We will locate the Surface Plasmon Resonance of a 50 nm silver film on glass at 500nm by analyzing the reflection and transmission as a function of the source angle of incidence. Angles with low reflection and transmission (high absorption) indicate that power from the source is exciting (coupling into) the SPR mode. We also calculate the dispersion relation of the SPR modes.
Finding the SPR mode at 500nm
For this simulation, we do a parameter sweep over the source incidence angle. We are looking for the source angle that excites the SPR mode (this happens when the y component of the source wave vector matches the wave vector of the SPR mode. We measure absorption in the Silver to determine the angle with the strongest coupling (since SPR modes have very high loss).
This is a convenient test case because an analytic solution exists.
Important settings to notice:
- The PML profile is set to "steep angle" to better absorb light propagating at large angles away from normal incidence.
- A mesh override region is used to force a finer mesh step size in the y direction (normal the silver film).
The plot to the left below shows the simulated reflection spectrum as a function of source angle in comparison with the analytic solution. The resonance angle for both the analytic solution and FDTD simulation are found at approximately 47 degrees. The plot on the right shows the E field intensity as a function of x for all of the angles of incidence. For a higher resolution of the E field intensity over x, the mesh accuracy setting in the FDTD simulation region object can be increased.
To recreate the plot, open sp_film_resonance.fsp. Run sp_film_resonance.lsf script file to run the parameter sweep, plot the results and compare them with theory.
Next, we calculate the dispersion relation of the SPR mode(s) using a technique described in the Bandstructure section. Basically, we do a parameter sweep over the wave vector ky and look for frequencies with strong resonances. To reproduce the following results, open spr_film_dispersion.fsp, run the parameter sweep, then run the script spr_film_dispersion.lsf.
In the following figures, two SPR modes are visible (Air:Ag:Glass and Glass:Ag:Air) as well as the Air and Glass light lines.
Raw dispersion data.
Dispersion data after peak finding routine.