An efficient numerical steepest descent path method to calculate the physical optics scattered fields with concave phase variations

In this work, we develop the numerical steepest descent path (NSDP) algorithm to calculate the physical optics (PO) integrals on surface with quadratic concave phase terms. The high frequency critical points contributions are studied in detail. Numerical results demonstrate that the NSDP method could achieve the frequency independent computational workload and obtain accurate results. Furthermore, to illustrate the transition effect of the critical points, we extend the NSDP method to calculate the PO integrals with the coalescence of the critical points.