1：Experimental Design and Method Selection:

The study formulates self-focusing as a coherence propagation phenomenon using theoretical models, including a master equation derived for non-interacting particles and electromagnetic waves. It involves simulating metamaterial behavior based on permittivity and permeability equations.

2：Sample Selection and Data Sources:

Four different metamaterial cells with specific dimensions (a = 7 mm, 6.5 mm, 6.0 mm, 5.5 mm) are used, with parameters such as r = 0.5 × 10^{-4} m, r1 = 3.0 × 10^{-3} m, d = 1.0 × 10^{-3} m.

3：5 mm, 0 mm, 5 mm) are used, with parameters such as r = 5 × 10^{-4} m, r1 = 0 × 10^{-3} m, d = 0 × 10^{-3} m. List of Experimental Equipment and Materials:

3. List of Experimental Equipment and Materials: No specific equipment or materials are listed; the study is theoretical and simulation-based, focusing on mathematical models and graphical simulations.

4：Experimental Procedures and Operational Workflow:

The methodology involves deriving equations for coherence length and simulating the permittivity, permeability, and coherence length for different cell sizes using the provided parameters.

5：Data Analysis Methods:

Graphical analysis of simulations to observe behavior changes, such as the presence of frequency filter windows and coherence length variations.