The complex Jacobi iterative method for three-dimensional wide-angle beam propagation.

Area of Science:

• Optics and Photonics
• Computational Electromagnetics
• Numerical Analysis

Background:

• Accurate simulation of optical propagation in waveguide structures is crucial for device design.
• Standard beam propagation methods struggle with evanescent waves and accuracy for wide-angle propagation.
• Direct matrix inversion can be computationally expensive for large-scale problems.

Purpose of the Study:

• To introduce a novel complex Jacobi iterative technique for three-dimensional (3D) wide-angle (WA) beam propagation.
• To enhance the accuracy of optical propagation modeling using a modified Padé(1,1) approximant operator.
• To compare the performance of the new iterative method against traditional direct matrix inversion.

Main Methods:

• Developed a new complex Jacobi iterative technique for solving the beam propagation equation.
• Utilized a novel modified Padé(1,1) approximant operator to improve the treatment of evanescent waves.
• Performed a comparative analysis of the iterative method and direct matrix inversion for WA-beam propagation.

Main Results:

• The modified Padé(1,1) operator provides better damping for evanescent waves.
• The complex Jacobi iterative technique offers more accurate approximations to the Helmholtz equation compared to standard operators.
• The iterative method demonstrates superior speed and suitability for large-scale problems over direct matrix inversion.

Conclusions:

• The proposed complex Jacobi iterative technique is an efficient and accurate method for 3D WA beam propagation.
• This approach offers significant advantages for simulating complex optical waveguide structures.
• The findings suggest a more computationally feasible solution for advanced optical modeling.