An Operator-Expansion TD-PO Method for Fast Near-Field UWB Scattering from Electrically Large, Dispersive Surfaces

To evaluate the influence of near-field ground scattering on ultra-wideband (UWB) fuze performance, this paper presents an efficient operator-expansion time-domain physical optics (OE-TD-PO) framework. This method extends conventional far-field TD-PO to electrically large, dispersive rough surfaces under near-field excitation. By leveraging the local plane wave approximation (LPA) and time-domain Kirchhoff approximation (KA), the complex scattering process is decomposed into independent element-wise responses, which reduces the coupling between geometry and wave propagation. The scattering physics of each facet are represented using closed-form material and geometric operators. The material operator accounts for frequency-dependent dispersion and polarimetric reflection, while the geometric operator models intra-facet delay spread in the time domain. An excitation-order expansion of the transient dipole radiation formula is introduced to decouple the source waveform from spatial facet loops, yielding radiation, induction, and static components corresponding to the derivative, proportional, and integral terms of the excitation signal. This decoupling reduces computational complexity while preserving physical fidelity. Validated against analytical and numerical benchmarks, the proposed method effectively quantifies terrain-induced ranging biases and initiation reliability, providing a rigorous basis for adaptive error compensation and gain control in UWB fuzes across diverse environments.