Adaptive Hermite-Gauss decomposition method to analyze optical dielectric waveguides

Area of Science:

• Computational electromagnetics
• Photonics and optical engineering
• Numerical analysis

Background:

• Accurate analysis of 3D dielectric structures is crucial for optical device design.
• Existing methods like Hermite-Gauss decomposition method (HGDM) have limitations in accuracy and computational efficiency, especially near mode cutoff.
• Optimization strategies for HGDM exist but can be computationally intensive.

Purpose of the Study:

• To introduce a novel spectral method, the adaptive Hermite-Gauss decomposition method (A-HGDM), for analyzing 3D dielectric structures.
• To develop an integrated optimization strategy for A-HGDM to automatically determine quasi-optimum numerical parameters efficiently.
• To evaluate the accuracy and computational performance of A-HGDM compared to existing methods.

Main Methods:

• Development of the adaptive Hermite-Gauss decomposition method (A-HGDM) incorporating variable transformation.
• Implementation of an automated optimization strategy for numerical parameters within A-HGDM.
• Testing A-HGDM on two standard 3D dielectric structures: rectangular step-index waveguide and rib-waveguide directional coupler.

Main Results:

• A-HGDM demonstrates increased accuracy compared to the standard HGDM, particularly for modes near cutoff.
• The method shows improved computational efficiency over previously published optimized HGDM strategies.
• Successful analysis of both rectangular step-index waveguides and rib-waveguide directional couplers was achieved.

Conclusions:

• The adaptive Hermite-Gauss decomposition method (A-HGDM) is an effective and efficient technique for analyzing 3D dielectric structures.
• A-HGDM offers enhanced accuracy, especially in challenging near-cutoff conditions.
• The integrated optimization strategy provides a computationally efficient approach to parameter selection.