Vector analysis of bending waveguides by using a modified finite-difference method in a local cylindrical coordinate...

Area of Science:

• Photonics and Waveguide Optics
• Computational Electromagnetics
• Numerical Methods in Physics

Background:

• Bending waveguides are crucial components in integrated photonic circuits.
• Accurate analysis of guided and leaky modes in bent waveguides is essential for device design.
• Existing methods may involve approximations or limitations in handling complex waveguide geometries.

Purpose of the Study:

• To develop a robust vector mode solver for analyzing bending waveguides.
• To incorporate perfectly matched layer absorbing boundary conditions for accurate simulations.
• To validate the solver's performance against established methods.

Main Methods:

• A modified finite-difference (FD) method is employed in a local cylindrical coordinate system.
• Taylor series expansion and continuity conditions are used to derive a matrix eigenvalue equation.
• The perfectly matched layer (PML) absorbing boundary conditions are integrated into the solver.

Main Results:

• The solver accurately calculates complex effective indexes and field distributions of leaky modes.
• Simulations were performed for a typical rib bending waveguide and a silicon wire bend.
• The obtained solutions show excellent agreement with results from the film mode matching method.

Conclusions:

• The developed vector mode solver is valid and useful for analyzing bending waveguides.
• The method provides accurate results without relying on the averaged index approximation.
• This solver offers a reliable tool for photonic device design and simulation.