Strongly coupled surface plasmons on thin shallow metallic gratings

The optical response of a thin metallic film with shallow corrugations on both surfaces is explored and the structure is found to support a strongly coupled surface plasmon polariton when transverse magnetic radiation is incident in a plane parallel to the grating grooves. Modeling confirms that this strongly excited mode is the short range surface plasmon polariton and its presence is confirmed experimentally in the visible part of the spectrum.

Figure 1

Schematic diagram illustrating the sample and coordinate system used in this study. Here, ${\lambda }_g$ is the grating pitch, $a$ is the grating amplitude, $d$ is the thickness of the silver layer, $\theta$ is the polar angle, and $\phi$ is the azimuth angle which is set to 90°. The silver layer is bounded by silica media. The orientation of the electric field $\left({\mathbf{E}}_{\mathrm{TM}}\right)$ for TM polarization at $\phi =90°$ is also shown.

Figure 2

Experimental reflection (open squares), transmission (open triangles), and absorption (open stars) together with the model fits (dashed, dotted, and solid lines) when TM polarized light is incident on a thin silver sinusoidal grating with a thickness of $23\mathrm{nm}$, a pitch of $252\mathrm{nm}$, and an amplitude of $8\mathrm{nm}$ at $\theta =65.0°$ and $\phi =90°$.

Figure 3

Theoretical absorption at $\theta =65.0°$ and $\phi =90°$ for (a) a $23\mathrm{nm}$ and (b) a $650\mathrm{nm}$ silver film with corrugation (solid line) and without corrugation (dashed line) together with the absorption difference (open circles). Lines without symbols are associated with the left axis and those with symbols with the right axis. (The grating has a pitch of $252\mathrm{nm}$ and an amplitude of $8\mathrm{nm}$.)

Figure 4

Instantaneous $E_{xy}$ vector fields at a resonant frequency of $f=0.595\times {10}^{15}\mathrm{Hz}$ for a thin silver film grating ($d=23\mathrm{nm}$, ${\lambda }_g=252\mathrm{nm}$, and $a=8\mathrm{nm}$) at $\theta =65.0°$ and $\phi =90°$. The continuous lines are the surfaces of the thin metal grating. The grayscale of the arrows represents the magnitude of the $E_{xy}$ fields.

Figure 5

Theoretical TM polarized absorption as a function of frequency and silver film thickness at $\theta =65.0°$ and $\phi =90°$ for a corrugated silver film of $8\mathrm{nm}$ amplitude and $252\mathrm{nm}$ pitch.

Figure 6

Theoretical TM excited SRSPP (open circles) and LRSPP (solid circles) absorption peak height as a function of amplitude at $\theta =65.0°$ and $\phi =90°$ for different film thicknesses (a) $d=23\mathrm{nm}$, (b) $d=50\mathrm{nm}$, and (c) $d=80\mathrm{nm}$. The absorption peak height for the TM excited SISPP (crosses) is also plotted in each of the graphs.