As far as I know there is no analytical solution for this problem (but I might be wrong). In such cases I would use two different Maxwell-solver for example an FDTD-based like FDTD solutions and a second one like a finite-element-based like the one that is used in COMSOL. If both solutions converge for decreasing mesh sizes you can consider yourself to be fairly safe. On a second thought, how about carrying out the corresponding experiment?... ;-)

For calculating the cross section of a nanoparticle in free space, Mie theory is an exact solution of the Maxwells equations. And for calculating the scattering cross section of a particle on a substrate or thin film, there are FDTD and FEM methods but they are not exact solution as Mie theory in free space. However, you can confirmed them by your experimental results.

Thank you Kaleem.

Thomas Mayerhofer,

Thanks for your suggestions. Sorry to respond late as i prepared a reproduction of FDTD vs experiment results from a published article. I took an experimental example published as seen below

Article Double-Resonance Plasmon Substrates for Surface-Enhanced Ram...

It is nanodisk on film system with SiO2 layer in between. I tried to reproduce Figure 3(a) result. Particularly disk diameter 130 nm and period of 500 nm. After several optimizations, I matched the experimental result.

So following are the critical conditions when you do 3D FEM or FDTD.

1) Mesh size (most common)

2) Size of Simulation region (especially Z direction when using a periodic condition)

3) Size and location of power monitors recording data

If there is a proper optimization of above mentioned parameters, then simulation results matches very well with experimental one.

Hi

I am trying to do similar on CST but effect from substrate is very strong there is no shift in extinction parameter with changing radius of NP. Could elaborate your method a little bit more in detail.

thank you

I am interesting with your paper

Vasanthan Devaraj Thomas Mayerhöfer Hello sir,

As I am simulating a gold nano disk (diameter 100; height 20; periodicity 200) on the silica substrate whenever I am calculating the value of extinction, absorption and scattering efficiency. There might be some error in calculation in scattering efficiency as you already benchmark the results. Kindly please let me know which point I am missing while calculation the scattering efficiency. The equation which I am using writing below:

For a single nano disk the Power-flow outwards of the Nano disk surface is integrated.

nrelPoav = nxemw.relPoavx + nyemw.relPoavy + nz*emw.relPoavz;

sigma_sc = (intop_surf(nrelPoav)/sigma_geom;

sigma_abs = intop_vol(emw.Qh)/sigma_geom;

where, intop_surf integrates over the surface of a single Nanodisk and sigma_geom is the geometric cross-section.

and S_in = E0^2/(2*Z0_const)

Thank you in Advance.

Sneha Verma

I assume you use COMSOL for the calculation (probably RF or wave optics module).

In that case there are two corrections:

First correction with relative normal poynting flux. It has to be as follows (when using waveoptics module):

nrelPoav = nx*ewfd2.relPoavx+ny*ewfd2.relPoavy+nz*ewfd2.relPoavz

Then with the cross-section calculations, you should use incident field instead of sigma_geom. Therefore, it has to be as follows:

sigma_sc = intop_surf(nrelPoav)/I0

sigma_abs = intop_vol(ewfd2.Qh)/I0

Where I0 is incident light.

Both intop surface and volume should applied to the plasmonic NP (ex. sphere, disk or cube, etc).

I hope this helps.

Prithu Roy

I think the methodology is simple straight forward. Make sure your Scattering and absorption monitors are placed in right positions close to the plasmonic nanostructure. Since I dont have experience in using CST, I dont know what kind of error you make. For other most important fundamentals, I think I had mentioned it earlier in my answers.

Thank you.

Hello Vasanthan Devaraj

First of all thanks for your response.

This is for your kind information I am using the RF model the equation which you have given me the same equation I am using.

I am surprised that my model is perfectly calculating the value of the absorption spectra that means the value of volume integral is also calculating perfectly. But there is a problem in surf integral because when I am calculating the value of the scattering cross section some random values I am getting.

Kindly let me know when you put volume integral you may be selecting the domains and for surface integral I think you are selecting the boundaries the same thing I am doing.:

sigma_sc = intop_surf(nrelPoav)/I0

Because these only two parameters are effecting the values of the scattering cross section. So may be there could be chance that I am calculating the nrelPoav wrong. I am calculating it without writing rel in

my equation: nx*emw.Poavx+ny*emw.Poavy+nz*emw.Poavz

Your equation: nx*ewfd2.relPoavx+ny*ewfd2.relPoavy+nz*ewfd2.relPoavz

In my case COMSOL is not recognising this term ewfd2.relPoavx. Can you please help me how i will calculate the real part of the power.

Thank you in advance