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We will calculate the transmission and reflection spectrum from an array of nanoholes in a metallic film. We will also consider the near field profiles at the surface of the film and the local field enhancements.

 

Solvers

FDTD

Associated files

sp_array.fsp

sp_array.lsf

See also

Surface Plasmons

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Simulation setup

The file sp_array.fsp can be used to simulate an array of nanoholes of radius 100 nm and pitch 400 nm in a 100 nm thick layer of gold. The gold layer uses the "Au (Gold) - CRC" model included in the default material database.  The plane wave source covers a wavelength range of 400 to 750 nm. A single unit cell of the array is modeled, and symmetric/anti-symmetric boundary conditions are used to further reduce the simulation volume by a factor of 4. (Please note that symmetric/anti-symmetric boundaries must be consistent with the source polarization.) With an FDTD mesh accuracy of 2, and a 10 nm mesh override in the gold, the simulation runs in a few seconds on a single computer. Some convergence testing of the mesh size should be done for each simulation and typically mesh sizes of 5 nm or less should be used for the final results.

Results

After running the simulation, run the script file sp_array.lsf. It will perform a series of representative calculations and create the figures shown below. We can see that there are a number of resonances with the strongest at approximately 675nm. The script also creates a figure of the transmission normalized to the area of the hole divided by the unit cell area, which makes it easy to see where we have extraordinary transmission.

 

Transmission and reflection vs wavelength

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Verification of the material properties

It is sometimes useful to verify that the gold material used in the FDTD simulation had the desired properties over the entire wavelength range. The following plot shows the index of the gold material used in the simulation as a function of wavelength.

 

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Near field plots

The following images show |E|2 at the surface of the gold, on the transmitted and reflected side. We can see that the local near field enhancement is very significant because the incident field intensity is 1 V/m.

 

Reflected surface

Transmitted surface

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The cross section in the x-z plane shown below has the colorbar adjusted to a range of 1 to 10. This makes it possible to easily see the region where the near field intensity enhancement is at least 10.

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The simulation will also make an mpeg movie called sp_array_nanohole_movie.mpg.

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