The goal of this example is to show how FDTD can be used to investigate the focusing properties of a single subwavelength aperture surrounded by grooves on the output surface. This is accomplished by reproducing theoretical results from a paper by Garcia-Vidal et al.
As shown above, the simulation contains a structure with a subwavelength aperture surrounded by grooves.
In order to reproduce the results from figure 2 of Garcia-Vidal et al, the structure in Garcia_Vidal.fsp has 20 grooves on the output surface with a period of 500nm. The groove width and depth are 40 nm and 83.5 nm respectively. Since the authors of the publication assume perfect metal boundary conditions in their theoretical calculations, the Perfect Electrical Conductor (PEC) material is used for the structure.
The structure is contained in a group so that it is easy to modify geometrical parameters such as the groove depth or width.
A 500-600 nm TE plane wave impinges on the structure from the left and a monitor is place in the near field to the right. The near field data from this monitor is used to get the fields as a function of x and y to the right of the aperture.
Note: Plane wave with PML
Usually we do not recommend using plane wave with PML boundaries at the sides since it leads to artificial diffraction and edge effects. This example is an exception. The edge effects will still present but since the simulation region span is much wider than the patterned region of the structure, the edge effects will be minimal in the central region, and the distorted fields at the edges near the PML will be reflected by the PEC slab and do not propagate to the monitor for result analysis.
An alternative to avoid edge effects is to use a TFSF source which is done in the Bullseye Aperture example.
After the simulation Garcia_Vidal.fsp has run to completion, run the script file, Garcia_Vidal.lsf. The script file uses far field projections of the data from the monitor to calculate the fields to the right of the aperture. The time that it takes to run the script file will depend on how many points are desired in the far field projection. The results below can be obtained by using 1000 points in x and 500 points in y. The attached script file is set to less in order to reduce the time it takes to run the script file.
Note that due to grid dispersion, using the far field projections is more accurate than simulating a large area at the output of the aperture and using a 2D monitor to measure the fields.
Once complete, the script file produces the three figures below. The script also calculates the focal width and length, and prints the results to the command prompt. The focal length is the distance from the aperture to the focal point and the focal width is the full width half maximum of the fields in the direction perpendicular to the field propagation. For the attached simulation, the focal length and width are
Focal length: 48.034 microns Focal width: 3.28657 microns
E field intensity profile as a function of x and y at 532nm.
Cut along the line y=0 from the previous picture. The peak occurs at the focal length determined to be 47.58 microns.
Cut along the line x = 47.58 microns
F. J. Garcia-Vidal, L. Martin-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83, 4500 (2003).