## Nanoparticle in inhomogeneous medium- substrate case (part II)

After testing definition of excitation field, PML performance and background meshing quality (See part I), we will solve metallic nanoparticle on the glass.

In order to show difference when exciting particle with p-polarized plane wave under normal or oblique incidence, I propose to solve gold nanobar (nanorod) sufficiently long that can support at least modes m=1 (or "lambda/2or "dipolar") and m=2 (or "lamda" mode). To do that nanobar with dimensions of 360x75x50nm will do just fine.

This example is suitable, because even modes (m=2) can be excited only by oblique incidence (incident angle of 30*pi/180 rad).

However, here I will show response of 500x50x50nm gold rod, which supports m=2 and m=3 modes for Lambda<1.2um.

In order to show difference when exciting particle with p-polarized plane wave under normal or oblique incidence, I propose to solve gold nanobar (nanorod) sufficiently long that can support at least modes m=1 (or "lambda/2or "dipolar") and m=2 (or "lamda" mode). To do that nanobar with dimensions of 360x75x50nm will do just fine.

This example is suitable, because even modes (m=2) can be excited only by oblique incidence (incident angle of 30*pi/180 rad).

However, here I will show response of 500x50x50nm gold rod, which supports m=2 and m=3 modes for Lambda<1.2um.

## Modeling

Setting up the modeling parameters is identical to Example 2 part I, and will not be repeated. Actually, you should always make full model, mesh everything (background and scatterer), and then turn your particle invisible (same refractive index as superstrate). If you plan to solve model for multiple wavelengths to get spectral information, then run first test for the smallest wavelength to are intending to sweep over in your spectra. Check amplitude of the scattered fields, and if they are sufficiently lower than amplitude (usually 0.001-0.00001 of incidence amplitude), or if there are some a bit more intense fields near PML boundaries but inside the geometry is fine, you can run your model with visible scatterer.

Since you have substrate, you will have interface also where two PMLs meet, and consequently there will be some hot spots, but with low amplitude. This is something you cannot prevent. There is article in Nanoletters proposing 2-step procedure, where you first solve empty geometry, and then you use solution of the 1st run (I guess Ei+scE, i.e. now total field) as incident field in the second run. The authors claimed that it will help to reduce aforementioned hot spots at PML interface!? Does this make any sense, I am not sure. If anyone want´s I can explain how to do this 2-step procedure. Last time I checked, the result was exactly the same when you do standard way (as I am "preaching" here) or 2-step procedure. Identical. Thus, 2-step procedure just takes more of your time, since for every wavelength you need to solve your model twice. In favor of this stand, I think that no one has ever mentioned 2-step procedure, and more COSMOL simulations have been published by the same authors.

Now we proceed to solution.

Since you have substrate, you will have interface also where two PMLs meet, and consequently there will be some hot spots, but with low amplitude. This is something you cannot prevent. There is article in Nanoletters proposing 2-step procedure, where you first solve empty geometry, and then you use solution of the 1st run (I guess Ei+scE, i.e. now total field) as incident field in the second run. The authors claimed that it will help to reduce aforementioned hot spots at PML interface!? Does this make any sense, I am not sure. If anyone want´s I can explain how to do this 2-step procedure. Last time I checked, the result was exactly the same when you do standard way (as I am "preaching" here) or 2-step procedure. Identical. Thus, 2-step procedure just takes more of your time, since for every wavelength you need to solve your model twice. In favor of this stand, I think that no one has ever mentioned 2-step procedure, and more COSMOL simulations have been published by the same authors.

Now we proceed to solution.