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Linearization of the T-matrix solution for quasi-homogeneous scatterers
Constantine A Valagiannopoulos1, Nikolaos L Tsitsas
11School of Electrical and Computer Engineering, National Technical University of Athens, 9 Iroon Polytechniou Str., Zografos, Athens 15773, Greece.
Summary
This study introduces a new method for analyzing electromagnetic wave scattering by quasi-homogeneous obstacles. The technique decomposes the scattering pattern into contributions from homogeneous scatterers and perturbations, aiding in optical and engineering applications.
Area of Science:
- Electromagnetic wave scattering
- Optical engineering
- Environmental science
- Biology
Background:
- Investigating electromagnetic wave scattering by radially inhomogeneous obstacles is crucial for various scientific and engineering fields.
- Quasi-homogeneous obstacles, characterized by wavenumbers with limited variations from an average value, present unique scattering challenges.
Purpose of the Study:
- To develop and analyze a novel method for plane-wave scattering by quasi-homogeneous obstacles in 1D, 2D, and 3D.
- To decompose the far-field scattering pattern into contributions from the homogeneous part and perturbations due to wavenumber variations.
Main Methods:
- A T-matrix method is applied to a step approximation of the obstacle's wavenumber, treating it as piecewise homogeneous.
- Taylor expansion is used to express field coefficients as linear combinations of wavenumber deviations, weighted by 'layer-factors'.
- The far-field pattern is decomposed into the homogeneous scatterer's pattern and a perturbation term.
Main Results:
- The proposed technique accurately computes far-field patterns, validated by comparison with the standard T-matrix method.
- The perturbation far-field pattern and layer-factors are investigated for various wavenumber profiles (linear, sinusoidal, Lunenburg, triangular).
- The decomposition provides insights into the influence of wavenumber variations on scattering behavior.
Conclusions:
- The developed method offers an effective approach for analyzing scattering from quasi-homogeneous obstacles.
- The layer-factor concept quantifies the contribution of different radial layers to the overall scattered field.
- This work provides a valuable tool for applications in optical and chemical engineering, environmental science, and biology.
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