High-accuracy analytical solver for guided and unguided complex modes of optical waveguides

Area of Science:

• Optics and Photonics
• Computational Electromagnetics

Background:

• Dielectric optical waveguides are crucial components in photonic integrated circuits.
• Accurate analysis of waveguide modes is essential for device design and performance optimization.
• Traditional numerical methods like finite difference may struggle with accuracy for complex modes.

Purpose of the Study:

• To develop a highly accurate, analytical solver for vector modes in dielectric optical waveguides.
• To overcome limitations of existing numerical methods for mode analysis.
• To provide a versatile tool for optical waveguide analysis and optimization.

Main Methods:

• The method employs analytical solutions for 1D slab waveguides to construct solutions for 2D channel waveguides.
• The standard mode matching method is applied to solve for full vectorial modes.
• Complex root searching algorithms, like particle swarm optimization, solve the transcendental equation for mode effective indices.

Main Results:

• The solver accurately determines both guided and un-guided complex modes.
• Analytical global functions describe modal fields, avoiding numerical discretization and round-off errors.
• Achieved accuracy for complex modes surpasses traditional numerical methods.

Conclusions:

• The developed analytical solver offers high accuracy and versatility for optical waveguide analysis.
• The method's analytical nature provides a powerful basis for propagation problems in non-uniform waveguides.
• This approach is expected to advance the design and optimization of photonic devices.