Can I simulate SPP propagation length of IMI waveguide using FDTD?


I want to compare the propagation length or the spatial extent of Surface Plasmon Polariton on IMI structure between different metal and dielectric materials.
Although there are some description about how to simulate dispersion, is it also possible to simulate propagation length and the spatial extent properties with FDTD?
This graph is an example of the comparison of those parameters for MIM and IMI structure.

I would appreciate if anybody help me.


Hi @sugimoto

The topic is new to me, but what I understood from the paper and plot, you can use a DFT monitor to record the field over the MIM or IMI structure. Then you can extract the proper field components (Ez or Hy) along the proper direction (z or x) for propagation length or spatial extent. You can use pinch command to select a specific data of interest:

I hope this answers your inquiry.


Thank you for your quick reply @bkhanaliloo.

As a starting point, I have simulated SPP excitation on the interface between a semi-infinite gold film and air. In this simulation, I used a electric dipole source to excite SPP. As you said, I the field components (Ez or Hy) can be measured by DFT monitors; however, the field of SPP is disturbed by the field radiated from the dipole source (i.e. concentric field is superposed to the SPP field). This makes it difficult to measure the spatial extent of the SPP field (by a line DFT monitor placed normal to the gold surface).

Additionally, the propagation length looks much shorter than analytically obtained one.
This graph shows the analytically obtained |Hy| of SPP (at 1nm from gold surface) as a function of propagation distance.
This result has been calculated based on below equation about TM field and the dispersion of SPP (from Plasmonics: Fundamentals and Applications (S.A. Maier)
image image

This graph shows |Hy| simulated using FDTD solutions. The dipole source is placed at x=0 nm.

180913_Test_SPP_1.fsp (3.5 MB)

Obviously, the attenuation of SPP is much faster in the result of FDTD solutions. I wonder this difference comes from the method of excitation.



Hi @sugimoto

The dipole filed can affect your results of course, a similar concern when we calculate the Q factor in the cavities:

To solve the problem, you can use apodization in the monitors to make sure that you are excluding the dipole fields:

Another approach would be to use MODE source instead:

Please repeat your calculation and let me know if you had any further quesitons.


Hi @bkhanaliloo,

Thank you for the suggestion. I agree that I have to exclude the dipole field to see the SPP fields. However, I think it is impossible to do that by apodization because SPPs, I believe, propagate together with the light injected from the dipole source (without delay).
Let me know if you think it is incorrect, or have any other suggestions.



Hi @sugimoto

I see your point, and it makes sense. If you are using dipole source, you can place DFT monitor far from the dipole source such that dipole field has decayed and only the SPPs have survived. Dipole source can excite the modes of waveguide (SPPs here), but the unsupported and lossy modes will decay faster than the SPPs.

You can also use mode source to excite the mode of interest and study its propagation. This might be a simpler approach to avoid the dipole fields.

Please let me know of your thoughts.