Multistep method for wide-angle beam propagation.

Area of Science:

• Computational physics
• Wave propagation modeling

Background:

• Accurate simulation of wave propagation is crucial in various scientific fields.
• Existing wide-angle propagation methods often face computational challenges or approximations.

Purpose of the Study:

• To introduce a new, efficient, and accurate beam-propagation method.
• To enable accurate approximations to true Helmholtz propagation.

Main Methods:

• Factoring the Padé approximant wide-angle propagation operator into simpler Padé (1, 1) operators.
• Developing a multistep method where each step is solvable using paraxial-like techniques.
• Utilizing the tridiagonal form of component steps for transparent boundary condition integration.

Main Results:

• The method provides accurate approximations to true Helmholtz propagation.
• The computational cost is only modestly increased compared to simpler methods.
• Seamless integration with previously reported transparent boundary conditions is achieved.

Conclusions:

• The presented beam-propagation method offers a robust and accurate solution for wave propagation problems.
• The multistep approach enhances computational efficiency and simplifies implementation.
• This method is suitable for applications requiring precise Helmholtz propagation modeling.