scholarly journals Efficient implementation of the invariant imbedding T-matrix method and the separation of variables method applied to large nonspherical inhomogeneous particles

2013 ◽  
Vol 116 ◽  
pp. 169-183 ◽  
Author(s):  
Lei Bi ◽  
Ping Yang ◽  
George W. Kattawar ◽  
Michael I. Mishchenko
Keyword(s):  
Matrix Method ◽  
Separation Of Variables ◽  
Efficient Implementation ◽  
Invariant Imbedding ◽  
Separation Of Variables Method ◽  
T Matrix

Invariant-imbedding T-matrix method

2020 ◽  
pp. 145-188 ◽  
Author(s):  
Bingqiang Sun ◽  
Lei Bi ◽  
Ping Yang ◽  
Michael Kahnert ◽  
George Kattawar
Keyword(s):  
Matrix Method ◽  
Invariant Imbedding ◽  
T Matrix

scholarly journals Design and Validation of the Invariant Imbedded T-Matrix Scattering Model for Atmospheric Particles with Arbitrary Shapes

2019 ◽  
Vol 9 (20) ◽  
pp. 4423 ◽  
Author(s):  
Shuai Hu ◽  
Lei Liu ◽  
Taichang Gao ◽  
Qingwei Zeng
Keyword(s):  
Light Scattering ◽  
Matrix Method ◽  
Mie Theory ◽  
Spherical Particles ◽  
Layer By Layer ◽  
Invariant Imbedding ◽  
Surface Integral ◽  
Spherical Coordinate ◽  
T Matrix ◽  
Arbitrary Shapes

Light scattering by non-spherical particles is an important factor influencing atmospheric radiative transfer. To accurately simulate the scattering properties of non-spherical particles, the Invariant Imbedded T-matrix method (IIM T-Matrix) is developed by combining the Lorenz–Mie theory and invariant imbedding technique. In this model, the non-spherical particle is regarded as an inhomogeneous sphere and discretized into multiple spherical layers in the spherical coordinate system. The T-matrix of the inscribed sphere is firstly calculated by the Lorenz–Mie theory, and then taking it as the initial value, the T-matrix is updated layer by layer by using the invariant imbedding technique. To improve the computational efficiency, the model is further parallelized by the OpenMP technique. To verify the simulation accuracy of the IIM T-Matrix method, the results of the model are compared with those of the EBCM (Extended Boundary Condition Method) T-Matrix method, DDA (Discrete Dipole Approximation) and MRTD (Multi-Resolution Time Domain). The results show that the scattering phase matrix simulated by the IIM T-Matrix method closely agrees with that of the well-tested models, indicating that the IIM T-Matrix method is a powerful tool for the light scattering simulation of non-spherical particles. Since the IIM T-Matrix method is derived from the volume integral equation, compared to the T-Matrix method which is based on surface integral principles (i.e., “EBCM” or the “null field method”), it can be applied to the scattering calculations of particle with arbitrary shapes and inhomogeneous compositions, which can greatly expand the application scope of the T-Matrix method.

Gustav Mie and the Evolving Discipline of Electromagnetic Scattering by Particles

2008 ◽  
Vol 89 (12) ◽  
pp. 1853-1862 ◽  
Author(s):  
Michael I. Mishchenko ◽  
Larry D. Travis
Keyword(s):  
Electromagnetic Scattering ◽  
Matrix Method ◽  
Separation Of Variables ◽  
Mie Theory ◽  
Biomedical Optics ◽  
Physical Reality ◽  
Spherical Particles ◽  
Scientific Publications ◽  
Seminal Paper ◽  
T Matrix

The year 2008 marks the centenary of the seminal paper by Gustav Mie on electromagnetic scattering by homogeneous spherical particles. Having been cited in almost 4,000 journal articles since 1955 (according to the Science Citation Index Expanded database), Mie s paper has been among the more influential scientific publications of the twentieth century. It has affected profoundly the development of a great variety of natural science disciplines including atmospheric radiation, meteorological optics, remote sensing, aerosol physics, astrophysics, and biomedical optics. Mies paper represented a fundamental advancement over the earlier publications by Ludvig Lorenz in that it was explicitly based on the Maxwell equations, gave the final solution in a convenient form suitable for practical computations, and imparted physical reality to the abstract concept of electromagnetic scattering. The Mie solution anticipated such general concepts as far-field scattering and the Sommerfeld-Silver-Müller boundary conditions at infinity as well as paved the way to such important extensions as the separation of variables method for spheroids and the T-matrix method. Key ingredients of the Mie theory are quite prominent in the superposition T-matrix method for clusters of particles and even in the recent microphysical derivation of the radiative transfer equation. Among the most illustrative uses of the Mie solution have been the explanation of the spectacular optical displays caused by cloud and rain droplets, the identification of sulfuric acid particles in the atmosphere of Venus from Earth-based polarimetry, and optical particle characterization based on measurements of morphology-dependent resonances. Yet it is clear that the full practical potential of the Mie theory is still to be revealed.

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