Debye Series Expansion of Electromagnetic Scattering by Inhomogeneous Particles and Its Applications
|School||Xi'an University of Electronic Science and Technology|
|Keywords||Electromagnetic scattering Mie theory Debye series Rainbow Shaped beam Particle sizing|
Most of particles encountered in many industrial process and scientific research have inhomogeneous structures caused by many effects for instance its character, mechanism of form, industrial process, practical need, etc. Biological particles, coated particles in the atmosphere, Graded-Index Polymer Optical Fiber (GI-POF), oil droplet in spray chamber and so on are all inhomogeneous particles. Of all theories of electromagnetic scattering, Debye series expansion (DSE) which is a rigorous theory can be employed to the analysis of scattering mechanism and is of great practial significance. On the basis of Debye series for homogeneous and coated spheres, this thesis is devoted to the systemic research on Debye series of plane wave and shaped beam scattering by inhomogeneous spherical and infinitely long cylindrical particles and its applications on many techniques, for instance particle sizing. The main works and achievements are summarized as follows:1. On the basis of Debye series expansion of electromagnetic scattering by homogeneous and coated spheres, Debye series formula for multilayered spheres is derived, which can clarify the physical origins of many effects that occur in electromagnetic scattering, and is of great importance to the study of scattering characteristics of particles. An efficient numerical algorithm is obtained as well.2. After numerical verifications, Debye series formula is employed to the research on a special rainbow, namely multi-first-order rainbows, which contains the information about the size and refractive index of each layer and is of great importance to the research on characteristics of multilayered spheres. Multi-first-order rainbows can be employed to the measurement of particle parameters. Because Debye series can isolate the effect of each contribution and be convenient to the study of single-rainbow intensities and interference intensities of mixed-order rainbows. This is a very important character of Debye series, and so provides an efficient way to the research on scattering characteristics of particles and scattering mechanism.3. Debye series formula for shaped beam scattering by inhomogeneous spherical particles is obtained, and the calculation of Beam Shaped Coefficients (BSC’s), Gaussian beam as example, is studied as well. On the basis of Integral Localized Approximation, BSC’s expression of Bessel functions for first-order Gaussian beam is obtained, and such formula can be employed to the simulation of strongly focused beam. Integral Localized Approximation is an efficient and stable algorithm to the calculation of BSC’s. First rainbow is mainly used in rainbow measurement method, so the obtained formula is employed to the research on scattering mechanism of first rainbow.4. Debye series formula of normally incident plane-wave scattering by an infinite multilayered cylinder is obtained too, and an efficient algorithm is presented as well. Simulations have been done on a personal computer Intel Pentium 4 CPU 2.93 GHz with 512 Mbytes of RAM. In this configuration we can calculate for a cylinder with size parameter as large as about 8000 with 1000 layers. The limit is due to the memory of the computer. Single-order rainbow intensities and interference intensities of mixed-order rainbow are simulated, and the intensity for spheres is compared with that for cylinders.5. On the basis of former job, the interaction between shaped beam and inhomogeneous cylinder is studied and presented Debye series formula. Taking Gaussian beam as example, Integral method and Localized Approximation for BSC’s is discussed. Finally the far-field scattered intensity is simulated.6. Generalized Debye Series Expansion (GDSE) is derived with matrix formulation for tilted incident plane-wave scattering by multilayered cylinders. When the electromagnetic waves illuminate diagonally the cylinder, the cross-polarization exists, and it is hard to obtain the formula if the common DSE is employed. On the basis of matrix formulation, GDSE can conveniently and easily obtain the formula.The far-field scattered intensities for ice cylinders and doubly clad image-transmitting fibers are simulated, and the results are compared with those published in the literature to verify the formula and code. The first-order rainbow intensities of different tilt angle are simulated, and the results are obtained that the rainbow angles increase with the increasing of tilt angles and that there is a qualitative similarity between varying the tilt angle and of the incident plane wave and varying the refractive index at normal incidence. The intensity of plane wave scattering by Graded-Index Polymer Optical Fiber (GI-POF) is finally simulated.