Rigorous solution for optical diffraction of a sub-wavelength real-metal slit.

We present a rigorous closed-form solution of the Sommerfeld integral for the optical scattering of a metal sub-wavelength slit. The two-dimensional (2D) field solution consists of the Surface Plasmon Polariton (SPP) mode at the metal surface and the 2D scattered field, which is the cylindrical harmonic of first order emitted by the electrical dipole and convolved with the 1D transient SPP along the interface. The creeping wave or quasi-cylindrical wave detected in the previous experiment is not an extra evanescent surface wave, but is the asymptotic behavior of the 2D scattered field at the proximity of the slit. Furthermore, our solution predicts a strong resonant enhancement of the scattered field at the proximity of the slit, depending on the materials and wavelength.