invasive optical technique for measurement of the thicknesses of thin solid and liquid films to sub-micron accuracy. TRM allows measurement of coating thicknesses in two separate ways: first, directly, by a measurement of the difference between two scattering angles; ; and second, by the analysis of a Moire pattern found in the superposition of two sets of interference fringes. In this paper we will examine the conditions under which twin-rainbow metrology can be used, the accuracy of measurements made by it, and its potential applications.

Analysis of the shadow-sausage effect caustic

We analyze the optical caustic produced by light refracted at the curved meniscus surrounding a cylindrical rod standing partially out of a liquid-filled container. When the rod is tilted from the vertical or when light is diagonally incident, the caustic is a four-cusped astroid with two of its cusps obscured by the rods shadow. If a portion of the flat end of the rod is raised above the water level, the caustic evolves into a pattern of five interlocking cusps. The five cusps result from symmetry breaking of a three-cusped surface perturbation caustic.

Rainbows in the grass. II. Arbitrary diagonal incidence

We consider external reflection rainbow caustics due to the reflection of light from a pendant droplet where the light rays are at an arbitrary angle with respect to the horizontal. We compare this theory to observation of glare spots from pendant drops on grass; we also consider the potential application of this theory to the determination of liquid surface tension.

A frequency selective atom interferometer magnetometer

In this article, we discuss the magnetic-field frequency selectivity of a time-domain interferometer based on the number and timing of intermediate pulses. We theoretically show that by adjusting the number of pulses and the -pulse timing, we can control the frequency selectivity of the interferometer to time varying and DC magnetic fields. We present experimental data demonstrating increased coherence time due to bandwidth filtering with the inclusion of a pulse between the initial and final pulses, which mitigates sensitivity to low frequency magnetic fields.