Debye Series Analysis of Forward Scattering by a Multi-layered Sphere

Abstract

A formula of Debye series for forward scattering by a multi-layered sphere is presented. The Debye series expansion allows for the decomposition of the global scattering process in a series of local interactions, and clarifies the physical origins of many effects that occur in electromagnetic scattering. The forward-scattering pattern contains many information about the properties, and the method is widely used for determining such properties on the basis of forward-scattering pattern. In the paper, the Debye series is employed to the study of forward scattering by a multi-layered sphere, which is of great importance to the study of characteristics of particles. DOI: 10.2529/PIERS060906223536 For many practical applications such as combustion, environmental control, fluid mechanics, and chemical reaction, we need to measure the properties of particles such as size and refractive indextemperature ratio quickly and precisely. The forward-scattering pattern contains many information about the properties, and it is widely used for determining such properties on the basis of forwardscattering pattern. The scattering of a plane electromagnetic wave by a single multilayered spherical particle has been extensively discussed within a theoretical framework similar to the Lorenz-Mie Theory (LMT) in many areas of theoretical and applied research, such as combustion, chemical engineering, remote sensing, communication, biology, and medicine [1]. The Mie theory is a rigorous solution of the Maxwell equations and contains all effects that contribute to the scattering [2, 3]. But it gives few clues to the various physical processes that are responsible for the scattering [2–4]. Full geometrical optics theory can be used with reasonable accuracy for forward direction light scattering computations related to particle sizing and characterization [5], and has been extended to forward scattering by coated particles [6]. But as soon as the scatters are complicated, for instance multi-layered sphere, the construction of the geometrical optics approximation formula is very difficult. The Debye series writes each term of the Mie series as another infinite series, and clarifies the physical origins of many effect that occur in electromagnetic scattering [2, 3], which is of great importance in the study of characteristics of electromagnetic scattering. The Debye series was originally formulated for scattering of a normally incident plane wave by a cylinder [7] and has been subsequently extended to scattering by a sphere [8, 9], the internal fields [10], scattering by a coated sphere [11], scattering of a plane wave diagonally incident on a cylinder [12], and scattering by a multilayered sphere [2] and a spherical Bragg grating [13]. We consider an l-layered dielectric sphere whose refractive index of any layer j is mj (region j) and whose radius a is embedded in a dielectric medium of refractive index ml+1 (region l + 1), as shown in Fig. 1. When the sphere is illuminated by a monochromatic plane wave of wavelength λ, the classic Mie coefficients an and b l n can be expanded in the Debye series [2] an bn }