Debye Series Research Articles

Asymptotics of eigenwaves of a smooth irregular spherical anisotropic waveguide

Based on the Debye series modified with respect to the method of horizontal beams and vertical modes, the asymptotics of eigenwaves of a smooth irregular anisotropic spherical anisotropic waveguide channel is constructed.

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.

Scattering by an elastic shell with nonconcentric cylindrical surfaces: Generalized Debye series expansion

The scattered pressure by a solid elastic shell defined by two nonconcentric cylindrical surfaces is considered; the cylinder axes are parallel. The shell is immersed in a fluid and is excited by a monochromatic plane wave impinging on it normally to the axis. The generalized Debye expansion (GDE) formalism is used to physically analyze all the local interactions involving in the scattering process. Two cylindrical coordinate systems, each associated with one cylindrical surface, are introduced. With this choice, all the needed cylindrical wave functions can be written either in one system or the other thanks to the Graf addition theorem and the boundary conditions can be simply expressed; the scattered pressure can be calculated. It is also possible to relate the elements of the S matrix to the local interaction coefficients, i.e., reflexion and transmission modal coefficients coming from the GDE. In next future, it allows to obtain an expression of the background which is useful to calculate the target resonances.

Assessing the contributions of surface waves and complex rays to far-field Mie scattering by use of the Debye series

The contributions of complex rays and the secondary radiation shed by surface waves to scattering by a dielectric sphere are calculated in the context of the Debye-series expansion of the Mie scattering amplitudes. Also, the contributions of geometrical rays are reviewed and compared with those of the Debye series. Interference effects among surface waves, complex rays, and geometrical rays are calculated, and the possibility of observing these interference effects is discussed. Experimental data supporting the observation of a surface-wave–geometrical-ray-interference pattern are presented.

Reflection and refraction of a heterogeneous plane wave by a solid layer

Reflection and refraction of harmonic heterogeneous waves by a plane, isotropic viscoelastic layer are described in the framework of linear acoustics. The reflection and transmission coefficients are obtained by two different approaches: firstly, using the well-known model of Brekhovskikh for the case of a homogeneous plane wave, secondly, using an expansion into a geometrical Debye's series through a matrix sum. the energy balance is also established. Some particular cases are analyzed and the results are discussed. For instance, although obeying the energy conservation law, the solution may have an unexpected behaviour due to heterogeneity.

Reflection/refraction of a solid layer by Debye's series expansion

The aim of this paper is to expand in a Debye's series the well-known solution of the reflection/refraction of a plane wave at a solid layer. In this form the solution can be considered as a series of countable interferences. Several methods of expansion into a geometrical Debye's series are considered: using a matrix sum (one summation); taking into account all double reflections/refractions on both interfaces (three summations); and, finally, analysing the elementary reflection/refraction on each interface separately (seven summations). Energy balance is then considered at the end of the paper.

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.

Debye-series approach in analysis of transient radiation from a Hertzian dipole antenna in a cavity in a medium

We present an analysis of the radiation produced when an electrically short transiently excited dipole antenna radiates from within a cavity in a medium. We show that, if one formulates the problem in terms of a Debye series in the Laplace domain, complete results may be obtained analytically in the lossless case. When loss is present in the surrounding medium, some numerical evaluations are required to obtain the complete solution. As an example we treat the problem of communication between a transmitting antenna located beneath a metal craft on the surface of a lake and a receiver some distance below the surface.