Efficient beam-propagation method based on Padé approximants in the propagation direction

Area of Science:

• Computational electromagnetics
• Wave propagation modeling
• Numerical methods

Background:

• Conventional beam-propagation methods (BPMs) face limitations in accuracy and efficiency for complex wave propagation scenarios.
• Higher-order approximations are needed to improve the fidelity of numerical simulations.

Purpose of the Study:

• To introduce a novel beam-propagation method (BPM) utilizing higher-order Padé approximants.
• To enhance the accuracy and efficiency of wave propagation simulations.

Main Methods:

• Developed a novel BPM incorporating higher-order Padé approximants in transverse and longitudinal directions.
• Extended Padé approximation to the propagation direction and employed a multistep method.
• Utilized phase analysis to predict accuracy and optimal propagation step size.

Main Results:

• The proposed method demonstrates superior accuracy and efficiency compared to conventional BPMs.
• Minimal increase in programming complexity was observed with the extended Padé approximation and multistep approach.
• Phase analysis effectively predicted the method's accuracy and appropriate step sizes.

Conclusions:

• The higher-order Padé approximant-based BPM offers a more accurate and efficient alternative for wave propagation simulations.
• The method provides a robust framework for computational electromagnetics with predictable performance characteristics.