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The generalized Wiener-Hopf equations for wave motion in angular regions: electromagnetic application
1Department of Electronics and Communications, Politecnico di Torino, 10129 Torino, Italy.
Proceedings. Mathematical, Physical, and Engineering Sciences
|February 14, 2022
Summary
This study presents a new method for deriving spectral functional equations and generalized Wiener-Hopf equations (GWHEs) for wave motion in angular regions. These GWHEs are applicable to electromagnetics and arbitrary linear media.
Area of Science:
- Electromagnetics
- Wave Propagation
- Mathematical Physics
Background:
- Wave motion in angular regions presents challenges in analysis.
- Existing methods may not cover arbitrary linear media or sources at infinity.
Purpose of the Study:
- Introduce a general method to deduce spectral functional equations.
- Derive generalized Wiener-Hopf equations (GWHEs) for wave motion.
- Apply the theory to electromagnetic wave problems.
Main Methods:
- Solving first-order vector differential equations to model wave motion.
- Applying boundary conditions to functional equations to obtain GWHEs.
- Developing a general theory for GWHEs.
Main Results:
- A general method for deducing spectral functional equations is established.
- Generalized Wiener-Hopf equations (GWHEs) are derived for wave motion in angular regions.
- The validity of GWHEs in electromagnetic applications is demonstrated.
Conclusions:
- The proposed method provides a general framework for spectral functional equations and GWHEs.
- The derived GWHEs are applicable to wave motion in arbitrary linear homogeneous media.
- This work validates GWHEs for electromagnetic applications and suggests future extensions.
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