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This study justifies Rayleigh's hypothesis for wave scattering, showing its T-matrix method correctly models near-fields. It also clarifies that overlapping obstacles can be modeled in multiple scattering scenarios.

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Area of Science:

  • Wave scattering
  • Electromagnetics
  • Acoustics

Background:

  • The Rayleigh hypothesis for wave scattering assumes scattered fields expand using outgoing eigensolutions.
  • Its correctness is crucial for near-field analysis and multiple scattering but remains unclarified.
  • Waterman's T-matrix method, using an extended boundary condition, avoids this uncertainty but restricts non-overlapping obstacles.

Purpose of the Study:

  • To justify the correctness of Rayleigh's hypothesis in wave scattering.
  • To clarify the implications of Rayleigh's hypothesis for modeling multiple scattering.
  • To investigate the applicability of Waterman's T-matrix method in scenarios with overlapping obstacles.

Main Methods:

  • Theoretical analysis of wave scattering and the Helmholtz equation.
  • Development and application of Waterman's T-matrix method.
  • Numerical simulations of multiple scattering with overlapping obstacles.

Main Results:

  • The study provides a theoretical justification for the correctness of Rayleigh's hypothesis.
  • It demonstrates that Waterman's T-matrix can represent near-fields within the critical region.
  • The findings indicate that overlapping obstacles do not necessarily need to be excluded in multiple scattering modeling.

Conclusions:

  • Rayleigh's hypothesis is validated for wave scattering from nonspherical obstacles.
  • Waterman's T-matrix method is applicable for near-field representation even in the critical region.
  • The restriction of non-overlapping obstacles in multiple scattering modeling can be relaxed.