Pulse delay and propagation through subwavelength metallic slits

The transmission properties of a 2D metallic grating are investigated at optical wavelengths for an incident Gaussian pulse having pulse widths from 100 fs to 10 ps. The slits in the grating are subwavelength which can nevertheless allow significant transmission in the narrow wavelength regions where the so-called surface plasmon polariton (SPP) and waveguide mode resonances occur. The solution is obtained for each spectral component of the pulse by using the rigorous coupled wave approach and then the temporally varying output pulse is reconstructed by the standard method of taking an inverse Fourier transform. The delay of the pulse and the output pulse widths are determined by taking the first and second order moments of the Poynting vector with respect to time. It is shown that the time delay may be significant, as much as 256 fs for a pulse width of 200 fs for the SPP resonance but quite small (32 fs) for the waveguide mode resonance. The focus of the work is on demonstrating how the pulse delay evolves as the pulse propagates in the half-space beyond the grating. It is shown that the distance over which the time delay develops is much larger than the actual longitudinal dimension of the grating structure and it is approximately the same distance over which the stored energy and the vortices of the Poynting vector extend.