Experimental observation of rainbow scattering by a coated cylinder: twin primary rainbows and thin-film interference

Inverse analysis of the rainbow for the case of low-coherent incident light to determine the diameter of a glass fiber

The aim of this paper is to discuss the possibility of a noninvasive, optical characterization of a transparent (glass) fiber on the basis of scattered light in the vicinity of a primary rainbow. Computational studies show that with the use of a spectrally adjusted incident beam of light, it is possible to form a rainbow with no strong nonlinearities typical for coherent light and that may be interpreted in terms of Airy's theory of rainbow. An inverse analysis is applied to obtain the fiber diameter with the help of a straightforward mathematical formula based on the Airy integral, corrected by comparison with the solution according to the complex angular momentum method.

Generalized Debye series expansion of electromagnetic plane wave scattering by an infinite multilayered cylinder at oblique incidence

The Debye series expansion expresses the Mie scattering coefficients into a series of Fresnel coefficients and gives physical interpretation of different scattering modes, but when an infinite multilayered cylinder is obliquely illuminated by electromagnetic plane waves, the scattering process becomes very complicated because of cross polarization. Based on the relation of boundary conditions between global scattering process and local scattering processes, the generalized Debye series expansion of plane wave scattering by an infinite multilayered cylinder at oblique incidence is derived in this paper. The formula and the code are verified by the comparison of the results with that of Lorenz-Mie theory in special cases and those presented in the literatures.

Assessment of refractive index gradients by standard rainbow thermometry

Up to now the application of rainbow thermometry has been limited to particle systems possessing a uniform refractive index. This is mostly due to the absence of an appropriate data inversion algorithm that takes into account the presence of a refractive index gradient. In this paper, for the first time to our knowledge, exploiting a generalization of the Airy theory, a data inversion algorithm for a single droplet, presenting a parabolic refractive index gradient, is proposed. This data inversion algorithm is used to compute the diameter and the refractive index at the core and at the surface of a simulated burning droplet. The results are compared to the analytical solutions showing a satisfactory agreement.

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 total-internal-reflection rainbows

A new class of rainbows is created when a droplet is illuminated from the inside by a point light source. The position of the rainbow depends on both the index of refraction of the droplet and the position of the light source, and the rainbow vanishes when the point source is too close to the center of the droplet. Here we experimentally measure the position of the transmission and one-internal-reflection total-internal-reflection rainbows, and the standard (primary) rainbow, as a function of light-source position.