Higher-order wide-angle split-step spectral method for non-paraxial beam propagation.

Area of Science:

• Computational physics
• Electromagnetics
• Numerical methods

Background:

• Accurate simulation of non-paraxial beam propagation is crucial in optics and photonics.
• Existing wide-angle split-step spectral (WASSS) methods offer a balance between accuracy and computational cost.
• Higher-order approximations are needed for enhanced precision in complex optical systems.

Purpose of the Study:

• To develop a higher-order method for non-paraxial beam propagation.
• To improve the accuracy and efficiency of the wide-angle split-step spectral method.
• To validate the new method using waveguide propagation problems.

Main Methods:

• Developed the higher-order WASSS (HOWASSS) method, incorporating terms up to third-order in the Magnus expansion of the Helmholtz equation.
• Employed a symmetric exponential operator splitting technique for operator simplification.
• Implemented the HOWASSS method on a graphics processing unit (GPU) for performance evaluation.

Main Results:

• The HOWASSS method demonstrates high accuracy and performance for non-paraxial beam propagation, validated against known analytical solutions for waveguide propagation.
• Significant speed enhancements were achieved through GPU implementation.
• HOWASSS proves substantially faster than the original WASSS method when high accuracy is required.

Conclusions:

• The HOWASSS method offers a superior approach for accurate and efficient non-paraxial beam propagation.
• The GPU implementation provides substantial performance gains, making it suitable for computationally intensive simulations.
• This method advances the simulation capabilities in optical and photonic research.