Stable and accurate method for modal analysis of multilayer waveguides using a graph approach

Area of Science:

• Optics and Photonics
• Waveguide Theory
• Computational Electromagnetics

Background:

• Multilayer planar waveguides are crucial in optical and photonic devices.
• Accurate calculation of guided and leaky modes is essential for device design.
• Existing methods may involve approximations or numerical instabilities.

Purpose of the Study:

• To present a new method for calculating propagation constants of allowed guided and leaky modes.
• To develop a two-way graph model for describing tangential fields in waveguides.
• To derive analytical and closed-form dispersion equations for TE and TM modes.

Main Methods:

• Development of a two-way graph model for waveguide tangential fields.
• Application of a topology scheme to derive dispersion equations.
• Comparison with series-expansion, approximation, and transfer-matrix methods.

Main Results:

• Analytical and closed-form dispersion equations for TE and TM modes were derived.
• The graph model method allows accurate eigenmode computation without series truncation.
• The derived dispersion equations are exact and avoid root loss or numerical instability.

Conclusions:

• The proposed graph model and derived dispersion equations offer an accurate and stable method for analyzing multilayer planar waveguides.
• This approach facilitates precise eigenmode determination, even for waveguides with thick layers.
• The method presents advantages over traditional techniques in numerical computation and accuracy.