Quartic form of the slowly decaying imaginary distance beam propagation method

Area of Science:

• Optics and Photonics
• Computational Electromagnetics
• Waveguide Theory

Background:

• Calculating eigenmodes in optical fibers and waveguides is crucial for understanding light propagation.
• Existing methods, including the imaginary distance beam propagation method (ID-BPM), have limitations in convergence speed and accuracy.
• The slowly decaying imaginary distance beam propagation method (SD-ID-BPM) offers improvements but can be further optimized.

Purpose of the Study:

• To further modify the governing equation of the SD-ID-BPM for enhanced eigenmode calculation in optical fibers and waveguides.
• To analyze the convergence properties of the modified SD-ID-BPM.
• To compare the performance of the modified SD-ID-BPM against its earlier version and other existing methods.

Main Methods:

• Modification of the governing partial differential equation for the SD-ID-BPM.
• Detailed analysis of the convergence behavior of the modified method.
• Comparative study of convergence speed and accuracy with previous SD-ID-BPM versions and alternative numerical techniques.

Main Results:

• The modified SD-ID-BPM demonstrates improved convergence properties.
• The enhanced method achieves the desired accuracy in fewer propagation steps compared to the earlier SD-ID-BPM and other methods.
• The study suggests exploring numerical techniques for higher-order partial differential equations for transverse discretization.

Conclusions:

• The modified SD-ID-BPM offers a more efficient approach for calculating eigenmodes in optical waveguides.
• The findings highlight the potential for further advancements by incorporating advanced numerical methods for solving higher-order PDEs.
• This research contributes to the development of faster and more accurate computational tools for optical device design.