Green dyadic calculations for inhomogeneous optical media

Area of Science:

• Electromagnetics and Wave Propagation
• Computational Physics
• Materials Science

Background:

• Analyzing electromagnetic wave propagation in complex dielectric media is crucial for various applications.
• Existing methods often face challenges with multilayered or continuously varying dielectric profiles.
• The Green dyadic formalism provides a powerful framework for solving electromagnetic boundary value problems.

Purpose of the Study:

• To develop and validate a difference equation approach for solving Green dyadic formalism in dielectric media.
• To extend the formalism to handle both discrete (multilayered) and continuous dielectric variations.
• To demonstrate the convergence and applicability of the developed numerical techniques.

Main Methods:

• Derivation of a difference equation from the reassociated Green dyadic formalism.
• Computation of limiting cases for progressively thinner layers to model continuous variations.
• Development of a hybrid formulation combining discrete and continuous numerical techniques.
• Numerical computation for a simple dipole source in a dielectric medium.

Main Results:

• The difference equation successfully yields solutions for multilayered dielectric media.
• A parallel development for continuously varying dielectrics is established through limiting processes.
• Numerical examples confirm the convergence of the difference equation solutions to the differential equation solution, validating the hybrid approach.

Conclusions:

• The developed difference equation offers an effective numerical tool for electromagnetic analysis in complex dielectric structures.
• The hybrid formulation provides a flexible approach for modeling diverse dielectric profiles.
• The study confirms the robustness and accuracy of the discrete numerical method for electromagnetic wave propagation problems.