MATLAB-Based Fast Vector Spherical Wave Expansion Implementation

An optimized direct vector spherical wave expansion (VSWE) implementation is presented. The orthogonal spherical bases are generated sequentially, leveraging their linkage through the recurrence formulas. This implementation encompasses three-dimensional field analysis and synthesis scenarios. Different beam types are numerically analyzed for validation and compared with the theoretical analysis. The execution time to compute all VSWE coefficients and beam synthesis is less than 2.5 seconds with a two-degree spatially-sampled far-field. The present study promotes the integration of the VSWE as a standalone essential tool for electromagnetic field analysis within the MATLAB antenna toolbox or scientific computation frameworks built in other script programming languages.