Debye-series analysis of the first-order rainbow produced in scattering of a diagonally incident plane wave by a circular cylinder

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

“…But in the context of catastrophe theory, 1 they are merely different manifestations of the same general caustic morphology if the assumptions of normal incidence and plane waves are relaxed. For example, if a plane wave illuminates the cylinder at a progressively steeper angle of incidence or, equivalently, if the refractive index of the cylinder progressively increases, 2 the two branches of the far-zone (p Ϫ 1)-order rainbow caustic approach each other, join together at infinity [3][4][5][6][7] in what has been called the caustic merging transition, and evolve into a near-zone focusing caustic. If the angle of incidence is further increased, the focal line of the near-zone caustic approaches the cylinder and touches its surface, and the caustic evolves into a cusp lying entirely within the cylinder.…”

High-order interior caustics produced in scattering of a diagonally incident plane wave by a circular cylinder

“…32 The p ϭ 1 cylindrical aberration caustic of a thin fiber at normal incidence has been studied by Benincasa et al 2 To the best of our knowledge, the caustics produced by a plane wave diagonally incident on a cylinder have not been analyzed in detail. The purposes of this paper and a companion paper 33 are to describe these caustics theoretically and to observe them experimentally. In this paper the caustics are described in terms of ray theory, and various of the 1 р p р 6 interior caustics are observed.…”

Debye series for light scattering by a nonspherical particle

“…(106) and (107). These equations can be written as a set of coupled matrix equations as C = R 11,TM/TE D + R 11,TM/TM C + T 21 …”

“…It is noteworthy that the Debye series with diagonal plane-wave incidence on a circular cylinder was derived in Ref. [21]. Generalizing the incident wave profile, the Debye series for shaped beam incidence was derived for a sphere through including a set of BSC's defined in GLMT [22].…”

“…(42) and (48), respectively. The partial wave internal transmission and external reflection amplitudes T 21 and R 22 are obtained using Eqs. (41) and (49), respectively.…”