Evanescent wave in multiple slit diffraction and n-array antennas in metamaterial using Cesàro convergence.

Area of Science:

• Electromagnetism and Optics
• Wave Phenomena
• Materials Science

Background:

• Negative refractive index (NRI) materials exhibit unique electromagnetic properties.
• Evanescent waves are typically confined to the near-field and decay rapidly.
• Understanding wave behavior in NRI media is crucial for novel device applications.

Purpose of the Study:

• To investigate the role and behavior of evanescent waves in NRI materials.
• To analyze multiple slit diffraction and antenna amplification in NRI environments.
• To explore the mathematical framework governing these phenomena, specifically using the Riemann zeta function.

Main Methods:

• Theoretical analysis of wave propagation in NRI materials.
• Calculation of diffraction intensity and antenna amplification factor (AF).
• Application of the Riemann zeta function to model wave convergence and nulls.

Main Results:

• Evanescent waves play a critical role in the near-field of NRI structures.
• Evanescent waves exhibit significant growth and Cesàro convergence in NRI media.
• The Riemann zeta function accurately describes diffraction intensity, AF, and introduces additional nulls.

Conclusions:

• Diffraction in NRI materials significantly enhances evanescent waves, leading to Cesàro convergence.
• The Riemann zeta function provides a powerful tool for analyzing wave phenomena in NRI.
• These findings have implications for advanced optical and antenna designs utilizing NRI materials.