Discontinuities in photonic waveguides: rigorous Maxwell-based 3D modeling with the finite element method

Area of Science:

• Computational Electromagnetics
• Waveguide Theory
• Plasmonics

Background:

• Studying discontinuities in open waveguides is crucial for designing advanced optical and sensing devices.
• Existing methods often struggle with complex, arbitrary shapes and rigorous vector analysis.
• Accurate modeling of plasmonic inclusions and periodic structures is challenging.

Purpose of the Study:

• To develop a general methodology for rigorous analysis of arbitrary discontinuities in open waveguides.
• To provide a framework for computing leaky modes and scattered fields.
• To validate the approach by comparing results with finite structures and demonstrating its applicability in infrared sensing.

Main Methods:

• Utilizing a full vector description based on Maxwell's equations within the finite element method (FEM).
• Computing leaky modes of the invariant structure and employing them as incident fields.
• Implementing a scattered field approach and projecting the scattered field onto the modes using bi-orthogonality.

Main Results:

• Successfully modeled general discontinuities, including arbitrary-shaped plasmonic inclusions.
• Computed complex propagation constants for periodically structured open waveguides.
• Demonstrated excellent agreement between the proposed method and finite structure simulations for an infrared sensing example.

Conclusions:

• The presented methodology offers a robust and general approach for analyzing complex waveguide discontinuities.
• The method accurately captures the behavior of open waveguides with arbitrary obstacles and periodic structuring.
• Open-source models are provided, facilitating reproducibility and further research in waveguide design and sensing applications.