Wavelet-Galerkin solver for the analysis of optical waveguides

Area of Science:

• Optics and Photonics
• Computational Electromagnetics
• Waveguide Theory

Background:

• Optical waveguides are crucial components in photonic integrated circuits.
• Efficient numerical methods are needed for accurate waveguide analysis.
• Existing basis functions can lead to computationally intensive solutions.

Purpose of the Study:

• To propose a new set of basis functions for optical waveguide analysis.
• To leverage the Galerkin method with truncated Gaussian wavelets.
• To enhance computational efficiency and reduce memory requirements.

Main Methods:

• Development of basis functions using truncated Gaussian wavelets.
• Application of the Galerkin method to solve the wave equation.
• Formulation of a sparse eigenvalue equation.

Main Results:

• The proposed basis functions result in a sparse eigenvalue equation.
• Integral computations for matrix elements are significantly faster.
• Reduced memory requirements compared to traditional methods.
• Demonstrated accuracy for diffused and step index planar and channel waveguides.

Conclusions:

• Truncated Gaussian wavelets offer an efficient and accurate approach for optical waveguide analysis.
• The method provides a substantial reduction in computation time.
• This technique is suitable for analyzing various waveguide types.