In this communication, we propose a frequency independent approach, the numerical steepest descent path method, for computing the physical optics scattered electromagnetic field on the quadratic hyperbolic surface. Due to the highly oscillatory nature of the physical optics integral, the proposed method relies on deforming the integration path of the integral into the numerical steepest descent path on the complex plane. Numerical results for the PO based EM fields from the hyperbolic surface illustrate that the proposed numerical steepest descent path method is frequency independent in computational cost and error controllable in accuracy.