Simple expressions for the maximum omnidirectional bandgap of bilayer photonic crystals

Area of Science:

• Photonics
• Materials Science
• Condensed Matter Physics

Background:

• One-dimensional photonic crystals (1DPCs) exhibit unique optical properties due to their periodic structure.
• The maximum omnidirectional gap (MODG) in 1DPCs is crucial for applications requiring broadband light reflection.
• Predicting MODG characteristics often involves complex calculations, limiting practical design flexibility.

Purpose of the Study:

• To develop simple, dimensionless approximate expressions for predicting MODG parameters.
• To provide a method for easily calculating the thickness filling factor, gap center, and gap width of the MODG.
• To enable the estimation of refractive indices from MODG properties.

Main Methods:

• Derivation of approximate analytical expressions.
• Focus on dimensionless parameters for broad applicability.
• Avoidance of trigonometric and inverse trigonometric functions for simplicity.

Main Results:

• Three novel dimensionless approximate expressions were derived.
• These expressions accurately predict the thickness filling factor, gap center, and gap width of the MODG.
• The formulas are applicable across a range of refractive indices.

Conclusions:

• The proposed expressions offer a simplified approach to MODG analysis in 1DPCs.
• These findings facilitate easier design and analysis of photonic crystal devices.
• The ability to estimate refractive indices from MODG expands the utility of these expressions.