Analytical Methods for Causality Evaluation of Photonic Materials.

Area of Science:

• Optics and Photonics
• Electrodynamics
• Materials Science

Background:

• Causality is a fundamental principle in physics, crucial for understanding material responses.
• Evaluating causality in photonic materials is complex, often requiring advanced mathematical tools.
• Existing material models may not always adhere to causality principles.

Purpose of the Study:

• To comprehensively review and formulate mathematical theorems for causality evaluation in photonic materials.
• To provide rigorous methods for determining the causality of material models.
• To correct and establish causal formulations for existing material models.

Main Methods:

• Collection and application of distributional theorems, including the distributional Titchmarsh theorem.
• Utilizing distribution theory to correct and formulate causal material models.
• Overview of five methods for assessing causality of dispersion relations, including Kramers-Krönig relations.

Main Results:

• A set of theorems is formulated for rigorous causality evaluation of material models.
• Distribution theory is applied to derive causal formulations for complex electromagnetic systems.
• Alternative methods to Kramers-Krönig relations are presented for challenging integral calculations.

Conclusions:

• The presented methodologies offer robust tools for analyzing causality in photonic materials.
• Scientists and engineers can utilize these methods to prove or disprove causality in electrodynamics and optics.
• The study emphasizes the importance of invoking mathematical distributions for advanced causality analysis.