Using Unpolarized Light to Calculate Reflectance and Transmittance


#1

Hi,

I’ve read the tutorial on using an unpolarized beam, and how to generate my results.
In the script file provided with the tutorial at

[https://kb.lumerical.com/en/ref_sim_obj_fdtd_coherence_unpolarized_beam.html]

They calculate this by simulating a beam with a polarization angle of 0 and then a beam with a polarization of angle 90, they then get the quantity <|E|2> referring to the time averaged electric field intensity of the unpolarized beam source as,

<|E|2> = 0.5 (<|E_0|>^2 + <|E_90|>^2)

In the script for the unpolarized beam they do the same additions for calculating transmission.

So, now if I’m simulating a gold nanoparticle of 10 nm radius, and follow the same procedure, while calculating the reflectance and transmission in each case using field and profile monitors. In order to get the averaged electric field intensity, all I have to do is something along the lines of:

T_unpol=0.5*(T_0+T_90);
R_unpol = 0.5*(R_0+R_90);
E2_unpol=0.5*(E2_0+E2_90);

Are the E2_0 and E2_90 referring to the E abs^2 variable in the field and profile monitor? Must I apply these same additions if I’m calculating power absorption or scattering/absorption cross sections using the pabs, and cross section analysis monitors?


#2

Hi @apmanuel,

That is correct. As long as you are dealing with a linear system, you can obtain the unpolarized results by incoherently averaging the results from 2 simulations using the 2 orthogonal polarization. This is valid for \(|E|^2\), as well as T and R, but also \(P_{abs}\) as

\[
P_{abs} = -{1 \over 2} \omega |E|^2 imag(\epsilon)
\]

so

\[
P_{abs} = -{1 \over 2} \omega \left( {1 \over 2} |E_0|^2 + {1 \over 2}|E_{90}|^2 \right) imag(\epsilon)
\]

Similarly, the cross section calculation is using the transmission through monitors to get the power ratio going through the monitors that is then normalized to the source intensity.

I hope this helps.


#3

Just a few questions:

(1) What do you mean by a linear system? What if I was looking at specific arrangements of nanorods in a certain shape?
(2) The imag(e) refers to the imaginary component of the dielectric constant?
(3) The last statement, you say that the cross section calculation using transmission through the planes of the monitor, so do I use the same incoherent average here as in T and R, or do I use that provided in Pabs?


#4

Hi @apmanuel,

I meant the response of the system is linear (it would be different if we were using non-linear materials).

Correct, \(imag(\epsilon)\) is the imaginary part of the permittivity. Note for dispersive materials, \(\epsilon\) is not a constant.

You can use the same incoherent average as in T and R. The cross section analysis group from the object library is using a box of monitors and get the transmissions through these monitors to calculate the cross section:

\[
\sigma = {\sum T_i} {sourcepower(f) \over sourceintensity(f)}
\]

Where \( \sum T_i\) is the sum of the transmission of each monitor. This is used, for instance, in the Mie scattering example.


#5

Hi,

Following your instructions I was able to set up my simulations accordingly. I wanted to do the unpolarized calculation on a nanotube where I’m using a TFSF source.
Basically I did one simulation with TFSF source of 0 degree polarization, and the second with the TFSF source of 90 degree polarization, with both sources having the light enter in from atop of the nanotube. While my 0 degree polarization simulation converged well and showed the relevant reflectance and transmittance behavior, my 90 degree polarization simulation didn’t converge at all with the autoshutoff level increasing from 1-200 by the end of the simulation. Could this have to do with how I’m using the 90 degree polarized TFSF source?


#6

Hi @apmanuel,

It’s difficult to say where the problem could be as there can be multiple causes for diverging simulation.
Can you eventually share the simulation file?