Study Of Shaped Beam Scattering By Eccentric Particle And Rainbow Properties Of Spheroids

Due to the important guidance roles as well as practical implications inthe development of various research fields, such as biomedicine, physics,chemistry, and so on, the analysis of electromagnetic wave (optical)scattering by regular and irregular objects has always been a hot researchtopic. In the literatures, the scattering characteristic of a homogeneoussphere illuminated by a plane wave has been vastly studied. Along with theadventure and widely application of the laser source, the interaction ofshaped beam with natural or artificial inhomogeneous particles as well asnon-spherical particles requires further discussion to improve the opticalmeasurement accuracy.Two parts of work are included in this thesis. The First Part analyses theinteraction of an eccentric sphere with an arbitrary incident shaped beamwithin the framework of generalized Lorenz-Mie theory (GLMT). Byapplying the Extended Boundary Condition method (EBCM), the sensitivityof rainbow technique to the nonsphericity of droplets is studied in theSecond Part. The main contributions of the thesis are as follows:1. By applying the rotational and translational addition theorem of thevector spherical wave functions (VSWFs), an arbitrary incident shaped beamis expressed in terms of VSWFs in any Cartesian coordinates. A generalformulation for the transformation of spherical beam shape coefficients(BSCs) among different coordinate systems is derived. Specifically, anaxisymmetric beam is analyzed as an example. Simplified analyticalexpressions for the transformation of spherical BSCs among differentcoordinate systems are given, which can be implemented directly innumerical calculations. More specifically, value of the spherical BSCs of afocused Gaussian beam is calculated by applying the modified LocalizedApproximation for demonstration. It is worthy to notice that the currentmodified Localized Approximation does not commute with rotations ofcoordinate systems, which indicates that the current modified LocalizedApproximation is only valid for parallel illumination.2. Within the framework of GLMT, the scattering equations for an eccentric sphere illuminated by a shaped beam in an arbitrary orientation arederived and solved by applying the translational addition theorem of theVSWFs. Based on the corresponding theoretical results, a program is writtenin FORTRAN language to predict various scattering characteristics of aneccentric sphere illuminated by a shaped beam in an arbitrary orientation.Compared with the published program, the following improvements shouldbe indicated:(I) Shaped beam is introduced in our program, which is capableof predicting the scattering characteristics of an eccentric sphere illuminatedby a shaped beam in an arbitrary orientation. The plane wave scattering isincluded as a simple special case.(II) Our program is capable in theprediction of the internal, near-surface and far-zone field distributions of theeccentric sphere.(III) The calculation of basic functions is optimized,including the Riccati-Bessel functions, the associated Legendre functions andso on. The calculation of translational coefficients is implemented by thealgorithm derived by Mackowski instead of the one given by Ngo. By doingthese, the steadiness of the computation is improved.(IV) Our program iswritten in FORTRAN90, which is much more readable and implantable.3. Distributions of internal, near-surface and far-zone scattered fields ofan eccentric sphere illuminated by a focused Gaussian beam are analyzed.The effects on the field distributions from various parameters of theeccentric sphere and shaped beam, such as the relative size of the inclusion,the distance between centers of two spheres, the beam waist radius and theincident angle of shaped beam, are analyzed. This study is essential to theunderstanding of physical interaction between particles and shaped beam,especially to the research of nonlinear optical phenomenon, such asstimulated Raman scattering, stimulated Brillouin scattering, and so on. Itwill also benefit the detection and identification of the internal structure ofsmall particles.4. Within the framework of GLMT, theoretical investigation of thebehavior of morphology-dependent resonances (MDRs) excited in aneccentric sphere illuminated by a tightly focused Gaussian beam is studied.Calculations of extinction efficiency spectra and backward scatteringintensity spectra are made for different locations and radii of the inclusionwith respect to the host sphere. Exemplifying field distributions inside of the eccentric sphere under off-resonance and on-resonance conditions areexhibited with an illumination of a tightly focused off-axis Gaussian beam aswell as with an illumination of a plane wave. The influences of the relativesize of the inclusion with respect to the host sphere and the separationdistance between the two sphere centers on the resonance positions and theamplitudes of the MDRs peaks are discussed.5. Within the framework of EBCM, the transition matrixes for anisotropic particle as well as for an anisotropic particle are derived. Based onphysical model of single scattering, analytical solution to the scattering of anensemble of particles in random orientation is given. By expanding theanalytical expressions of the elements in the ensemble-averaged scatteringmatrix in terms of generalized spherical functions, the calculation speed ofthe scattering prediction is accelerated. By using the EBCM, light scatteringproperties around the rainbow angle for an ensemble of spheroids in randomorientations illuminated by a plane wave are studied. By using a programbased on the Nussenzveig theory for spheres combined with theNon-Negative Least Square method, refractive index and size distribution ofdroplets are extracted from simulated rainbow signals obtained fromsimulations experiments of an ensemble of spheroids. By comparing theextracted parameters with those original parameters used in the simulationexperiments, the sensitivity of the rainbow technique to the non-sphericity ofdroplets is quantified.