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Asymptotic Representation for the Scattering Pattern

Asymptotic Representation for the Scattering Pattern

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The pattern of the scattered field in the far zone, in principle, can be determined by applying a Fourier transform to the asymptotic representations for the current. However, this chapter shows one should not do this since the expressions obtained using this approach do not satisfy the reciprocity theorem. Because of this, an asymptotic relationship was sought for the field in the far zone, proceeding from the exact solutions and functional equations derived from the previous chapter.

Chapter Contents:

  • 10.1 Exact Expressions for the Scattering Pattern and Some Properties of ξ n (α,α0)
  • 10.2 Asymptotic Representations for ξ n (α,α0)
  • 10.2.1 Asymptotic Series for ξ n (α,α0)
  • 10.2.2 Estimate of Un,2 (α,α0)
  • 10.2.3 Asymptotic Representation for φ m+n (α,α0)
  • 10.3 First-Order Approximation for the Scattering Pattern
  • 10.4 Nth-Order Approximation for the Scattering Pattern
  • 10.4.1 Derivation of an Approximate Formula
  • 10.4.2 Verification of the Boundary Conditions
  • 10.4.3 Estimate of the Error
  • 10.4.4 Total Scattering Cross Section
  • 10.5 Relationship Between Approximations for the Current and the Scattering Pattern
  • 10.6 Additional Comments

Inspec keywords: functional analysis; electromagnetic wave scattering

Other keywords: scattered field pattern; reciprocity theorem; asymptotic relationship; scattering pattern; asymptotic representation

Subjects: Electromagnetic waves: theory; Electromagnetic wave propagation; Functional analysis (numerical analysis); Function theory, analysis

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