Approximate analysis and design of rectangular-lattice photonic crystals

Area of Science:

• Photonics and Wave Physics
• Materials Science
• Computational Physics

Background:

• Photonic crystals exhibit unique wave propagation properties based on their periodic refractive index.
• Analyzing complex refractive index profiles in photonic crystals is computationally challenging.
• Understanding band structures and Bloch waves is crucial for photonic crystal applications.

Purpose of the Study:

• To introduce a simplified theoretical model for analyzing wave propagation in photonic crystals.
• To develop a method for approximating arbitrary refractive-index profiles in photonic crystals.
• To demonstrate the effectiveness of the staircase approximation for studying photonic crystal properties.

Main Methods:

• Approximating arbitrary refractive-index functions with a tunable staircase profile.
• Decomposing the 2D wave equation into two 1D equations using a decoupling parameter.
• Analyzing the resulting band structures and Bloch waves theoretically.

Main Results:

• The staircase profile effectively approximates desired photonic crystal structures over a wide frequency range.
• The decomposition into 1D equations simplifies the theoretical analysis.
• Key features of photonic crystal band structures and Bloch waves are accurately captured.

Conclusions:

• The staircase approximation provides a powerful and simplified tool for theoretical analysis of photonic crystals.
• This method facilitates the study of wave propagation and band structures in various photonic crystal designs.
• The approach offers insights into the fundamental physics governing photonic crystal behavior.