We will calculate the transmission through a sub-wavelength aperture in a thin silver film. Surface plasmon modes created by a series of rings around the aperture are used to enhance the transmission. Simulation results will be compared to the experimental results published by Lezec et al.
The file sp_bullseye.fsp contains a simulation of the structure shown in Figure 1 from Lezec. A bullseye pattern of concentric circles is etched from a free standing 300nm thick silver layer. The central hole has a radius of 150nm, and goes completely through the silver layer. Four 60 nm deep circular grooves are etched in both the top and bottom of the layer surrounding the central hole. Please note that the silver material fitting parameters has been adjusted from the default settings to improve the fit.
A mesh override region is used to force a fine mesh around the structures and TFSF source region.
A broadband Total Field Scattered Field (TFSF) plane wave source (400-1000 nm) is incident on the lower surface. A frequency domain power monitor is located above the upper surface and will be used to measure transmission through the aperture. Note that we need the unpolarized result, which usually requires running two simulations with orthogonal source polarizations. For more information on calculating response for unpolarized an incoherent illumination, see the Polarization incoherence page. For this particular structure, since it has rotational symmetry, the unpolarized far field projection results can be obtained from a single simulation by summing the result with the transpose of the result. This analysis is performed in the analysis script in the "farfield_unpolarized" analysis group.
In order to analyze the enhancement in the transmission due to the addition of the concentric circle groove pattern, two simulations are required, one with and one without the grooves. In the structure group named "Bullseye", the variable "make_grooves" allows you to choose if the grooves should be added to the simulation. Set "make_grooves" to 1 to add the grooves, and 0 to leave them out. By comparing the simulations, enhancement due to the grooves can be determined. For initial results, the mesh override region can be deleted. This will make the simulation faster and require less memory, but produce less accurate results. As soon as each of the simulations are complete, run the script sp_bullseye_analysis.lsf. It will calculate a series of far field projections for that simulation and create three figures. Results for the simulation with and without grooves are shown below.
Fig.1a Transmission at various collection angles, with grooves
Fig.1b Transmission at various collection angles, without grooves
Fig.1 produced by the script shows the far field projection of the transmission monitor as a function of frequency at a series of collection angles. It is important to note the difference in scale in the two cases. The peak transmission with the bullseye grooves is about 1.2e-11 at 660 nm. Without the grooves, the transmission at 660 nm is about 2.5e-14. This shows that the grooves improve transmission by three orders of magnitude. This result shows very good agreement with Figure 1.B in Lezec, et al.
Fig.2a far field projection at the wavelength with the peak transmission
Fig.2b far field projection at the wavelength with the peak transmission
Fig.3a far field projection at the wavelength with the peak transmission
Fig.3b far field projection at the wavelength with the peak transmission
The second figure from the analysis script shows the far field projection at the wavelength with the peak transmission. The third figure shows a 1D slice of the same data. The above figures show the far field projections at 660 nm. It is clear that adding the grooves results in a much more focused beam. The divergence angle with the grooves is 5 degrees, compared to 45 degrees without the grooves.
Fig. 4 poynting vector in the xy plane
The above image is a vector plot of the Poynting vector in the xy plane, above the feature. It is often more meaningful to plot the Poynting vector rather than the fields, as is the case here (plots of the electric field will often contain vectors pointing in different directions representing the oscillation in the field direction). With a vector plot of the the Poynting vector you can see the direction of power flow. It can be helpful to create an electric field vector plot to study circularly polarized or elliptically polarized beams.
H. J. Lezec, et al., "Beaming light from a subwavelength aperture", Science 297, 802 (2002).