Propagation of Surface Plasmon Polaritons on Semiconductor Gratings

We present time-domain measurements of terahertz surface plasmon polaritons (SPPs) propagating on gratings structured on silicon surfaces. Using single-cycle pulses of terahertz radiation to excite SPPs in a broad frequency range, we observe that the efficient SPPs scattering on the semiconductor periodic structure introduces significant dispersion and modifies the SPPs propagation. A stop gap, or a frequency range where SPPs are Bragg reflected, is formed by the structure. This gap depends strongly on the Si doping density and type. The resonant scattering at the edge of the gap reduces the group velocity by more than a factor of 2. The measurements show a good agreement with our numerical calculations based on the reduced Rayleigh equation.

Figure 1

Terahertz SPP transients. The gray curve corresponds to SPPs propagating on a flat $n$-doped Si surface with a carrier density of $N\approx {10}^{18}{\mathrm{c}\mathrm{m}}^{-3}$. The black curve corresponds to a SPP transient transmitted through a grating of 30 grooves with a lattice constant of $442\mu \mathrm{m}$, groove depth of $100\mu \mathrm{m}$, and groove width of $221\mu \mathrm{m}$ structured on a similar Si wafer. Inset: scanning electron microscope image of a SPP grating.

Figure 2

Transmittance as a function of the frequency of SPPs propagating on gratings of grooves structured on Si wafers. The open circles are measurements and the solid curves numerical calculations. (a) corresponds to a grating structured on $n$-doped Si, while (b) corresponds to a similar grating structured on $p$-doped Si.

Figure 3

Dispersion relation of SPPs on a grating of grooves structured on an $n$-doped silicon wafer. The open circles are measurements, while the solid curve is a calculation. The dashed curve represents the dispersion relation of SPPs on a flat Si surface.

Figure 4

Group velocity of SPPs on gratings normalized by the velocity of SPPs on flat surfaces. The open circles correspond to measurements, while the solid curves are numerical calculations. (a) corresponds to a grating structured on an $n$-doped Si wafer, while (b) corresponds to a similar grating on a $p$-doped Si wafer.