Fast beam shape coefficient computation from continuous surface fields

A computationally efficient method is presented for computing beam shape coefficients (BSCs) from electromagnetic fields defined on regular, compact surfaces. By reformulating the BSC calculation as a continuous surface integral, the method eliminates the need for pointwise vector spherical harmonic (VSH) expansions, resulting in dramatic reductions in computation time. It enables fast and rigorous modeling of incident fields on planar surfaces and yields accurate approximations on curved surfaces with radii exceeding two wavelengths. Demonstrated runtime reductions exceed 1000× on consumer-level hardware. Applications include optical tweezers, optical force analysis, and advanced beam synthesis.