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.

Rigorous solution for the transient Surface Plasmon Polariton launched by subwavelength slit scattering.

We demonstrate by a rigorous theoretical calculation the transient Surface Plasmon Polariton (SPP) mode, which is launched by a beam impinging onto a sub-wavelength real metallic slit in addition to the conventional long-range SPP. Different from the previous works, we find a direct closed-form solution of the Maxwell's equations by the Sommerfeld branch-cut integrals without approximation. The transient wave is a SPP with a complex-valued envelope, expressed as the exponential integral. Its rapid damping may be asymptotically approximated as - ln(x), 1/ x1/2 and 1/x, respectively, depending on the distance range away from the slit. The transit SPP may be considered as a cylindrical wave, which is radiated from the slit, takes the SPP propagation constant at the interface and propagates with additional drop due to the loss of energy pumped to the SPP.