Physical Consequences of Anomalies in Nonlocal Potential Problems

An s-wave two-body separable potential may give rise to several phenomena which are absent for nonsingular local potentials. We examine the physical implications of a well known example of such phenomena, the continuum bound state, as well as of two lesser known anomalies, the so-called positive energy spurious state and negative energy bound states with improper long-range behavior. By examining these anomalies in light of Levinson\u27s theorem, Wigner\u27s phase shift inequality, and the effect of a perturbation on the anomalous states by their insertion in a three-body scattering situation, we find in agreement with previous studies that the continuum bound state acts as a resonance of negligible width. However, we find it difficult to see how the presence of a spurious state can be detected experimentally

Light and Color in the Open Air: Introduction to the Feature Issue

This special feature of Applied Optics reports the results of new experimental and theoretical research concerning a number of naked-eye optical phenomena, including ice-crystal halo displays, mirages, rainbows, glories, optical caustics, clear-sky phenomena, cloud coronas, cloud iridescence, and the extinction of skylight. (C) 2003 Optical Society of America

Light and Color in the Open Air: Introduction to the Feature Issue

This special feature of Applied Optics reports the results of new experimental and theoretical research concerning a number of naked-eye optical phenomena, including ice-crystal halo displays, mirages, rainbows, glories, optical caustics, clear-sky phenomena, cloud coronas, cloud iridescence, and the extinction of skylight. (C) 2003 Optical Society of America

Exterior Caustics Produced in Scattering of a Diagonally Incident Plane Wave by a Circular Cylinder: Semiclassical Scattering Theory Analysis

Rie 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 far-zone 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. (C) 2000 Optical Society of America [S0740-3232(00)01010-3]. OCIS codes: 080.1510, 290.4020

Exterior Caustics Produced in Scattering of a Diagonally Incident Plane Wave by a Circular Cylinder: Semiclassical Scattering Theory Analysis

Rie 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 far-zone 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. (C) 2000 Optical Society of America [S0740-3232(00)01010-3]. OCIS codes: 080.1510, 290.4020

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 rod\u27s rotation angle, into a Fourier series and find that the rod\u27s 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 rod\u27s 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. (C) 1998 Optical Society of America

Rainbows in the Grass. I. External Reflection Rainbows from Pendant Droplets

In the mid-morning on a sunny day one can sometimes see glare spots associated with uncolored rainbow (i.e., fold) caustics due to the sunlight reflected from the surface of dew or guttation drops. We show that these dewdrop reflection rainbows are due to places on the droplet (i.e., from an inflection circle ) where its Gaussian curvature becomes zero. We work out the theory of such caustics with horizontally incident light and present a comparison of the theory to measurements made in the laboratory. (C) 2008 Optical Society of Americ

Rainbows in the Grass. II. Arbitrary Diagonal Incidence

We consider external reflection rainbow caustic,,; 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. (C) 2008 Optical Society of Americ