Excitation of surface plasmon polaritons on silicon with an intense femtosecond laser pulse

We report the experimental observation of anomalies appearing in the reflection of intense $p$-polarized 100-femtosecond (fs) laser pulses at a nonmetallic material surface with a grating structure. The reflectivity was measured in air as a function of the angle of incidence at a Si grating. The results have exhibited an abrupt decrease to create a sharp dip at a specific incident angle of $\sim {24}^{\circ }$, where the grating surface was deeply ablated along the edge of the grooves. Similar to the so-called Wood's anomalies, the observed angle-dependent reflectivity provides direct evidence that surface plasmon polaritons (SPPs) can resonantly be excited at the interface between air and the nonmetallic material surface, as the intense fs laser pulse produces a high density of free electrons to form a metal-like layer on the Si grating surface. Calculation for a model target reproduces well the experimental results to confirm the excitation of SPPs on the Si grating, demonstrating the generation of enhanced near fields for the periodic ablation of a target surface.

Figure 1

(a) SPM image and (b) its lateral ($x\text{−}z$) scan of the Si grating surface. (c) Schematic diagram of the optical configuration for the reflectivity measurement. Two lenses for expansion of the reflected laser beam and a CCD camera are set on an isolated breadboard (dashed square) that can be rotated around the focal point. White arrows denote the direction of rotation of the target and the breadboard. HWP, half-wave plate; P, polarizer; L, lens.

Figure 2

Reflectivity $R$ for (a) the flat Si substrate and (b) the Si grating, measured as a function of the incident angle $\theta$ of the fs laser pulse, at $F_1=40\mathrm{mJ}/\mathrm{c}{\mathrm{m}}^2$ (squares) and $F_2=700\mathrm{mJ}/\mathrm{c}{\mathrm{m}}^2$ (circles), where the solid and open symbols correspond to $R$ observed with $p$ and $s$ polarizations, respectively. The thick and thin solid curves represent the calculated reflectivity $R_{\mathrm{cal}}$ of light with $p$ and $s$ polarizations, respectively, at the Si surfaces. The dashed and dotted curves in (a) are the calculated results of $R_{\mathrm{cal}}$ for $p$ and $s$ polarizations, respectively, at the flat Si substrate including $N_{\mathrm{e}}=0.8\times {10}^{22}\mathrm{c}{\mathrm{m}}^{-3}$.

Figure 3

Calculated reflectivity $R_{\mathrm{cal}}$ for the $p$-polarized light at the Si grating surface with $N_{\mathrm{e}}=0.8\times {10}^{22}\mathrm{c}{\mathrm{m}}^{-3}$ (dotted), $1.0\times {10}^{22}\mathrm{c}{\mathrm{m}}^{-3}$ (dashed), $2.0\times {10}^{22}\mathrm{c}{\mathrm{m}}^{-3}$ (thin solid), and $3.0\times {10}^{22}\mathrm{c}{\mathrm{m}}^{-3}$ (thick solid). For comparison, $R$ measured at $F_2$ is replotted with gray circles.

Figure 4

SPM images of the Si grating surface after irradiation at (a) $\theta ={15}^{\circ }$ and (b) $\theta ={24}^{\circ }$ with a single shot of the $p$-polarized fs pulse at $F_2$, where the arrow in (a) denotes the incident direction of the laser pulse. (c) Depth of grooves measured as a function of $\theta$ for the Si grating, where the dashed line indicates the groove depth on the original surface, and the gray lines simply connect the data points for easier tracking of the dependence.

Figure 5

Calculated intensity distribution of the electric field around the Si grating surface irradiated by the incident $p$-polarized field of $E=1\mathrm{V}/\mathrm{m}$ at (a) $\theta ={15}^{\circ }$ and (b) $\theta ={24}^{\circ }$, where $N_{\mathrm{e}}=2.0\times {10}^{22}\mathrm{c}{\mathrm{m}}^{-3}$ is assumed, and the arrow denotes the incident direction of the beam.