Order-one quadrature rules for flat facets

In this paper, we build on the method of implementing a robust numerical integration based on the method of steepest descents. To our knowledge, this is the first algorithm that works a double integral in a fashion that is asymptotically frequency-independent, or order-1, with some cases yielding error that actually decreases with frequency. We restrict our attention to TE scattering from a flat strip, which has dominant phases {k_q} = (-k, k_x, k), where k_x is the component of the incident field tangential to the strip.