Wave propagation through penetrable scatterers in a waveguide and through a penetrable grating

Area of Science:

• Electromagnetics and Wave Propagation
• Computational Physics
• Materials Science

Background:

• Analyzing wave propagation through complex scatterers is crucial for various physical phenomena.
• Existing methods like rigorous coupled wave analysis (RCWA) have limitations in handling arbitrary shapes and certain approximations.

Purpose of the Study:

• To develop a robust multimodal method for analyzing wave propagation through arbitrary scatterers.
• To provide a unified framework for both numerical and analytical solutions in scattering problems.
• To investigate the properties of the proposed admittance matrix method.

Main Methods:

• A multimodal method based on the admittance matrix formulation.
• Reduction of wave propagation problems to systems of first-order differential equations.
• Numerical solution using the admittance matrix for stability and convergence.
• Analytical solutions via weak scattering approximation and plane wave approximation.

Main Results:

• The admittance matrix method provides a stable numerical approach for wave propagation analysis.
• It allows for analytical solutions in the weak scattering regime, generalizing the Webster equation.
• The method is applicable to waveguides with scatterers and plane wave scattering from periodic structures.
• Analysis of Wood anomalies and Fano resonances is facilitated by this approach.

Conclusions:

• The admittance matrix method is a versatile and stable technique for analyzing wave scattering from arbitrary structures.
• It bridges numerical and analytical approaches, offering deeper insights into scattering phenomena.
• The method's properties, including convergence and energy conservation, are well-defined, ensuring reliability.