A quantitative theory and the generalized Bragg condition for surface plasmon Bragg reflectors

Area of Science:

• Photonics and Nanophotonics
• Electromagnetics
• Materials Science

Background:

• Surface plasmon polariton (SPP) Bragg reflectors are crucial optical components.
• Designing these reflectors often involves complex simulations due to their intricate structures and optical properties.
• Existing models may not efficiently account for various loss mechanisms and higher-order modes.

Purpose of the Study:

• To propose a quantitative theory for SPP-Bragg reflectors with arbitrary geometry and refractive index profiles.
• To develop a recursive coupled-mode model that simplifies calculations for reflectors with multiple defects.
• To introduce a generalized Bragg condition for enhanced design flexibility.

Main Methods:

• Development of a surface plasmon polariton (SPP) coupled-mode model.
• Formulation of a recursive model for efficient computation of reflectance and transmittance.
• Incorporation of SPP absorption loss, high-order modes, and radiation loss into the model.
• Derivation and verification of a generalized Bragg condition.

Main Results:

• The developed recursive SPP coupled-mode model is shown to be equivalent to the coupled-mode model.
• The model efficiently incorporates various loss mechanisms and higher-order modes.
• Computational cost for analyzing N-defect reflectors is reduced to that of a single defect.
• Model predictions align well with full vectorial computation data.
• A generalized Bragg condition is proposed and verified for diverse SPP-Bragg reflector structures.

Conclusions:

• The proposed quantitative theory and recursive model significantly simplify the design and analysis of SPP-Bragg reflectors.
• The generalized Bragg condition offers a more versatile approach to designing these optical devices.
• This work provides a powerful tool for optimizing SPP-Bragg reflector performance.